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 qpolynomial
34 #include <isl_list_templ.c>
37 #define EL_BASE pw_qpolynomial
39 #include <isl_list_templ.c>
41 static unsigned pos(__isl_keep isl_space
*space
, enum isl_dim_type type
)
44 case isl_dim_param
: return 0;
45 case isl_dim_in
: return space
->nparam
;
46 case isl_dim_out
: return space
->nparam
+ space
->n_in
;
51 isl_bool
isl_poly_is_cst(__isl_keep isl_poly
*poly
)
54 return isl_bool_error
;
56 return isl_bool_ok(poly
->var
< 0);
59 __isl_keep isl_poly_cst
*isl_poly_as_cst(__isl_keep isl_poly
*poly
)
64 isl_assert(poly
->ctx
, poly
->var
< 0, return NULL
);
66 return (isl_poly_cst
*) poly
;
69 __isl_keep isl_poly_rec
*isl_poly_as_rec(__isl_keep isl_poly
*poly
)
74 isl_assert(poly
->ctx
, poly
->var
>= 0, return NULL
);
76 return (isl_poly_rec
*) poly
;
79 /* Compare two polynomials.
81 * Return -1 if "poly1" is "smaller" than "poly2", 1 if "poly1" is "greater"
82 * than "poly2" and 0 if they are equal.
84 static int isl_poly_plain_cmp(__isl_keep isl_poly
*poly1
,
85 __isl_keep isl_poly
*poly2
)
89 isl_poly_rec
*rec1
, *rec2
;
93 is_cst1
= isl_poly_is_cst(poly1
);
98 if (poly1
->var
!= poly2
->var
)
99 return poly1
->var
- poly2
->var
;
102 isl_poly_cst
*cst1
, *cst2
;
105 cst1
= isl_poly_as_cst(poly1
);
106 cst2
= isl_poly_as_cst(poly2
);
109 cmp
= isl_int_cmp(cst1
->n
, cst2
->n
);
112 return isl_int_cmp(cst1
->d
, cst2
->d
);
115 rec1
= isl_poly_as_rec(poly1
);
116 rec2
= isl_poly_as_rec(poly2
);
120 if (rec1
->n
!= rec2
->n
)
121 return rec1
->n
- rec2
->n
;
123 for (i
= 0; i
< rec1
->n
; ++i
) {
124 int cmp
= isl_poly_plain_cmp(rec1
->p
[i
], rec2
->p
[i
]);
132 isl_bool
isl_poly_is_equal(__isl_keep isl_poly
*poly1
,
133 __isl_keep isl_poly
*poly2
)
137 isl_poly_rec
*rec1
, *rec2
;
139 is_cst1
= isl_poly_is_cst(poly1
);
140 if (is_cst1
< 0 || !poly2
)
141 return isl_bool_error
;
143 return isl_bool_true
;
144 if (poly1
->var
!= poly2
->var
)
145 return isl_bool_false
;
147 isl_poly_cst
*cst1
, *cst2
;
149 cst1
= isl_poly_as_cst(poly1
);
150 cst2
= isl_poly_as_cst(poly2
);
152 return isl_bool_error
;
153 r
= isl_int_eq(cst1
->n
, cst2
->n
) &&
154 isl_int_eq(cst1
->d
, cst2
->d
);
155 return isl_bool_ok(r
);
158 rec1
= isl_poly_as_rec(poly1
);
159 rec2
= isl_poly_as_rec(poly2
);
161 return isl_bool_error
;
163 if (rec1
->n
!= rec2
->n
)
164 return isl_bool_false
;
166 for (i
= 0; i
< rec1
->n
; ++i
) {
167 isl_bool eq
= isl_poly_is_equal(rec1
->p
[i
], rec2
->p
[i
]);
172 return isl_bool_true
;
175 isl_bool
isl_poly_is_zero(__isl_keep isl_poly
*poly
)
180 is_cst
= isl_poly_is_cst(poly
);
181 if (is_cst
< 0 || !is_cst
)
184 cst
= isl_poly_as_cst(poly
);
186 return isl_bool_error
;
188 return isl_bool_ok(isl_int_is_zero(cst
->n
) && isl_int_is_pos(cst
->d
));
191 int isl_poly_sgn(__isl_keep isl_poly
*poly
)
196 is_cst
= isl_poly_is_cst(poly
);
197 if (is_cst
< 0 || !is_cst
)
200 cst
= isl_poly_as_cst(poly
);
204 return isl_int_sgn(cst
->n
);
207 isl_bool
isl_poly_is_nan(__isl_keep isl_poly
*poly
)
212 is_cst
= isl_poly_is_cst(poly
);
213 if (is_cst
< 0 || !is_cst
)
216 cst
= isl_poly_as_cst(poly
);
218 return isl_bool_error
;
220 return isl_bool_ok(isl_int_is_zero(cst
->n
) && isl_int_is_zero(cst
->d
));
223 isl_bool
isl_poly_is_infty(__isl_keep isl_poly
*poly
)
228 is_cst
= isl_poly_is_cst(poly
);
229 if (is_cst
< 0 || !is_cst
)
232 cst
= isl_poly_as_cst(poly
);
234 return isl_bool_error
;
236 return isl_bool_ok(isl_int_is_pos(cst
->n
) && isl_int_is_zero(cst
->d
));
239 isl_bool
isl_poly_is_neginfty(__isl_keep isl_poly
*poly
)
244 is_cst
= isl_poly_is_cst(poly
);
245 if (is_cst
< 0 || !is_cst
)
248 cst
= isl_poly_as_cst(poly
);
250 return isl_bool_error
;
252 return isl_bool_ok(isl_int_is_neg(cst
->n
) && isl_int_is_zero(cst
->d
));
255 isl_bool
isl_poly_is_one(__isl_keep isl_poly
*poly
)
261 is_cst
= isl_poly_is_cst(poly
);
262 if (is_cst
< 0 || !is_cst
)
265 cst
= isl_poly_as_cst(poly
);
267 return isl_bool_error
;
269 r
= isl_int_eq(cst
->n
, cst
->d
) && isl_int_is_pos(cst
->d
);
270 return isl_bool_ok(r
);
273 isl_bool
isl_poly_is_negone(__isl_keep isl_poly
*poly
)
278 is_cst
= isl_poly_is_cst(poly
);
279 if (is_cst
< 0 || !is_cst
)
282 cst
= isl_poly_as_cst(poly
);
284 return isl_bool_error
;
286 return isl_bool_ok(isl_int_is_negone(cst
->n
) && isl_int_is_one(cst
->d
));
289 __isl_give isl_poly_cst
*isl_poly_cst_alloc(isl_ctx
*ctx
)
293 cst
= isl_alloc_type(ctx
, struct isl_poly_cst
);
302 isl_int_init(cst
->n
);
303 isl_int_init(cst
->d
);
308 __isl_give isl_poly
*isl_poly_zero(isl_ctx
*ctx
)
312 cst
= isl_poly_cst_alloc(ctx
);
316 isl_int_set_si(cst
->n
, 0);
317 isl_int_set_si(cst
->d
, 1);
322 __isl_give isl_poly
*isl_poly_one(isl_ctx
*ctx
)
326 cst
= isl_poly_cst_alloc(ctx
);
330 isl_int_set_si(cst
->n
, 1);
331 isl_int_set_si(cst
->d
, 1);
336 __isl_give isl_poly
*isl_poly_infty(isl_ctx
*ctx
)
340 cst
= isl_poly_cst_alloc(ctx
);
344 isl_int_set_si(cst
->n
, 1);
345 isl_int_set_si(cst
->d
, 0);
350 __isl_give isl_poly
*isl_poly_neginfty(isl_ctx
*ctx
)
354 cst
= isl_poly_cst_alloc(ctx
);
358 isl_int_set_si(cst
->n
, -1);
359 isl_int_set_si(cst
->d
, 0);
364 __isl_give isl_poly
*isl_poly_nan(isl_ctx
*ctx
)
368 cst
= isl_poly_cst_alloc(ctx
);
372 isl_int_set_si(cst
->n
, 0);
373 isl_int_set_si(cst
->d
, 0);
378 __isl_give isl_poly
*isl_poly_rat_cst(isl_ctx
*ctx
, isl_int n
, isl_int d
)
382 cst
= isl_poly_cst_alloc(ctx
);
386 isl_int_set(cst
->n
, n
);
387 isl_int_set(cst
->d
, d
);
392 __isl_give isl_poly_rec
*isl_poly_alloc_rec(isl_ctx
*ctx
, int var
, int size
)
396 isl_assert(ctx
, var
>= 0, return NULL
);
397 isl_assert(ctx
, size
>= 0, return NULL
);
398 rec
= isl_calloc(ctx
, struct isl_poly_rec
,
399 sizeof(struct isl_poly_rec
) +
400 size
* sizeof(struct isl_poly
*));
415 /* Return the domain space of "qp".
416 * This may be either a copy or the space itself
417 * if there is only one reference to "qp".
418 * This allows the space to be modified inplace
419 * if both the quasi-polynomial and its domain space
420 * have only a single reference.
421 * The caller is not allowed to modify "qp" between this call and
422 * a subsequent call to isl_qpolynomial_restore_domain_space.
423 * The only exception is that isl_qpolynomial_free can be called instead.
425 static __isl_give isl_space
*isl_qpolynomial_take_domain_space(
426 __isl_keep isl_qpolynomial
*qp
)
433 return isl_qpolynomial_get_domain_space(qp
);
439 /* Set the domain space of "qp" to "space",
440 * where the domain space of "qp" may be missing
441 * due to a preceding call to isl_qpolynomial_take_domain_space.
442 * However, in this case, "qp" only has a single reference and
443 * then the call to isl_qpolynomial_cow has no effect.
445 static __isl_give isl_qpolynomial
*isl_qpolynomial_restore_domain_space(
446 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*space
)
451 if (qp
->dim
== space
) {
452 isl_space_free(space
);
456 qp
= isl_qpolynomial_cow(qp
);
459 isl_space_free(qp
->dim
);
464 isl_qpolynomial_free(qp
);
465 isl_space_free(space
);
469 __isl_give isl_qpolynomial
*isl_qpolynomial_reset_domain_space(
470 __isl_keep isl_qpolynomial
*qp
, __isl_take isl_space
*space
)
472 return isl_qpolynomial_restore_domain_space(qp
, space
);
475 /* Reset the space of "qp". This function is called from isl_pw_templ.c
476 * and doesn't know if the space of an element object is represented
477 * directly or through its domain. It therefore passes along both.
479 __isl_give isl_qpolynomial
*isl_qpolynomial_reset_space_and_domain(
480 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*space
,
481 __isl_take isl_space
*domain
)
483 isl_space_free(space
);
484 return isl_qpolynomial_reset_domain_space(qp
, domain
);
487 isl_ctx
*isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial
*qp
)
489 return qp
? qp
->dim
->ctx
: NULL
;
492 /* Return the domain space of "qp".
494 static __isl_keep isl_space
*isl_qpolynomial_peek_domain_space(
495 __isl_keep isl_qpolynomial
*qp
)
497 return qp
? qp
->dim
: NULL
;
500 /* Return a copy of the domain space of "qp".
502 __isl_give isl_space
*isl_qpolynomial_get_domain_space(
503 __isl_keep isl_qpolynomial
*qp
)
505 return isl_space_copy(isl_qpolynomial_peek_domain_space(qp
));
509 #define TYPE isl_qpolynomial
511 #define PEEK_SPACE peek_domain_space
514 #include "isl_type_has_equal_space_bin_templ.c"
516 #include "isl_type_check_equal_space_templ.c"
520 /* Return a copy of the local space on which "qp" is defined.
522 static __isl_give isl_local_space
*isl_qpolynomial_get_domain_local_space(
523 __isl_keep isl_qpolynomial
*qp
)
530 space
= isl_qpolynomial_get_domain_space(qp
);
531 return isl_local_space_alloc_div(space
, isl_mat_copy(qp
->div
));
534 __isl_give isl_space
*isl_qpolynomial_get_space(__isl_keep isl_qpolynomial
*qp
)
539 space
= isl_space_copy(qp
->dim
);
540 space
= isl_space_from_domain(space
);
541 space
= isl_space_add_dims(space
, isl_dim_out
, 1);
545 /* Return the number of variables of the given type in the domain of "qp".
547 isl_size
isl_qpolynomial_domain_dim(__isl_keep isl_qpolynomial
*qp
,
548 enum isl_dim_type type
)
553 space
= isl_qpolynomial_peek_domain_space(qp
);
556 return isl_size_error
;
557 if (type
== isl_dim_div
)
558 return qp
->div
->n_row
;
559 dim
= isl_space_dim(space
, type
);
561 return isl_size_error
;
562 if (type
== isl_dim_all
) {
565 n_div
= isl_qpolynomial_domain_dim(qp
, isl_dim_div
);
567 return isl_size_error
;
573 /* Given the type of a dimension of an isl_qpolynomial,
574 * return the type of the corresponding dimension in its domain.
575 * This function is only called for "type" equal to isl_dim_in or
578 static enum isl_dim_type
domain_type(enum isl_dim_type type
)
580 return type
== isl_dim_in
? isl_dim_set
: type
;
583 /* Externally, an isl_qpolynomial has a map space, but internally, the
584 * ls field corresponds to the domain of that space.
586 isl_size
isl_qpolynomial_dim(__isl_keep isl_qpolynomial
*qp
,
587 enum isl_dim_type type
)
590 return isl_size_error
;
591 if (type
== isl_dim_out
)
593 type
= domain_type(type
);
594 return isl_qpolynomial_domain_dim(qp
, type
);
597 /* Return the offset of the first variable of type "type" within
598 * the variables of the domain of "qp".
600 static isl_size
isl_qpolynomial_domain_var_offset(
601 __isl_keep isl_qpolynomial
*qp
, enum isl_dim_type type
)
605 space
= isl_qpolynomial_peek_domain_space(qp
);
609 case isl_dim_set
: return isl_space_offset(space
, type
);
610 case isl_dim_div
: return isl_space_dim(space
, isl_dim_all
);
613 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
614 "invalid dimension type", return isl_size_error
);
618 /* Return the offset of the first coefficient of type "type" in
619 * the domain of "qp".
621 unsigned isl_qpolynomial_domain_offset(__isl_keep isl_qpolynomial
*qp
,
622 enum isl_dim_type type
)
630 return 1 + isl_qpolynomial_domain_var_offset(qp
, type
);
636 isl_bool
isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial
*qp
)
638 return qp
? isl_poly_is_zero(qp
->poly
) : isl_bool_error
;
641 isl_bool
isl_qpolynomial_is_one(__isl_keep isl_qpolynomial
*qp
)
643 return qp
? isl_poly_is_one(qp
->poly
) : isl_bool_error
;
646 isl_bool
isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial
*qp
)
648 return qp
? isl_poly_is_nan(qp
->poly
) : isl_bool_error
;
651 isl_bool
isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial
*qp
)
653 return qp
? isl_poly_is_infty(qp
->poly
) : isl_bool_error
;
656 isl_bool
isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial
*qp
)
658 return qp
? isl_poly_is_neginfty(qp
->poly
) : isl_bool_error
;
661 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial
*qp
)
663 return qp
? isl_poly_sgn(qp
->poly
) : 0;
666 static void poly_free_cst(__isl_take isl_poly_cst
*cst
)
668 isl_int_clear(cst
->n
);
669 isl_int_clear(cst
->d
);
672 static void poly_free_rec(__isl_take isl_poly_rec
*rec
)
676 for (i
= 0; i
< rec
->n
; ++i
)
677 isl_poly_free(rec
->p
[i
]);
680 __isl_give isl_poly
*isl_poly_copy(__isl_keep isl_poly
*poly
)
689 __isl_give isl_poly
*isl_poly_dup_cst(__isl_keep isl_poly
*poly
)
694 cst
= isl_poly_as_cst(poly
);
698 dup
= isl_poly_as_cst(isl_poly_zero(poly
->ctx
));
701 isl_int_set(dup
->n
, cst
->n
);
702 isl_int_set(dup
->d
, cst
->d
);
707 __isl_give isl_poly
*isl_poly_dup_rec(__isl_keep isl_poly
*poly
)
713 rec
= isl_poly_as_rec(poly
);
717 dup
= isl_poly_alloc_rec(poly
->ctx
, poly
->var
, rec
->n
);
721 for (i
= 0; i
< rec
->n
; ++i
) {
722 dup
->p
[i
] = isl_poly_copy(rec
->p
[i
]);
730 isl_poly_free(&dup
->poly
);
734 __isl_give isl_poly
*isl_poly_dup(__isl_keep isl_poly
*poly
)
738 is_cst
= isl_poly_is_cst(poly
);
742 return isl_poly_dup_cst(poly
);
744 return isl_poly_dup_rec(poly
);
747 __isl_give isl_poly
*isl_poly_cow(__isl_take isl_poly
*poly
)
755 return isl_poly_dup(poly
);
758 __isl_null isl_poly
*isl_poly_free(__isl_take isl_poly
*poly
)
767 poly_free_cst((isl_poly_cst
*) poly
);
769 poly_free_rec((isl_poly_rec
*) poly
);
771 isl_ctx_deref(poly
->ctx
);
776 static void isl_poly_cst_reduce(__isl_keep isl_poly_cst
*cst
)
781 isl_int_gcd(gcd
, cst
->n
, cst
->d
);
782 if (!isl_int_is_zero(gcd
) && !isl_int_is_one(gcd
)) {
783 isl_int_divexact(cst
->n
, cst
->n
, gcd
);
784 isl_int_divexact(cst
->d
, cst
->d
, gcd
);
789 __isl_give isl_poly
*isl_poly_sum_cst(__isl_take isl_poly
*poly1
,
790 __isl_take isl_poly
*poly2
)
795 poly1
= isl_poly_cow(poly1
);
796 if (!poly1
|| !poly2
)
799 cst1
= isl_poly_as_cst(poly1
);
800 cst2
= isl_poly_as_cst(poly2
);
802 if (isl_int_eq(cst1
->d
, cst2
->d
))
803 isl_int_add(cst1
->n
, cst1
->n
, cst2
->n
);
805 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->d
);
806 isl_int_addmul(cst1
->n
, cst2
->n
, cst1
->d
);
807 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
810 isl_poly_cst_reduce(cst1
);
812 isl_poly_free(poly2
);
815 isl_poly_free(poly1
);
816 isl_poly_free(poly2
);
820 static __isl_give isl_poly
*replace_by_zero(__isl_take isl_poly
*poly
)
828 return isl_poly_zero(ctx
);
831 static __isl_give isl_poly
*replace_by_constant_term(__isl_take isl_poly
*poly
)
839 rec
= isl_poly_as_rec(poly
);
842 cst
= isl_poly_copy(rec
->p
[0]);
850 __isl_give isl_poly
*isl_poly_sum(__isl_take isl_poly
*poly1
,
851 __isl_take isl_poly
*poly2
)
854 isl_bool is_zero
, is_nan
, is_cst
;
855 isl_poly_rec
*rec1
, *rec2
;
857 if (!poly1
|| !poly2
)
860 is_nan
= isl_poly_is_nan(poly1
);
864 isl_poly_free(poly2
);
868 is_nan
= isl_poly_is_nan(poly2
);
872 isl_poly_free(poly1
);
876 is_zero
= isl_poly_is_zero(poly1
);
880 isl_poly_free(poly1
);
884 is_zero
= isl_poly_is_zero(poly2
);
888 isl_poly_free(poly2
);
892 if (poly1
->var
< poly2
->var
)
893 return isl_poly_sum(poly2
, poly1
);
895 if (poly2
->var
< poly1
->var
) {
899 is_infty
= isl_poly_is_infty(poly2
);
900 if (is_infty
>= 0 && !is_infty
)
901 is_infty
= isl_poly_is_neginfty(poly2
);
905 isl_poly_free(poly1
);
908 poly1
= isl_poly_cow(poly1
);
909 rec
= isl_poly_as_rec(poly1
);
912 rec
->p
[0] = isl_poly_sum(rec
->p
[0], poly2
);
914 poly1
= replace_by_constant_term(poly1
);
918 is_cst
= isl_poly_is_cst(poly1
);
922 return isl_poly_sum_cst(poly1
, poly2
);
924 rec1
= isl_poly_as_rec(poly1
);
925 rec2
= isl_poly_as_rec(poly2
);
929 if (rec1
->n
< rec2
->n
)
930 return isl_poly_sum(poly2
, poly1
);
932 poly1
= isl_poly_cow(poly1
);
933 rec1
= isl_poly_as_rec(poly1
);
937 for (i
= rec2
->n
- 1; i
>= 0; --i
) {
940 rec1
->p
[i
] = isl_poly_sum(rec1
->p
[i
],
941 isl_poly_copy(rec2
->p
[i
]));
944 if (i
!= rec1
->n
- 1)
946 is_zero
= isl_poly_is_zero(rec1
->p
[i
]);
950 isl_poly_free(rec1
->p
[i
]);
956 poly1
= replace_by_zero(poly1
);
957 else if (rec1
->n
== 1)
958 poly1
= replace_by_constant_term(poly1
);
960 isl_poly_free(poly2
);
964 isl_poly_free(poly1
);
965 isl_poly_free(poly2
);
969 __isl_give isl_poly
*isl_poly_cst_add_isl_int(__isl_take isl_poly
*poly
,
974 poly
= isl_poly_cow(poly
);
978 cst
= isl_poly_as_cst(poly
);
980 isl_int_addmul(cst
->n
, cst
->d
, v
);
985 __isl_give isl_poly
*isl_poly_add_isl_int(__isl_take isl_poly
*poly
, isl_int v
)
990 is_cst
= isl_poly_is_cst(poly
);
992 return isl_poly_free(poly
);
994 return isl_poly_cst_add_isl_int(poly
, v
);
996 poly
= isl_poly_cow(poly
);
997 rec
= isl_poly_as_rec(poly
);
1001 rec
->p
[0] = isl_poly_add_isl_int(rec
->p
[0], v
);
1007 isl_poly_free(poly
);
1011 __isl_give isl_poly
*isl_poly_cst_mul_isl_int(__isl_take isl_poly
*poly
,
1017 is_zero
= isl_poly_is_zero(poly
);
1019 return isl_poly_free(poly
);
1023 poly
= isl_poly_cow(poly
);
1027 cst
= isl_poly_as_cst(poly
);
1029 isl_int_mul(cst
->n
, cst
->n
, v
);
1034 __isl_give isl_poly
*isl_poly_mul_isl_int(__isl_take isl_poly
*poly
, isl_int v
)
1040 is_cst
= isl_poly_is_cst(poly
);
1042 return isl_poly_free(poly
);
1044 return isl_poly_cst_mul_isl_int(poly
, v
);
1046 poly
= isl_poly_cow(poly
);
1047 rec
= isl_poly_as_rec(poly
);
1051 for (i
= 0; i
< rec
->n
; ++i
) {
1052 rec
->p
[i
] = isl_poly_mul_isl_int(rec
->p
[i
], v
);
1059 isl_poly_free(poly
);
1063 /* Multiply the constant polynomial "poly" by "v".
1065 static __isl_give isl_poly
*isl_poly_cst_scale_val(__isl_take isl_poly
*poly
,
1066 __isl_keep isl_val
*v
)
1071 is_zero
= isl_poly_is_zero(poly
);
1073 return isl_poly_free(poly
);
1077 poly
= isl_poly_cow(poly
);
1081 cst
= isl_poly_as_cst(poly
);
1083 isl_int_mul(cst
->n
, cst
->n
, v
->n
);
1084 isl_int_mul(cst
->d
, cst
->d
, v
->d
);
1085 isl_poly_cst_reduce(cst
);
1090 /* Multiply the polynomial "poly" by "v".
1092 static __isl_give isl_poly
*isl_poly_scale_val(__isl_take isl_poly
*poly
,
1093 __isl_keep isl_val
*v
)
1099 is_cst
= isl_poly_is_cst(poly
);
1101 return isl_poly_free(poly
);
1103 return isl_poly_cst_scale_val(poly
, v
);
1105 poly
= isl_poly_cow(poly
);
1106 rec
= isl_poly_as_rec(poly
);
1110 for (i
= 0; i
< rec
->n
; ++i
) {
1111 rec
->p
[i
] = isl_poly_scale_val(rec
->p
[i
], v
);
1118 isl_poly_free(poly
);
1122 __isl_give isl_poly
*isl_poly_mul_cst(__isl_take isl_poly
*poly1
,
1123 __isl_take isl_poly
*poly2
)
1128 poly1
= isl_poly_cow(poly1
);
1129 if (!poly1
|| !poly2
)
1132 cst1
= isl_poly_as_cst(poly1
);
1133 cst2
= isl_poly_as_cst(poly2
);
1135 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->n
);
1136 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
1138 isl_poly_cst_reduce(cst1
);
1140 isl_poly_free(poly2
);
1143 isl_poly_free(poly1
);
1144 isl_poly_free(poly2
);
1148 __isl_give isl_poly
*isl_poly_mul_rec(__isl_take isl_poly
*poly1
,
1149 __isl_take isl_poly
*poly2
)
1153 isl_poly_rec
*res
= NULL
;
1157 rec1
= isl_poly_as_rec(poly1
);
1158 rec2
= isl_poly_as_rec(poly2
);
1161 size
= rec1
->n
+ rec2
->n
- 1;
1162 res
= isl_poly_alloc_rec(poly1
->ctx
, poly1
->var
, size
);
1166 for (i
= 0; i
< rec1
->n
; ++i
) {
1167 res
->p
[i
] = isl_poly_mul(isl_poly_copy(rec2
->p
[0]),
1168 isl_poly_copy(rec1
->p
[i
]));
1173 for (; i
< size
; ++i
) {
1174 res
->p
[i
] = isl_poly_zero(poly1
->ctx
);
1179 for (i
= 0; i
< rec1
->n
; ++i
) {
1180 for (j
= 1; j
< rec2
->n
; ++j
) {
1182 poly
= isl_poly_mul(isl_poly_copy(rec2
->p
[j
]),
1183 isl_poly_copy(rec1
->p
[i
]));
1184 res
->p
[i
+ j
] = isl_poly_sum(res
->p
[i
+ j
], poly
);
1190 isl_poly_free(poly1
);
1191 isl_poly_free(poly2
);
1195 isl_poly_free(poly1
);
1196 isl_poly_free(poly2
);
1197 isl_poly_free(&res
->poly
);
1201 __isl_give isl_poly
*isl_poly_mul(__isl_take isl_poly
*poly1
,
1202 __isl_take isl_poly
*poly2
)
1204 isl_bool is_zero
, is_nan
, is_one
, is_cst
;
1206 if (!poly1
|| !poly2
)
1209 is_nan
= isl_poly_is_nan(poly1
);
1213 isl_poly_free(poly2
);
1217 is_nan
= isl_poly_is_nan(poly2
);
1221 isl_poly_free(poly1
);
1225 is_zero
= isl_poly_is_zero(poly1
);
1229 isl_poly_free(poly2
);
1233 is_zero
= isl_poly_is_zero(poly2
);
1237 isl_poly_free(poly1
);
1241 is_one
= isl_poly_is_one(poly1
);
1245 isl_poly_free(poly1
);
1249 is_one
= isl_poly_is_one(poly2
);
1253 isl_poly_free(poly2
);
1257 if (poly1
->var
< poly2
->var
)
1258 return isl_poly_mul(poly2
, poly1
);
1260 if (poly2
->var
< poly1
->var
) {
1265 is_infty
= isl_poly_is_infty(poly2
);
1266 if (is_infty
>= 0 && !is_infty
)
1267 is_infty
= isl_poly_is_neginfty(poly2
);
1271 isl_ctx
*ctx
= poly1
->ctx
;
1272 isl_poly_free(poly1
);
1273 isl_poly_free(poly2
);
1274 return isl_poly_nan(ctx
);
1276 poly1
= isl_poly_cow(poly1
);
1277 rec
= isl_poly_as_rec(poly1
);
1281 for (i
= 0; i
< rec
->n
; ++i
) {
1282 rec
->p
[i
] = isl_poly_mul(rec
->p
[i
],
1283 isl_poly_copy(poly2
));
1287 isl_poly_free(poly2
);
1291 is_cst
= isl_poly_is_cst(poly1
);
1295 return isl_poly_mul_cst(poly1
, poly2
);
1297 return isl_poly_mul_rec(poly1
, poly2
);
1299 isl_poly_free(poly1
);
1300 isl_poly_free(poly2
);
1304 __isl_give isl_poly
*isl_poly_pow(__isl_take isl_poly
*poly
, unsigned power
)
1314 res
= isl_poly_copy(poly
);
1316 res
= isl_poly_one(poly
->ctx
);
1318 while (power
>>= 1) {
1319 poly
= isl_poly_mul(poly
, isl_poly_copy(poly
));
1321 res
= isl_poly_mul(res
, isl_poly_copy(poly
));
1324 isl_poly_free(poly
);
1328 __isl_give isl_qpolynomial
*isl_qpolynomial_alloc(__isl_take isl_space
*space
,
1329 unsigned n_div
, __isl_take isl_poly
*poly
)
1331 struct isl_qpolynomial
*qp
= NULL
;
1334 total
= isl_space_dim(space
, isl_dim_all
);
1335 if (total
< 0 || !poly
)
1338 if (!isl_space_is_set(space
))
1339 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
1340 "domain of polynomial should be a set", goto error
);
1342 qp
= isl_calloc_type(space
->ctx
, struct isl_qpolynomial
);
1347 qp
->div
= isl_mat_alloc(space
->ctx
, n_div
, 1 + 1 + total
+ n_div
);
1356 isl_space_free(space
);
1357 isl_poly_free(poly
);
1358 isl_qpolynomial_free(qp
);
1362 __isl_give isl_qpolynomial
*isl_qpolynomial_copy(__isl_keep isl_qpolynomial
*qp
)
1371 __isl_give isl_qpolynomial
*isl_qpolynomial_dup(__isl_keep isl_qpolynomial
*qp
)
1373 struct isl_qpolynomial
*dup
;
1378 dup
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
), qp
->div
->n_row
,
1379 isl_poly_copy(qp
->poly
));
1382 isl_mat_free(dup
->div
);
1383 dup
->div
= isl_mat_copy(qp
->div
);
1389 isl_qpolynomial_free(dup
);
1393 __isl_give isl_qpolynomial
*isl_qpolynomial_cow(__isl_take isl_qpolynomial
*qp
)
1401 return isl_qpolynomial_dup(qp
);
1404 __isl_null isl_qpolynomial
*isl_qpolynomial_free(
1405 __isl_take isl_qpolynomial
*qp
)
1413 isl_space_free(qp
->dim
);
1414 isl_mat_free(qp
->div
);
1415 isl_poly_free(qp
->poly
);
1421 __isl_give isl_poly
*isl_poly_var_pow(isl_ctx
*ctx
, int pos
, int power
)
1427 rec
= isl_poly_alloc_rec(ctx
, pos
, 1 + power
);
1430 for (i
= 0; i
< 1 + power
; ++i
) {
1431 rec
->p
[i
] = isl_poly_zero(ctx
);
1436 cst
= isl_poly_as_cst(rec
->p
[power
]);
1437 isl_int_set_si(cst
->n
, 1);
1441 isl_poly_free(&rec
->poly
);
1445 /* r array maps original positions to new positions.
1447 static __isl_give isl_poly
*reorder(__isl_take isl_poly
*poly
, int *r
)
1455 is_cst
= isl_poly_is_cst(poly
);
1457 return isl_poly_free(poly
);
1461 rec
= isl_poly_as_rec(poly
);
1465 isl_assert(poly
->ctx
, rec
->n
>= 1, goto error
);
1467 base
= isl_poly_var_pow(poly
->ctx
, r
[poly
->var
], 1);
1468 res
= reorder(isl_poly_copy(rec
->p
[rec
->n
- 1]), r
);
1470 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1471 res
= isl_poly_mul(res
, isl_poly_copy(base
));
1472 res
= isl_poly_sum(res
, reorder(isl_poly_copy(rec
->p
[i
]), r
));
1475 isl_poly_free(base
);
1476 isl_poly_free(poly
);
1480 isl_poly_free(poly
);
1484 static isl_bool
compatible_divs(__isl_keep isl_mat
*div1
,
1485 __isl_keep isl_mat
*div2
)
1490 isl_assert(div1
->ctx
, div1
->n_row
>= div2
->n_row
&&
1491 div1
->n_col
>= div2
->n_col
,
1492 return isl_bool_error
);
1494 if (div1
->n_row
== div2
->n_row
)
1495 return isl_mat_is_equal(div1
, div2
);
1497 n_row
= div1
->n_row
;
1498 n_col
= div1
->n_col
;
1499 div1
->n_row
= div2
->n_row
;
1500 div1
->n_col
= div2
->n_col
;
1502 equal
= isl_mat_is_equal(div1
, div2
);
1504 div1
->n_row
= n_row
;
1505 div1
->n_col
= n_col
;
1510 static int cmp_row(__isl_keep isl_mat
*div
, int i
, int j
)
1514 li
= isl_seq_last_non_zero(div
->row
[i
], div
->n_col
);
1515 lj
= isl_seq_last_non_zero(div
->row
[j
], div
->n_col
);
1520 return isl_seq_cmp(div
->row
[i
], div
->row
[j
], div
->n_col
);
1523 struct isl_div_sort_info
{
1528 static int div_sort_cmp(const void *p1
, const void *p2
)
1530 const struct isl_div_sort_info
*i1
, *i2
;
1531 i1
= (const struct isl_div_sort_info
*) p1
;
1532 i2
= (const struct isl_div_sort_info
*) p2
;
1534 return cmp_row(i1
->div
, i1
->row
, i2
->row
);
1537 /* Sort divs and remove duplicates.
1539 static __isl_give isl_qpolynomial
*sort_divs(__isl_take isl_qpolynomial
*qp
)
1544 struct isl_div_sort_info
*array
= NULL
;
1545 int *pos
= NULL
, *at
= NULL
;
1546 int *reordering
= NULL
;
1551 if (qp
->div
->n_row
<= 1)
1554 div_pos
= isl_qpolynomial_domain_var_offset(qp
, isl_dim_div
);
1556 return isl_qpolynomial_free(qp
);
1558 array
= isl_alloc_array(qp
->div
->ctx
, struct isl_div_sort_info
,
1560 pos
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1561 at
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1562 len
= qp
->div
->n_col
- 2;
1563 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
1564 if (!array
|| !pos
|| !at
|| !reordering
)
1567 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1568 array
[i
].div
= qp
->div
;
1574 qsort(array
, qp
->div
->n_row
, sizeof(struct isl_div_sort_info
),
1577 for (i
= 0; i
< div_pos
; ++i
)
1580 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1581 if (pos
[array
[i
].row
] == i
)
1583 qp
->div
= isl_mat_swap_rows(qp
->div
, i
, pos
[array
[i
].row
]);
1584 pos
[at
[i
]] = pos
[array
[i
].row
];
1585 at
[pos
[array
[i
].row
]] = at
[i
];
1586 at
[i
] = array
[i
].row
;
1587 pos
[array
[i
].row
] = i
;
1591 for (i
= 0; i
< len
- div_pos
; ++i
) {
1593 isl_seq_eq(qp
->div
->row
[i
- skip
- 1],
1594 qp
->div
->row
[i
- skip
], qp
->div
->n_col
)) {
1595 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
1596 isl_mat_col_add(qp
->div
, 2 + div_pos
+ i
- skip
- 1,
1597 2 + div_pos
+ i
- skip
);
1598 qp
->div
= isl_mat_drop_cols(qp
->div
,
1599 2 + div_pos
+ i
- skip
, 1);
1602 reordering
[div_pos
+ array
[i
].row
] = div_pos
+ i
- skip
;
1605 qp
->poly
= reorder(qp
->poly
, reordering
);
1607 if (!qp
->poly
|| !qp
->div
)
1621 isl_qpolynomial_free(qp
);
1625 static __isl_give isl_poly
*expand(__isl_take isl_poly
*poly
, int *exp
,
1632 is_cst
= isl_poly_is_cst(poly
);
1634 return isl_poly_free(poly
);
1638 if (poly
->var
< first
)
1641 if (exp
[poly
->var
- first
] == poly
->var
- first
)
1644 poly
= isl_poly_cow(poly
);
1648 poly
->var
= exp
[poly
->var
- first
] + first
;
1650 rec
= isl_poly_as_rec(poly
);
1654 for (i
= 0; i
< rec
->n
; ++i
) {
1655 rec
->p
[i
] = expand(rec
->p
[i
], exp
, first
);
1662 isl_poly_free(poly
);
1666 static __isl_give isl_qpolynomial
*with_merged_divs(
1667 __isl_give isl_qpolynomial
*(*fn
)(__isl_take isl_qpolynomial
*qp1
,
1668 __isl_take isl_qpolynomial
*qp2
),
1669 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
1673 isl_mat
*div
= NULL
;
1676 qp1
= isl_qpolynomial_cow(qp1
);
1677 qp2
= isl_qpolynomial_cow(qp2
);
1682 isl_assert(qp1
->div
->ctx
, qp1
->div
->n_row
>= qp2
->div
->n_row
&&
1683 qp1
->div
->n_col
>= qp2
->div
->n_col
, goto error
);
1685 n_div1
= qp1
->div
->n_row
;
1686 n_div2
= qp2
->div
->n_row
;
1687 exp1
= isl_alloc_array(qp1
->div
->ctx
, int, n_div1
);
1688 exp2
= isl_alloc_array(qp2
->div
->ctx
, int, n_div2
);
1689 if ((n_div1
&& !exp1
) || (n_div2
&& !exp2
))
1692 div
= isl_merge_divs(qp1
->div
, qp2
->div
, exp1
, exp2
);
1696 isl_mat_free(qp1
->div
);
1697 qp1
->div
= isl_mat_copy(div
);
1698 isl_mat_free(qp2
->div
);
1699 qp2
->div
= isl_mat_copy(div
);
1701 qp1
->poly
= expand(qp1
->poly
, exp1
, div
->n_col
- div
->n_row
- 2);
1702 qp2
->poly
= expand(qp2
->poly
, exp2
, div
->n_col
- div
->n_row
- 2);
1704 if (!qp1
->poly
|| !qp2
->poly
)
1711 return fn(qp1
, qp2
);
1716 isl_qpolynomial_free(qp1
);
1717 isl_qpolynomial_free(qp2
);
1721 __isl_give isl_qpolynomial
*isl_qpolynomial_add(__isl_take isl_qpolynomial
*qp1
,
1722 __isl_take isl_qpolynomial
*qp2
)
1724 isl_bool compatible
;
1726 qp1
= isl_qpolynomial_cow(qp1
);
1728 if (isl_qpolynomial_check_equal_space(qp1
, qp2
) < 0)
1731 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1732 return isl_qpolynomial_add(qp2
, qp1
);
1734 compatible
= compatible_divs(qp1
->div
, qp2
->div
);
1738 return with_merged_divs(isl_qpolynomial_add
, qp1
, qp2
);
1740 qp1
->poly
= isl_poly_sum(qp1
->poly
, isl_poly_copy(qp2
->poly
));
1744 isl_qpolynomial_free(qp2
);
1748 isl_qpolynomial_free(qp1
);
1749 isl_qpolynomial_free(qp2
);
1753 __isl_give isl_qpolynomial
*isl_qpolynomial_add_on_domain(
1754 __isl_keep isl_set
*dom
,
1755 __isl_take isl_qpolynomial
*qp1
,
1756 __isl_take isl_qpolynomial
*qp2
)
1758 qp1
= isl_qpolynomial_add(qp1
, qp2
);
1759 qp1
= isl_qpolynomial_gist(qp1
, isl_set_copy(dom
));
1763 __isl_give isl_qpolynomial
*isl_qpolynomial_sub(__isl_take isl_qpolynomial
*qp1
,
1764 __isl_take isl_qpolynomial
*qp2
)
1766 return isl_qpolynomial_add(qp1
, isl_qpolynomial_neg(qp2
));
1769 __isl_give isl_qpolynomial
*isl_qpolynomial_add_isl_int(
1770 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1772 if (isl_int_is_zero(v
))
1775 qp
= isl_qpolynomial_cow(qp
);
1779 qp
->poly
= isl_poly_add_isl_int(qp
->poly
, v
);
1785 isl_qpolynomial_free(qp
);
1790 __isl_give isl_qpolynomial
*isl_qpolynomial_neg(__isl_take isl_qpolynomial
*qp
)
1795 return isl_qpolynomial_mul_isl_int(qp
, qp
->dim
->ctx
->negone
);
1798 __isl_give isl_qpolynomial
*isl_qpolynomial_mul_isl_int(
1799 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1801 if (isl_int_is_one(v
))
1804 if (qp
&& isl_int_is_zero(v
)) {
1805 isl_qpolynomial
*zero
;
1806 zero
= isl_qpolynomial_zero_on_domain(isl_space_copy(qp
->dim
));
1807 isl_qpolynomial_free(qp
);
1811 qp
= isl_qpolynomial_cow(qp
);
1815 qp
->poly
= isl_poly_mul_isl_int(qp
->poly
, v
);
1821 isl_qpolynomial_free(qp
);
1825 __isl_give isl_qpolynomial
*isl_qpolynomial_scale(
1826 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1828 return isl_qpolynomial_mul_isl_int(qp
, v
);
1831 /* Multiply "qp" by "v".
1833 __isl_give isl_qpolynomial
*isl_qpolynomial_scale_val(
1834 __isl_take isl_qpolynomial
*qp
, __isl_take isl_val
*v
)
1839 if (!isl_val_is_rat(v
))
1840 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
1841 "expecting rational factor", goto error
);
1843 if (isl_val_is_one(v
)) {
1848 if (isl_val_is_zero(v
)) {
1851 space
= isl_qpolynomial_get_domain_space(qp
);
1852 isl_qpolynomial_free(qp
);
1854 return isl_qpolynomial_zero_on_domain(space
);
1857 qp
= isl_qpolynomial_cow(qp
);
1861 qp
->poly
= isl_poly_scale_val(qp
->poly
, v
);
1863 qp
= isl_qpolynomial_free(qp
);
1869 isl_qpolynomial_free(qp
);
1873 /* Divide "qp" by "v".
1875 __isl_give isl_qpolynomial
*isl_qpolynomial_scale_down_val(
1876 __isl_take isl_qpolynomial
*qp
, __isl_take isl_val
*v
)
1881 if (!isl_val_is_rat(v
))
1882 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
1883 "expecting rational factor", goto error
);
1884 if (isl_val_is_zero(v
))
1885 isl_die(isl_val_get_ctx(v
), isl_error_invalid
,
1886 "cannot scale down by zero", goto error
);
1888 return isl_qpolynomial_scale_val(qp
, isl_val_inv(v
));
1891 isl_qpolynomial_free(qp
);
1895 __isl_give isl_qpolynomial
*isl_qpolynomial_mul(__isl_take isl_qpolynomial
*qp1
,
1896 __isl_take isl_qpolynomial
*qp2
)
1898 isl_bool compatible
;
1900 qp1
= isl_qpolynomial_cow(qp1
);
1902 if (isl_qpolynomial_check_equal_space(qp1
, qp2
) < 0)
1905 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1906 return isl_qpolynomial_mul(qp2
, qp1
);
1908 compatible
= compatible_divs(qp1
->div
, qp2
->div
);
1912 return with_merged_divs(isl_qpolynomial_mul
, qp1
, qp2
);
1914 qp1
->poly
= isl_poly_mul(qp1
->poly
, isl_poly_copy(qp2
->poly
));
1918 isl_qpolynomial_free(qp2
);
1922 isl_qpolynomial_free(qp1
);
1923 isl_qpolynomial_free(qp2
);
1927 __isl_give isl_qpolynomial
*isl_qpolynomial_pow(__isl_take isl_qpolynomial
*qp
,
1930 qp
= isl_qpolynomial_cow(qp
);
1935 qp
->poly
= isl_poly_pow(qp
->poly
, power
);
1941 isl_qpolynomial_free(qp
);
1945 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_pow(
1946 __isl_take isl_pw_qpolynomial
*pwqp
, unsigned power
)
1953 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
1957 for (i
= 0; i
< pwqp
->n
; ++i
) {
1958 pwqp
->p
[i
].qp
= isl_qpolynomial_pow(pwqp
->p
[i
].qp
, power
);
1960 return isl_pw_qpolynomial_free(pwqp
);
1966 __isl_give isl_qpolynomial
*isl_qpolynomial_zero_on_domain(
1967 __isl_take isl_space
*domain
)
1971 return isl_qpolynomial_alloc(domain
, 0, isl_poly_zero(domain
->ctx
));
1974 __isl_give isl_qpolynomial
*isl_qpolynomial_one_on_domain(
1975 __isl_take isl_space
*domain
)
1979 return isl_qpolynomial_alloc(domain
, 0, isl_poly_one(domain
->ctx
));
1982 __isl_give isl_qpolynomial
*isl_qpolynomial_infty_on_domain(
1983 __isl_take isl_space
*domain
)
1987 return isl_qpolynomial_alloc(domain
, 0, isl_poly_infty(domain
->ctx
));
1990 __isl_give isl_qpolynomial
*isl_qpolynomial_neginfty_on_domain(
1991 __isl_take isl_space
*domain
)
1995 return isl_qpolynomial_alloc(domain
, 0, isl_poly_neginfty(domain
->ctx
));
1998 __isl_give isl_qpolynomial
*isl_qpolynomial_nan_on_domain(
1999 __isl_take isl_space
*domain
)
2003 return isl_qpolynomial_alloc(domain
, 0, isl_poly_nan(domain
->ctx
));
2006 __isl_give isl_qpolynomial
*isl_qpolynomial_cst_on_domain(
2007 __isl_take isl_space
*domain
,
2010 struct isl_qpolynomial
*qp
;
2013 qp
= isl_qpolynomial_zero_on_domain(domain
);
2017 cst
= isl_poly_as_cst(qp
->poly
);
2018 isl_int_set(cst
->n
, v
);
2023 isl_bool
isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial
*qp
,
2024 isl_int
*n
, isl_int
*d
)
2030 return isl_bool_error
;
2032 is_cst
= isl_poly_is_cst(qp
->poly
);
2033 if (is_cst
< 0 || !is_cst
)
2036 cst
= isl_poly_as_cst(qp
->poly
);
2038 return isl_bool_error
;
2041 isl_int_set(*n
, cst
->n
);
2043 isl_int_set(*d
, cst
->d
);
2045 return isl_bool_true
;
2048 /* Return the constant term of "poly".
2050 static __isl_give isl_val
*isl_poly_get_constant_val(__isl_keep isl_poly
*poly
)
2058 while ((is_cst
= isl_poly_is_cst(poly
)) == isl_bool_false
) {
2061 rec
= isl_poly_as_rec(poly
);
2069 cst
= isl_poly_as_cst(poly
);
2072 return isl_val_rat_from_isl_int(cst
->poly
.ctx
, cst
->n
, cst
->d
);
2075 /* Return the constant term of "qp".
2077 __isl_give isl_val
*isl_qpolynomial_get_constant_val(
2078 __isl_keep isl_qpolynomial
*qp
)
2083 return isl_poly_get_constant_val(qp
->poly
);
2086 isl_bool
isl_poly_is_affine(__isl_keep isl_poly
*poly
)
2092 return isl_bool_error
;
2095 return isl_bool_true
;
2097 rec
= isl_poly_as_rec(poly
);
2099 return isl_bool_error
;
2102 return isl_bool_false
;
2104 isl_assert(poly
->ctx
, rec
->n
> 1, return isl_bool_error
);
2106 is_cst
= isl_poly_is_cst(rec
->p
[1]);
2107 if (is_cst
< 0 || !is_cst
)
2110 return isl_poly_is_affine(rec
->p
[0]);
2113 isl_bool
isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial
*qp
)
2116 return isl_bool_error
;
2118 if (qp
->div
->n_row
> 0)
2119 return isl_bool_false
;
2121 return isl_poly_is_affine(qp
->poly
);
2124 static void update_coeff(__isl_keep isl_vec
*aff
,
2125 __isl_keep isl_poly_cst
*cst
, int pos
)
2130 if (isl_int_is_zero(cst
->n
))
2135 isl_int_gcd(gcd
, cst
->d
, aff
->el
[0]);
2136 isl_int_divexact(f
, cst
->d
, gcd
);
2137 isl_int_divexact(gcd
, aff
->el
[0], gcd
);
2138 isl_seq_scale(aff
->el
, aff
->el
, f
, aff
->size
);
2139 isl_int_mul(aff
->el
[1 + pos
], gcd
, cst
->n
);
2144 int isl_poly_update_affine(__isl_keep isl_poly
*poly
, __isl_keep isl_vec
*aff
)
2152 if (poly
->var
< 0) {
2155 cst
= isl_poly_as_cst(poly
);
2158 update_coeff(aff
, cst
, 0);
2162 rec
= isl_poly_as_rec(poly
);
2165 isl_assert(poly
->ctx
, rec
->n
== 2, return -1);
2167 cst
= isl_poly_as_cst(rec
->p
[1]);
2170 update_coeff(aff
, cst
, 1 + poly
->var
);
2172 return isl_poly_update_affine(rec
->p
[0], aff
);
2175 __isl_give isl_vec
*isl_qpolynomial_extract_affine(
2176 __isl_keep isl_qpolynomial
*qp
)
2181 d
= isl_qpolynomial_domain_dim(qp
, isl_dim_all
);
2185 aff
= isl_vec_alloc(qp
->div
->ctx
, 2 + d
);
2189 isl_seq_clr(aff
->el
+ 1, 1 + d
);
2190 isl_int_set_si(aff
->el
[0], 1);
2192 if (isl_poly_update_affine(qp
->poly
, aff
) < 0)
2201 /* Compare two quasi-polynomials.
2203 * Return -1 if "qp1" is "smaller" than "qp2", 1 if "qp1" is "greater"
2204 * than "qp2" and 0 if they are equal.
2206 int isl_qpolynomial_plain_cmp(__isl_keep isl_qpolynomial
*qp1
,
2207 __isl_keep isl_qpolynomial
*qp2
)
2218 cmp
= isl_space_cmp(qp1
->dim
, qp2
->dim
);
2222 cmp
= isl_local_cmp(qp1
->div
, qp2
->div
);
2226 return isl_poly_plain_cmp(qp1
->poly
, qp2
->poly
);
2229 /* Is "qp1" obviously equal to "qp2"?
2231 * NaN is not equal to anything, not even to another NaN.
2233 isl_bool
isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial
*qp1
,
2234 __isl_keep isl_qpolynomial
*qp2
)
2239 return isl_bool_error
;
2241 if (isl_qpolynomial_is_nan(qp1
) || isl_qpolynomial_is_nan(qp2
))
2242 return isl_bool_false
;
2244 equal
= isl_space_is_equal(qp1
->dim
, qp2
->dim
);
2245 if (equal
< 0 || !equal
)
2248 equal
= isl_mat_is_equal(qp1
->div
, qp2
->div
);
2249 if (equal
< 0 || !equal
)
2252 return isl_poly_is_equal(qp1
->poly
, qp2
->poly
);
2255 static isl_stat
poly_update_den(__isl_keep isl_poly
*poly
, isl_int
*d
)
2261 is_cst
= isl_poly_is_cst(poly
);
2263 return isl_stat_error
;
2266 cst
= isl_poly_as_cst(poly
);
2268 return isl_stat_error
;
2269 isl_int_lcm(*d
, *d
, cst
->d
);
2273 rec
= isl_poly_as_rec(poly
);
2275 return isl_stat_error
;
2277 for (i
= 0; i
< rec
->n
; ++i
)
2278 poly_update_den(rec
->p
[i
], d
);
2283 __isl_give isl_val
*isl_qpolynomial_get_den(__isl_keep isl_qpolynomial
*qp
)
2289 d
= isl_val_one(isl_qpolynomial_get_ctx(qp
));
2292 if (poly_update_den(qp
->poly
, &d
->n
) < 0)
2293 return isl_val_free(d
);
2297 __isl_give isl_qpolynomial
*isl_qpolynomial_var_pow_on_domain(
2298 __isl_take isl_space
*domain
, int pos
, int power
)
2300 struct isl_ctx
*ctx
;
2307 return isl_qpolynomial_alloc(domain
, 0,
2308 isl_poly_var_pow(ctx
, pos
, power
));
2311 __isl_give isl_qpolynomial
*isl_qpolynomial_var_on_domain(
2312 __isl_take isl_space
*domain
, enum isl_dim_type type
, unsigned pos
)
2316 if (isl_space_check_is_set(domain
) < 0)
2318 if (isl_space_check_range(domain
, type
, pos
, 1) < 0)
2321 off
= isl_space_offset(domain
, type
);
2325 return isl_qpolynomial_var_pow_on_domain(domain
, off
+ pos
, 1);
2327 isl_space_free(domain
);
2331 __isl_give isl_poly
*isl_poly_subs(__isl_take isl_poly
*poly
,
2332 unsigned first
, unsigned n
, __isl_keep isl_poly
**subs
)
2337 isl_poly
*base
, *res
;
2339 is_cst
= isl_poly_is_cst(poly
);
2341 return isl_poly_free(poly
);
2345 if (poly
->var
< first
)
2348 rec
= isl_poly_as_rec(poly
);
2352 isl_assert(poly
->ctx
, rec
->n
>= 1, goto error
);
2354 if (poly
->var
>= first
+ n
)
2355 base
= isl_poly_var_pow(poly
->ctx
, poly
->var
, 1);
2357 base
= isl_poly_copy(subs
[poly
->var
- first
]);
2359 res
= isl_poly_subs(isl_poly_copy(rec
->p
[rec
->n
- 1]), first
, n
, subs
);
2360 for (i
= rec
->n
- 2; i
>= 0; --i
) {
2362 t
= isl_poly_subs(isl_poly_copy(rec
->p
[i
]), first
, n
, subs
);
2363 res
= isl_poly_mul(res
, isl_poly_copy(base
));
2364 res
= isl_poly_sum(res
, t
);
2367 isl_poly_free(base
);
2368 isl_poly_free(poly
);
2372 isl_poly_free(poly
);
2376 __isl_give isl_poly
*isl_poly_from_affine(isl_ctx
*ctx
, isl_int
*f
,
2377 isl_int denom
, unsigned len
)
2382 isl_assert(ctx
, len
>= 1, return NULL
);
2384 poly
= isl_poly_rat_cst(ctx
, f
[0], denom
);
2385 for (i
= 0; i
< len
- 1; ++i
) {
2389 if (isl_int_is_zero(f
[1 + i
]))
2392 c
= isl_poly_rat_cst(ctx
, f
[1 + i
], denom
);
2393 t
= isl_poly_var_pow(ctx
, i
, 1);
2394 t
= isl_poly_mul(c
, t
);
2395 poly
= isl_poly_sum(poly
, t
);
2401 /* Remove common factor of non-constant terms and denominator.
2403 static void normalize_div(__isl_keep isl_qpolynomial
*qp
, int div
)
2405 isl_ctx
*ctx
= qp
->div
->ctx
;
2406 unsigned total
= qp
->div
->n_col
- 2;
2408 isl_seq_gcd(qp
->div
->row
[div
] + 2, total
, &ctx
->normalize_gcd
);
2409 isl_int_gcd(ctx
->normalize_gcd
,
2410 ctx
->normalize_gcd
, qp
->div
->row
[div
][0]);
2411 if (isl_int_is_one(ctx
->normalize_gcd
))
2414 isl_seq_scale_down(qp
->div
->row
[div
] + 2, qp
->div
->row
[div
] + 2,
2415 ctx
->normalize_gcd
, total
);
2416 isl_int_divexact(qp
->div
->row
[div
][0], qp
->div
->row
[div
][0],
2417 ctx
->normalize_gcd
);
2418 isl_int_fdiv_q(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1],
2419 ctx
->normalize_gcd
);
2422 /* Replace the integer division identified by "div" by the polynomial "s".
2423 * The integer division is assumed not to appear in the definition
2424 * of any other integer divisions.
2426 static __isl_give isl_qpolynomial
*substitute_div(
2427 __isl_take isl_qpolynomial
*qp
, int div
, __isl_take isl_poly
*s
)
2437 qp
= isl_qpolynomial_cow(qp
);
2441 div_pos
= isl_qpolynomial_domain_var_offset(qp
, isl_dim_div
);
2444 qp
->poly
= isl_poly_subs(qp
->poly
, div_pos
+ div
, 1, &s
);
2448 ctx
= isl_qpolynomial_get_ctx(qp
);
2449 reordering
= isl_alloc_array(ctx
, int, div_pos
+ qp
->div
->n_row
);
2452 for (i
= 0; i
< div_pos
+ div
; ++i
)
2454 for (i
= div_pos
+ div
+ 1; i
< div_pos
+ qp
->div
->n_row
; ++i
)
2455 reordering
[i
] = i
- 1;
2456 qp
->div
= isl_mat_drop_rows(qp
->div
, div
, 1);
2457 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + div_pos
+ div
, 1);
2458 qp
->poly
= reorder(qp
->poly
, reordering
);
2461 if (!qp
->poly
|| !qp
->div
)
2467 isl_qpolynomial_free(qp
);
2472 /* Replace all integer divisions [e/d] that turn out to not actually be integer
2473 * divisions because d is equal to 1 by their definition, i.e., e.
2475 static __isl_give isl_qpolynomial
*substitute_non_divs(
2476 __isl_take isl_qpolynomial
*qp
)
2482 div_pos
= isl_qpolynomial_domain_var_offset(qp
, isl_dim_div
);
2484 return isl_qpolynomial_free(qp
);
2486 for (i
= 0; qp
&& i
< qp
->div
->n_row
; ++i
) {
2487 if (!isl_int_is_one(qp
->div
->row
[i
][0]))
2489 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
2490 if (isl_int_is_zero(qp
->div
->row
[j
][2 + div_pos
+ i
]))
2492 isl_seq_combine(qp
->div
->row
[j
] + 1,
2493 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
2494 qp
->div
->row
[j
][2 + div_pos
+ i
],
2495 qp
->div
->row
[i
] + 1, 1 + div_pos
+ i
);
2496 isl_int_set_si(qp
->div
->row
[j
][2 + div_pos
+ i
], 0);
2497 normalize_div(qp
, j
);
2499 s
= isl_poly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
2500 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
2501 qp
= substitute_div(qp
, i
, s
);
2508 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
2509 * with d the denominator. When replacing the coefficient e of x by
2510 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
2511 * inside the division, so we need to add floor(e/d) * x outside.
2512 * That is, we replace q by q' + floor(e/d) * x and we therefore need
2513 * to adjust the coefficient of x in each later div that depends on the
2514 * current div "div" and also in the affine expressions in the rows of "mat"
2515 * (if they too depend on "div").
2517 static void reduce_div(__isl_keep isl_qpolynomial
*qp
, int div
,
2518 __isl_keep isl_mat
**mat
)
2522 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
2525 for (i
= 0; i
< 1 + total
+ div
; ++i
) {
2526 if (isl_int_is_nonneg(qp
->div
->row
[div
][1 + i
]) &&
2527 isl_int_lt(qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]))
2529 isl_int_fdiv_q(v
, qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
2530 isl_int_fdiv_r(qp
->div
->row
[div
][1 + i
],
2531 qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
2532 *mat
= isl_mat_col_addmul(*mat
, i
, v
, 1 + total
+ div
);
2533 for (j
= div
+ 1; j
< qp
->div
->n_row
; ++j
) {
2534 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ div
]))
2536 isl_int_addmul(qp
->div
->row
[j
][1 + i
],
2537 v
, qp
->div
->row
[j
][2 + total
+ div
]);
2543 /* Check if the last non-zero coefficient is bigger that half of the
2544 * denominator. If so, we will invert the div to further reduce the number
2545 * of distinct divs that may appear.
2546 * If the last non-zero coefficient is exactly half the denominator,
2547 * then we continue looking for earlier coefficients that are bigger
2548 * than half the denominator.
2550 static int needs_invert(__isl_keep isl_mat
*div
, int row
)
2555 for (i
= div
->n_col
- 1; i
>= 1; --i
) {
2556 if (isl_int_is_zero(div
->row
[row
][i
]))
2558 isl_int_mul_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
2559 cmp
= isl_int_cmp(div
->row
[row
][i
], div
->row
[row
][0]);
2560 isl_int_divexact_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
2570 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
2571 * We only invert the coefficients of e (and the coefficient of q in
2572 * later divs and in the rows of "mat"). After calling this function, the
2573 * coefficients of e should be reduced again.
2575 static void invert_div(__isl_keep isl_qpolynomial
*qp
, int div
,
2576 __isl_keep isl_mat
**mat
)
2578 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
2580 isl_seq_neg(qp
->div
->row
[div
] + 1,
2581 qp
->div
->row
[div
] + 1, qp
->div
->n_col
- 1);
2582 isl_int_sub_ui(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1], 1);
2583 isl_int_add(qp
->div
->row
[div
][1],
2584 qp
->div
->row
[div
][1], qp
->div
->row
[div
][0]);
2585 *mat
= isl_mat_col_neg(*mat
, 1 + total
+ div
);
2586 isl_mat_col_mul(qp
->div
, 2 + total
+ div
,
2587 qp
->div
->ctx
->negone
, 2 + total
+ div
);
2590 /* Reduce all divs of "qp" to have coefficients
2591 * in the interval [0, d-1], with d the denominator and such that the
2592 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2593 * The modifications to the integer divisions need to be reflected
2594 * in the factors of the polynomial that refer to the original
2595 * integer divisions. To this end, the modifications are collected
2596 * as a set of affine expressions and then plugged into the polynomial.
2598 * After the reduction, some divs may have become redundant or identical,
2599 * so we call substitute_non_divs and sort_divs. If these functions
2600 * eliminate divs or merge two or more divs into one, the coefficients
2601 * of the enclosing divs may have to be reduced again, so we call
2602 * ourselves recursively if the number of divs decreases.
2604 static __isl_give isl_qpolynomial
*reduce_divs(__isl_take isl_qpolynomial
*qp
)
2611 isl_size n_div
, total
, new_n_div
;
2613 total
= isl_qpolynomial_domain_dim(qp
, isl_dim_all
);
2614 n_div
= isl_qpolynomial_domain_dim(qp
, isl_dim_div
);
2615 o_div
= isl_qpolynomial_domain_offset(qp
, isl_dim_div
);
2616 if (total
< 0 || n_div
< 0)
2617 return isl_qpolynomial_free(qp
);
2618 ctx
= isl_qpolynomial_get_ctx(qp
);
2619 mat
= isl_mat_zero(ctx
, n_div
, 1 + total
);
2621 for (i
= 0; i
< n_div
; ++i
)
2622 mat
= isl_mat_set_element_si(mat
, i
, o_div
+ i
, 1);
2624 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2625 normalize_div(qp
, i
);
2626 reduce_div(qp
, i
, &mat
);
2627 if (needs_invert(qp
->div
, i
)) {
2628 invert_div(qp
, i
, &mat
);
2629 reduce_div(qp
, i
, &mat
);
2635 s
= isl_alloc_array(ctx
, struct isl_poly
*, n_div
);
2638 for (i
= 0; i
< n_div
; ++i
)
2639 s
[i
] = isl_poly_from_affine(ctx
, mat
->row
[i
], ctx
->one
,
2641 qp
->poly
= isl_poly_subs(qp
->poly
, o_div
- 1, n_div
, s
);
2642 for (i
= 0; i
< n_div
; ++i
)
2643 isl_poly_free(s
[i
]);
2650 qp
= substitute_non_divs(qp
);
2652 new_n_div
= isl_qpolynomial_domain_dim(qp
, isl_dim_div
);
2654 return isl_qpolynomial_free(qp
);
2655 if (new_n_div
< n_div
)
2656 return reduce_divs(qp
);
2660 isl_qpolynomial_free(qp
);
2665 __isl_give isl_qpolynomial
*isl_qpolynomial_rat_cst_on_domain(
2666 __isl_take isl_space
*domain
, const isl_int n
, const isl_int d
)
2668 struct isl_qpolynomial
*qp
;
2671 qp
= isl_qpolynomial_zero_on_domain(domain
);
2675 cst
= isl_poly_as_cst(qp
->poly
);
2676 isl_int_set(cst
->n
, n
);
2677 isl_int_set(cst
->d
, d
);
2682 /* Return an isl_qpolynomial that is equal to "val" on domain space "domain".
2684 __isl_give isl_qpolynomial
*isl_qpolynomial_val_on_domain(
2685 __isl_take isl_space
*domain
, __isl_take isl_val
*val
)
2687 isl_qpolynomial
*qp
;
2690 qp
= isl_qpolynomial_zero_on_domain(domain
);
2694 cst
= isl_poly_as_cst(qp
->poly
);
2695 isl_int_set(cst
->n
, val
->n
);
2696 isl_int_set(cst
->d
, val
->d
);
2702 isl_qpolynomial_free(qp
);
2706 static isl_stat
poly_set_active(__isl_keep isl_poly
*poly
, int *active
, int d
)
2712 is_cst
= isl_poly_is_cst(poly
);
2714 return isl_stat_error
;
2719 active
[poly
->var
] = 1;
2721 rec
= isl_poly_as_rec(poly
);
2722 for (i
= 0; i
< rec
->n
; ++i
)
2723 if (poly_set_active(rec
->p
[i
], active
, d
) < 0)
2724 return isl_stat_error
;
2729 static isl_stat
set_active(__isl_keep isl_qpolynomial
*qp
, int *active
)
2735 space
= isl_qpolynomial_peek_domain_space(qp
);
2736 d
= isl_space_dim(space
, isl_dim_all
);
2737 if (d
< 0 || !active
)
2738 return isl_stat_error
;
2740 for (i
= 0; i
< d
; ++i
)
2741 for (j
= 0; j
< qp
->div
->n_row
; ++j
) {
2742 if (isl_int_is_zero(qp
->div
->row
[j
][2 + i
]))
2748 return poly_set_active(qp
->poly
, active
, d
);
2752 #define TYPE isl_qpolynomial
2754 #include "check_type_range_templ.c"
2756 isl_bool
isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial
*qp
,
2757 enum isl_dim_type type
, unsigned first
, unsigned n
)
2761 isl_bool involves
= isl_bool_false
;
2767 return isl_bool_error
;
2769 return isl_bool_false
;
2771 if (isl_qpolynomial_check_range(qp
, type
, first
, n
) < 0)
2772 return isl_bool_error
;
2773 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2774 type
== isl_dim_in
, return isl_bool_error
);
2776 space
= isl_qpolynomial_peek_domain_space(qp
);
2777 d
= isl_space_dim(space
, isl_dim_all
);
2779 return isl_bool_error
;
2780 active
= isl_calloc_array(qp
->dim
->ctx
, int, d
);
2781 if (set_active(qp
, active
) < 0)
2784 offset
= isl_qpolynomial_domain_var_offset(qp
, domain_type(type
));
2788 for (i
= 0; i
< n
; ++i
)
2789 if (active
[first
+ i
]) {
2790 involves
= isl_bool_true
;
2799 return isl_bool_error
;
2802 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2803 * of the divs that do appear in the quasi-polynomial.
2805 static __isl_give isl_qpolynomial
*remove_redundant_divs(
2806 __isl_take isl_qpolynomial
*qp
)
2813 int *reordering
= NULL
;
2820 if (qp
->div
->n_row
== 0)
2823 div_pos
= isl_qpolynomial_domain_var_offset(qp
, isl_dim_div
);
2825 return isl_qpolynomial_free(qp
);
2826 len
= qp
->div
->n_col
- 2;
2827 ctx
= isl_qpolynomial_get_ctx(qp
);
2828 active
= isl_calloc_array(ctx
, int, len
);
2832 if (poly_set_active(qp
->poly
, active
, len
) < 0)
2835 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
2836 if (!active
[div_pos
+ i
]) {
2840 for (j
= 0; j
< i
; ++j
) {
2841 if (isl_int_is_zero(qp
->div
->row
[i
][2 + div_pos
+ j
]))
2843 active
[div_pos
+ j
] = 1;
2853 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
2857 for (i
= 0; i
< div_pos
; ++i
)
2861 n_div
= qp
->div
->n_row
;
2862 for (i
= 0; i
< n_div
; ++i
) {
2863 if (!active
[div_pos
+ i
]) {
2864 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
2865 qp
->div
= isl_mat_drop_cols(qp
->div
,
2866 2 + div_pos
+ i
- skip
, 1);
2869 reordering
[div_pos
+ i
] = div_pos
+ i
- skip
;
2872 qp
->poly
= reorder(qp
->poly
, reordering
);
2874 if (!qp
->poly
|| !qp
->div
)
2884 isl_qpolynomial_free(qp
);
2888 __isl_give isl_poly
*isl_poly_drop(__isl_take isl_poly
*poly
,
2889 unsigned first
, unsigned n
)
2896 if (n
== 0 || poly
->var
< 0 || poly
->var
< first
)
2898 if (poly
->var
< first
+ n
) {
2899 poly
= replace_by_constant_term(poly
);
2900 return isl_poly_drop(poly
, first
, n
);
2902 poly
= isl_poly_cow(poly
);
2906 rec
= isl_poly_as_rec(poly
);
2910 for (i
= 0; i
< rec
->n
; ++i
) {
2911 rec
->p
[i
] = isl_poly_drop(rec
->p
[i
], first
, n
);
2918 isl_poly_free(poly
);
2922 __isl_give isl_qpolynomial
*isl_qpolynomial_set_dim_name(
2923 __isl_take isl_qpolynomial
*qp
,
2924 enum isl_dim_type type
, unsigned pos
, const char *s
)
2930 if (type
== isl_dim_out
)
2931 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
2932 "cannot set name of output/set dimension",
2933 return isl_qpolynomial_free(qp
));
2934 type
= domain_type(type
);
2935 space
= isl_qpolynomial_take_domain_space(qp
);
2936 space
= isl_space_set_dim_name(space
, type
, pos
, s
);
2937 qp
= isl_qpolynomial_restore_domain_space(qp
, space
);
2941 __isl_give isl_qpolynomial
*isl_qpolynomial_drop_dims(
2942 __isl_take isl_qpolynomial
*qp
,
2943 enum isl_dim_type type
, unsigned first
, unsigned n
)
2950 if (type
== isl_dim_out
)
2951 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
2952 "cannot drop output/set dimension",
2954 if (isl_qpolynomial_check_range(qp
, type
, first
, n
) < 0)
2955 return isl_qpolynomial_free(qp
);
2956 type
= domain_type(type
);
2957 if (n
== 0 && !isl_space_is_named_or_nested(qp
->dim
, type
))
2961 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2962 type
== isl_dim_set
, goto error
);
2964 space
= isl_qpolynomial_take_domain_space(qp
);
2965 space
= isl_space_drop_dims(space
, type
, first
, n
);
2966 qp
= isl_qpolynomial_restore_domain_space(qp
, space
);
2968 qp
= isl_qpolynomial_cow(qp
);
2972 offset
= isl_qpolynomial_domain_var_offset(qp
, type
);
2977 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + first
, n
);
2981 qp
->poly
= isl_poly_drop(qp
->poly
, first
, n
);
2987 isl_qpolynomial_free(qp
);
2991 /* Project the domain of the quasi-polynomial onto its parameter space.
2992 * The quasi-polynomial may not involve any of the domain dimensions.
2994 __isl_give isl_qpolynomial
*isl_qpolynomial_project_domain_on_params(
2995 __isl_take isl_qpolynomial
*qp
)
3001 n
= isl_qpolynomial_dim(qp
, isl_dim_in
);
3003 return isl_qpolynomial_free(qp
);
3004 involves
= isl_qpolynomial_involves_dims(qp
, isl_dim_in
, 0, n
);
3006 return isl_qpolynomial_free(qp
);
3008 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
3009 "polynomial involves some of the domain dimensions",
3010 return isl_qpolynomial_free(qp
));
3011 qp
= isl_qpolynomial_drop_dims(qp
, isl_dim_in
, 0, n
);
3012 space
= isl_qpolynomial_get_domain_space(qp
);
3013 space
= isl_space_params(space
);
3014 qp
= isl_qpolynomial_reset_domain_space(qp
, space
);
3018 static __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities_lifted(
3019 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
3029 if (eq
->n_eq
== 0) {
3030 isl_basic_set_free(eq
);
3034 qp
= isl_qpolynomial_cow(qp
);
3037 qp
->div
= isl_mat_cow(qp
->div
);
3041 total
= isl_basic_set_offset(eq
, isl_dim_div
);
3043 isl_int_init(denom
);
3044 for (i
= 0; i
< eq
->n_eq
; ++i
) {
3045 j
= isl_seq_last_non_zero(eq
->eq
[i
], total
+ n_div
);
3046 if (j
< 0 || j
== 0 || j
>= total
)
3049 for (k
= 0; k
< qp
->div
->n_row
; ++k
) {
3050 if (isl_int_is_zero(qp
->div
->row
[k
][1 + j
]))
3052 isl_seq_elim(qp
->div
->row
[k
] + 1, eq
->eq
[i
], j
, total
,
3053 &qp
->div
->row
[k
][0]);
3054 normalize_div(qp
, k
);
3057 if (isl_int_is_pos(eq
->eq
[i
][j
]))
3058 isl_seq_neg(eq
->eq
[i
], eq
->eq
[i
], total
);
3059 isl_int_abs(denom
, eq
->eq
[i
][j
]);
3060 isl_int_set_si(eq
->eq
[i
][j
], 0);
3062 poly
= isl_poly_from_affine(qp
->dim
->ctx
,
3063 eq
->eq
[i
], denom
, total
);
3064 qp
->poly
= isl_poly_subs(qp
->poly
, j
- 1, 1, &poly
);
3065 isl_poly_free(poly
);
3067 isl_int_clear(denom
);
3072 isl_basic_set_free(eq
);
3074 qp
= substitute_non_divs(qp
);
3079 isl_basic_set_free(eq
);
3080 isl_qpolynomial_free(qp
);
3084 /* Exploit the equalities in "eq" to simplify the quasi-polynomial.
3086 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities(
3087 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
3091 if (qp
->div
->n_row
> 0)
3092 eq
= isl_basic_set_add_dims(eq
, isl_dim_set
, qp
->div
->n_row
);
3093 return isl_qpolynomial_substitute_equalities_lifted(qp
, eq
);
3095 isl_basic_set_free(eq
);
3096 isl_qpolynomial_free(qp
);
3100 /* Look for equalities among the variables shared by context and qp
3101 * and the integer divisions of qp, if any.
3102 * The equalities are then used to eliminate variables and/or integer
3103 * divisions from qp.
3105 __isl_give isl_qpolynomial
*isl_qpolynomial_gist(
3106 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
3108 isl_local_space
*ls
;
3111 ls
= isl_qpolynomial_get_domain_local_space(qp
);
3112 context
= isl_local_space_lift_set(ls
, context
);
3114 aff
= isl_set_affine_hull(context
);
3115 return isl_qpolynomial_substitute_equalities_lifted(qp
, aff
);
3118 __isl_give isl_qpolynomial
*isl_qpolynomial_gist_params(
3119 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
3121 isl_space
*space
= isl_qpolynomial_get_domain_space(qp
);
3122 isl_set
*dom_context
= isl_set_universe(space
);
3123 dom_context
= isl_set_intersect_params(dom_context
, context
);
3124 return isl_qpolynomial_gist(qp
, dom_context
);
3127 /* Return a zero isl_qpolynomial in the given space.
3129 * This is a helper function for isl_pw_*_as_* that ensures a uniform
3130 * interface over all piecewise types.
3132 static __isl_give isl_qpolynomial
*isl_qpolynomial_zero_in_space(
3133 __isl_take isl_space
*space
)
3135 return isl_qpolynomial_zero_on_domain(isl_space_domain(space
));
3138 #define isl_qpolynomial_involves_nan isl_qpolynomial_is_nan
3141 #define PW isl_pw_qpolynomial
3143 #define BASE qpolynomial
3145 #define EL_IS_ZERO is_zero
3149 #define IS_ZERO is_zero
3152 #undef DEFAULT_IS_ZERO
3153 #define DEFAULT_IS_ZERO 1
3155 #include <isl_pw_templ.c>
3156 #include <isl_pw_un_op_templ.c>
3157 #include <isl_pw_add_disjoint_templ.c>
3158 #include <isl_pw_eval.c>
3159 #include <isl_pw_fix_templ.c>
3160 #include <isl_pw_from_range_templ.c>
3161 #include <isl_pw_insert_dims_templ.c>
3162 #include <isl_pw_lift_templ.c>
3163 #include <isl_pw_morph_templ.c>
3164 #include <isl_pw_move_dims_templ.c>
3165 #include <isl_pw_neg_templ.c>
3166 #include <isl_pw_opt_templ.c>
3167 #include <isl_pw_split_dims_templ.c>
3168 #include <isl_pw_sub_templ.c>
3171 #define BASE pw_qpolynomial
3173 #include <isl_union_single.c>
3174 #include <isl_union_eval.c>
3175 #include <isl_union_neg.c>
3176 #include <isl_union_sub_templ.c>
3178 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial
*pwqp
)
3186 if (!isl_set_plain_is_universe(pwqp
->p
[0].set
))
3189 return isl_qpolynomial_is_one(pwqp
->p
[0].qp
);
3192 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add(
3193 __isl_take isl_pw_qpolynomial
*pwqp1
,
3194 __isl_take isl_pw_qpolynomial
*pwqp2
)
3196 return isl_pw_qpolynomial_union_add_(pwqp1
, pwqp2
);
3199 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_mul(
3200 __isl_take isl_pw_qpolynomial
*pwqp1
,
3201 __isl_take isl_pw_qpolynomial
*pwqp2
)
3204 struct isl_pw_qpolynomial
*res
;
3206 if (!pwqp1
|| !pwqp2
)
3209 isl_assert(pwqp1
->dim
->ctx
, isl_space_is_equal(pwqp1
->dim
, pwqp2
->dim
),
3212 if (isl_pw_qpolynomial_is_zero(pwqp1
)) {
3213 isl_pw_qpolynomial_free(pwqp2
);
3217 if (isl_pw_qpolynomial_is_zero(pwqp2
)) {
3218 isl_pw_qpolynomial_free(pwqp1
);
3222 if (isl_pw_qpolynomial_is_one(pwqp1
)) {
3223 isl_pw_qpolynomial_free(pwqp1
);
3227 if (isl_pw_qpolynomial_is_one(pwqp2
)) {
3228 isl_pw_qpolynomial_free(pwqp2
);
3232 n
= pwqp1
->n
* pwqp2
->n
;
3233 res
= isl_pw_qpolynomial_alloc_size(isl_space_copy(pwqp1
->dim
), n
);
3235 for (i
= 0; i
< pwqp1
->n
; ++i
) {
3236 for (j
= 0; j
< pwqp2
->n
; ++j
) {
3237 struct isl_set
*common
;
3238 struct isl_qpolynomial
*prod
;
3239 common
= isl_set_intersect(isl_set_copy(pwqp1
->p
[i
].set
),
3240 isl_set_copy(pwqp2
->p
[j
].set
));
3241 if (isl_set_plain_is_empty(common
)) {
3242 isl_set_free(common
);
3246 prod
= isl_qpolynomial_mul(
3247 isl_qpolynomial_copy(pwqp1
->p
[i
].qp
),
3248 isl_qpolynomial_copy(pwqp2
->p
[j
].qp
));
3250 res
= isl_pw_qpolynomial_add_piece(res
, common
, prod
);
3254 isl_pw_qpolynomial_free(pwqp1
);
3255 isl_pw_qpolynomial_free(pwqp2
);
3259 isl_pw_qpolynomial_free(pwqp1
);
3260 isl_pw_qpolynomial_free(pwqp2
);
3264 __isl_give isl_val
*isl_poly_eval(__isl_take isl_poly
*poly
,
3265 __isl_take isl_vec
*vec
)
3273 is_cst
= isl_poly_is_cst(poly
);
3278 res
= isl_poly_get_constant_val(poly
);
3279 isl_poly_free(poly
);
3283 rec
= isl_poly_as_rec(poly
);
3287 isl_assert(poly
->ctx
, rec
->n
>= 1, goto error
);
3289 base
= isl_val_rat_from_isl_int(poly
->ctx
,
3290 vec
->el
[1 + poly
->var
], vec
->el
[0]);
3292 res
= isl_poly_eval(isl_poly_copy(rec
->p
[rec
->n
- 1]),
3295 for (i
= rec
->n
- 2; i
>= 0; --i
) {
3296 res
= isl_val_mul(res
, isl_val_copy(base
));
3297 res
= isl_val_add(res
, isl_poly_eval(isl_poly_copy(rec
->p
[i
]),
3298 isl_vec_copy(vec
)));
3302 isl_poly_free(poly
);
3306 isl_poly_free(poly
);
3311 /* Evaluate "qp" in the void point "pnt".
3312 * In particular, return the value NaN.
3314 static __isl_give isl_val
*eval_void(__isl_take isl_qpolynomial
*qp
,
3315 __isl_take isl_point
*pnt
)
3319 ctx
= isl_point_get_ctx(pnt
);
3320 isl_qpolynomial_free(qp
);
3321 isl_point_free(pnt
);
3322 return isl_val_nan(ctx
);
3325 __isl_give isl_val
*isl_qpolynomial_eval(__isl_take isl_qpolynomial
*qp
,
3326 __isl_take isl_point
*pnt
)
3334 isl_assert(pnt
->dim
->ctx
, isl_space_is_equal(pnt
->dim
, qp
->dim
), goto error
);
3335 is_void
= isl_point_is_void(pnt
);
3339 return eval_void(qp
, pnt
);
3341 ext
= isl_local_extend_point_vec(qp
->div
, isl_vec_copy(pnt
->vec
));
3343 v
= isl_poly_eval(isl_poly_copy(qp
->poly
), ext
);
3345 isl_qpolynomial_free(qp
);
3346 isl_point_free(pnt
);
3350 isl_qpolynomial_free(qp
);
3351 isl_point_free(pnt
);
3355 int isl_poly_cmp(__isl_keep isl_poly_cst
*cst1
, __isl_keep isl_poly_cst
*cst2
)
3360 isl_int_mul(t
, cst1
->n
, cst2
->d
);
3361 isl_int_submul(t
, cst2
->n
, cst1
->d
);
3362 cmp
= isl_int_sgn(t
);
3367 __isl_give isl_qpolynomial
*isl_qpolynomial_insert_dims(
3368 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
,
3369 unsigned first
, unsigned n
)
3378 if (type
== isl_dim_out
)
3379 isl_die(qp
->div
->ctx
, isl_error_invalid
,
3380 "cannot insert output/set dimensions",
3382 if (isl_qpolynomial_check_range(qp
, type
, first
, 0) < 0)
3383 return isl_qpolynomial_free(qp
);
3384 type
= domain_type(type
);
3385 if (n
== 0 && !isl_space_is_named_or_nested(qp
->dim
, type
))
3388 qp
= isl_qpolynomial_cow(qp
);
3392 g_pos
= pos(qp
->dim
, type
) + first
;
3394 qp
->div
= isl_mat_insert_zero_cols(qp
->div
, 2 + g_pos
, n
);
3398 total
= qp
->div
->n_col
- 2;
3399 if (total
> g_pos
) {
3401 exp
= isl_alloc_array(qp
->div
->ctx
, int, total
- g_pos
);
3404 for (i
= 0; i
< total
- g_pos
; ++i
)
3406 qp
->poly
= expand(qp
->poly
, exp
, g_pos
);
3412 space
= isl_qpolynomial_take_domain_space(qp
);
3413 space
= isl_space_insert_dims(space
, type
, first
, n
);
3414 qp
= isl_qpolynomial_restore_domain_space(qp
, space
);
3418 isl_qpolynomial_free(qp
);
3422 __isl_give isl_qpolynomial
*isl_qpolynomial_add_dims(
3423 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
, unsigned n
)
3427 pos
= isl_qpolynomial_dim(qp
, type
);
3429 return isl_qpolynomial_free(qp
);
3431 return isl_qpolynomial_insert_dims(qp
, type
, pos
, n
);
3434 static int *reordering_move(isl_ctx
*ctx
,
3435 unsigned len
, unsigned dst
, unsigned src
, unsigned n
)
3440 reordering
= isl_alloc_array(ctx
, int, len
);
3445 for (i
= 0; i
< dst
; ++i
)
3447 for (i
= 0; i
< n
; ++i
)
3448 reordering
[src
+ i
] = dst
+ i
;
3449 for (i
= 0; i
< src
- dst
; ++i
)
3450 reordering
[dst
+ i
] = dst
+ n
+ i
;
3451 for (i
= 0; i
< len
- src
- n
; ++i
)
3452 reordering
[src
+ n
+ i
] = src
+ n
+ i
;
3454 for (i
= 0; i
< src
; ++i
)
3456 for (i
= 0; i
< n
; ++i
)
3457 reordering
[src
+ i
] = dst
+ i
;
3458 for (i
= 0; i
< dst
- src
; ++i
)
3459 reordering
[src
+ n
+ i
] = src
+ i
;
3460 for (i
= 0; i
< len
- dst
- n
; ++i
)
3461 reordering
[dst
+ n
+ i
] = dst
+ n
+ i
;
3467 __isl_give isl_qpolynomial
*isl_qpolynomial_move_dims(
3468 __isl_take isl_qpolynomial
*qp
,
3469 enum isl_dim_type dst_type
, unsigned dst_pos
,
3470 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
3476 isl_size src_off
, dst_off
;
3483 ctx
= isl_qpolynomial_get_ctx(qp
);
3484 if (dst_type
== isl_dim_out
|| src_type
== isl_dim_out
)
3485 isl_die(ctx
, isl_error_invalid
,
3486 "cannot move output/set dimension",
3487 return isl_qpolynomial_free(qp
));
3488 if (src_type
== isl_dim_div
|| dst_type
== isl_dim_div
)
3489 isl_die(ctx
, isl_error_invalid
, "cannot move local variables",
3490 return isl_qpolynomial_free(qp
));
3491 if (isl_qpolynomial_check_range(qp
, src_type
, src_pos
, n
) < 0)
3492 return isl_qpolynomial_free(qp
);
3493 if (dst_type
== isl_dim_in
)
3494 dst_type
= isl_dim_set
;
3495 if (src_type
== isl_dim_in
)
3496 src_type
= isl_dim_set
;
3499 !isl_space_is_named_or_nested(qp
->dim
, src_type
) &&
3500 !isl_space_is_named_or_nested(qp
->dim
, dst_type
))
3503 qp
= isl_qpolynomial_cow(qp
);
3504 src_off
= isl_qpolynomial_domain_var_offset(qp
, src_type
);
3505 dst_off
= isl_qpolynomial_domain_var_offset(qp
, dst_type
);
3506 if (src_off
< 0 || dst_off
< 0)
3507 return isl_qpolynomial_free(qp
);
3509 g_dst_pos
= dst_off
+ dst_pos
;
3510 g_src_pos
= src_off
+ src_pos
;
3511 if (dst_type
> src_type
)
3514 qp
->div
= isl_local_move_vars(qp
->div
, g_dst_pos
, g_src_pos
, n
);
3516 return isl_qpolynomial_free(qp
);
3519 total
= isl_qpolynomial_domain_dim(qp
, isl_dim_all
);
3521 return isl_qpolynomial_free(qp
);
3522 reordering
= reordering_move(ctx
, total
, g_dst_pos
, g_src_pos
, n
);
3524 return isl_qpolynomial_free(qp
);
3526 qp
->poly
= reorder(qp
->poly
, reordering
);
3529 return isl_qpolynomial_free(qp
);
3531 space
= isl_qpolynomial_take_domain_space(qp
);
3532 space
= isl_space_move_dims(space
, dst_type
, dst_pos
,
3533 src_type
, src_pos
, n
);
3534 qp
= isl_qpolynomial_restore_domain_space(qp
, space
);
3539 __isl_give isl_qpolynomial
*isl_qpolynomial_from_affine(
3540 __isl_take isl_space
*space
, isl_int
*f
, isl_int denom
)
3545 space
= isl_space_domain(space
);
3549 d
= isl_space_dim(space
, isl_dim_all
);
3550 poly
= d
< 0 ? NULL
: isl_poly_from_affine(space
->ctx
, f
, denom
, 1 + d
);
3552 return isl_qpolynomial_alloc(space
, 0, poly
);
3555 __isl_give isl_qpolynomial
*isl_qpolynomial_from_aff(__isl_take isl_aff
*aff
)
3559 isl_qpolynomial
*qp
;
3564 ctx
= isl_aff_get_ctx(aff
);
3565 poly
= isl_poly_from_affine(ctx
, aff
->v
->el
+ 1, aff
->v
->el
[0],
3568 qp
= isl_qpolynomial_alloc(isl_aff_get_domain_space(aff
),
3569 aff
->ls
->div
->n_row
, poly
);
3573 isl_mat_free(qp
->div
);
3574 qp
->div
= isl_mat_copy(aff
->ls
->div
);
3575 qp
->div
= isl_mat_cow(qp
->div
);
3580 qp
= reduce_divs(qp
);
3581 qp
= remove_redundant_divs(qp
);
3585 return isl_qpolynomial_free(qp
);
3588 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_from_pw_aff(
3589 __isl_take isl_pw_aff
*pwaff
)
3592 isl_pw_qpolynomial
*pwqp
;
3597 pwqp
= isl_pw_qpolynomial_alloc_size(isl_pw_aff_get_space(pwaff
),
3600 for (i
= 0; i
< pwaff
->n
; ++i
) {
3602 isl_qpolynomial
*qp
;
3604 dom
= isl_set_copy(pwaff
->p
[i
].set
);
3605 qp
= isl_qpolynomial_from_aff(isl_aff_copy(pwaff
->p
[i
].aff
));
3606 pwqp
= isl_pw_qpolynomial_add_piece(pwqp
, dom
, qp
);
3609 isl_pw_aff_free(pwaff
);
3613 __isl_give isl_qpolynomial
*isl_qpolynomial_from_constraint(
3614 __isl_take isl_constraint
*c
, enum isl_dim_type type
, unsigned pos
)
3618 aff
= isl_constraint_get_bound(c
, type
, pos
);
3619 isl_constraint_free(c
);
3620 return isl_qpolynomial_from_aff(aff
);
3623 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3624 * in "qp" by subs[i].
3626 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute(
3627 __isl_take isl_qpolynomial
*qp
,
3628 enum isl_dim_type type
, unsigned first
, unsigned n
,
3629 __isl_keep isl_qpolynomial
**subs
)
3637 qp
= isl_qpolynomial_cow(qp
);
3641 if (type
== isl_dim_out
)
3642 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
3643 "cannot substitute output/set dimension",
3645 if (isl_qpolynomial_check_range(qp
, type
, first
, n
) < 0)
3646 return isl_qpolynomial_free(qp
);
3647 type
= domain_type(type
);
3649 for (i
= 0; i
< n
; ++i
)
3653 for (i
= 0; i
< n
; ++i
)
3654 if (isl_qpolynomial_check_equal_space(qp
, subs
[i
]) < 0)
3657 isl_assert(qp
->dim
->ctx
, qp
->div
->n_row
== 0, goto error
);
3658 for (i
= 0; i
< n
; ++i
)
3659 isl_assert(qp
->dim
->ctx
, subs
[i
]->div
->n_row
== 0, goto error
);
3661 first
+= pos(qp
->dim
, type
);
3663 polys
= isl_alloc_array(qp
->dim
->ctx
, struct isl_poly
*, n
);
3666 for (i
= 0; i
< n
; ++i
)
3667 polys
[i
] = subs
[i
]->poly
;
3669 qp
->poly
= isl_poly_subs(qp
->poly
, first
, n
, polys
);
3678 isl_qpolynomial_free(qp
);
3682 /* Extend "bset" with extra set dimensions for each integer division
3683 * in "qp" and then call "fn" with the extended bset and the polynomial
3684 * that results from replacing each of the integer divisions by the
3685 * corresponding extra set dimension.
3687 isl_stat
isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial
*qp
,
3688 __isl_keep isl_basic_set
*bset
,
3689 isl_stat (*fn
)(__isl_take isl_basic_set
*bset
,
3690 __isl_take isl_qpolynomial
*poly
, void *user
), void *user
)
3693 isl_local_space
*ls
;
3694 isl_qpolynomial
*poly
;
3697 return isl_stat_error
;
3698 if (qp
->div
->n_row
== 0)
3699 return fn(isl_basic_set_copy(bset
), isl_qpolynomial_copy(qp
),
3702 space
= isl_space_copy(qp
->dim
);
3703 space
= isl_space_add_dims(space
, isl_dim_set
, qp
->div
->n_row
);
3704 poly
= isl_qpolynomial_alloc(space
, 0, isl_poly_copy(qp
->poly
));
3705 bset
= isl_basic_set_copy(bset
);
3706 ls
= isl_qpolynomial_get_domain_local_space(qp
);
3707 bset
= isl_local_space_lift_basic_set(ls
, bset
);
3709 return fn(bset
, poly
, user
);
3712 /* Return total degree in variables first (inclusive) up to last (exclusive).
3714 int isl_poly_degree(__isl_keep isl_poly
*poly
, int first
, int last
)
3718 isl_bool is_zero
, is_cst
;
3721 is_zero
= isl_poly_is_zero(poly
);
3726 is_cst
= isl_poly_is_cst(poly
);
3729 if (is_cst
|| poly
->var
< first
)
3732 rec
= isl_poly_as_rec(poly
);
3736 for (i
= 0; i
< rec
->n
; ++i
) {
3739 is_zero
= isl_poly_is_zero(rec
->p
[i
]);
3744 d
= isl_poly_degree(rec
->p
[i
], first
, last
);
3745 if (poly
->var
< last
)
3754 /* Return total degree in set variables.
3756 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial
*poly
)
3764 ovar
= isl_space_offset(poly
->dim
, isl_dim_set
);
3765 nvar
= isl_space_dim(poly
->dim
, isl_dim_set
);
3766 if (ovar
< 0 || nvar
< 0)
3768 return isl_poly_degree(poly
->poly
, ovar
, ovar
+ nvar
);
3771 __isl_give isl_poly
*isl_poly_coeff(__isl_keep isl_poly
*poly
,
3772 unsigned pos
, int deg
)
3778 is_cst
= isl_poly_is_cst(poly
);
3781 if (is_cst
|| poly
->var
< pos
) {
3783 return isl_poly_copy(poly
);
3785 return isl_poly_zero(poly
->ctx
);
3788 rec
= isl_poly_as_rec(poly
);
3792 if (poly
->var
== pos
) {
3794 return isl_poly_copy(rec
->p
[deg
]);
3796 return isl_poly_zero(poly
->ctx
);
3799 poly
= isl_poly_copy(poly
);
3800 poly
= isl_poly_cow(poly
);
3801 rec
= isl_poly_as_rec(poly
);
3805 for (i
= 0; i
< rec
->n
; ++i
) {
3807 t
= isl_poly_coeff(rec
->p
[i
], pos
, deg
);
3810 isl_poly_free(rec
->p
[i
]);
3816 isl_poly_free(poly
);
3820 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3822 __isl_give isl_qpolynomial
*isl_qpolynomial_coeff(
3823 __isl_keep isl_qpolynomial
*qp
,
3824 enum isl_dim_type type
, unsigned t_pos
, int deg
)
3833 if (type
== isl_dim_out
)
3834 isl_die(qp
->div
->ctx
, isl_error_invalid
,
3835 "output/set dimension does not have a coefficient",
3837 if (isl_qpolynomial_check_range(qp
, type
, t_pos
, 1) < 0)
3839 type
= domain_type(type
);
3841 g_pos
= pos(qp
->dim
, type
) + t_pos
;
3842 poly
= isl_poly_coeff(qp
->poly
, g_pos
, deg
);
3844 c
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
),
3845 qp
->div
->n_row
, poly
);
3848 isl_mat_free(c
->div
);
3849 c
->div
= isl_mat_copy(qp
->div
);
3854 isl_qpolynomial_free(c
);
3858 /* Homogenize the polynomial in the variables first (inclusive) up to
3859 * last (exclusive) by inserting powers of variable first.
3860 * Variable first is assumed not to appear in the input.
3862 __isl_give isl_poly
*isl_poly_homogenize(__isl_take isl_poly
*poly
, int deg
,
3863 int target
, int first
, int last
)
3866 isl_bool is_zero
, is_cst
;
3869 is_zero
= isl_poly_is_zero(poly
);
3871 return isl_poly_free(poly
);
3876 is_cst
= isl_poly_is_cst(poly
);
3878 return isl_poly_free(poly
);
3879 if (is_cst
|| poly
->var
< first
) {
3882 hom
= isl_poly_var_pow(poly
->ctx
, first
, target
- deg
);
3885 rec
= isl_poly_as_rec(hom
);
3886 rec
->p
[target
- deg
] = isl_poly_mul(rec
->p
[target
- deg
], poly
);
3891 poly
= isl_poly_cow(poly
);
3892 rec
= isl_poly_as_rec(poly
);
3896 for (i
= 0; i
< rec
->n
; ++i
) {
3897 is_zero
= isl_poly_is_zero(rec
->p
[i
]);
3899 return isl_poly_free(poly
);
3902 rec
->p
[i
] = isl_poly_homogenize(rec
->p
[i
],
3903 poly
->var
< last
? deg
+ i
: i
, target
,
3911 isl_poly_free(poly
);
3915 /* Homogenize the polynomial in the set variables by introducing
3916 * powers of an extra set variable at position 0.
3918 __isl_give isl_qpolynomial
*isl_qpolynomial_homogenize(
3919 __isl_take isl_qpolynomial
*poly
)
3923 int deg
= isl_qpolynomial_degree(poly
);
3928 poly
= isl_qpolynomial_insert_dims(poly
, isl_dim_in
, 0, 1);
3929 poly
= isl_qpolynomial_cow(poly
);
3933 ovar
= isl_space_offset(poly
->dim
, isl_dim_set
);
3934 nvar
= isl_space_dim(poly
->dim
, isl_dim_set
);
3935 if (ovar
< 0 || nvar
< 0)
3936 return isl_qpolynomial_free(poly
);
3937 poly
->poly
= isl_poly_homogenize(poly
->poly
, 0, deg
, ovar
, ovar
+ nvar
);
3943 isl_qpolynomial_free(poly
);
3947 __isl_give isl_term
*isl_term_alloc(__isl_take isl_space
*space
,
3948 __isl_take isl_mat
*div
)
3954 d
= isl_space_dim(space
, isl_dim_all
);
3960 term
= isl_calloc(space
->ctx
, struct isl_term
,
3961 sizeof(struct isl_term
) + (n
- 1) * sizeof(int));
3968 isl_int_init(term
->n
);
3969 isl_int_init(term
->d
);
3973 isl_space_free(space
);
3978 __isl_give isl_term
*isl_term_copy(__isl_keep isl_term
*term
)
3987 __isl_give isl_term
*isl_term_dup(__isl_keep isl_term
*term
)
3993 total
= isl_term_dim(term
, isl_dim_all
);
3997 dup
= isl_term_alloc(isl_space_copy(term
->dim
), isl_mat_copy(term
->div
));
4001 isl_int_set(dup
->n
, term
->n
);
4002 isl_int_set(dup
->d
, term
->d
);
4004 for (i
= 0; i
< total
; ++i
)
4005 dup
->pow
[i
] = term
->pow
[i
];
4010 __isl_give isl_term
*isl_term_cow(__isl_take isl_term
*term
)
4018 return isl_term_dup(term
);
4021 __isl_null isl_term
*isl_term_free(__isl_take isl_term
*term
)
4026 if (--term
->ref
> 0)
4029 isl_space_free(term
->dim
);
4030 isl_mat_free(term
->div
);
4031 isl_int_clear(term
->n
);
4032 isl_int_clear(term
->d
);
4038 isl_size
isl_term_dim(__isl_keep isl_term
*term
, enum isl_dim_type type
)
4043 return isl_size_error
;
4048 case isl_dim_out
: return isl_space_dim(term
->dim
, type
);
4049 case isl_dim_div
: return term
->div
->n_row
;
4050 case isl_dim_all
: dim
= isl_space_dim(term
->dim
, isl_dim_all
);
4052 return isl_size_error
;
4053 return dim
+ term
->div
->n_row
;
4054 default: return isl_size_error
;
4058 /* Return the space of "term".
4060 static __isl_keep isl_space
*isl_term_peek_space(__isl_keep isl_term
*term
)
4062 return term
? term
->dim
: NULL
;
4065 /* Return the offset of the first variable of type "type" within
4066 * the variables of "term".
4068 static isl_size
isl_term_offset(__isl_keep isl_term
*term
,
4069 enum isl_dim_type type
)
4073 space
= isl_term_peek_space(term
);
4075 return isl_size_error
;
4079 case isl_dim_set
: return isl_space_offset(space
, type
);
4080 case isl_dim_div
: return isl_space_dim(space
, isl_dim_all
);
4082 isl_die(isl_term_get_ctx(term
), isl_error_invalid
,
4083 "invalid dimension type", return isl_size_error
);
4087 isl_ctx
*isl_term_get_ctx(__isl_keep isl_term
*term
)
4089 return term
? term
->dim
->ctx
: NULL
;
4092 void isl_term_get_num(__isl_keep isl_term
*term
, isl_int
*n
)
4096 isl_int_set(*n
, term
->n
);
4099 /* Return the coefficient of the term "term".
4101 __isl_give isl_val
*isl_term_get_coefficient_val(__isl_keep isl_term
*term
)
4106 return isl_val_rat_from_isl_int(isl_term_get_ctx(term
),
4111 #define TYPE isl_term
4113 #include "check_type_range_templ.c"
4115 isl_size
isl_term_get_exp(__isl_keep isl_term
*term
,
4116 enum isl_dim_type type
, unsigned pos
)
4120 if (isl_term_check_range(term
, type
, pos
, 1) < 0)
4121 return isl_size_error
;
4122 offset
= isl_term_offset(term
, type
);
4124 return isl_size_error
;
4126 return term
->pow
[offset
+ pos
];
4129 __isl_give isl_aff
*isl_term_get_div(__isl_keep isl_term
*term
, unsigned pos
)
4131 isl_local_space
*ls
;
4134 if (isl_term_check_range(term
, isl_dim_div
, pos
, 1) < 0)
4137 ls
= isl_local_space_alloc_div(isl_space_copy(term
->dim
),
4138 isl_mat_copy(term
->div
));
4139 aff
= isl_aff_alloc(ls
);
4143 isl_seq_cpy(aff
->v
->el
, term
->div
->row
[pos
], aff
->v
->size
);
4145 aff
= isl_aff_normalize(aff
);
4150 __isl_give isl_term
*isl_poly_foreach_term(__isl_keep isl_poly
*poly
,
4151 isl_stat (*fn
)(__isl_take isl_term
*term
, void *user
),
4152 __isl_take isl_term
*term
, void *user
)
4155 isl_bool is_zero
, is_bad
, is_cst
;
4158 is_zero
= isl_poly_is_zero(poly
);
4159 if (is_zero
< 0 || !term
)
4165 is_cst
= isl_poly_is_cst(poly
);
4166 is_bad
= isl_poly_is_nan(poly
);
4167 if (is_bad
>= 0 && !is_bad
)
4168 is_bad
= isl_poly_is_infty(poly
);
4169 if (is_bad
>= 0 && !is_bad
)
4170 is_bad
= isl_poly_is_neginfty(poly
);
4171 if (is_cst
< 0 || is_bad
< 0)
4172 return isl_term_free(term
);
4174 isl_die(isl_term_get_ctx(term
), isl_error_invalid
,
4175 "cannot handle NaN/infty polynomial",
4176 return isl_term_free(term
));
4180 cst
= isl_poly_as_cst(poly
);
4183 term
= isl_term_cow(term
);
4186 isl_int_set(term
->n
, cst
->n
);
4187 isl_int_set(term
->d
, cst
->d
);
4188 if (fn(isl_term_copy(term
), user
) < 0)
4193 rec
= isl_poly_as_rec(poly
);
4197 for (i
= 0; i
< rec
->n
; ++i
) {
4198 term
= isl_term_cow(term
);
4201 term
->pow
[poly
->var
] = i
;
4202 term
= isl_poly_foreach_term(rec
->p
[i
], fn
, term
, user
);
4206 term
= isl_term_cow(term
);
4209 term
->pow
[poly
->var
] = 0;
4213 isl_term_free(term
);
4217 isl_stat
isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial
*qp
,
4218 isl_stat (*fn
)(__isl_take isl_term
*term
, void *user
), void *user
)
4223 return isl_stat_error
;
4225 term
= isl_term_alloc(isl_space_copy(qp
->dim
), isl_mat_copy(qp
->div
));
4227 return isl_stat_error
;
4229 term
= isl_poly_foreach_term(qp
->poly
, fn
, term
, user
);
4231 isl_term_free(term
);
4233 return term
? isl_stat_ok
: isl_stat_error
;
4236 __isl_give isl_qpolynomial
*isl_qpolynomial_from_term(__isl_take isl_term
*term
)
4239 isl_qpolynomial
*qp
;
4243 n
= isl_term_dim(term
, isl_dim_all
);
4245 term
= isl_term_free(term
);
4249 poly
= isl_poly_rat_cst(term
->dim
->ctx
, term
->n
, term
->d
);
4250 for (i
= 0; i
< n
; ++i
) {
4253 poly
= isl_poly_mul(poly
,
4254 isl_poly_var_pow(term
->dim
->ctx
, i
, term
->pow
[i
]));
4257 qp
= isl_qpolynomial_alloc(isl_space_copy(term
->dim
),
4258 term
->div
->n_row
, poly
);
4261 isl_mat_free(qp
->div
);
4262 qp
->div
= isl_mat_copy(term
->div
);
4266 isl_term_free(term
);
4269 isl_qpolynomial_free(qp
);
4270 isl_term_free(term
);
4274 __isl_give isl_qpolynomial
*isl_qpolynomial_lift(__isl_take isl_qpolynomial
*qp
,
4275 __isl_take isl_space
*space
)
4279 isl_size total
, d_set
, d_qp
;
4284 if (isl_space_is_equal(qp
->dim
, space
)) {
4285 isl_space_free(space
);
4289 qp
= isl_qpolynomial_cow(qp
);
4293 d_set
= isl_space_dim(space
, isl_dim_set
);
4294 d_qp
= isl_qpolynomial_domain_dim(qp
, isl_dim_set
);
4295 extra
= d_set
- d_qp
;
4296 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4297 if (d_set
< 0 || d_qp
< 0 || total
< 0)
4299 if (qp
->div
->n_row
) {
4302 exp
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
4305 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4307 qp
->poly
= expand(qp
->poly
, exp
, total
);
4312 qp
->div
= isl_mat_insert_cols(qp
->div
, 2 + total
, extra
);
4315 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4316 isl_seq_clr(qp
->div
->row
[i
] + 2 + total
, extra
);
4318 isl_space_free(isl_qpolynomial_take_domain_space(qp
));
4319 qp
= isl_qpolynomial_restore_domain_space(qp
, space
);
4323 isl_space_free(space
);
4324 isl_qpolynomial_free(qp
);
4328 /* For each parameter or variable that does not appear in qp,
4329 * first eliminate the variable from all constraints and then set it to zero.
4331 static __isl_give isl_set
*fix_inactive(__isl_take isl_set
*set
,
4332 __isl_keep isl_qpolynomial
*qp
)
4340 d
= isl_set_dim(set
, isl_dim_all
);
4344 active
= isl_calloc_array(set
->ctx
, int, d
);
4345 if (set_active(qp
, active
) < 0)
4348 for (i
= 0; i
< d
; ++i
)
4357 nparam
= isl_set_dim(set
, isl_dim_param
);
4358 nvar
= isl_set_dim(set
, isl_dim_set
);
4359 if (nparam
< 0 || nvar
< 0)
4361 for (i
= 0; i
< nparam
; ++i
) {
4364 set
= isl_set_eliminate(set
, isl_dim_param
, i
, 1);
4365 set
= isl_set_fix_si(set
, isl_dim_param
, i
, 0);
4367 for (i
= 0; i
< nvar
; ++i
) {
4368 if (active
[nparam
+ i
])
4370 set
= isl_set_eliminate(set
, isl_dim_set
, i
, 1);
4371 set
= isl_set_fix_si(set
, isl_dim_set
, i
, 0);
4383 struct isl_opt_data
{
4384 isl_qpolynomial
*qp
;
4390 static isl_stat
opt_fn(__isl_take isl_point
*pnt
, void *user
)
4392 struct isl_opt_data
*data
= (struct isl_opt_data
*)user
;
4395 val
= isl_qpolynomial_eval(isl_qpolynomial_copy(data
->qp
), pnt
);
4399 } else if (data
->max
) {
4400 data
->opt
= isl_val_max(data
->opt
, val
);
4402 data
->opt
= isl_val_min(data
->opt
, val
);
4408 __isl_give isl_val
*isl_qpolynomial_opt_on_domain(
4409 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*set
, int max
)
4411 struct isl_opt_data data
= { NULL
, 1, NULL
, max
};
4417 is_cst
= isl_poly_is_cst(qp
->poly
);
4422 data
.opt
= isl_qpolynomial_get_constant_val(qp
);
4423 isl_qpolynomial_free(qp
);
4427 set
= fix_inactive(set
, qp
);
4430 if (isl_set_foreach_point(set
, opt_fn
, &data
) < 0)
4434 data
.opt
= isl_val_zero(isl_set_get_ctx(set
));
4437 isl_qpolynomial_free(qp
);
4441 isl_qpolynomial_free(qp
);
4442 isl_val_free(data
.opt
);
4446 __isl_give isl_qpolynomial
*isl_qpolynomial_morph_domain(
4447 __isl_take isl_qpolynomial
*qp
, __isl_take isl_morph
*morph
)
4454 isl_mat
*mat
, *diag
;
4456 qp
= isl_qpolynomial_cow(qp
);
4458 space
= isl_qpolynomial_peek_domain_space(qp
);
4459 if (isl_morph_check_applies(morph
, space
) < 0)
4462 ctx
= isl_qpolynomial_get_ctx(qp
);
4463 n_sub
= morph
->inv
->n_row
- 1;
4464 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
4465 n_sub
+= qp
->div
->n_row
;
4466 subs
= isl_calloc_array(ctx
, struct isl_poly
*, n_sub
);
4470 for (i
= 0; 1 + i
< morph
->inv
->n_row
; ++i
)
4471 subs
[i
] = isl_poly_from_affine(ctx
, morph
->inv
->row
[1 + i
],
4472 morph
->inv
->row
[0][0], morph
->inv
->n_col
);
4473 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
4474 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4475 subs
[morph
->inv
->n_row
- 1 + i
] =
4476 isl_poly_var_pow(ctx
, morph
->inv
->n_col
- 1 + i
, 1);
4478 qp
->poly
= isl_poly_subs(qp
->poly
, 0, n_sub
, subs
);
4480 for (i
= 0; i
< n_sub
; ++i
)
4481 isl_poly_free(subs
[i
]);
4484 diag
= isl_mat_diag(ctx
, 1, morph
->inv
->row
[0][0]);
4485 mat
= isl_mat_diagonal(diag
, isl_mat_copy(morph
->inv
));
4486 diag
= isl_mat_diag(ctx
, qp
->div
->n_row
, morph
->inv
->row
[0][0]);
4487 mat
= isl_mat_diagonal(mat
, diag
);
4488 qp
->div
= isl_mat_product(qp
->div
, mat
);
4490 if (!qp
->poly
|| !qp
->div
)
4493 isl_space_free(isl_qpolynomial_take_domain_space(qp
));
4494 space
= isl_space_copy(morph
->ran
->dim
);
4495 qp
= isl_qpolynomial_restore_domain_space(qp
, space
);
4497 isl_morph_free(morph
);
4501 isl_qpolynomial_free(qp
);
4502 isl_morph_free(morph
);
4506 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_mul(
4507 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
4508 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
4510 return isl_union_pw_qpolynomial_match_bin_op(upwqp1
, upwqp2
,
4511 &isl_pw_qpolynomial_mul
);
4514 /* Reorder the dimension of "qp" according to the given reordering.
4516 __isl_give isl_qpolynomial
*isl_qpolynomial_realign_domain(
4517 __isl_take isl_qpolynomial
*qp
, __isl_take isl_reordering
*r
)
4521 qp
= isl_qpolynomial_cow(qp
);
4525 r
= isl_reordering_extend(r
, qp
->div
->n_row
);
4529 qp
->div
= isl_local_reorder(qp
->div
, isl_reordering_copy(r
));
4533 qp
->poly
= reorder(qp
->poly
, r
->pos
);
4537 space
= isl_reordering_get_space(r
);
4538 qp
= isl_qpolynomial_reset_domain_space(qp
, space
);
4540 isl_reordering_free(r
);
4543 isl_qpolynomial_free(qp
);
4544 isl_reordering_free(r
);
4548 __isl_give isl_qpolynomial
*isl_qpolynomial_align_params(
4549 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*model
)
4551 isl_space
*domain_space
;
4552 isl_bool equal_params
;
4554 domain_space
= isl_qpolynomial_peek_domain_space(qp
);
4555 equal_params
= isl_space_has_equal_params(domain_space
, model
);
4556 if (equal_params
< 0)
4558 if (!equal_params
) {
4559 isl_reordering
*exp
;
4561 exp
= isl_parameter_alignment_reordering(domain_space
, model
);
4562 qp
= isl_qpolynomial_realign_domain(qp
, exp
);
4565 isl_space_free(model
);
4568 isl_space_free(model
);
4569 isl_qpolynomial_free(qp
);
4573 struct isl_split_periods_data
{
4575 isl_pw_qpolynomial
*res
;
4578 /* Create a slice where the integer division "div" has the fixed value "v".
4579 * In particular, if "div" refers to floor(f/m), then create a slice
4581 * m v <= f <= m v + (m - 1)
4586 * -f + m v + (m - 1) >= 0
4588 static __isl_give isl_set
*set_div_slice(__isl_take isl_space
*space
,
4589 __isl_keep isl_qpolynomial
*qp
, int div
, isl_int v
)
4592 isl_basic_set
*bset
= NULL
;
4595 total
= isl_space_dim(space
, isl_dim_all
);
4596 if (total
< 0 || !qp
)
4599 bset
= isl_basic_set_alloc_space(isl_space_copy(space
), 0, 0, 2);
4601 k
= isl_basic_set_alloc_inequality(bset
);
4604 isl_seq_cpy(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4605 isl_int_submul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4607 k
= isl_basic_set_alloc_inequality(bset
);
4610 isl_seq_neg(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4611 isl_int_addmul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4612 isl_int_add(bset
->ineq
[k
][0], bset
->ineq
[k
][0], qp
->div
->row
[div
][0]);
4613 isl_int_sub_ui(bset
->ineq
[k
][0], bset
->ineq
[k
][0], 1);
4615 isl_space_free(space
);
4616 return isl_set_from_basic_set(bset
);
4618 isl_basic_set_free(bset
);
4619 isl_space_free(space
);
4623 static isl_stat
split_periods(__isl_take isl_set
*set
,
4624 __isl_take isl_qpolynomial
*qp
, void *user
);
4626 /* Create a slice of the domain "set" such that integer division "div"
4627 * has the fixed value "v" and add the results to data->res,
4628 * replacing the integer division by "v" in "qp".
4630 static isl_stat
set_div(__isl_take isl_set
*set
,
4631 __isl_take isl_qpolynomial
*qp
, int div
, isl_int v
,
4632 struct isl_split_periods_data
*data
)
4639 slice
= set_div_slice(isl_set_get_space(set
), qp
, div
, v
);
4640 set
= isl_set_intersect(set
, slice
);
4642 div_pos
= isl_qpolynomial_domain_var_offset(qp
, isl_dim_div
);
4646 for (i
= div
+ 1; i
< qp
->div
->n_row
; ++i
) {
4647 if (isl_int_is_zero(qp
->div
->row
[i
][2 + div_pos
+ div
]))
4649 isl_int_addmul(qp
->div
->row
[i
][1],
4650 qp
->div
->row
[i
][2 + div_pos
+ div
], v
);
4651 isl_int_set_si(qp
->div
->row
[i
][2 + div_pos
+ div
], 0);
4654 cst
= isl_poly_rat_cst(qp
->dim
->ctx
, v
, qp
->dim
->ctx
->one
);
4655 qp
= substitute_div(qp
, div
, cst
);
4657 return split_periods(set
, qp
, data
);
4660 isl_qpolynomial_free(qp
);
4661 return isl_stat_error
;
4664 /* Split the domain "set" such that integer division "div"
4665 * has a fixed value (ranging from "min" to "max") on each slice
4666 * and add the results to data->res.
4668 static isl_stat
split_div(__isl_take isl_set
*set
,
4669 __isl_take isl_qpolynomial
*qp
, int div
, isl_int min
, isl_int max
,
4670 struct isl_split_periods_data
*data
)
4672 for (; isl_int_le(min
, max
); isl_int_add_ui(min
, min
, 1)) {
4673 isl_set
*set_i
= isl_set_copy(set
);
4674 isl_qpolynomial
*qp_i
= isl_qpolynomial_copy(qp
);
4676 if (set_div(set_i
, qp_i
, div
, min
, data
) < 0)
4680 isl_qpolynomial_free(qp
);
4684 isl_qpolynomial_free(qp
);
4685 return isl_stat_error
;
4688 /* If "qp" refers to any integer division
4689 * that can only attain "max_periods" distinct values on "set"
4690 * then split the domain along those distinct values.
4691 * Add the results (or the original if no splitting occurs)
4694 static isl_stat
split_periods(__isl_take isl_set
*set
,
4695 __isl_take isl_qpolynomial
*qp
, void *user
)
4698 isl_pw_qpolynomial
*pwqp
;
4699 struct isl_split_periods_data
*data
;
4702 isl_stat r
= isl_stat_ok
;
4704 data
= (struct isl_split_periods_data
*)user
;
4709 if (qp
->div
->n_row
== 0) {
4710 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4711 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4715 div_pos
= isl_qpolynomial_domain_var_offset(qp
, isl_dim_div
);
4721 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4722 enum isl_lp_result lp_res
;
4724 if (isl_seq_first_non_zero(qp
->div
->row
[i
] + 2 + div_pos
,
4725 qp
->div
->n_row
) != -1)
4728 lp_res
= isl_set_solve_lp(set
, 0, qp
->div
->row
[i
] + 1,
4729 set
->ctx
->one
, &min
, NULL
, NULL
);
4730 if (lp_res
== isl_lp_error
)
4732 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4734 isl_int_fdiv_q(min
, min
, qp
->div
->row
[i
][0]);
4736 lp_res
= isl_set_solve_lp(set
, 1, qp
->div
->row
[i
] + 1,
4737 set
->ctx
->one
, &max
, NULL
, NULL
);
4738 if (lp_res
== isl_lp_error
)
4740 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4742 isl_int_fdiv_q(max
, max
, qp
->div
->row
[i
][0]);
4744 isl_int_sub(max
, max
, min
);
4745 if (isl_int_cmp_si(max
, data
->max_periods
) < 0) {
4746 isl_int_add(max
, max
, min
);
4751 if (i
< qp
->div
->n_row
) {
4752 r
= split_div(set
, qp
, i
, min
, max
, data
);
4754 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4755 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4767 isl_qpolynomial_free(qp
);
4768 return isl_stat_error
;
4771 /* If any quasi-polynomial in pwqp refers to any integer division
4772 * that can only attain "max_periods" distinct values on its domain
4773 * then split the domain along those distinct values.
4775 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_split_periods(
4776 __isl_take isl_pw_qpolynomial
*pwqp
, int max_periods
)
4778 struct isl_split_periods_data data
;
4780 data
.max_periods
= max_periods
;
4781 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp
));
4783 if (isl_pw_qpolynomial_foreach_piece(pwqp
, &split_periods
, &data
) < 0)
4786 isl_pw_qpolynomial_free(pwqp
);
4790 isl_pw_qpolynomial_free(data
.res
);
4791 isl_pw_qpolynomial_free(pwqp
);
4795 /* Construct a piecewise quasipolynomial that is constant on the given
4796 * domain. In particular, it is
4799 * infinity if cst == -1
4801 * If cst == -1, then explicitly check whether the domain is empty and,
4802 * if so, return 0 instead.
4804 static __isl_give isl_pw_qpolynomial
*constant_on_domain(
4805 __isl_take isl_basic_set
*bset
, int cst
)
4808 isl_qpolynomial
*qp
;
4810 if (cst
< 0 && isl_basic_set_is_empty(bset
) == isl_bool_true
)
4815 bset
= isl_basic_set_params(bset
);
4816 space
= isl_basic_set_get_space(bset
);
4818 qp
= isl_qpolynomial_infty_on_domain(space
);
4820 qp
= isl_qpolynomial_zero_on_domain(space
);
4822 qp
= isl_qpolynomial_one_on_domain(space
);
4823 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset
), qp
);
4826 /* Internal data structure for multiplicative_call_factor_pw_qpolynomial.
4827 * "fn" is the function that is called on each factor.
4828 * "pwpq" collects the results.
4830 struct isl_multiplicative_call_data_pw_qpolynomial
{
4831 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
);
4832 isl_pw_qpolynomial
*pwqp
;
4835 /* Call "fn" on "bset" and return the result,
4836 * but first check if "bset" has any redundant constraints or
4837 * implicit equality constraints.
4838 * If so, there may be further opportunities for detecting factors or
4839 * removing equality constraints, so recursively call
4840 * the top-level isl_basic_set_multiplicative_call.
4842 static __isl_give isl_pw_qpolynomial
*multiplicative_call_base(
4843 __isl_take isl_basic_set
*bset
,
4844 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4846 isl_size n1
, n2
, n_eq
;
4848 n1
= isl_basic_set_n_constraint(bset
);
4850 bset
= isl_basic_set_free(bset
);
4851 bset
= isl_basic_set_remove_redundancies(bset
);
4852 bset
= isl_basic_set_detect_equalities(bset
);
4853 n2
= isl_basic_set_n_constraint(bset
);
4854 n_eq
= isl_basic_set_n_equality(bset
);
4855 if (n2
< 0 || n_eq
< 0)
4856 bset
= isl_basic_set_free(bset
);
4857 else if (n2
< n1
|| n_eq
> 0)
4858 return isl_basic_set_multiplicative_call(bset
, fn
);
4862 /* isl_factorizer_every_factor_basic_set callback that applies
4863 * data->fn to the factor "bset" and multiplies in the result
4866 static isl_bool
multiplicative_call_factor_pw_qpolynomial(
4867 __isl_keep isl_basic_set
*bset
, void *user
)
4869 struct isl_multiplicative_call_data_pw_qpolynomial
*data
= user
;
4870 isl_pw_qpolynomial
*res
;
4872 bset
= isl_basic_set_copy(bset
);
4873 res
= multiplicative_call_base(bset
, data
->fn
);
4874 data
->pwqp
= isl_pw_qpolynomial_mul(data
->pwqp
, res
);
4876 return isl_bool_error
;
4878 return isl_bool_true
;
4881 /* Factor bset, call fn on each of the factors and return the product.
4883 * If no factors can be found, simply call fn on the input.
4884 * Otherwise, construct the factors based on the factorizer,
4885 * call fn on each factor and compute the product.
4887 static __isl_give isl_pw_qpolynomial
*compressed_multiplicative_call(
4888 __isl_take isl_basic_set
*bset
,
4889 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4891 struct isl_multiplicative_call_data_pw_qpolynomial data
= { fn
};
4895 isl_qpolynomial
*qp
;
4898 f
= isl_basic_set_factorizer(bset
);
4901 if (f
->n_group
== 0) {
4902 isl_factorizer_free(f
);
4903 return multiplicative_call_base(bset
, fn
);
4906 space
= isl_basic_set_get_space(bset
);
4907 space
= isl_space_params(space
);
4908 set
= isl_set_universe(isl_space_copy(space
));
4909 qp
= isl_qpolynomial_one_on_domain(space
);
4910 data
.pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4912 every
= isl_factorizer_every_factor_basic_set(f
,
4913 &multiplicative_call_factor_pw_qpolynomial
, &data
);
4915 data
.pwqp
= isl_pw_qpolynomial_free(data
.pwqp
);
4917 isl_basic_set_free(bset
);
4918 isl_factorizer_free(f
);
4922 isl_basic_set_free(bset
);
4926 /* Factor bset, call fn on each of the factors and return the product.
4927 * The function is assumed to evaluate to zero on empty domains,
4928 * to one on zero-dimensional domains and to infinity on unbounded domains
4929 * and will not be called explicitly on zero-dimensional or unbounded domains.
4931 * We first check for some special cases and remove all equalities.
4932 * Then we hand over control to compressed_multiplicative_call.
4934 __isl_give isl_pw_qpolynomial
*isl_basic_set_multiplicative_call(
4935 __isl_take isl_basic_set
*bset
,
4936 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4941 isl_pw_qpolynomial
*pwqp
;
4946 if (isl_basic_set_plain_is_empty(bset
))
4947 return constant_on_domain(bset
, 0);
4949 dim
= isl_basic_set_dim(bset
, isl_dim_set
);
4953 return constant_on_domain(bset
, 1);
4955 bounded
= isl_basic_set_is_bounded(bset
);
4959 return constant_on_domain(bset
, -1);
4961 if (bset
->n_eq
== 0)
4962 return compressed_multiplicative_call(bset
, fn
);
4964 morph
= isl_basic_set_full_compression(bset
);
4965 bset
= isl_morph_basic_set(isl_morph_copy(morph
), bset
);
4967 pwqp
= compressed_multiplicative_call(bset
, fn
);
4969 morph
= isl_morph_dom_params(morph
);
4970 morph
= isl_morph_ran_params(morph
);
4971 morph
= isl_morph_inverse(morph
);
4973 pwqp
= isl_pw_qpolynomial_morph_domain(pwqp
, morph
);
4977 isl_basic_set_free(bset
);
4981 /* Drop all floors in "qp", turning each integer division [a/m] into
4982 * a rational division a/m. If "down" is set, then the integer division
4983 * is replaced by (a-(m-1))/m instead.
4985 static __isl_give isl_qpolynomial
*qp_drop_floors(
4986 __isl_take isl_qpolynomial
*qp
, int down
)
4993 if (qp
->div
->n_row
== 0)
4996 qp
= isl_qpolynomial_cow(qp
);
5000 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
5002 isl_int_sub(qp
->div
->row
[i
][1],
5003 qp
->div
->row
[i
][1], qp
->div
->row
[i
][0]);
5004 isl_int_add_ui(qp
->div
->row
[i
][1],
5005 qp
->div
->row
[i
][1], 1);
5007 s
= isl_poly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
5008 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
5009 qp
= substitute_div(qp
, i
, s
);
5017 /* Drop all floors in "pwqp", turning each integer division [a/m] into
5018 * a rational division a/m.
5020 static __isl_give isl_pw_qpolynomial
*pwqp_drop_floors(
5021 __isl_take isl_pw_qpolynomial
*pwqp
)
5028 if (isl_pw_qpolynomial_is_zero(pwqp
))
5031 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
5035 for (i
= 0; i
< pwqp
->n
; ++i
) {
5036 pwqp
->p
[i
].qp
= qp_drop_floors(pwqp
->p
[i
].qp
, 0);
5043 isl_pw_qpolynomial_free(pwqp
);
5047 /* Adjust all the integer divisions in "qp" such that they are at least
5048 * one over the given orthant (identified by "signs"). This ensures
5049 * that they will still be non-negative even after subtracting (m-1)/m.
5051 * In particular, f is replaced by f' + v, changing f = [a/m]
5052 * to f' = [(a - m v)/m].
5053 * If the constant term k in a is smaller than m,
5054 * the constant term of v is set to floor(k/m) - 1.
5055 * For any other term, if the coefficient c and the variable x have
5056 * the same sign, then no changes are needed.
5057 * Otherwise, if the variable is positive (and c is negative),
5058 * then the coefficient of x in v is set to floor(c/m).
5059 * If the variable is negative (and c is positive),
5060 * then the coefficient of x in v is set to ceil(c/m).
5062 static __isl_give isl_qpolynomial
*make_divs_pos(__isl_take isl_qpolynomial
*qp
,
5070 qp
= isl_qpolynomial_cow(qp
);
5071 div_pos
= isl_qpolynomial_domain_var_offset(qp
, isl_dim_div
);
5073 return isl_qpolynomial_free(qp
);
5074 qp
->div
= isl_mat_cow(qp
->div
);
5078 v
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
5080 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
5081 isl_int
*row
= qp
->div
->row
[i
];
5085 if (isl_int_lt(row
[1], row
[0])) {
5086 isl_int_fdiv_q(v
->el
[0], row
[1], row
[0]);
5087 isl_int_sub_ui(v
->el
[0], v
->el
[0], 1);
5088 isl_int_submul(row
[1], row
[0], v
->el
[0]);
5090 for (j
= 0; j
< div_pos
; ++j
) {
5091 if (isl_int_sgn(row
[2 + j
]) * signs
[j
] >= 0)
5094 isl_int_cdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
5096 isl_int_fdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
5097 isl_int_submul(row
[2 + j
], row
[0], v
->el
[1 + j
]);
5099 for (j
= 0; j
< i
; ++j
) {
5100 if (isl_int_sgn(row
[2 + div_pos
+ j
]) >= 0)
5102 isl_int_fdiv_q(v
->el
[1 + div_pos
+ j
],
5103 row
[2 + div_pos
+ j
], row
[0]);
5104 isl_int_submul(row
[2 + div_pos
+ j
],
5105 row
[0], v
->el
[1 + div_pos
+ j
]);
5107 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
5108 if (isl_int_is_zero(qp
->div
->row
[j
][2 + div_pos
+ i
]))
5110 isl_seq_combine(qp
->div
->row
[j
] + 1,
5111 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
5112 qp
->div
->row
[j
][2 + div_pos
+ i
], v
->el
,
5115 isl_int_set_si(v
->el
[1 + div_pos
+ i
], 1);
5116 s
= isl_poly_from_affine(qp
->dim
->ctx
, v
->el
,
5117 qp
->div
->ctx
->one
, v
->size
);
5118 qp
->poly
= isl_poly_subs(qp
->poly
, div_pos
+ i
, 1, &s
);
5128 isl_qpolynomial_free(qp
);
5132 struct isl_to_poly_data
{
5134 isl_pw_qpolynomial
*res
;
5135 isl_qpolynomial
*qp
;
5138 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
5139 * We first make all integer divisions positive and then split the
5140 * quasipolynomials into terms with sign data->sign (the direction
5141 * of the requested approximation) and terms with the opposite sign.
5142 * In the first set of terms, each integer division [a/m] is
5143 * overapproximated by a/m, while in the second it is underapproximated
5146 static isl_stat
to_polynomial_on_orthant(__isl_take isl_set
*orthant
,
5147 int *signs
, void *user
)
5149 struct isl_to_poly_data
*data
= user
;
5150 isl_pw_qpolynomial
*t
;
5151 isl_qpolynomial
*qp
, *up
, *down
;
5153 qp
= isl_qpolynomial_copy(data
->qp
);
5154 qp
= make_divs_pos(qp
, signs
);
5156 up
= isl_qpolynomial_terms_of_sign(qp
, signs
, data
->sign
);
5157 up
= qp_drop_floors(up
, 0);
5158 down
= isl_qpolynomial_terms_of_sign(qp
, signs
, -data
->sign
);
5159 down
= qp_drop_floors(down
, 1);
5161 isl_qpolynomial_free(qp
);
5162 qp
= isl_qpolynomial_add(up
, down
);
5164 t
= isl_pw_qpolynomial_alloc(orthant
, qp
);
5165 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, t
);
5170 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
5171 * the polynomial will be an overapproximation. If "sign" is negative,
5172 * it will be an underapproximation. If "sign" is zero, the approximation
5173 * will lie somewhere in between.
5175 * In particular, is sign == 0, we simply drop the floors, turning
5176 * the integer divisions into rational divisions.
5177 * Otherwise, we split the domains into orthants, make all integer divisions
5178 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
5179 * depending on the requested sign and the sign of the term in which
5180 * the integer division appears.
5182 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_to_polynomial(
5183 __isl_take isl_pw_qpolynomial
*pwqp
, int sign
)
5186 struct isl_to_poly_data data
;
5189 return pwqp_drop_floors(pwqp
);
5195 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp
));
5197 for (i
= 0; i
< pwqp
->n
; ++i
) {
5198 if (pwqp
->p
[i
].qp
->div
->n_row
== 0) {
5199 isl_pw_qpolynomial
*t
;
5200 t
= isl_pw_qpolynomial_alloc(
5201 isl_set_copy(pwqp
->p
[i
].set
),
5202 isl_qpolynomial_copy(pwqp
->p
[i
].qp
));
5203 data
.res
= isl_pw_qpolynomial_add_disjoint(data
.res
, t
);
5206 data
.qp
= pwqp
->p
[i
].qp
;
5207 if (isl_set_foreach_orthant(pwqp
->p
[i
].set
,
5208 &to_polynomial_on_orthant
, &data
) < 0)
5212 isl_pw_qpolynomial_free(pwqp
);
5216 isl_pw_qpolynomial_free(pwqp
);
5217 isl_pw_qpolynomial_free(data
.res
);
5221 static __isl_give isl_pw_qpolynomial
*poly_entry(
5222 __isl_take isl_pw_qpolynomial
*pwqp
, void *user
)
5226 return isl_pw_qpolynomial_to_polynomial(pwqp
, *sign
);
5229 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_to_polynomial(
5230 __isl_take isl_union_pw_qpolynomial
*upwqp
, int sign
)
5232 return isl_union_pw_qpolynomial_transform_inplace(upwqp
,
5233 &poly_entry
, &sign
);
5236 __isl_give isl_basic_map
*isl_basic_map_from_qpolynomial(
5237 __isl_take isl_qpolynomial
*qp
)
5239 isl_local_space
*ls
;
5242 isl_basic_map
*bmap
;
5247 is_affine
= isl_poly_is_affine(qp
->poly
);
5251 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
5252 "input quasi-polynomial not affine", goto error
);
5253 ls
= isl_qpolynomial_get_domain_local_space(qp
);
5254 vec
= isl_qpolynomial_extract_affine(qp
);
5255 aff
= isl_aff_alloc_vec(ls
, vec
);
5256 bmap
= isl_basic_map_from_aff(aff
);
5257 isl_qpolynomial_free(qp
);
5260 isl_qpolynomial_free(qp
);