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 __isl_give isl_qpolynomial
*isl_qpolynomial_reset_domain_space(
416 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*space
)
418 qp
= isl_qpolynomial_cow(qp
);
422 isl_space_free(qp
->dim
);
427 isl_qpolynomial_free(qp
);
428 isl_space_free(space
);
432 /* Reset the space of "qp". This function is called from isl_pw_templ.c
433 * and doesn't know if the space of an element object is represented
434 * directly or through its domain. It therefore passes along both.
436 __isl_give isl_qpolynomial
*isl_qpolynomial_reset_space_and_domain(
437 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*space
,
438 __isl_take isl_space
*domain
)
440 isl_space_free(space
);
441 return isl_qpolynomial_reset_domain_space(qp
, domain
);
444 isl_ctx
*isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial
*qp
)
446 return qp
? qp
->dim
->ctx
: NULL
;
449 /* Return the domain space of "qp".
451 static __isl_keep isl_space
*isl_qpolynomial_peek_domain_space(
452 __isl_keep isl_qpolynomial
*qp
)
454 return qp
? qp
->dim
: NULL
;
457 /* Return a copy of the domain space of "qp".
459 __isl_give isl_space
*isl_qpolynomial_get_domain_space(
460 __isl_keep isl_qpolynomial
*qp
)
462 return isl_space_copy(isl_qpolynomial_peek_domain_space(qp
));
466 #define TYPE isl_qpolynomial
468 #define PEEK_SPACE peek_domain_space
471 #include "isl_type_has_equal_space_bin_templ.c"
473 #include "isl_type_check_equal_space_templ.c"
477 /* Return a copy of the local space on which "qp" is defined.
479 static __isl_give isl_local_space
*isl_qpolynomial_get_domain_local_space(
480 __isl_keep isl_qpolynomial
*qp
)
487 space
= isl_qpolynomial_get_domain_space(qp
);
488 return isl_local_space_alloc_div(space
, isl_mat_copy(qp
->div
));
491 __isl_give isl_space
*isl_qpolynomial_get_space(__isl_keep isl_qpolynomial
*qp
)
496 space
= isl_space_copy(qp
->dim
);
497 space
= isl_space_from_domain(space
);
498 space
= isl_space_add_dims(space
, isl_dim_out
, 1);
502 /* Return the number of variables of the given type in the domain of "qp".
504 isl_size
isl_qpolynomial_domain_dim(__isl_keep isl_qpolynomial
*qp
,
505 enum isl_dim_type type
)
510 space
= isl_qpolynomial_peek_domain_space(qp
);
513 return isl_size_error
;
514 if (type
== isl_dim_div
)
515 return qp
->div
->n_row
;
516 dim
= isl_space_dim(space
, type
);
518 return isl_size_error
;
519 if (type
== isl_dim_all
) {
522 n_div
= isl_qpolynomial_domain_dim(qp
, isl_dim_div
);
524 return isl_size_error
;
530 /* Given the type of a dimension of an isl_qpolynomial,
531 * return the type of the corresponding dimension in its domain.
532 * This function is only called for "type" equal to isl_dim_in or
535 static enum isl_dim_type
domain_type(enum isl_dim_type type
)
537 return type
== isl_dim_in
? isl_dim_set
: type
;
540 /* Externally, an isl_qpolynomial has a map space, but internally, the
541 * ls field corresponds to the domain of that space.
543 isl_size
isl_qpolynomial_dim(__isl_keep isl_qpolynomial
*qp
,
544 enum isl_dim_type type
)
547 return isl_size_error
;
548 if (type
== isl_dim_out
)
550 type
= domain_type(type
);
551 return isl_qpolynomial_domain_dim(qp
, type
);
554 /* Return the offset of the first variable of type "type" within
555 * the variables of the domain of "qp".
557 static isl_size
isl_qpolynomial_domain_var_offset(
558 __isl_keep isl_qpolynomial
*qp
, enum isl_dim_type type
)
562 space
= isl_qpolynomial_peek_domain_space(qp
);
564 return isl_size_error
;
568 case isl_dim_set
: return isl_space_offset(space
, type
);
569 case isl_dim_div
: return isl_space_dim(space
, isl_dim_all
);
572 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
573 "invalid dimension type", return isl_size_error
);
577 /* Return the offset of the first coefficient of type "type" in
578 * the domain of "qp".
580 unsigned isl_qpolynomial_domain_offset(__isl_keep isl_qpolynomial
*qp
,
581 enum isl_dim_type type
)
589 return 1 + isl_qpolynomial_domain_var_offset(qp
, type
);
595 isl_bool
isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial
*qp
)
597 return qp
? isl_poly_is_zero(qp
->poly
) : isl_bool_error
;
600 isl_bool
isl_qpolynomial_is_one(__isl_keep isl_qpolynomial
*qp
)
602 return qp
? isl_poly_is_one(qp
->poly
) : isl_bool_error
;
605 isl_bool
isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial
*qp
)
607 return qp
? isl_poly_is_nan(qp
->poly
) : isl_bool_error
;
610 isl_bool
isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial
*qp
)
612 return qp
? isl_poly_is_infty(qp
->poly
) : isl_bool_error
;
615 isl_bool
isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial
*qp
)
617 return qp
? isl_poly_is_neginfty(qp
->poly
) : isl_bool_error
;
620 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial
*qp
)
622 return qp
? isl_poly_sgn(qp
->poly
) : 0;
625 static void poly_free_cst(__isl_take isl_poly_cst
*cst
)
627 isl_int_clear(cst
->n
);
628 isl_int_clear(cst
->d
);
631 static void poly_free_rec(__isl_take isl_poly_rec
*rec
)
635 for (i
= 0; i
< rec
->n
; ++i
)
636 isl_poly_free(rec
->p
[i
]);
639 __isl_give isl_poly
*isl_poly_copy(__isl_keep isl_poly
*poly
)
648 __isl_give isl_poly
*isl_poly_dup_cst(__isl_keep isl_poly
*poly
)
653 cst
= isl_poly_as_cst(poly
);
657 dup
= isl_poly_as_cst(isl_poly_zero(poly
->ctx
));
660 isl_int_set(dup
->n
, cst
->n
);
661 isl_int_set(dup
->d
, cst
->d
);
666 __isl_give isl_poly
*isl_poly_dup_rec(__isl_keep isl_poly
*poly
)
672 rec
= isl_poly_as_rec(poly
);
676 dup
= isl_poly_alloc_rec(poly
->ctx
, poly
->var
, rec
->n
);
680 for (i
= 0; i
< rec
->n
; ++i
) {
681 dup
->p
[i
] = isl_poly_copy(rec
->p
[i
]);
689 isl_poly_free(&dup
->poly
);
693 __isl_give isl_poly
*isl_poly_dup(__isl_keep isl_poly
*poly
)
697 is_cst
= isl_poly_is_cst(poly
);
701 return isl_poly_dup_cst(poly
);
703 return isl_poly_dup_rec(poly
);
706 __isl_give isl_poly
*isl_poly_cow(__isl_take isl_poly
*poly
)
714 return isl_poly_dup(poly
);
717 __isl_null isl_poly
*isl_poly_free(__isl_take isl_poly
*poly
)
726 poly_free_cst((isl_poly_cst
*) poly
);
728 poly_free_rec((isl_poly_rec
*) poly
);
730 isl_ctx_deref(poly
->ctx
);
735 static void isl_poly_cst_reduce(__isl_keep isl_poly_cst
*cst
)
740 isl_int_gcd(gcd
, cst
->n
, cst
->d
);
741 if (!isl_int_is_zero(gcd
) && !isl_int_is_one(gcd
)) {
742 isl_int_divexact(cst
->n
, cst
->n
, gcd
);
743 isl_int_divexact(cst
->d
, cst
->d
, gcd
);
748 __isl_give isl_poly
*isl_poly_sum_cst(__isl_take isl_poly
*poly1
,
749 __isl_take isl_poly
*poly2
)
754 poly1
= isl_poly_cow(poly1
);
755 if (!poly1
|| !poly2
)
758 cst1
= isl_poly_as_cst(poly1
);
759 cst2
= isl_poly_as_cst(poly2
);
761 if (isl_int_eq(cst1
->d
, cst2
->d
))
762 isl_int_add(cst1
->n
, cst1
->n
, cst2
->n
);
764 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->d
);
765 isl_int_addmul(cst1
->n
, cst2
->n
, cst1
->d
);
766 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
769 isl_poly_cst_reduce(cst1
);
771 isl_poly_free(poly2
);
774 isl_poly_free(poly1
);
775 isl_poly_free(poly2
);
779 static __isl_give isl_poly
*replace_by_zero(__isl_take isl_poly
*poly
)
787 return isl_poly_zero(ctx
);
790 static __isl_give isl_poly
*replace_by_constant_term(__isl_take isl_poly
*poly
)
798 rec
= isl_poly_as_rec(poly
);
801 cst
= isl_poly_copy(rec
->p
[0]);
809 __isl_give isl_poly
*isl_poly_sum(__isl_take isl_poly
*poly1
,
810 __isl_take isl_poly
*poly2
)
813 isl_bool is_zero
, is_nan
, is_cst
;
814 isl_poly_rec
*rec1
, *rec2
;
816 if (!poly1
|| !poly2
)
819 is_nan
= isl_poly_is_nan(poly1
);
823 isl_poly_free(poly2
);
827 is_nan
= isl_poly_is_nan(poly2
);
831 isl_poly_free(poly1
);
835 is_zero
= isl_poly_is_zero(poly1
);
839 isl_poly_free(poly1
);
843 is_zero
= isl_poly_is_zero(poly2
);
847 isl_poly_free(poly2
);
851 if (poly1
->var
< poly2
->var
)
852 return isl_poly_sum(poly2
, poly1
);
854 if (poly2
->var
< poly1
->var
) {
858 is_infty
= isl_poly_is_infty(poly2
);
859 if (is_infty
>= 0 && !is_infty
)
860 is_infty
= isl_poly_is_neginfty(poly2
);
864 isl_poly_free(poly1
);
867 poly1
= isl_poly_cow(poly1
);
868 rec
= isl_poly_as_rec(poly1
);
871 rec
->p
[0] = isl_poly_sum(rec
->p
[0], poly2
);
873 poly1
= replace_by_constant_term(poly1
);
877 is_cst
= isl_poly_is_cst(poly1
);
881 return isl_poly_sum_cst(poly1
, poly2
);
883 rec1
= isl_poly_as_rec(poly1
);
884 rec2
= isl_poly_as_rec(poly2
);
888 if (rec1
->n
< rec2
->n
)
889 return isl_poly_sum(poly2
, poly1
);
891 poly1
= isl_poly_cow(poly1
);
892 rec1
= isl_poly_as_rec(poly1
);
896 for (i
= rec2
->n
- 1; i
>= 0; --i
) {
899 rec1
->p
[i
] = isl_poly_sum(rec1
->p
[i
],
900 isl_poly_copy(rec2
->p
[i
]));
903 if (i
!= rec1
->n
- 1)
905 is_zero
= isl_poly_is_zero(rec1
->p
[i
]);
909 isl_poly_free(rec1
->p
[i
]);
915 poly1
= replace_by_zero(poly1
);
916 else if (rec1
->n
== 1)
917 poly1
= replace_by_constant_term(poly1
);
919 isl_poly_free(poly2
);
923 isl_poly_free(poly1
);
924 isl_poly_free(poly2
);
928 __isl_give isl_poly
*isl_poly_cst_add_isl_int(__isl_take isl_poly
*poly
,
933 poly
= isl_poly_cow(poly
);
937 cst
= isl_poly_as_cst(poly
);
939 isl_int_addmul(cst
->n
, cst
->d
, v
);
944 __isl_give isl_poly
*isl_poly_add_isl_int(__isl_take isl_poly
*poly
, isl_int v
)
949 is_cst
= isl_poly_is_cst(poly
);
951 return isl_poly_free(poly
);
953 return isl_poly_cst_add_isl_int(poly
, v
);
955 poly
= isl_poly_cow(poly
);
956 rec
= isl_poly_as_rec(poly
);
960 rec
->p
[0] = isl_poly_add_isl_int(rec
->p
[0], v
);
970 __isl_give isl_poly
*isl_poly_cst_mul_isl_int(__isl_take isl_poly
*poly
,
976 is_zero
= isl_poly_is_zero(poly
);
978 return isl_poly_free(poly
);
982 poly
= isl_poly_cow(poly
);
986 cst
= isl_poly_as_cst(poly
);
988 isl_int_mul(cst
->n
, cst
->n
, v
);
993 __isl_give isl_poly
*isl_poly_mul_isl_int(__isl_take isl_poly
*poly
, isl_int v
)
999 is_cst
= isl_poly_is_cst(poly
);
1001 return isl_poly_free(poly
);
1003 return isl_poly_cst_mul_isl_int(poly
, v
);
1005 poly
= isl_poly_cow(poly
);
1006 rec
= isl_poly_as_rec(poly
);
1010 for (i
= 0; i
< rec
->n
; ++i
) {
1011 rec
->p
[i
] = isl_poly_mul_isl_int(rec
->p
[i
], v
);
1018 isl_poly_free(poly
);
1022 /* Multiply the constant polynomial "poly" by "v".
1024 static __isl_give isl_poly
*isl_poly_cst_scale_val(__isl_take isl_poly
*poly
,
1025 __isl_keep isl_val
*v
)
1030 is_zero
= isl_poly_is_zero(poly
);
1032 return isl_poly_free(poly
);
1036 poly
= isl_poly_cow(poly
);
1040 cst
= isl_poly_as_cst(poly
);
1042 isl_int_mul(cst
->n
, cst
->n
, v
->n
);
1043 isl_int_mul(cst
->d
, cst
->d
, v
->d
);
1044 isl_poly_cst_reduce(cst
);
1049 /* Multiply the polynomial "poly" by "v".
1051 static __isl_give isl_poly
*isl_poly_scale_val(__isl_take isl_poly
*poly
,
1052 __isl_keep isl_val
*v
)
1058 is_cst
= isl_poly_is_cst(poly
);
1060 return isl_poly_free(poly
);
1062 return isl_poly_cst_scale_val(poly
, v
);
1064 poly
= isl_poly_cow(poly
);
1065 rec
= isl_poly_as_rec(poly
);
1069 for (i
= 0; i
< rec
->n
; ++i
) {
1070 rec
->p
[i
] = isl_poly_scale_val(rec
->p
[i
], v
);
1077 isl_poly_free(poly
);
1081 __isl_give isl_poly
*isl_poly_mul_cst(__isl_take isl_poly
*poly1
,
1082 __isl_take isl_poly
*poly2
)
1087 poly1
= isl_poly_cow(poly1
);
1088 if (!poly1
|| !poly2
)
1091 cst1
= isl_poly_as_cst(poly1
);
1092 cst2
= isl_poly_as_cst(poly2
);
1094 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->n
);
1095 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
1097 isl_poly_cst_reduce(cst1
);
1099 isl_poly_free(poly2
);
1102 isl_poly_free(poly1
);
1103 isl_poly_free(poly2
);
1107 __isl_give isl_poly
*isl_poly_mul_rec(__isl_take isl_poly
*poly1
,
1108 __isl_take isl_poly
*poly2
)
1112 isl_poly_rec
*res
= NULL
;
1116 rec1
= isl_poly_as_rec(poly1
);
1117 rec2
= isl_poly_as_rec(poly2
);
1120 size
= rec1
->n
+ rec2
->n
- 1;
1121 res
= isl_poly_alloc_rec(poly1
->ctx
, poly1
->var
, size
);
1125 for (i
= 0; i
< rec1
->n
; ++i
) {
1126 res
->p
[i
] = isl_poly_mul(isl_poly_copy(rec2
->p
[0]),
1127 isl_poly_copy(rec1
->p
[i
]));
1132 for (; i
< size
; ++i
) {
1133 res
->p
[i
] = isl_poly_zero(poly1
->ctx
);
1138 for (i
= 0; i
< rec1
->n
; ++i
) {
1139 for (j
= 1; j
< rec2
->n
; ++j
) {
1141 poly
= isl_poly_mul(isl_poly_copy(rec2
->p
[j
]),
1142 isl_poly_copy(rec1
->p
[i
]));
1143 res
->p
[i
+ j
] = isl_poly_sum(res
->p
[i
+ j
], poly
);
1149 isl_poly_free(poly1
);
1150 isl_poly_free(poly2
);
1154 isl_poly_free(poly1
);
1155 isl_poly_free(poly2
);
1156 isl_poly_free(&res
->poly
);
1160 __isl_give isl_poly
*isl_poly_mul(__isl_take isl_poly
*poly1
,
1161 __isl_take isl_poly
*poly2
)
1163 isl_bool is_zero
, is_nan
, is_one
, is_cst
;
1165 if (!poly1
|| !poly2
)
1168 is_nan
= isl_poly_is_nan(poly1
);
1172 isl_poly_free(poly2
);
1176 is_nan
= isl_poly_is_nan(poly2
);
1180 isl_poly_free(poly1
);
1184 is_zero
= isl_poly_is_zero(poly1
);
1188 isl_poly_free(poly2
);
1192 is_zero
= isl_poly_is_zero(poly2
);
1196 isl_poly_free(poly1
);
1200 is_one
= isl_poly_is_one(poly1
);
1204 isl_poly_free(poly1
);
1208 is_one
= isl_poly_is_one(poly2
);
1212 isl_poly_free(poly2
);
1216 if (poly1
->var
< poly2
->var
)
1217 return isl_poly_mul(poly2
, poly1
);
1219 if (poly2
->var
< poly1
->var
) {
1224 is_infty
= isl_poly_is_infty(poly2
);
1225 if (is_infty
>= 0 && !is_infty
)
1226 is_infty
= isl_poly_is_neginfty(poly2
);
1230 isl_ctx
*ctx
= poly1
->ctx
;
1231 isl_poly_free(poly1
);
1232 isl_poly_free(poly2
);
1233 return isl_poly_nan(ctx
);
1235 poly1
= isl_poly_cow(poly1
);
1236 rec
= isl_poly_as_rec(poly1
);
1240 for (i
= 0; i
< rec
->n
; ++i
) {
1241 rec
->p
[i
] = isl_poly_mul(rec
->p
[i
],
1242 isl_poly_copy(poly2
));
1246 isl_poly_free(poly2
);
1250 is_cst
= isl_poly_is_cst(poly1
);
1254 return isl_poly_mul_cst(poly1
, poly2
);
1256 return isl_poly_mul_rec(poly1
, poly2
);
1258 isl_poly_free(poly1
);
1259 isl_poly_free(poly2
);
1263 __isl_give isl_poly
*isl_poly_pow(__isl_take isl_poly
*poly
, unsigned power
)
1273 res
= isl_poly_copy(poly
);
1275 res
= isl_poly_one(poly
->ctx
);
1277 while (power
>>= 1) {
1278 poly
= isl_poly_mul(poly
, isl_poly_copy(poly
));
1280 res
= isl_poly_mul(res
, isl_poly_copy(poly
));
1283 isl_poly_free(poly
);
1287 __isl_give isl_qpolynomial
*isl_qpolynomial_alloc(__isl_take isl_space
*space
,
1288 unsigned n_div
, __isl_take isl_poly
*poly
)
1290 struct isl_qpolynomial
*qp
= NULL
;
1293 total
= isl_space_dim(space
, isl_dim_all
);
1294 if (total
< 0 || !poly
)
1297 if (!isl_space_is_set(space
))
1298 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
1299 "domain of polynomial should be a set", goto error
);
1301 qp
= isl_calloc_type(space
->ctx
, struct isl_qpolynomial
);
1306 qp
->div
= isl_mat_alloc(space
->ctx
, n_div
, 1 + 1 + total
+ n_div
);
1315 isl_space_free(space
);
1316 isl_poly_free(poly
);
1317 isl_qpolynomial_free(qp
);
1321 __isl_give isl_qpolynomial
*isl_qpolynomial_copy(__isl_keep isl_qpolynomial
*qp
)
1330 __isl_give isl_qpolynomial
*isl_qpolynomial_dup(__isl_keep isl_qpolynomial
*qp
)
1332 struct isl_qpolynomial
*dup
;
1337 dup
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
), qp
->div
->n_row
,
1338 isl_poly_copy(qp
->poly
));
1341 isl_mat_free(dup
->div
);
1342 dup
->div
= isl_mat_copy(qp
->div
);
1348 isl_qpolynomial_free(dup
);
1352 __isl_give isl_qpolynomial
*isl_qpolynomial_cow(__isl_take isl_qpolynomial
*qp
)
1360 return isl_qpolynomial_dup(qp
);
1363 __isl_null isl_qpolynomial
*isl_qpolynomial_free(
1364 __isl_take isl_qpolynomial
*qp
)
1372 isl_space_free(qp
->dim
);
1373 isl_mat_free(qp
->div
);
1374 isl_poly_free(qp
->poly
);
1380 __isl_give isl_poly
*isl_poly_var_pow(isl_ctx
*ctx
, int pos
, int power
)
1386 rec
= isl_poly_alloc_rec(ctx
, pos
, 1 + power
);
1389 for (i
= 0; i
< 1 + power
; ++i
) {
1390 rec
->p
[i
] = isl_poly_zero(ctx
);
1395 cst
= isl_poly_as_cst(rec
->p
[power
]);
1396 isl_int_set_si(cst
->n
, 1);
1400 isl_poly_free(&rec
->poly
);
1404 /* r array maps original positions to new positions.
1406 static __isl_give isl_poly
*reorder(__isl_take isl_poly
*poly
, int *r
)
1414 is_cst
= isl_poly_is_cst(poly
);
1416 return isl_poly_free(poly
);
1420 rec
= isl_poly_as_rec(poly
);
1424 isl_assert(poly
->ctx
, rec
->n
>= 1, goto error
);
1426 base
= isl_poly_var_pow(poly
->ctx
, r
[poly
->var
], 1);
1427 res
= reorder(isl_poly_copy(rec
->p
[rec
->n
- 1]), r
);
1429 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1430 res
= isl_poly_mul(res
, isl_poly_copy(base
));
1431 res
= isl_poly_sum(res
, reorder(isl_poly_copy(rec
->p
[i
]), r
));
1434 isl_poly_free(base
);
1435 isl_poly_free(poly
);
1439 isl_poly_free(poly
);
1443 static isl_bool
compatible_divs(__isl_keep isl_mat
*div1
,
1444 __isl_keep isl_mat
*div2
)
1449 isl_assert(div1
->ctx
, div1
->n_row
>= div2
->n_row
&&
1450 div1
->n_col
>= div2
->n_col
,
1451 return isl_bool_error
);
1453 if (div1
->n_row
== div2
->n_row
)
1454 return isl_mat_is_equal(div1
, div2
);
1456 n_row
= div1
->n_row
;
1457 n_col
= div1
->n_col
;
1458 div1
->n_row
= div2
->n_row
;
1459 div1
->n_col
= div2
->n_col
;
1461 equal
= isl_mat_is_equal(div1
, div2
);
1463 div1
->n_row
= n_row
;
1464 div1
->n_col
= n_col
;
1469 static int cmp_row(__isl_keep isl_mat
*div
, int i
, int j
)
1473 li
= isl_seq_last_non_zero(div
->row
[i
], div
->n_col
);
1474 lj
= isl_seq_last_non_zero(div
->row
[j
], div
->n_col
);
1479 return isl_seq_cmp(div
->row
[i
], div
->row
[j
], div
->n_col
);
1482 struct isl_div_sort_info
{
1487 static int div_sort_cmp(const void *p1
, const void *p2
)
1489 const struct isl_div_sort_info
*i1
, *i2
;
1490 i1
= (const struct isl_div_sort_info
*) p1
;
1491 i2
= (const struct isl_div_sort_info
*) p2
;
1493 return cmp_row(i1
->div
, i1
->row
, i2
->row
);
1496 /* Sort divs and remove duplicates.
1498 static __isl_give isl_qpolynomial
*sort_divs(__isl_take isl_qpolynomial
*qp
)
1503 struct isl_div_sort_info
*array
= NULL
;
1504 int *pos
= NULL
, *at
= NULL
;
1505 int *reordering
= NULL
;
1510 if (qp
->div
->n_row
<= 1)
1513 div_pos
= isl_qpolynomial_domain_var_offset(qp
, isl_dim_div
);
1515 return isl_qpolynomial_free(qp
);
1517 array
= isl_alloc_array(qp
->div
->ctx
, struct isl_div_sort_info
,
1519 pos
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1520 at
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1521 len
= qp
->div
->n_col
- 2;
1522 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
1523 if (!array
|| !pos
|| !at
|| !reordering
)
1526 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1527 array
[i
].div
= qp
->div
;
1533 qsort(array
, qp
->div
->n_row
, sizeof(struct isl_div_sort_info
),
1536 for (i
= 0; i
< div_pos
; ++i
)
1539 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1540 if (pos
[array
[i
].row
] == i
)
1542 qp
->div
= isl_mat_swap_rows(qp
->div
, i
, pos
[array
[i
].row
]);
1543 pos
[at
[i
]] = pos
[array
[i
].row
];
1544 at
[pos
[array
[i
].row
]] = at
[i
];
1545 at
[i
] = array
[i
].row
;
1546 pos
[array
[i
].row
] = i
;
1550 for (i
= 0; i
< len
- div_pos
; ++i
) {
1552 isl_seq_eq(qp
->div
->row
[i
- skip
- 1],
1553 qp
->div
->row
[i
- skip
], qp
->div
->n_col
)) {
1554 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
1555 isl_mat_col_add(qp
->div
, 2 + div_pos
+ i
- skip
- 1,
1556 2 + div_pos
+ i
- skip
);
1557 qp
->div
= isl_mat_drop_cols(qp
->div
,
1558 2 + div_pos
+ i
- skip
, 1);
1561 reordering
[div_pos
+ array
[i
].row
] = div_pos
+ i
- skip
;
1564 qp
->poly
= reorder(qp
->poly
, reordering
);
1566 if (!qp
->poly
|| !qp
->div
)
1580 isl_qpolynomial_free(qp
);
1584 static __isl_give isl_poly
*expand(__isl_take isl_poly
*poly
, int *exp
,
1591 is_cst
= isl_poly_is_cst(poly
);
1593 return isl_poly_free(poly
);
1597 if (poly
->var
< first
)
1600 if (exp
[poly
->var
- first
] == poly
->var
- first
)
1603 poly
= isl_poly_cow(poly
);
1607 poly
->var
= exp
[poly
->var
- first
] + first
;
1609 rec
= isl_poly_as_rec(poly
);
1613 for (i
= 0; i
< rec
->n
; ++i
) {
1614 rec
->p
[i
] = expand(rec
->p
[i
], exp
, first
);
1621 isl_poly_free(poly
);
1625 static __isl_give isl_qpolynomial
*with_merged_divs(
1626 __isl_give isl_qpolynomial
*(*fn
)(__isl_take isl_qpolynomial
*qp1
,
1627 __isl_take isl_qpolynomial
*qp2
),
1628 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
1632 isl_mat
*div
= NULL
;
1635 qp1
= isl_qpolynomial_cow(qp1
);
1636 qp2
= isl_qpolynomial_cow(qp2
);
1641 isl_assert(qp1
->div
->ctx
, qp1
->div
->n_row
>= qp2
->div
->n_row
&&
1642 qp1
->div
->n_col
>= qp2
->div
->n_col
, goto error
);
1644 n_div1
= qp1
->div
->n_row
;
1645 n_div2
= qp2
->div
->n_row
;
1646 exp1
= isl_alloc_array(qp1
->div
->ctx
, int, n_div1
);
1647 exp2
= isl_alloc_array(qp2
->div
->ctx
, int, n_div2
);
1648 if ((n_div1
&& !exp1
) || (n_div2
&& !exp2
))
1651 div
= isl_merge_divs(qp1
->div
, qp2
->div
, exp1
, exp2
);
1655 isl_mat_free(qp1
->div
);
1656 qp1
->div
= isl_mat_copy(div
);
1657 isl_mat_free(qp2
->div
);
1658 qp2
->div
= isl_mat_copy(div
);
1660 qp1
->poly
= expand(qp1
->poly
, exp1
, div
->n_col
- div
->n_row
- 2);
1661 qp2
->poly
= expand(qp2
->poly
, exp2
, div
->n_col
- div
->n_row
- 2);
1663 if (!qp1
->poly
|| !qp2
->poly
)
1670 return fn(qp1
, qp2
);
1675 isl_qpolynomial_free(qp1
);
1676 isl_qpolynomial_free(qp2
);
1680 __isl_give isl_qpolynomial
*isl_qpolynomial_add(__isl_take isl_qpolynomial
*qp1
,
1681 __isl_take isl_qpolynomial
*qp2
)
1683 isl_bool compatible
;
1685 qp1
= isl_qpolynomial_cow(qp1
);
1687 if (isl_qpolynomial_check_equal_space(qp1
, qp2
) < 0)
1690 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1691 return isl_qpolynomial_add(qp2
, qp1
);
1693 compatible
= compatible_divs(qp1
->div
, qp2
->div
);
1697 return with_merged_divs(isl_qpolynomial_add
, qp1
, qp2
);
1699 qp1
->poly
= isl_poly_sum(qp1
->poly
, isl_poly_copy(qp2
->poly
));
1703 isl_qpolynomial_free(qp2
);
1707 isl_qpolynomial_free(qp1
);
1708 isl_qpolynomial_free(qp2
);
1712 __isl_give isl_qpolynomial
*isl_qpolynomial_add_on_domain(
1713 __isl_keep isl_set
*dom
,
1714 __isl_take isl_qpolynomial
*qp1
,
1715 __isl_take isl_qpolynomial
*qp2
)
1717 qp1
= isl_qpolynomial_add(qp1
, qp2
);
1718 qp1
= isl_qpolynomial_gist(qp1
, isl_set_copy(dom
));
1722 __isl_give isl_qpolynomial
*isl_qpolynomial_sub(__isl_take isl_qpolynomial
*qp1
,
1723 __isl_take isl_qpolynomial
*qp2
)
1725 return isl_qpolynomial_add(qp1
, isl_qpolynomial_neg(qp2
));
1728 __isl_give isl_qpolynomial
*isl_qpolynomial_add_isl_int(
1729 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1731 if (isl_int_is_zero(v
))
1734 qp
= isl_qpolynomial_cow(qp
);
1738 qp
->poly
= isl_poly_add_isl_int(qp
->poly
, v
);
1744 isl_qpolynomial_free(qp
);
1749 __isl_give isl_qpolynomial
*isl_qpolynomial_neg(__isl_take isl_qpolynomial
*qp
)
1754 return isl_qpolynomial_mul_isl_int(qp
, qp
->dim
->ctx
->negone
);
1757 __isl_give isl_qpolynomial
*isl_qpolynomial_mul_isl_int(
1758 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1760 if (isl_int_is_one(v
))
1763 if (qp
&& isl_int_is_zero(v
)) {
1764 isl_qpolynomial
*zero
;
1765 zero
= isl_qpolynomial_zero_on_domain(isl_space_copy(qp
->dim
));
1766 isl_qpolynomial_free(qp
);
1770 qp
= isl_qpolynomial_cow(qp
);
1774 qp
->poly
= isl_poly_mul_isl_int(qp
->poly
, v
);
1780 isl_qpolynomial_free(qp
);
1784 __isl_give isl_qpolynomial
*isl_qpolynomial_scale(
1785 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1787 return isl_qpolynomial_mul_isl_int(qp
, v
);
1790 /* Multiply "qp" by "v".
1792 __isl_give isl_qpolynomial
*isl_qpolynomial_scale_val(
1793 __isl_take isl_qpolynomial
*qp
, __isl_take isl_val
*v
)
1798 if (!isl_val_is_rat(v
))
1799 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
1800 "expecting rational factor", goto error
);
1802 if (isl_val_is_one(v
)) {
1807 if (isl_val_is_zero(v
)) {
1810 space
= isl_qpolynomial_get_domain_space(qp
);
1811 isl_qpolynomial_free(qp
);
1813 return isl_qpolynomial_zero_on_domain(space
);
1816 qp
= isl_qpolynomial_cow(qp
);
1820 qp
->poly
= isl_poly_scale_val(qp
->poly
, v
);
1822 qp
= isl_qpolynomial_free(qp
);
1828 isl_qpolynomial_free(qp
);
1832 /* Divide "qp" by "v".
1834 __isl_give isl_qpolynomial
*isl_qpolynomial_scale_down_val(
1835 __isl_take isl_qpolynomial
*qp
, __isl_take isl_val
*v
)
1840 if (!isl_val_is_rat(v
))
1841 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
1842 "expecting rational factor", goto error
);
1843 if (isl_val_is_zero(v
))
1844 isl_die(isl_val_get_ctx(v
), isl_error_invalid
,
1845 "cannot scale down by zero", goto error
);
1847 return isl_qpolynomial_scale_val(qp
, isl_val_inv(v
));
1850 isl_qpolynomial_free(qp
);
1854 __isl_give isl_qpolynomial
*isl_qpolynomial_mul(__isl_take isl_qpolynomial
*qp1
,
1855 __isl_take isl_qpolynomial
*qp2
)
1857 isl_bool compatible
;
1859 qp1
= isl_qpolynomial_cow(qp1
);
1861 if (isl_qpolynomial_check_equal_space(qp1
, qp2
) < 0)
1864 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1865 return isl_qpolynomial_mul(qp2
, qp1
);
1867 compatible
= compatible_divs(qp1
->div
, qp2
->div
);
1871 return with_merged_divs(isl_qpolynomial_mul
, qp1
, qp2
);
1873 qp1
->poly
= isl_poly_mul(qp1
->poly
, isl_poly_copy(qp2
->poly
));
1877 isl_qpolynomial_free(qp2
);
1881 isl_qpolynomial_free(qp1
);
1882 isl_qpolynomial_free(qp2
);
1886 __isl_give isl_qpolynomial
*isl_qpolynomial_pow(__isl_take isl_qpolynomial
*qp
,
1889 qp
= isl_qpolynomial_cow(qp
);
1894 qp
->poly
= isl_poly_pow(qp
->poly
, power
);
1900 isl_qpolynomial_free(qp
);
1904 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_pow(
1905 __isl_take isl_pw_qpolynomial
*pwqp
, unsigned power
)
1912 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
1916 for (i
= 0; i
< pwqp
->n
; ++i
) {
1917 pwqp
->p
[i
].qp
= isl_qpolynomial_pow(pwqp
->p
[i
].qp
, power
);
1919 return isl_pw_qpolynomial_free(pwqp
);
1925 __isl_give isl_qpolynomial
*isl_qpolynomial_zero_on_domain(
1926 __isl_take isl_space
*domain
)
1930 return isl_qpolynomial_alloc(domain
, 0, isl_poly_zero(domain
->ctx
));
1933 __isl_give isl_qpolynomial
*isl_qpolynomial_one_on_domain(
1934 __isl_take isl_space
*domain
)
1938 return isl_qpolynomial_alloc(domain
, 0, isl_poly_one(domain
->ctx
));
1941 __isl_give isl_qpolynomial
*isl_qpolynomial_infty_on_domain(
1942 __isl_take isl_space
*domain
)
1946 return isl_qpolynomial_alloc(domain
, 0, isl_poly_infty(domain
->ctx
));
1949 __isl_give isl_qpolynomial
*isl_qpolynomial_neginfty_on_domain(
1950 __isl_take isl_space
*domain
)
1954 return isl_qpolynomial_alloc(domain
, 0, isl_poly_neginfty(domain
->ctx
));
1957 __isl_give isl_qpolynomial
*isl_qpolynomial_nan_on_domain(
1958 __isl_take isl_space
*domain
)
1962 return isl_qpolynomial_alloc(domain
, 0, isl_poly_nan(domain
->ctx
));
1965 __isl_give isl_qpolynomial
*isl_qpolynomial_cst_on_domain(
1966 __isl_take isl_space
*domain
,
1969 struct isl_qpolynomial
*qp
;
1972 qp
= isl_qpolynomial_zero_on_domain(domain
);
1976 cst
= isl_poly_as_cst(qp
->poly
);
1977 isl_int_set(cst
->n
, v
);
1982 isl_bool
isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial
*qp
,
1983 isl_int
*n
, isl_int
*d
)
1989 return isl_bool_error
;
1991 is_cst
= isl_poly_is_cst(qp
->poly
);
1992 if (is_cst
< 0 || !is_cst
)
1995 cst
= isl_poly_as_cst(qp
->poly
);
1997 return isl_bool_error
;
2000 isl_int_set(*n
, cst
->n
);
2002 isl_int_set(*d
, cst
->d
);
2004 return isl_bool_true
;
2007 /* Return the constant term of "poly".
2009 static __isl_give isl_val
*isl_poly_get_constant_val(__isl_keep isl_poly
*poly
)
2017 while ((is_cst
= isl_poly_is_cst(poly
)) == isl_bool_false
) {
2020 rec
= isl_poly_as_rec(poly
);
2028 cst
= isl_poly_as_cst(poly
);
2031 return isl_val_rat_from_isl_int(cst
->poly
.ctx
, cst
->n
, cst
->d
);
2034 /* Return the constant term of "qp".
2036 __isl_give isl_val
*isl_qpolynomial_get_constant_val(
2037 __isl_keep isl_qpolynomial
*qp
)
2042 return isl_poly_get_constant_val(qp
->poly
);
2045 isl_bool
isl_poly_is_affine(__isl_keep isl_poly
*poly
)
2051 return isl_bool_error
;
2054 return isl_bool_true
;
2056 rec
= isl_poly_as_rec(poly
);
2058 return isl_bool_error
;
2061 return isl_bool_false
;
2063 isl_assert(poly
->ctx
, rec
->n
> 1, return isl_bool_error
);
2065 is_cst
= isl_poly_is_cst(rec
->p
[1]);
2066 if (is_cst
< 0 || !is_cst
)
2069 return isl_poly_is_affine(rec
->p
[0]);
2072 isl_bool
isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial
*qp
)
2075 return isl_bool_error
;
2077 if (qp
->div
->n_row
> 0)
2078 return isl_bool_false
;
2080 return isl_poly_is_affine(qp
->poly
);
2083 static void update_coeff(__isl_keep isl_vec
*aff
,
2084 __isl_keep isl_poly_cst
*cst
, int pos
)
2089 if (isl_int_is_zero(cst
->n
))
2094 isl_int_gcd(gcd
, cst
->d
, aff
->el
[0]);
2095 isl_int_divexact(f
, cst
->d
, gcd
);
2096 isl_int_divexact(gcd
, aff
->el
[0], gcd
);
2097 isl_seq_scale(aff
->el
, aff
->el
, f
, aff
->size
);
2098 isl_int_mul(aff
->el
[1 + pos
], gcd
, cst
->n
);
2103 int isl_poly_update_affine(__isl_keep isl_poly
*poly
, __isl_keep isl_vec
*aff
)
2111 if (poly
->var
< 0) {
2114 cst
= isl_poly_as_cst(poly
);
2117 update_coeff(aff
, cst
, 0);
2121 rec
= isl_poly_as_rec(poly
);
2124 isl_assert(poly
->ctx
, rec
->n
== 2, return -1);
2126 cst
= isl_poly_as_cst(rec
->p
[1]);
2129 update_coeff(aff
, cst
, 1 + poly
->var
);
2131 return isl_poly_update_affine(rec
->p
[0], aff
);
2134 __isl_give isl_vec
*isl_qpolynomial_extract_affine(
2135 __isl_keep isl_qpolynomial
*qp
)
2140 d
= isl_qpolynomial_domain_dim(qp
, isl_dim_all
);
2144 aff
= isl_vec_alloc(qp
->div
->ctx
, 2 + d
);
2148 isl_seq_clr(aff
->el
+ 1, 1 + d
);
2149 isl_int_set_si(aff
->el
[0], 1);
2151 if (isl_poly_update_affine(qp
->poly
, aff
) < 0)
2160 /* Compare two quasi-polynomials.
2162 * Return -1 if "qp1" is "smaller" than "qp2", 1 if "qp1" is "greater"
2163 * than "qp2" and 0 if they are equal.
2165 int isl_qpolynomial_plain_cmp(__isl_keep isl_qpolynomial
*qp1
,
2166 __isl_keep isl_qpolynomial
*qp2
)
2177 cmp
= isl_space_cmp(qp1
->dim
, qp2
->dim
);
2181 cmp
= isl_local_cmp(qp1
->div
, qp2
->div
);
2185 return isl_poly_plain_cmp(qp1
->poly
, qp2
->poly
);
2188 /* Is "qp1" obviously equal to "qp2"?
2190 * NaN is not equal to anything, not even to another NaN.
2192 isl_bool
isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial
*qp1
,
2193 __isl_keep isl_qpolynomial
*qp2
)
2198 return isl_bool_error
;
2200 if (isl_qpolynomial_is_nan(qp1
) || isl_qpolynomial_is_nan(qp2
))
2201 return isl_bool_false
;
2203 equal
= isl_space_is_equal(qp1
->dim
, qp2
->dim
);
2204 if (equal
< 0 || !equal
)
2207 equal
= isl_mat_is_equal(qp1
->div
, qp2
->div
);
2208 if (equal
< 0 || !equal
)
2211 return isl_poly_is_equal(qp1
->poly
, qp2
->poly
);
2214 static isl_stat
poly_update_den(__isl_keep isl_poly
*poly
, isl_int
*d
)
2220 is_cst
= isl_poly_is_cst(poly
);
2222 return isl_stat_error
;
2225 cst
= isl_poly_as_cst(poly
);
2227 return isl_stat_error
;
2228 isl_int_lcm(*d
, *d
, cst
->d
);
2232 rec
= isl_poly_as_rec(poly
);
2234 return isl_stat_error
;
2236 for (i
= 0; i
< rec
->n
; ++i
)
2237 poly_update_den(rec
->p
[i
], d
);
2242 __isl_give isl_val
*isl_qpolynomial_get_den(__isl_keep isl_qpolynomial
*qp
)
2248 d
= isl_val_one(isl_qpolynomial_get_ctx(qp
));
2251 if (poly_update_den(qp
->poly
, &d
->n
) < 0)
2252 return isl_val_free(d
);
2256 __isl_give isl_qpolynomial
*isl_qpolynomial_var_pow_on_domain(
2257 __isl_take isl_space
*domain
, int pos
, int power
)
2259 struct isl_ctx
*ctx
;
2266 return isl_qpolynomial_alloc(domain
, 0,
2267 isl_poly_var_pow(ctx
, pos
, power
));
2270 __isl_give isl_qpolynomial
*isl_qpolynomial_var_on_domain(
2271 __isl_take isl_space
*domain
, enum isl_dim_type type
, unsigned pos
)
2273 if (isl_space_check_is_set(domain
) < 0)
2275 if (isl_space_check_range(domain
, type
, pos
, 1) < 0)
2278 pos
+= isl_space_offset(domain
, type
);
2280 return isl_qpolynomial_var_pow_on_domain(domain
, pos
, 1);
2282 isl_space_free(domain
);
2286 __isl_give isl_poly
*isl_poly_subs(__isl_take isl_poly
*poly
,
2287 unsigned first
, unsigned n
, __isl_keep isl_poly
**subs
)
2292 isl_poly
*base
, *res
;
2294 is_cst
= isl_poly_is_cst(poly
);
2296 return isl_poly_free(poly
);
2300 if (poly
->var
< first
)
2303 rec
= isl_poly_as_rec(poly
);
2307 isl_assert(poly
->ctx
, rec
->n
>= 1, goto error
);
2309 if (poly
->var
>= first
+ n
)
2310 base
= isl_poly_var_pow(poly
->ctx
, poly
->var
, 1);
2312 base
= isl_poly_copy(subs
[poly
->var
- first
]);
2314 res
= isl_poly_subs(isl_poly_copy(rec
->p
[rec
->n
- 1]), first
, n
, subs
);
2315 for (i
= rec
->n
- 2; i
>= 0; --i
) {
2317 t
= isl_poly_subs(isl_poly_copy(rec
->p
[i
]), first
, n
, subs
);
2318 res
= isl_poly_mul(res
, isl_poly_copy(base
));
2319 res
= isl_poly_sum(res
, t
);
2322 isl_poly_free(base
);
2323 isl_poly_free(poly
);
2327 isl_poly_free(poly
);
2331 __isl_give isl_poly
*isl_poly_from_affine(isl_ctx
*ctx
, isl_int
*f
,
2332 isl_int denom
, unsigned len
)
2337 isl_assert(ctx
, len
>= 1, return NULL
);
2339 poly
= isl_poly_rat_cst(ctx
, f
[0], denom
);
2340 for (i
= 0; i
< len
- 1; ++i
) {
2344 if (isl_int_is_zero(f
[1 + i
]))
2347 c
= isl_poly_rat_cst(ctx
, f
[1 + i
], denom
);
2348 t
= isl_poly_var_pow(ctx
, i
, 1);
2349 t
= isl_poly_mul(c
, t
);
2350 poly
= isl_poly_sum(poly
, t
);
2356 /* Remove common factor of non-constant terms and denominator.
2358 static void normalize_div(__isl_keep isl_qpolynomial
*qp
, int div
)
2360 isl_ctx
*ctx
= qp
->div
->ctx
;
2361 unsigned total
= qp
->div
->n_col
- 2;
2363 isl_seq_gcd(qp
->div
->row
[div
] + 2, total
, &ctx
->normalize_gcd
);
2364 isl_int_gcd(ctx
->normalize_gcd
,
2365 ctx
->normalize_gcd
, qp
->div
->row
[div
][0]);
2366 if (isl_int_is_one(ctx
->normalize_gcd
))
2369 isl_seq_scale_down(qp
->div
->row
[div
] + 2, qp
->div
->row
[div
] + 2,
2370 ctx
->normalize_gcd
, total
);
2371 isl_int_divexact(qp
->div
->row
[div
][0], qp
->div
->row
[div
][0],
2372 ctx
->normalize_gcd
);
2373 isl_int_fdiv_q(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1],
2374 ctx
->normalize_gcd
);
2377 /* Replace the integer division identified by "div" by the polynomial "s".
2378 * The integer division is assumed not to appear in the definition
2379 * of any other integer divisions.
2381 static __isl_give isl_qpolynomial
*substitute_div(
2382 __isl_take isl_qpolynomial
*qp
, int div
, __isl_take isl_poly
*s
)
2392 qp
= isl_qpolynomial_cow(qp
);
2396 div_pos
= isl_qpolynomial_domain_var_offset(qp
, isl_dim_div
);
2399 qp
->poly
= isl_poly_subs(qp
->poly
, div_pos
+ div
, 1, &s
);
2403 ctx
= isl_qpolynomial_get_ctx(qp
);
2404 reordering
= isl_alloc_array(ctx
, int, div_pos
+ qp
->div
->n_row
);
2407 for (i
= 0; i
< div_pos
+ div
; ++i
)
2409 for (i
= div_pos
+ div
+ 1; i
< div_pos
+ qp
->div
->n_row
; ++i
)
2410 reordering
[i
] = i
- 1;
2411 qp
->div
= isl_mat_drop_rows(qp
->div
, div
, 1);
2412 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + div_pos
+ div
, 1);
2413 qp
->poly
= reorder(qp
->poly
, reordering
);
2416 if (!qp
->poly
|| !qp
->div
)
2422 isl_qpolynomial_free(qp
);
2427 /* Replace all integer divisions [e/d] that turn out to not actually be integer
2428 * divisions because d is equal to 1 by their definition, i.e., e.
2430 static __isl_give isl_qpolynomial
*substitute_non_divs(
2431 __isl_take isl_qpolynomial
*qp
)
2437 div_pos
= isl_qpolynomial_domain_var_offset(qp
, isl_dim_div
);
2439 return isl_qpolynomial_free(qp
);
2441 for (i
= 0; qp
&& i
< qp
->div
->n_row
; ++i
) {
2442 if (!isl_int_is_one(qp
->div
->row
[i
][0]))
2444 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
2445 if (isl_int_is_zero(qp
->div
->row
[j
][2 + div_pos
+ i
]))
2447 isl_seq_combine(qp
->div
->row
[j
] + 1,
2448 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
2449 qp
->div
->row
[j
][2 + div_pos
+ i
],
2450 qp
->div
->row
[i
] + 1, 1 + div_pos
+ i
);
2451 isl_int_set_si(qp
->div
->row
[j
][2 + div_pos
+ i
], 0);
2452 normalize_div(qp
, j
);
2454 s
= isl_poly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
2455 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
2456 qp
= substitute_div(qp
, i
, s
);
2463 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
2464 * with d the denominator. When replacing the coefficient e of x by
2465 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
2466 * inside the division, so we need to add floor(e/d) * x outside.
2467 * That is, we replace q by q' + floor(e/d) * x and we therefore need
2468 * to adjust the coefficient of x in each later div that depends on the
2469 * current div "div" and also in the affine expressions in the rows of "mat"
2470 * (if they too depend on "div").
2472 static void reduce_div(__isl_keep isl_qpolynomial
*qp
, int div
,
2473 __isl_keep isl_mat
**mat
)
2477 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
2480 for (i
= 0; i
< 1 + total
+ div
; ++i
) {
2481 if (isl_int_is_nonneg(qp
->div
->row
[div
][1 + i
]) &&
2482 isl_int_lt(qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]))
2484 isl_int_fdiv_q(v
, qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
2485 isl_int_fdiv_r(qp
->div
->row
[div
][1 + i
],
2486 qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
2487 *mat
= isl_mat_col_addmul(*mat
, i
, v
, 1 + total
+ div
);
2488 for (j
= div
+ 1; j
< qp
->div
->n_row
; ++j
) {
2489 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ div
]))
2491 isl_int_addmul(qp
->div
->row
[j
][1 + i
],
2492 v
, qp
->div
->row
[j
][2 + total
+ div
]);
2498 /* Check if the last non-zero coefficient is bigger that half of the
2499 * denominator. If so, we will invert the div to further reduce the number
2500 * of distinct divs that may appear.
2501 * If the last non-zero coefficient is exactly half the denominator,
2502 * then we continue looking for earlier coefficients that are bigger
2503 * than half the denominator.
2505 static int needs_invert(__isl_keep isl_mat
*div
, int row
)
2510 for (i
= div
->n_col
- 1; i
>= 1; --i
) {
2511 if (isl_int_is_zero(div
->row
[row
][i
]))
2513 isl_int_mul_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
2514 cmp
= isl_int_cmp(div
->row
[row
][i
], div
->row
[row
][0]);
2515 isl_int_divexact_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
2525 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
2526 * We only invert the coefficients of e (and the coefficient of q in
2527 * later divs and in the rows of "mat"). After calling this function, the
2528 * coefficients of e should be reduced again.
2530 static void invert_div(__isl_keep isl_qpolynomial
*qp
, int div
,
2531 __isl_keep isl_mat
**mat
)
2533 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
2535 isl_seq_neg(qp
->div
->row
[div
] + 1,
2536 qp
->div
->row
[div
] + 1, qp
->div
->n_col
- 1);
2537 isl_int_sub_ui(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1], 1);
2538 isl_int_add(qp
->div
->row
[div
][1],
2539 qp
->div
->row
[div
][1], qp
->div
->row
[div
][0]);
2540 *mat
= isl_mat_col_neg(*mat
, 1 + total
+ div
);
2541 isl_mat_col_mul(qp
->div
, 2 + total
+ div
,
2542 qp
->div
->ctx
->negone
, 2 + total
+ div
);
2545 /* Reduce all divs of "qp" to have coefficients
2546 * in the interval [0, d-1], with d the denominator and such that the
2547 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2548 * The modifications to the integer divisions need to be reflected
2549 * in the factors of the polynomial that refer to the original
2550 * integer divisions. To this end, the modifications are collected
2551 * as a set of affine expressions and then plugged into the polynomial.
2553 * After the reduction, some divs may have become redundant or identical,
2554 * so we call substitute_non_divs and sort_divs. If these functions
2555 * eliminate divs or merge two or more divs into one, the coefficients
2556 * of the enclosing divs may have to be reduced again, so we call
2557 * ourselves recursively if the number of divs decreases.
2559 static __isl_give isl_qpolynomial
*reduce_divs(__isl_take isl_qpolynomial
*qp
)
2566 isl_size n_div
, total
, new_n_div
;
2568 total
= isl_qpolynomial_domain_dim(qp
, isl_dim_all
);
2569 n_div
= isl_qpolynomial_domain_dim(qp
, isl_dim_div
);
2570 o_div
= isl_qpolynomial_domain_offset(qp
, isl_dim_div
);
2571 if (total
< 0 || n_div
< 0)
2572 return isl_qpolynomial_free(qp
);
2573 ctx
= isl_qpolynomial_get_ctx(qp
);
2574 mat
= isl_mat_zero(ctx
, n_div
, 1 + total
);
2576 for (i
= 0; i
< n_div
; ++i
)
2577 mat
= isl_mat_set_element_si(mat
, i
, o_div
+ i
, 1);
2579 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2580 normalize_div(qp
, i
);
2581 reduce_div(qp
, i
, &mat
);
2582 if (needs_invert(qp
->div
, i
)) {
2583 invert_div(qp
, i
, &mat
);
2584 reduce_div(qp
, i
, &mat
);
2590 s
= isl_alloc_array(ctx
, struct isl_poly
*, n_div
);
2593 for (i
= 0; i
< n_div
; ++i
)
2594 s
[i
] = isl_poly_from_affine(ctx
, mat
->row
[i
], ctx
->one
,
2596 qp
->poly
= isl_poly_subs(qp
->poly
, o_div
- 1, n_div
, s
);
2597 for (i
= 0; i
< n_div
; ++i
)
2598 isl_poly_free(s
[i
]);
2605 qp
= substitute_non_divs(qp
);
2607 new_n_div
= isl_qpolynomial_domain_dim(qp
, isl_dim_div
);
2609 return isl_qpolynomial_free(qp
);
2610 if (new_n_div
< n_div
)
2611 return reduce_divs(qp
);
2615 isl_qpolynomial_free(qp
);
2620 __isl_give isl_qpolynomial
*isl_qpolynomial_rat_cst_on_domain(
2621 __isl_take isl_space
*domain
, const isl_int n
, const isl_int d
)
2623 struct isl_qpolynomial
*qp
;
2626 qp
= isl_qpolynomial_zero_on_domain(domain
);
2630 cst
= isl_poly_as_cst(qp
->poly
);
2631 isl_int_set(cst
->n
, n
);
2632 isl_int_set(cst
->d
, d
);
2637 /* Return an isl_qpolynomial that is equal to "val" on domain space "domain".
2639 __isl_give isl_qpolynomial
*isl_qpolynomial_val_on_domain(
2640 __isl_take isl_space
*domain
, __isl_take isl_val
*val
)
2642 isl_qpolynomial
*qp
;
2645 qp
= isl_qpolynomial_zero_on_domain(domain
);
2649 cst
= isl_poly_as_cst(qp
->poly
);
2650 isl_int_set(cst
->n
, val
->n
);
2651 isl_int_set(cst
->d
, val
->d
);
2657 isl_qpolynomial_free(qp
);
2661 static isl_stat
poly_set_active(__isl_keep isl_poly
*poly
, int *active
, int d
)
2667 is_cst
= isl_poly_is_cst(poly
);
2669 return isl_stat_error
;
2674 active
[poly
->var
] = 1;
2676 rec
= isl_poly_as_rec(poly
);
2677 for (i
= 0; i
< rec
->n
; ++i
)
2678 if (poly_set_active(rec
->p
[i
], active
, d
) < 0)
2679 return isl_stat_error
;
2684 static isl_stat
set_active(__isl_keep isl_qpolynomial
*qp
, int *active
)
2690 space
= isl_qpolynomial_peek_domain_space(qp
);
2691 d
= isl_space_dim(space
, isl_dim_all
);
2692 if (d
< 0 || !active
)
2693 return isl_stat_error
;
2695 for (i
= 0; i
< d
; ++i
)
2696 for (j
= 0; j
< qp
->div
->n_row
; ++j
) {
2697 if (isl_int_is_zero(qp
->div
->row
[j
][2 + i
]))
2703 return poly_set_active(qp
->poly
, active
, d
);
2707 #define TYPE isl_qpolynomial
2709 #include "check_type_range_templ.c"
2711 isl_bool
isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial
*qp
,
2712 enum isl_dim_type type
, unsigned first
, unsigned n
)
2716 isl_bool involves
= isl_bool_false
;
2722 return isl_bool_error
;
2724 return isl_bool_false
;
2726 if (isl_qpolynomial_check_range(qp
, type
, first
, n
) < 0)
2727 return isl_bool_error
;
2728 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2729 type
== isl_dim_in
, return isl_bool_error
);
2731 space
= isl_qpolynomial_peek_domain_space(qp
);
2732 d
= isl_space_dim(space
, isl_dim_all
);
2734 return isl_bool_error
;
2735 active
= isl_calloc_array(qp
->dim
->ctx
, int, d
);
2736 if (set_active(qp
, active
) < 0)
2739 offset
= isl_qpolynomial_domain_var_offset(qp
, domain_type(type
));
2743 for (i
= 0; i
< n
; ++i
)
2744 if (active
[first
+ i
]) {
2745 involves
= isl_bool_true
;
2754 return isl_bool_error
;
2757 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2758 * of the divs that do appear in the quasi-polynomial.
2760 static __isl_give isl_qpolynomial
*remove_redundant_divs(
2761 __isl_take isl_qpolynomial
*qp
)
2768 int *reordering
= NULL
;
2775 if (qp
->div
->n_row
== 0)
2778 div_pos
= isl_qpolynomial_domain_var_offset(qp
, isl_dim_div
);
2780 return isl_qpolynomial_free(qp
);
2781 len
= qp
->div
->n_col
- 2;
2782 ctx
= isl_qpolynomial_get_ctx(qp
);
2783 active
= isl_calloc_array(ctx
, int, len
);
2787 if (poly_set_active(qp
->poly
, active
, len
) < 0)
2790 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
2791 if (!active
[div_pos
+ i
]) {
2795 for (j
= 0; j
< i
; ++j
) {
2796 if (isl_int_is_zero(qp
->div
->row
[i
][2 + div_pos
+ j
]))
2798 active
[div_pos
+ j
] = 1;
2808 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
2812 for (i
= 0; i
< div_pos
; ++i
)
2816 n_div
= qp
->div
->n_row
;
2817 for (i
= 0; i
< n_div
; ++i
) {
2818 if (!active
[div_pos
+ i
]) {
2819 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
2820 qp
->div
= isl_mat_drop_cols(qp
->div
,
2821 2 + div_pos
+ i
- skip
, 1);
2824 reordering
[div_pos
+ i
] = div_pos
+ i
- skip
;
2827 qp
->poly
= reorder(qp
->poly
, reordering
);
2829 if (!qp
->poly
|| !qp
->div
)
2839 isl_qpolynomial_free(qp
);
2843 __isl_give isl_poly
*isl_poly_drop(__isl_take isl_poly
*poly
,
2844 unsigned first
, unsigned n
)
2851 if (n
== 0 || poly
->var
< 0 || poly
->var
< first
)
2853 if (poly
->var
< first
+ n
) {
2854 poly
= replace_by_constant_term(poly
);
2855 return isl_poly_drop(poly
, first
, n
);
2857 poly
= isl_poly_cow(poly
);
2861 rec
= isl_poly_as_rec(poly
);
2865 for (i
= 0; i
< rec
->n
; ++i
) {
2866 rec
->p
[i
] = isl_poly_drop(rec
->p
[i
], first
, n
);
2873 isl_poly_free(poly
);
2877 __isl_give isl_qpolynomial
*isl_qpolynomial_set_dim_name(
2878 __isl_take isl_qpolynomial
*qp
,
2879 enum isl_dim_type type
, unsigned pos
, const char *s
)
2881 qp
= isl_qpolynomial_cow(qp
);
2884 if (type
== isl_dim_out
)
2885 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
2886 "cannot set name of output/set dimension",
2887 return isl_qpolynomial_free(qp
));
2888 type
= domain_type(type
);
2889 qp
->dim
= isl_space_set_dim_name(qp
->dim
, type
, pos
, s
);
2894 isl_qpolynomial_free(qp
);
2898 __isl_give isl_qpolynomial
*isl_qpolynomial_drop_dims(
2899 __isl_take isl_qpolynomial
*qp
,
2900 enum isl_dim_type type
, unsigned first
, unsigned n
)
2906 if (type
== isl_dim_out
)
2907 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
2908 "cannot drop output/set dimension",
2910 if (isl_qpolynomial_check_range(qp
, type
, first
, n
) < 0)
2911 return isl_qpolynomial_free(qp
);
2912 type
= domain_type(type
);
2913 if (n
== 0 && !isl_space_is_named_or_nested(qp
->dim
, type
))
2916 qp
= isl_qpolynomial_cow(qp
);
2920 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2921 type
== isl_dim_set
, goto error
);
2923 qp
->dim
= isl_space_drop_dims(qp
->dim
, type
, first
, n
);
2927 offset
= isl_qpolynomial_domain_var_offset(qp
, type
);
2932 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + first
, n
);
2936 qp
->poly
= isl_poly_drop(qp
->poly
, first
, n
);
2942 isl_qpolynomial_free(qp
);
2946 /* Project the domain of the quasi-polynomial onto its parameter space.
2947 * The quasi-polynomial may not involve any of the domain dimensions.
2949 __isl_give isl_qpolynomial
*isl_qpolynomial_project_domain_on_params(
2950 __isl_take isl_qpolynomial
*qp
)
2956 n
= isl_qpolynomial_dim(qp
, isl_dim_in
);
2958 return isl_qpolynomial_free(qp
);
2959 involves
= isl_qpolynomial_involves_dims(qp
, isl_dim_in
, 0, n
);
2961 return isl_qpolynomial_free(qp
);
2963 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
2964 "polynomial involves some of the domain dimensions",
2965 return isl_qpolynomial_free(qp
));
2966 qp
= isl_qpolynomial_drop_dims(qp
, isl_dim_in
, 0, n
);
2967 space
= isl_qpolynomial_get_domain_space(qp
);
2968 space
= isl_space_params(space
);
2969 qp
= isl_qpolynomial_reset_domain_space(qp
, space
);
2973 static __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities_lifted(
2974 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2984 if (eq
->n_eq
== 0) {
2985 isl_basic_set_free(eq
);
2989 qp
= isl_qpolynomial_cow(qp
);
2992 qp
->div
= isl_mat_cow(qp
->div
);
2996 total
= isl_basic_set_offset(eq
, isl_dim_div
);
2998 isl_int_init(denom
);
2999 for (i
= 0; i
< eq
->n_eq
; ++i
) {
3000 j
= isl_seq_last_non_zero(eq
->eq
[i
], total
+ n_div
);
3001 if (j
< 0 || j
== 0 || j
>= total
)
3004 for (k
= 0; k
< qp
->div
->n_row
; ++k
) {
3005 if (isl_int_is_zero(qp
->div
->row
[k
][1 + j
]))
3007 isl_seq_elim(qp
->div
->row
[k
] + 1, eq
->eq
[i
], j
, total
,
3008 &qp
->div
->row
[k
][0]);
3009 normalize_div(qp
, k
);
3012 if (isl_int_is_pos(eq
->eq
[i
][j
]))
3013 isl_seq_neg(eq
->eq
[i
], eq
->eq
[i
], total
);
3014 isl_int_abs(denom
, eq
->eq
[i
][j
]);
3015 isl_int_set_si(eq
->eq
[i
][j
], 0);
3017 poly
= isl_poly_from_affine(qp
->dim
->ctx
,
3018 eq
->eq
[i
], denom
, total
);
3019 qp
->poly
= isl_poly_subs(qp
->poly
, j
- 1, 1, &poly
);
3020 isl_poly_free(poly
);
3022 isl_int_clear(denom
);
3027 isl_basic_set_free(eq
);
3029 qp
= substitute_non_divs(qp
);
3034 isl_basic_set_free(eq
);
3035 isl_qpolynomial_free(qp
);
3039 /* Exploit the equalities in "eq" to simplify the quasi-polynomial.
3041 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities(
3042 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
3046 if (qp
->div
->n_row
> 0)
3047 eq
= isl_basic_set_add_dims(eq
, isl_dim_set
, qp
->div
->n_row
);
3048 return isl_qpolynomial_substitute_equalities_lifted(qp
, eq
);
3050 isl_basic_set_free(eq
);
3051 isl_qpolynomial_free(qp
);
3055 /* Look for equalities among the variables shared by context and qp
3056 * and the integer divisions of qp, if any.
3057 * The equalities are then used to eliminate variables and/or integer
3058 * divisions from qp.
3060 __isl_give isl_qpolynomial
*isl_qpolynomial_gist(
3061 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
3063 isl_local_space
*ls
;
3066 ls
= isl_qpolynomial_get_domain_local_space(qp
);
3067 context
= isl_local_space_lift_set(ls
, context
);
3069 aff
= isl_set_affine_hull(context
);
3070 return isl_qpolynomial_substitute_equalities_lifted(qp
, aff
);
3073 __isl_give isl_qpolynomial
*isl_qpolynomial_gist_params(
3074 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
3076 isl_space
*space
= isl_qpolynomial_get_domain_space(qp
);
3077 isl_set
*dom_context
= isl_set_universe(space
);
3078 dom_context
= isl_set_intersect_params(dom_context
, context
);
3079 return isl_qpolynomial_gist(qp
, dom_context
);
3082 /* Return a zero isl_qpolynomial in the given space.
3084 * This is a helper function for isl_pw_*_as_* that ensures a uniform
3085 * interface over all piecewise types.
3087 static __isl_give isl_qpolynomial
*isl_qpolynomial_zero_in_space(
3088 __isl_take isl_space
*space
)
3090 return isl_qpolynomial_zero_on_domain(isl_space_domain(space
));
3093 #define isl_qpolynomial_involves_nan isl_qpolynomial_is_nan
3096 #define PW isl_pw_qpolynomial
3098 #define BASE qpolynomial
3100 #define EL_IS_ZERO is_zero
3104 #define IS_ZERO is_zero
3107 #undef DEFAULT_IS_ZERO
3108 #define DEFAULT_IS_ZERO 1
3110 #include <isl_pw_templ.c>
3111 #include <isl_pw_eval.c>
3112 #include <isl_pw_insert_dims_templ.c>
3113 #include <isl_pw_lift_templ.c>
3114 #include <isl_pw_morph_templ.c>
3115 #include <isl_pw_move_dims_templ.c>
3116 #include <isl_pw_neg_templ.c>
3117 #include <isl_pw_opt_templ.c>
3118 #include <isl_pw_sub_templ.c>
3121 #define BASE pw_qpolynomial
3123 #include <isl_union_single.c>
3124 #include <isl_union_eval.c>
3125 #include <isl_union_neg.c>
3127 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial
*pwqp
)
3135 if (!isl_set_plain_is_universe(pwqp
->p
[0].set
))
3138 return isl_qpolynomial_is_one(pwqp
->p
[0].qp
);
3141 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add(
3142 __isl_take isl_pw_qpolynomial
*pwqp1
,
3143 __isl_take isl_pw_qpolynomial
*pwqp2
)
3145 return isl_pw_qpolynomial_union_add_(pwqp1
, pwqp2
);
3148 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_mul(
3149 __isl_take isl_pw_qpolynomial
*pwqp1
,
3150 __isl_take isl_pw_qpolynomial
*pwqp2
)
3153 struct isl_pw_qpolynomial
*res
;
3155 if (!pwqp1
|| !pwqp2
)
3158 isl_assert(pwqp1
->dim
->ctx
, isl_space_is_equal(pwqp1
->dim
, pwqp2
->dim
),
3161 if (isl_pw_qpolynomial_is_zero(pwqp1
)) {
3162 isl_pw_qpolynomial_free(pwqp2
);
3166 if (isl_pw_qpolynomial_is_zero(pwqp2
)) {
3167 isl_pw_qpolynomial_free(pwqp1
);
3171 if (isl_pw_qpolynomial_is_one(pwqp1
)) {
3172 isl_pw_qpolynomial_free(pwqp1
);
3176 if (isl_pw_qpolynomial_is_one(pwqp2
)) {
3177 isl_pw_qpolynomial_free(pwqp2
);
3181 n
= pwqp1
->n
* pwqp2
->n
;
3182 res
= isl_pw_qpolynomial_alloc_size(isl_space_copy(pwqp1
->dim
), n
);
3184 for (i
= 0; i
< pwqp1
->n
; ++i
) {
3185 for (j
= 0; j
< pwqp2
->n
; ++j
) {
3186 struct isl_set
*common
;
3187 struct isl_qpolynomial
*prod
;
3188 common
= isl_set_intersect(isl_set_copy(pwqp1
->p
[i
].set
),
3189 isl_set_copy(pwqp2
->p
[j
].set
));
3190 if (isl_set_plain_is_empty(common
)) {
3191 isl_set_free(common
);
3195 prod
= isl_qpolynomial_mul(
3196 isl_qpolynomial_copy(pwqp1
->p
[i
].qp
),
3197 isl_qpolynomial_copy(pwqp2
->p
[j
].qp
));
3199 res
= isl_pw_qpolynomial_add_piece(res
, common
, prod
);
3203 isl_pw_qpolynomial_free(pwqp1
);
3204 isl_pw_qpolynomial_free(pwqp2
);
3208 isl_pw_qpolynomial_free(pwqp1
);
3209 isl_pw_qpolynomial_free(pwqp2
);
3213 __isl_give isl_val
*isl_poly_eval(__isl_take isl_poly
*poly
,
3214 __isl_take isl_vec
*vec
)
3222 is_cst
= isl_poly_is_cst(poly
);
3227 res
= isl_poly_get_constant_val(poly
);
3228 isl_poly_free(poly
);
3232 rec
= isl_poly_as_rec(poly
);
3236 isl_assert(poly
->ctx
, rec
->n
>= 1, goto error
);
3238 base
= isl_val_rat_from_isl_int(poly
->ctx
,
3239 vec
->el
[1 + poly
->var
], vec
->el
[0]);
3241 res
= isl_poly_eval(isl_poly_copy(rec
->p
[rec
->n
- 1]),
3244 for (i
= rec
->n
- 2; i
>= 0; --i
) {
3245 res
= isl_val_mul(res
, isl_val_copy(base
));
3246 res
= isl_val_add(res
, isl_poly_eval(isl_poly_copy(rec
->p
[i
]),
3247 isl_vec_copy(vec
)));
3251 isl_poly_free(poly
);
3255 isl_poly_free(poly
);
3260 /* Evaluate "qp" in the void point "pnt".
3261 * In particular, return the value NaN.
3263 static __isl_give isl_val
*eval_void(__isl_take isl_qpolynomial
*qp
,
3264 __isl_take isl_point
*pnt
)
3268 ctx
= isl_point_get_ctx(pnt
);
3269 isl_qpolynomial_free(qp
);
3270 isl_point_free(pnt
);
3271 return isl_val_nan(ctx
);
3274 __isl_give isl_val
*isl_qpolynomial_eval(__isl_take isl_qpolynomial
*qp
,
3275 __isl_take isl_point
*pnt
)
3283 isl_assert(pnt
->dim
->ctx
, isl_space_is_equal(pnt
->dim
, qp
->dim
), goto error
);
3284 is_void
= isl_point_is_void(pnt
);
3288 return eval_void(qp
, pnt
);
3290 ext
= isl_local_extend_point_vec(qp
->div
, isl_vec_copy(pnt
->vec
));
3292 v
= isl_poly_eval(isl_poly_copy(qp
->poly
), ext
);
3294 isl_qpolynomial_free(qp
);
3295 isl_point_free(pnt
);
3299 isl_qpolynomial_free(qp
);
3300 isl_point_free(pnt
);
3304 int isl_poly_cmp(__isl_keep isl_poly_cst
*cst1
, __isl_keep isl_poly_cst
*cst2
)
3309 isl_int_mul(t
, cst1
->n
, cst2
->d
);
3310 isl_int_submul(t
, cst2
->n
, cst1
->d
);
3311 cmp
= isl_int_sgn(t
);
3316 __isl_give isl_qpolynomial
*isl_qpolynomial_insert_dims(
3317 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
,
3318 unsigned first
, unsigned n
)
3326 if (type
== isl_dim_out
)
3327 isl_die(qp
->div
->ctx
, isl_error_invalid
,
3328 "cannot insert output/set dimensions",
3330 if (isl_qpolynomial_check_range(qp
, type
, first
, 0) < 0)
3331 return isl_qpolynomial_free(qp
);
3332 type
= domain_type(type
);
3333 if (n
== 0 && !isl_space_is_named_or_nested(qp
->dim
, type
))
3336 qp
= isl_qpolynomial_cow(qp
);
3340 g_pos
= pos(qp
->dim
, type
) + first
;
3342 qp
->div
= isl_mat_insert_zero_cols(qp
->div
, 2 + g_pos
, n
);
3346 total
= qp
->div
->n_col
- 2;
3347 if (total
> g_pos
) {
3349 exp
= isl_alloc_array(qp
->div
->ctx
, int, total
- g_pos
);
3352 for (i
= 0; i
< total
- g_pos
; ++i
)
3354 qp
->poly
= expand(qp
->poly
, exp
, g_pos
);
3360 qp
->dim
= isl_space_insert_dims(qp
->dim
, type
, first
, n
);
3366 isl_qpolynomial_free(qp
);
3370 __isl_give isl_qpolynomial
*isl_qpolynomial_add_dims(
3371 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
, unsigned n
)
3375 pos
= isl_qpolynomial_dim(qp
, type
);
3377 return isl_qpolynomial_free(qp
);
3379 return isl_qpolynomial_insert_dims(qp
, type
, pos
, n
);
3382 static int *reordering_move(isl_ctx
*ctx
,
3383 unsigned len
, unsigned dst
, unsigned src
, unsigned n
)
3388 reordering
= isl_alloc_array(ctx
, int, len
);
3393 for (i
= 0; i
< dst
; ++i
)
3395 for (i
= 0; i
< n
; ++i
)
3396 reordering
[src
+ i
] = dst
+ i
;
3397 for (i
= 0; i
< src
- dst
; ++i
)
3398 reordering
[dst
+ i
] = dst
+ n
+ i
;
3399 for (i
= 0; i
< len
- src
- n
; ++i
)
3400 reordering
[src
+ n
+ i
] = src
+ n
+ i
;
3402 for (i
= 0; i
< src
; ++i
)
3404 for (i
= 0; i
< n
; ++i
)
3405 reordering
[src
+ i
] = dst
+ i
;
3406 for (i
= 0; i
< dst
- src
; ++i
)
3407 reordering
[src
+ n
+ i
] = src
+ i
;
3408 for (i
= 0; i
< len
- dst
- n
; ++i
)
3409 reordering
[dst
+ n
+ i
] = dst
+ n
+ i
;
3415 __isl_give isl_qpolynomial
*isl_qpolynomial_move_dims(
3416 __isl_take isl_qpolynomial
*qp
,
3417 enum isl_dim_type dst_type
, unsigned dst_pos
,
3418 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
3427 if (dst_type
== isl_dim_out
|| src_type
== isl_dim_out
)
3428 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
3429 "cannot move output/set dimension",
3431 if (isl_qpolynomial_check_range(qp
, src_type
, src_pos
, n
) < 0)
3432 return isl_qpolynomial_free(qp
);
3433 if (dst_type
== isl_dim_in
)
3434 dst_type
= isl_dim_set
;
3435 if (src_type
== isl_dim_in
)
3436 src_type
= isl_dim_set
;
3439 !isl_space_is_named_or_nested(qp
->dim
, src_type
) &&
3440 !isl_space_is_named_or_nested(qp
->dim
, dst_type
))
3443 qp
= isl_qpolynomial_cow(qp
);
3447 g_dst_pos
= pos(qp
->dim
, dst_type
) + dst_pos
;
3448 g_src_pos
= pos(qp
->dim
, src_type
) + src_pos
;
3449 if (dst_type
> src_type
)
3452 qp
->div
= isl_mat_move_cols(qp
->div
, 2 + g_dst_pos
, 2 + g_src_pos
, n
);
3459 reordering
= reordering_move(qp
->dim
->ctx
,
3460 qp
->div
->n_col
- 2, g_dst_pos
, g_src_pos
, n
);
3464 qp
->poly
= reorder(qp
->poly
, reordering
);
3469 qp
->dim
= isl_space_move_dims(qp
->dim
, dst_type
, dst_pos
, src_type
, src_pos
, n
);
3475 isl_qpolynomial_free(qp
);
3479 __isl_give isl_qpolynomial
*isl_qpolynomial_from_affine(
3480 __isl_take isl_space
*space
, isl_int
*f
, isl_int denom
)
3485 space
= isl_space_domain(space
);
3489 d
= isl_space_dim(space
, isl_dim_all
);
3490 poly
= d
< 0 ? NULL
: isl_poly_from_affine(space
->ctx
, f
, denom
, 1 + d
);
3492 return isl_qpolynomial_alloc(space
, 0, poly
);
3495 __isl_give isl_qpolynomial
*isl_qpolynomial_from_aff(__isl_take isl_aff
*aff
)
3499 isl_qpolynomial
*qp
;
3504 ctx
= isl_aff_get_ctx(aff
);
3505 poly
= isl_poly_from_affine(ctx
, aff
->v
->el
+ 1, aff
->v
->el
[0],
3508 qp
= isl_qpolynomial_alloc(isl_aff_get_domain_space(aff
),
3509 aff
->ls
->div
->n_row
, poly
);
3513 isl_mat_free(qp
->div
);
3514 qp
->div
= isl_mat_copy(aff
->ls
->div
);
3515 qp
->div
= isl_mat_cow(qp
->div
);
3520 qp
= reduce_divs(qp
);
3521 qp
= remove_redundant_divs(qp
);
3525 return isl_qpolynomial_free(qp
);
3528 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_from_pw_aff(
3529 __isl_take isl_pw_aff
*pwaff
)
3532 isl_pw_qpolynomial
*pwqp
;
3537 pwqp
= isl_pw_qpolynomial_alloc_size(isl_pw_aff_get_space(pwaff
),
3540 for (i
= 0; i
< pwaff
->n
; ++i
) {
3542 isl_qpolynomial
*qp
;
3544 dom
= isl_set_copy(pwaff
->p
[i
].set
);
3545 qp
= isl_qpolynomial_from_aff(isl_aff_copy(pwaff
->p
[i
].aff
));
3546 pwqp
= isl_pw_qpolynomial_add_piece(pwqp
, dom
, qp
);
3549 isl_pw_aff_free(pwaff
);
3553 __isl_give isl_qpolynomial
*isl_qpolynomial_from_constraint(
3554 __isl_take isl_constraint
*c
, enum isl_dim_type type
, unsigned pos
)
3558 aff
= isl_constraint_get_bound(c
, type
, pos
);
3559 isl_constraint_free(c
);
3560 return isl_qpolynomial_from_aff(aff
);
3563 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3564 * in "qp" by subs[i].
3566 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute(
3567 __isl_take isl_qpolynomial
*qp
,
3568 enum isl_dim_type type
, unsigned first
, unsigned n
,
3569 __isl_keep isl_qpolynomial
**subs
)
3577 qp
= isl_qpolynomial_cow(qp
);
3581 if (type
== isl_dim_out
)
3582 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
3583 "cannot substitute output/set dimension",
3585 if (isl_qpolynomial_check_range(qp
, type
, first
, n
) < 0)
3586 return isl_qpolynomial_free(qp
);
3587 type
= domain_type(type
);
3589 for (i
= 0; i
< n
; ++i
)
3593 for (i
= 0; i
< n
; ++i
)
3594 if (isl_qpolynomial_check_equal_space(qp
, subs
[i
]) < 0)
3597 isl_assert(qp
->dim
->ctx
, qp
->div
->n_row
== 0, goto error
);
3598 for (i
= 0; i
< n
; ++i
)
3599 isl_assert(qp
->dim
->ctx
, subs
[i
]->div
->n_row
== 0, goto error
);
3601 first
+= pos(qp
->dim
, type
);
3603 polys
= isl_alloc_array(qp
->dim
->ctx
, struct isl_poly
*, n
);
3606 for (i
= 0; i
< n
; ++i
)
3607 polys
[i
] = subs
[i
]->poly
;
3609 qp
->poly
= isl_poly_subs(qp
->poly
, first
, n
, polys
);
3618 isl_qpolynomial_free(qp
);
3622 /* Extend "bset" with extra set dimensions for each integer division
3623 * in "qp" and then call "fn" with the extended bset and the polynomial
3624 * that results from replacing each of the integer divisions by the
3625 * corresponding extra set dimension.
3627 isl_stat
isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial
*qp
,
3628 __isl_keep isl_basic_set
*bset
,
3629 isl_stat (*fn
)(__isl_take isl_basic_set
*bset
,
3630 __isl_take isl_qpolynomial
*poly
, void *user
), void *user
)
3633 isl_local_space
*ls
;
3634 isl_qpolynomial
*poly
;
3637 return isl_stat_error
;
3638 if (qp
->div
->n_row
== 0)
3639 return fn(isl_basic_set_copy(bset
), isl_qpolynomial_copy(qp
),
3642 space
= isl_space_copy(qp
->dim
);
3643 space
= isl_space_add_dims(space
, isl_dim_set
, qp
->div
->n_row
);
3644 poly
= isl_qpolynomial_alloc(space
, 0, isl_poly_copy(qp
->poly
));
3645 bset
= isl_basic_set_copy(bset
);
3646 ls
= isl_qpolynomial_get_domain_local_space(qp
);
3647 bset
= isl_local_space_lift_basic_set(ls
, bset
);
3649 return fn(bset
, poly
, user
);
3652 /* Return total degree in variables first (inclusive) up to last (exclusive).
3654 int isl_poly_degree(__isl_keep isl_poly
*poly
, int first
, int last
)
3658 isl_bool is_zero
, is_cst
;
3661 is_zero
= isl_poly_is_zero(poly
);
3666 is_cst
= isl_poly_is_cst(poly
);
3669 if (is_cst
|| poly
->var
< first
)
3672 rec
= isl_poly_as_rec(poly
);
3676 for (i
= 0; i
< rec
->n
; ++i
) {
3679 is_zero
= isl_poly_is_zero(rec
->p
[i
]);
3684 d
= isl_poly_degree(rec
->p
[i
], first
, last
);
3685 if (poly
->var
< last
)
3694 /* Return total degree in set variables.
3696 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial
*poly
)
3704 ovar
= isl_space_offset(poly
->dim
, isl_dim_set
);
3705 nvar
= isl_space_dim(poly
->dim
, isl_dim_set
);
3708 return isl_poly_degree(poly
->poly
, ovar
, ovar
+ nvar
);
3711 __isl_give isl_poly
*isl_poly_coeff(__isl_keep isl_poly
*poly
,
3712 unsigned pos
, int deg
)
3718 is_cst
= isl_poly_is_cst(poly
);
3721 if (is_cst
|| poly
->var
< pos
) {
3723 return isl_poly_copy(poly
);
3725 return isl_poly_zero(poly
->ctx
);
3728 rec
= isl_poly_as_rec(poly
);
3732 if (poly
->var
== pos
) {
3734 return isl_poly_copy(rec
->p
[deg
]);
3736 return isl_poly_zero(poly
->ctx
);
3739 poly
= isl_poly_copy(poly
);
3740 poly
= isl_poly_cow(poly
);
3741 rec
= isl_poly_as_rec(poly
);
3745 for (i
= 0; i
< rec
->n
; ++i
) {
3747 t
= isl_poly_coeff(rec
->p
[i
], pos
, deg
);
3750 isl_poly_free(rec
->p
[i
]);
3756 isl_poly_free(poly
);
3760 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3762 __isl_give isl_qpolynomial
*isl_qpolynomial_coeff(
3763 __isl_keep isl_qpolynomial
*qp
,
3764 enum isl_dim_type type
, unsigned t_pos
, int deg
)
3773 if (type
== isl_dim_out
)
3774 isl_die(qp
->div
->ctx
, isl_error_invalid
,
3775 "output/set dimension does not have a coefficient",
3777 if (isl_qpolynomial_check_range(qp
, type
, t_pos
, 1) < 0)
3779 type
= domain_type(type
);
3781 g_pos
= pos(qp
->dim
, type
) + t_pos
;
3782 poly
= isl_poly_coeff(qp
->poly
, g_pos
, deg
);
3784 c
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
),
3785 qp
->div
->n_row
, poly
);
3788 isl_mat_free(c
->div
);
3789 c
->div
= isl_mat_copy(qp
->div
);
3794 isl_qpolynomial_free(c
);
3798 /* Homogenize the polynomial in the variables first (inclusive) up to
3799 * last (exclusive) by inserting powers of variable first.
3800 * Variable first is assumed not to appear in the input.
3802 __isl_give isl_poly
*isl_poly_homogenize(__isl_take isl_poly
*poly
, int deg
,
3803 int target
, int first
, int last
)
3806 isl_bool is_zero
, is_cst
;
3809 is_zero
= isl_poly_is_zero(poly
);
3811 return isl_poly_free(poly
);
3816 is_cst
= isl_poly_is_cst(poly
);
3818 return isl_poly_free(poly
);
3819 if (is_cst
|| poly
->var
< first
) {
3822 hom
= isl_poly_var_pow(poly
->ctx
, first
, target
- deg
);
3825 rec
= isl_poly_as_rec(hom
);
3826 rec
->p
[target
- deg
] = isl_poly_mul(rec
->p
[target
- deg
], poly
);
3831 poly
= isl_poly_cow(poly
);
3832 rec
= isl_poly_as_rec(poly
);
3836 for (i
= 0; i
< rec
->n
; ++i
) {
3837 is_zero
= isl_poly_is_zero(rec
->p
[i
]);
3839 return isl_poly_free(poly
);
3842 rec
->p
[i
] = isl_poly_homogenize(rec
->p
[i
],
3843 poly
->var
< last
? deg
+ i
: i
, target
,
3851 isl_poly_free(poly
);
3855 /* Homogenize the polynomial in the set variables by introducing
3856 * powers of an extra set variable at position 0.
3858 __isl_give isl_qpolynomial
*isl_qpolynomial_homogenize(
3859 __isl_take isl_qpolynomial
*poly
)
3863 int deg
= isl_qpolynomial_degree(poly
);
3868 poly
= isl_qpolynomial_insert_dims(poly
, isl_dim_in
, 0, 1);
3869 poly
= isl_qpolynomial_cow(poly
);
3873 ovar
= isl_space_offset(poly
->dim
, isl_dim_set
);
3874 nvar
= isl_space_dim(poly
->dim
, isl_dim_set
);
3876 return isl_qpolynomial_free(poly
);
3877 poly
->poly
= isl_poly_homogenize(poly
->poly
, 0, deg
, ovar
, ovar
+ nvar
);
3883 isl_qpolynomial_free(poly
);
3887 __isl_give isl_term
*isl_term_alloc(__isl_take isl_space
*space
,
3888 __isl_take isl_mat
*div
)
3894 d
= isl_space_dim(space
, isl_dim_all
);
3900 term
= isl_calloc(space
->ctx
, struct isl_term
,
3901 sizeof(struct isl_term
) + (n
- 1) * sizeof(int));
3908 isl_int_init(term
->n
);
3909 isl_int_init(term
->d
);
3913 isl_space_free(space
);
3918 __isl_give isl_term
*isl_term_copy(__isl_keep isl_term
*term
)
3927 __isl_give isl_term
*isl_term_dup(__isl_keep isl_term
*term
)
3933 total
= isl_term_dim(term
, isl_dim_all
);
3937 dup
= isl_term_alloc(isl_space_copy(term
->dim
), isl_mat_copy(term
->div
));
3941 isl_int_set(dup
->n
, term
->n
);
3942 isl_int_set(dup
->d
, term
->d
);
3944 for (i
= 0; i
< total
; ++i
)
3945 dup
->pow
[i
] = term
->pow
[i
];
3950 __isl_give isl_term
*isl_term_cow(__isl_take isl_term
*term
)
3958 return isl_term_dup(term
);
3961 __isl_null isl_term
*isl_term_free(__isl_take isl_term
*term
)
3966 if (--term
->ref
> 0)
3969 isl_space_free(term
->dim
);
3970 isl_mat_free(term
->div
);
3971 isl_int_clear(term
->n
);
3972 isl_int_clear(term
->d
);
3978 isl_size
isl_term_dim(__isl_keep isl_term
*term
, enum isl_dim_type type
)
3983 return isl_size_error
;
3988 case isl_dim_out
: return isl_space_dim(term
->dim
, type
);
3989 case isl_dim_div
: return term
->div
->n_row
;
3990 case isl_dim_all
: dim
= isl_space_dim(term
->dim
, isl_dim_all
);
3992 return isl_size_error
;
3993 return dim
+ term
->div
->n_row
;
3994 default: return isl_size_error
;
3998 /* Return the space of "term".
4000 static __isl_keep isl_space
*isl_term_peek_space(__isl_keep isl_term
*term
)
4002 return term
? term
->dim
: NULL
;
4005 /* Return the offset of the first variable of type "type" within
4006 * the variables of "term".
4008 static isl_size
isl_term_offset(__isl_keep isl_term
*term
,
4009 enum isl_dim_type type
)
4013 space
= isl_term_peek_space(term
);
4015 return isl_size_error
;
4019 case isl_dim_set
: return isl_space_offset(space
, type
);
4020 case isl_dim_div
: return isl_space_dim(space
, isl_dim_all
);
4022 isl_die(isl_term_get_ctx(term
), isl_error_invalid
,
4023 "invalid dimension type", return isl_size_error
);
4027 isl_ctx
*isl_term_get_ctx(__isl_keep isl_term
*term
)
4029 return term
? term
->dim
->ctx
: NULL
;
4032 void isl_term_get_num(__isl_keep isl_term
*term
, isl_int
*n
)
4036 isl_int_set(*n
, term
->n
);
4039 /* Return the coefficient of the term "term".
4041 __isl_give isl_val
*isl_term_get_coefficient_val(__isl_keep isl_term
*term
)
4046 return isl_val_rat_from_isl_int(isl_term_get_ctx(term
),
4051 #define TYPE isl_term
4053 #include "check_type_range_templ.c"
4055 isl_size
isl_term_get_exp(__isl_keep isl_term
*term
,
4056 enum isl_dim_type type
, unsigned pos
)
4060 if (isl_term_check_range(term
, type
, pos
, 1) < 0)
4061 return isl_size_error
;
4062 offset
= isl_term_offset(term
, type
);
4064 return isl_size_error
;
4066 return term
->pow
[offset
+ pos
];
4069 __isl_give isl_aff
*isl_term_get_div(__isl_keep isl_term
*term
, unsigned pos
)
4071 isl_local_space
*ls
;
4074 if (isl_term_check_range(term
, isl_dim_div
, pos
, 1) < 0)
4077 ls
= isl_local_space_alloc_div(isl_space_copy(term
->dim
),
4078 isl_mat_copy(term
->div
));
4079 aff
= isl_aff_alloc(ls
);
4083 isl_seq_cpy(aff
->v
->el
, term
->div
->row
[pos
], aff
->v
->size
);
4085 aff
= isl_aff_normalize(aff
);
4090 __isl_give isl_term
*isl_poly_foreach_term(__isl_keep isl_poly
*poly
,
4091 isl_stat (*fn
)(__isl_take isl_term
*term
, void *user
),
4092 __isl_take isl_term
*term
, void *user
)
4095 isl_bool is_zero
, is_bad
, is_cst
;
4098 is_zero
= isl_poly_is_zero(poly
);
4099 if (is_zero
< 0 || !term
)
4105 is_cst
= isl_poly_is_cst(poly
);
4106 is_bad
= isl_poly_is_nan(poly
);
4107 if (is_bad
>= 0 && !is_bad
)
4108 is_bad
= isl_poly_is_infty(poly
);
4109 if (is_bad
>= 0 && !is_bad
)
4110 is_bad
= isl_poly_is_neginfty(poly
);
4111 if (is_cst
< 0 || is_bad
< 0)
4112 return isl_term_free(term
);
4114 isl_die(isl_term_get_ctx(term
), isl_error_invalid
,
4115 "cannot handle NaN/infty polynomial",
4116 return isl_term_free(term
));
4120 cst
= isl_poly_as_cst(poly
);
4123 term
= isl_term_cow(term
);
4126 isl_int_set(term
->n
, cst
->n
);
4127 isl_int_set(term
->d
, cst
->d
);
4128 if (fn(isl_term_copy(term
), user
) < 0)
4133 rec
= isl_poly_as_rec(poly
);
4137 for (i
= 0; i
< rec
->n
; ++i
) {
4138 term
= isl_term_cow(term
);
4141 term
->pow
[poly
->var
] = i
;
4142 term
= isl_poly_foreach_term(rec
->p
[i
], fn
, term
, user
);
4146 term
= isl_term_cow(term
);
4149 term
->pow
[poly
->var
] = 0;
4153 isl_term_free(term
);
4157 isl_stat
isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial
*qp
,
4158 isl_stat (*fn
)(__isl_take isl_term
*term
, void *user
), void *user
)
4163 return isl_stat_error
;
4165 term
= isl_term_alloc(isl_space_copy(qp
->dim
), isl_mat_copy(qp
->div
));
4167 return isl_stat_error
;
4169 term
= isl_poly_foreach_term(qp
->poly
, fn
, term
, user
);
4171 isl_term_free(term
);
4173 return term
? isl_stat_ok
: isl_stat_error
;
4176 __isl_give isl_qpolynomial
*isl_qpolynomial_from_term(__isl_take isl_term
*term
)
4179 isl_qpolynomial
*qp
;
4183 n
= isl_term_dim(term
, isl_dim_all
);
4185 term
= isl_term_free(term
);
4189 poly
= isl_poly_rat_cst(term
->dim
->ctx
, term
->n
, term
->d
);
4190 for (i
= 0; i
< n
; ++i
) {
4193 poly
= isl_poly_mul(poly
,
4194 isl_poly_var_pow(term
->dim
->ctx
, i
, term
->pow
[i
]));
4197 qp
= isl_qpolynomial_alloc(isl_space_copy(term
->dim
),
4198 term
->div
->n_row
, poly
);
4201 isl_mat_free(qp
->div
);
4202 qp
->div
= isl_mat_copy(term
->div
);
4206 isl_term_free(term
);
4209 isl_qpolynomial_free(qp
);
4210 isl_term_free(term
);
4214 __isl_give isl_qpolynomial
*isl_qpolynomial_lift(__isl_take isl_qpolynomial
*qp
,
4215 __isl_take isl_space
*space
)
4219 isl_size total
, d_set
, d_qp
;
4224 if (isl_space_is_equal(qp
->dim
, space
)) {
4225 isl_space_free(space
);
4229 qp
= isl_qpolynomial_cow(qp
);
4233 d_set
= isl_space_dim(space
, isl_dim_set
);
4234 d_qp
= isl_qpolynomial_domain_dim(qp
, isl_dim_set
);
4235 extra
= d_set
- d_qp
;
4236 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4237 if (d_set
< 0 || d_qp
< 0 || total
< 0)
4239 if (qp
->div
->n_row
) {
4242 exp
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
4245 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4247 qp
->poly
= expand(qp
->poly
, exp
, total
);
4252 qp
->div
= isl_mat_insert_cols(qp
->div
, 2 + total
, extra
);
4255 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4256 isl_seq_clr(qp
->div
->row
[i
] + 2 + total
, extra
);
4258 isl_space_free(qp
->dim
);
4263 isl_space_free(space
);
4264 isl_qpolynomial_free(qp
);
4268 /* For each parameter or variable that does not appear in qp,
4269 * first eliminate the variable from all constraints and then set it to zero.
4271 static __isl_give isl_set
*fix_inactive(__isl_take isl_set
*set
,
4272 __isl_keep isl_qpolynomial
*qp
)
4280 d
= isl_set_dim(set
, isl_dim_all
);
4284 active
= isl_calloc_array(set
->ctx
, int, d
);
4285 if (set_active(qp
, active
) < 0)
4288 for (i
= 0; i
< d
; ++i
)
4297 nparam
= isl_set_dim(set
, isl_dim_param
);
4298 nvar
= isl_set_dim(set
, isl_dim_set
);
4299 if (nparam
< 0 || nvar
< 0)
4301 for (i
= 0; i
< nparam
; ++i
) {
4304 set
= isl_set_eliminate(set
, isl_dim_param
, i
, 1);
4305 set
= isl_set_fix_si(set
, isl_dim_param
, i
, 0);
4307 for (i
= 0; i
< nvar
; ++i
) {
4308 if (active
[nparam
+ i
])
4310 set
= isl_set_eliminate(set
, isl_dim_set
, i
, 1);
4311 set
= isl_set_fix_si(set
, isl_dim_set
, i
, 0);
4323 struct isl_opt_data
{
4324 isl_qpolynomial
*qp
;
4330 static isl_stat
opt_fn(__isl_take isl_point
*pnt
, void *user
)
4332 struct isl_opt_data
*data
= (struct isl_opt_data
*)user
;
4335 val
= isl_qpolynomial_eval(isl_qpolynomial_copy(data
->qp
), pnt
);
4339 } else if (data
->max
) {
4340 data
->opt
= isl_val_max(data
->opt
, val
);
4342 data
->opt
= isl_val_min(data
->opt
, val
);
4348 __isl_give isl_val
*isl_qpolynomial_opt_on_domain(
4349 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*set
, int max
)
4351 struct isl_opt_data data
= { NULL
, 1, NULL
, max
};
4357 is_cst
= isl_poly_is_cst(qp
->poly
);
4362 data
.opt
= isl_qpolynomial_get_constant_val(qp
);
4363 isl_qpolynomial_free(qp
);
4367 set
= fix_inactive(set
, qp
);
4370 if (isl_set_foreach_point(set
, opt_fn
, &data
) < 0)
4374 data
.opt
= isl_val_zero(isl_set_get_ctx(set
));
4377 isl_qpolynomial_free(qp
);
4381 isl_qpolynomial_free(qp
);
4382 isl_val_free(data
.opt
);
4386 __isl_give isl_qpolynomial
*isl_qpolynomial_morph_domain(
4387 __isl_take isl_qpolynomial
*qp
, __isl_take isl_morph
*morph
)
4394 isl_mat
*mat
, *diag
;
4396 qp
= isl_qpolynomial_cow(qp
);
4398 space
= isl_qpolynomial_peek_domain_space(qp
);
4399 if (isl_morph_check_applies(morph
, space
) < 0)
4402 ctx
= isl_qpolynomial_get_ctx(qp
);
4403 n_sub
= morph
->inv
->n_row
- 1;
4404 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
4405 n_sub
+= qp
->div
->n_row
;
4406 subs
= isl_calloc_array(ctx
, struct isl_poly
*, n_sub
);
4410 for (i
= 0; 1 + i
< morph
->inv
->n_row
; ++i
)
4411 subs
[i
] = isl_poly_from_affine(ctx
, morph
->inv
->row
[1 + i
],
4412 morph
->inv
->row
[0][0], morph
->inv
->n_col
);
4413 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
4414 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4415 subs
[morph
->inv
->n_row
- 1 + i
] =
4416 isl_poly_var_pow(ctx
, morph
->inv
->n_col
- 1 + i
, 1);
4418 qp
->poly
= isl_poly_subs(qp
->poly
, 0, n_sub
, subs
);
4420 for (i
= 0; i
< n_sub
; ++i
)
4421 isl_poly_free(subs
[i
]);
4424 diag
= isl_mat_diag(ctx
, 1, morph
->inv
->row
[0][0]);
4425 mat
= isl_mat_diagonal(diag
, isl_mat_copy(morph
->inv
));
4426 diag
= isl_mat_diag(ctx
, qp
->div
->n_row
, morph
->inv
->row
[0][0]);
4427 mat
= isl_mat_diagonal(mat
, diag
);
4428 qp
->div
= isl_mat_product(qp
->div
, mat
);
4429 isl_space_free(qp
->dim
);
4430 qp
->dim
= isl_space_copy(morph
->ran
->dim
);
4432 if (!qp
->poly
|| !qp
->div
|| !qp
->dim
)
4435 isl_morph_free(morph
);
4439 isl_qpolynomial_free(qp
);
4440 isl_morph_free(morph
);
4444 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_mul(
4445 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
4446 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
4448 return isl_union_pw_qpolynomial_match_bin_op(upwqp1
, upwqp2
,
4449 &isl_pw_qpolynomial_mul
);
4452 /* Reorder the dimension of "qp" according to the given reordering.
4454 __isl_give isl_qpolynomial
*isl_qpolynomial_realign_domain(
4455 __isl_take isl_qpolynomial
*qp
, __isl_take isl_reordering
*r
)
4459 qp
= isl_qpolynomial_cow(qp
);
4463 r
= isl_reordering_extend(r
, qp
->div
->n_row
);
4467 qp
->div
= isl_local_reorder(qp
->div
, isl_reordering_copy(r
));
4471 qp
->poly
= reorder(qp
->poly
, r
->pos
);
4475 space
= isl_reordering_get_space(r
);
4476 qp
= isl_qpolynomial_reset_domain_space(qp
, space
);
4478 isl_reordering_free(r
);
4481 isl_qpolynomial_free(qp
);
4482 isl_reordering_free(r
);
4486 __isl_give isl_qpolynomial
*isl_qpolynomial_align_params(
4487 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*model
)
4489 isl_bool equal_params
;
4494 equal_params
= isl_space_has_equal_params(qp
->dim
, model
);
4495 if (equal_params
< 0)
4497 if (!equal_params
) {
4498 isl_reordering
*exp
;
4500 exp
= isl_parameter_alignment_reordering(qp
->dim
, model
);
4501 exp
= isl_reordering_extend_space(exp
,
4502 isl_qpolynomial_get_domain_space(qp
));
4503 qp
= isl_qpolynomial_realign_domain(qp
, exp
);
4506 isl_space_free(model
);
4509 isl_space_free(model
);
4510 isl_qpolynomial_free(qp
);
4514 struct isl_split_periods_data
{
4516 isl_pw_qpolynomial
*res
;
4519 /* Create a slice where the integer division "div" has the fixed value "v".
4520 * In particular, if "div" refers to floor(f/m), then create a slice
4522 * m v <= f <= m v + (m - 1)
4527 * -f + m v + (m - 1) >= 0
4529 static __isl_give isl_set
*set_div_slice(__isl_take isl_space
*space
,
4530 __isl_keep isl_qpolynomial
*qp
, int div
, isl_int v
)
4533 isl_basic_set
*bset
= NULL
;
4536 total
= isl_space_dim(space
, isl_dim_all
);
4537 if (total
< 0 || !qp
)
4540 bset
= isl_basic_set_alloc_space(isl_space_copy(space
), 0, 0, 2);
4542 k
= isl_basic_set_alloc_inequality(bset
);
4545 isl_seq_cpy(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4546 isl_int_submul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4548 k
= isl_basic_set_alloc_inequality(bset
);
4551 isl_seq_neg(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4552 isl_int_addmul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4553 isl_int_add(bset
->ineq
[k
][0], bset
->ineq
[k
][0], qp
->div
->row
[div
][0]);
4554 isl_int_sub_ui(bset
->ineq
[k
][0], bset
->ineq
[k
][0], 1);
4556 isl_space_free(space
);
4557 return isl_set_from_basic_set(bset
);
4559 isl_basic_set_free(bset
);
4560 isl_space_free(space
);
4564 static isl_stat
split_periods(__isl_take isl_set
*set
,
4565 __isl_take isl_qpolynomial
*qp
, void *user
);
4567 /* Create a slice of the domain "set" such that integer division "div"
4568 * has the fixed value "v" and add the results to data->res,
4569 * replacing the integer division by "v" in "qp".
4571 static isl_stat
set_div(__isl_take isl_set
*set
,
4572 __isl_take isl_qpolynomial
*qp
, int div
, isl_int v
,
4573 struct isl_split_periods_data
*data
)
4580 slice
= set_div_slice(isl_set_get_space(set
), qp
, div
, v
);
4581 set
= isl_set_intersect(set
, slice
);
4583 div_pos
= isl_qpolynomial_domain_var_offset(qp
, isl_dim_div
);
4587 for (i
= div
+ 1; i
< qp
->div
->n_row
; ++i
) {
4588 if (isl_int_is_zero(qp
->div
->row
[i
][2 + div_pos
+ div
]))
4590 isl_int_addmul(qp
->div
->row
[i
][1],
4591 qp
->div
->row
[i
][2 + div_pos
+ div
], v
);
4592 isl_int_set_si(qp
->div
->row
[i
][2 + div_pos
+ div
], 0);
4595 cst
= isl_poly_rat_cst(qp
->dim
->ctx
, v
, qp
->dim
->ctx
->one
);
4596 qp
= substitute_div(qp
, div
, cst
);
4598 return split_periods(set
, qp
, data
);
4601 isl_qpolynomial_free(qp
);
4602 return isl_stat_error
;
4605 /* Split the domain "set" such that integer division "div"
4606 * has a fixed value (ranging from "min" to "max") on each slice
4607 * and add the results to data->res.
4609 static isl_stat
split_div(__isl_take isl_set
*set
,
4610 __isl_take isl_qpolynomial
*qp
, int div
, isl_int min
, isl_int max
,
4611 struct isl_split_periods_data
*data
)
4613 for (; isl_int_le(min
, max
); isl_int_add_ui(min
, min
, 1)) {
4614 isl_set
*set_i
= isl_set_copy(set
);
4615 isl_qpolynomial
*qp_i
= isl_qpolynomial_copy(qp
);
4617 if (set_div(set_i
, qp_i
, div
, min
, data
) < 0)
4621 isl_qpolynomial_free(qp
);
4625 isl_qpolynomial_free(qp
);
4626 return isl_stat_error
;
4629 /* If "qp" refers to any integer division
4630 * that can only attain "max_periods" distinct values on "set"
4631 * then split the domain along those distinct values.
4632 * Add the results (or the original if no splitting occurs)
4635 static isl_stat
split_periods(__isl_take isl_set
*set
,
4636 __isl_take isl_qpolynomial
*qp
, void *user
)
4639 isl_pw_qpolynomial
*pwqp
;
4640 struct isl_split_periods_data
*data
;
4643 isl_stat r
= isl_stat_ok
;
4645 data
= (struct isl_split_periods_data
*)user
;
4650 if (qp
->div
->n_row
== 0) {
4651 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4652 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4656 div_pos
= isl_qpolynomial_domain_var_offset(qp
, isl_dim_div
);
4662 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4663 enum isl_lp_result lp_res
;
4665 if (isl_seq_first_non_zero(qp
->div
->row
[i
] + 2 + div_pos
,
4666 qp
->div
->n_row
) != -1)
4669 lp_res
= isl_set_solve_lp(set
, 0, qp
->div
->row
[i
] + 1,
4670 set
->ctx
->one
, &min
, NULL
, NULL
);
4671 if (lp_res
== isl_lp_error
)
4673 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4675 isl_int_fdiv_q(min
, min
, qp
->div
->row
[i
][0]);
4677 lp_res
= isl_set_solve_lp(set
, 1, qp
->div
->row
[i
] + 1,
4678 set
->ctx
->one
, &max
, NULL
, NULL
);
4679 if (lp_res
== isl_lp_error
)
4681 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4683 isl_int_fdiv_q(max
, max
, qp
->div
->row
[i
][0]);
4685 isl_int_sub(max
, max
, min
);
4686 if (isl_int_cmp_si(max
, data
->max_periods
) < 0) {
4687 isl_int_add(max
, max
, min
);
4692 if (i
< qp
->div
->n_row
) {
4693 r
= split_div(set
, qp
, i
, min
, max
, data
);
4695 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4696 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4708 isl_qpolynomial_free(qp
);
4709 return isl_stat_error
;
4712 /* If any quasi-polynomial in pwqp refers to any integer division
4713 * that can only attain "max_periods" distinct values on its domain
4714 * then split the domain along those distinct values.
4716 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_split_periods(
4717 __isl_take isl_pw_qpolynomial
*pwqp
, int max_periods
)
4719 struct isl_split_periods_data data
;
4721 data
.max_periods
= max_periods
;
4722 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp
));
4724 if (isl_pw_qpolynomial_foreach_piece(pwqp
, &split_periods
, &data
) < 0)
4727 isl_pw_qpolynomial_free(pwqp
);
4731 isl_pw_qpolynomial_free(data
.res
);
4732 isl_pw_qpolynomial_free(pwqp
);
4736 /* Construct a piecewise quasipolynomial that is constant on the given
4737 * domain. In particular, it is
4740 * infinity if cst == -1
4742 * If cst == -1, then explicitly check whether the domain is empty and,
4743 * if so, return 0 instead.
4745 static __isl_give isl_pw_qpolynomial
*constant_on_domain(
4746 __isl_take isl_basic_set
*bset
, int cst
)
4749 isl_qpolynomial
*qp
;
4751 if (cst
< 0 && isl_basic_set_is_empty(bset
) == isl_bool_true
)
4756 bset
= isl_basic_set_params(bset
);
4757 space
= isl_basic_set_get_space(bset
);
4759 qp
= isl_qpolynomial_infty_on_domain(space
);
4761 qp
= isl_qpolynomial_zero_on_domain(space
);
4763 qp
= isl_qpolynomial_one_on_domain(space
);
4764 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset
), qp
);
4767 /* Internal data structure for multiplicative_call_factor_pw_qpolynomial.
4768 * "fn" is the function that is called on each factor.
4769 * "pwpq" collects the results.
4771 struct isl_multiplicative_call_data_pw_qpolynomial
{
4772 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
);
4773 isl_pw_qpolynomial
*pwqp
;
4776 /* Call "fn" on "bset" and return the result,
4777 * but first check if "bset" has any redundant constraints or
4778 * implicit equality constraints.
4779 * If so, there may be further opportunities for detecting factors or
4780 * removing equality constraints, so recursively call
4781 * the top-level isl_basic_set_multiplicative_call.
4783 static __isl_give isl_pw_qpolynomial
*multiplicative_call_base(
4784 __isl_take isl_basic_set
*bset
,
4785 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4787 isl_size n1
, n2
, n_eq
;
4789 n1
= isl_basic_set_n_constraint(bset
);
4791 bset
= isl_basic_set_free(bset
);
4792 bset
= isl_basic_set_remove_redundancies(bset
);
4793 bset
= isl_basic_set_detect_equalities(bset
);
4794 n2
= isl_basic_set_n_constraint(bset
);
4795 n_eq
= isl_basic_set_n_equality(bset
);
4796 if (n2
< 0 || n_eq
< 0)
4797 bset
= isl_basic_set_free(bset
);
4798 else if (n2
< n1
|| n_eq
> 0)
4799 return isl_basic_set_multiplicative_call(bset
, fn
);
4803 /* isl_factorizer_every_factor_basic_set callback that applies
4804 * data->fn to the factor "bset" and multiplies in the result
4807 static isl_bool
multiplicative_call_factor_pw_qpolynomial(
4808 __isl_keep isl_basic_set
*bset
, void *user
)
4810 struct isl_multiplicative_call_data_pw_qpolynomial
*data
= user
;
4811 isl_pw_qpolynomial
*res
;
4813 bset
= isl_basic_set_copy(bset
);
4814 res
= multiplicative_call_base(bset
, data
->fn
);
4815 data
->pwqp
= isl_pw_qpolynomial_mul(data
->pwqp
, res
);
4817 return isl_bool_error
;
4819 return isl_bool_true
;
4822 /* Factor bset, call fn on each of the factors and return the product.
4824 * If no factors can be found, simply call fn on the input.
4825 * Otherwise, construct the factors based on the factorizer,
4826 * call fn on each factor and compute the product.
4828 static __isl_give isl_pw_qpolynomial
*compressed_multiplicative_call(
4829 __isl_take isl_basic_set
*bset
,
4830 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4832 struct isl_multiplicative_call_data_pw_qpolynomial data
= { fn
};
4836 isl_qpolynomial
*qp
;
4839 f
= isl_basic_set_factorizer(bset
);
4842 if (f
->n_group
== 0) {
4843 isl_factorizer_free(f
);
4844 return multiplicative_call_base(bset
, fn
);
4847 space
= isl_basic_set_get_space(bset
);
4848 space
= isl_space_params(space
);
4849 set
= isl_set_universe(isl_space_copy(space
));
4850 qp
= isl_qpolynomial_one_on_domain(space
);
4851 data
.pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4853 every
= isl_factorizer_every_factor_basic_set(f
,
4854 &multiplicative_call_factor_pw_qpolynomial
, &data
);
4856 data
.pwqp
= isl_pw_qpolynomial_free(data
.pwqp
);
4858 isl_basic_set_free(bset
);
4859 isl_factorizer_free(f
);
4863 isl_basic_set_free(bset
);
4867 /* Factor bset, call fn on each of the factors and return the product.
4868 * The function is assumed to evaluate to zero on empty domains,
4869 * to one on zero-dimensional domains and to infinity on unbounded domains
4870 * and will not be called explicitly on zero-dimensional or unbounded domains.
4872 * We first check for some special cases and remove all equalities.
4873 * Then we hand over control to compressed_multiplicative_call.
4875 __isl_give isl_pw_qpolynomial
*isl_basic_set_multiplicative_call(
4876 __isl_take isl_basic_set
*bset
,
4877 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4882 isl_pw_qpolynomial
*pwqp
;
4887 if (isl_basic_set_plain_is_empty(bset
))
4888 return constant_on_domain(bset
, 0);
4890 dim
= isl_basic_set_dim(bset
, isl_dim_set
);
4894 return constant_on_domain(bset
, 1);
4896 bounded
= isl_basic_set_is_bounded(bset
);
4900 return constant_on_domain(bset
, -1);
4902 if (bset
->n_eq
== 0)
4903 return compressed_multiplicative_call(bset
, fn
);
4905 morph
= isl_basic_set_full_compression(bset
);
4906 bset
= isl_morph_basic_set(isl_morph_copy(morph
), bset
);
4908 pwqp
= compressed_multiplicative_call(bset
, fn
);
4910 morph
= isl_morph_dom_params(morph
);
4911 morph
= isl_morph_ran_params(morph
);
4912 morph
= isl_morph_inverse(morph
);
4914 pwqp
= isl_pw_qpolynomial_morph_domain(pwqp
, morph
);
4918 isl_basic_set_free(bset
);
4922 /* Drop all floors in "qp", turning each integer division [a/m] into
4923 * a rational division a/m. If "down" is set, then the integer division
4924 * is replaced by (a-(m-1))/m instead.
4926 static __isl_give isl_qpolynomial
*qp_drop_floors(
4927 __isl_take isl_qpolynomial
*qp
, int down
)
4934 if (qp
->div
->n_row
== 0)
4937 qp
= isl_qpolynomial_cow(qp
);
4941 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
4943 isl_int_sub(qp
->div
->row
[i
][1],
4944 qp
->div
->row
[i
][1], qp
->div
->row
[i
][0]);
4945 isl_int_add_ui(qp
->div
->row
[i
][1],
4946 qp
->div
->row
[i
][1], 1);
4948 s
= isl_poly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
4949 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
4950 qp
= substitute_div(qp
, i
, s
);
4958 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4959 * a rational division a/m.
4961 static __isl_give isl_pw_qpolynomial
*pwqp_drop_floors(
4962 __isl_take isl_pw_qpolynomial
*pwqp
)
4969 if (isl_pw_qpolynomial_is_zero(pwqp
))
4972 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
4976 for (i
= 0; i
< pwqp
->n
; ++i
) {
4977 pwqp
->p
[i
].qp
= qp_drop_floors(pwqp
->p
[i
].qp
, 0);
4984 isl_pw_qpolynomial_free(pwqp
);
4988 /* Adjust all the integer divisions in "qp" such that they are at least
4989 * one over the given orthant (identified by "signs"). This ensures
4990 * that they will still be non-negative even after subtracting (m-1)/m.
4992 * In particular, f is replaced by f' + v, changing f = [a/m]
4993 * to f' = [(a - m v)/m].
4994 * If the constant term k in a is smaller than m,
4995 * the constant term of v is set to floor(k/m) - 1.
4996 * For any other term, if the coefficient c and the variable x have
4997 * the same sign, then no changes are needed.
4998 * Otherwise, if the variable is positive (and c is negative),
4999 * then the coefficient of x in v is set to floor(c/m).
5000 * If the variable is negative (and c is positive),
5001 * then the coefficient of x in v is set to ceil(c/m).
5003 static __isl_give isl_qpolynomial
*make_divs_pos(__isl_take isl_qpolynomial
*qp
,
5011 qp
= isl_qpolynomial_cow(qp
);
5012 div_pos
= isl_qpolynomial_domain_var_offset(qp
, isl_dim_div
);
5014 return isl_qpolynomial_free(qp
);
5015 qp
->div
= isl_mat_cow(qp
->div
);
5019 v
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
5021 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
5022 isl_int
*row
= qp
->div
->row
[i
];
5026 if (isl_int_lt(row
[1], row
[0])) {
5027 isl_int_fdiv_q(v
->el
[0], row
[1], row
[0]);
5028 isl_int_sub_ui(v
->el
[0], v
->el
[0], 1);
5029 isl_int_submul(row
[1], row
[0], v
->el
[0]);
5031 for (j
= 0; j
< div_pos
; ++j
) {
5032 if (isl_int_sgn(row
[2 + j
]) * signs
[j
] >= 0)
5035 isl_int_cdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
5037 isl_int_fdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
5038 isl_int_submul(row
[2 + j
], row
[0], v
->el
[1 + j
]);
5040 for (j
= 0; j
< i
; ++j
) {
5041 if (isl_int_sgn(row
[2 + div_pos
+ j
]) >= 0)
5043 isl_int_fdiv_q(v
->el
[1 + div_pos
+ j
],
5044 row
[2 + div_pos
+ j
], row
[0]);
5045 isl_int_submul(row
[2 + div_pos
+ j
],
5046 row
[0], v
->el
[1 + div_pos
+ j
]);
5048 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
5049 if (isl_int_is_zero(qp
->div
->row
[j
][2 + div_pos
+ i
]))
5051 isl_seq_combine(qp
->div
->row
[j
] + 1,
5052 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
5053 qp
->div
->row
[j
][2 + div_pos
+ i
], v
->el
,
5056 isl_int_set_si(v
->el
[1 + div_pos
+ i
], 1);
5057 s
= isl_poly_from_affine(qp
->dim
->ctx
, v
->el
,
5058 qp
->div
->ctx
->one
, v
->size
);
5059 qp
->poly
= isl_poly_subs(qp
->poly
, div_pos
+ i
, 1, &s
);
5069 isl_qpolynomial_free(qp
);
5073 struct isl_to_poly_data
{
5075 isl_pw_qpolynomial
*res
;
5076 isl_qpolynomial
*qp
;
5079 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
5080 * We first make all integer divisions positive and then split the
5081 * quasipolynomials into terms with sign data->sign (the direction
5082 * of the requested approximation) and terms with the opposite sign.
5083 * In the first set of terms, each integer division [a/m] is
5084 * overapproximated by a/m, while in the second it is underapproximated
5087 static isl_stat
to_polynomial_on_orthant(__isl_take isl_set
*orthant
,
5088 int *signs
, void *user
)
5090 struct isl_to_poly_data
*data
= user
;
5091 isl_pw_qpolynomial
*t
;
5092 isl_qpolynomial
*qp
, *up
, *down
;
5094 qp
= isl_qpolynomial_copy(data
->qp
);
5095 qp
= make_divs_pos(qp
, signs
);
5097 up
= isl_qpolynomial_terms_of_sign(qp
, signs
, data
->sign
);
5098 up
= qp_drop_floors(up
, 0);
5099 down
= isl_qpolynomial_terms_of_sign(qp
, signs
, -data
->sign
);
5100 down
= qp_drop_floors(down
, 1);
5102 isl_qpolynomial_free(qp
);
5103 qp
= isl_qpolynomial_add(up
, down
);
5105 t
= isl_pw_qpolynomial_alloc(orthant
, qp
);
5106 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, t
);
5111 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
5112 * the polynomial will be an overapproximation. If "sign" is negative,
5113 * it will be an underapproximation. If "sign" is zero, the approximation
5114 * will lie somewhere in between.
5116 * In particular, is sign == 0, we simply drop the floors, turning
5117 * the integer divisions into rational divisions.
5118 * Otherwise, we split the domains into orthants, make all integer divisions
5119 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
5120 * depending on the requested sign and the sign of the term in which
5121 * the integer division appears.
5123 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_to_polynomial(
5124 __isl_take isl_pw_qpolynomial
*pwqp
, int sign
)
5127 struct isl_to_poly_data data
;
5130 return pwqp_drop_floors(pwqp
);
5136 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp
));
5138 for (i
= 0; i
< pwqp
->n
; ++i
) {
5139 if (pwqp
->p
[i
].qp
->div
->n_row
== 0) {
5140 isl_pw_qpolynomial
*t
;
5141 t
= isl_pw_qpolynomial_alloc(
5142 isl_set_copy(pwqp
->p
[i
].set
),
5143 isl_qpolynomial_copy(pwqp
->p
[i
].qp
));
5144 data
.res
= isl_pw_qpolynomial_add_disjoint(data
.res
, t
);
5147 data
.qp
= pwqp
->p
[i
].qp
;
5148 if (isl_set_foreach_orthant(pwqp
->p
[i
].set
,
5149 &to_polynomial_on_orthant
, &data
) < 0)
5153 isl_pw_qpolynomial_free(pwqp
);
5157 isl_pw_qpolynomial_free(pwqp
);
5158 isl_pw_qpolynomial_free(data
.res
);
5162 static __isl_give isl_pw_qpolynomial
*poly_entry(
5163 __isl_take isl_pw_qpolynomial
*pwqp
, void *user
)
5167 return isl_pw_qpolynomial_to_polynomial(pwqp
, *sign
);
5170 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_to_polynomial(
5171 __isl_take isl_union_pw_qpolynomial
*upwqp
, int sign
)
5173 return isl_union_pw_qpolynomial_transform_inplace(upwqp
,
5174 &poly_entry
, &sign
);
5177 __isl_give isl_basic_map
*isl_basic_map_from_qpolynomial(
5178 __isl_take isl_qpolynomial
*qp
)
5182 isl_vec
*aff
= NULL
;
5183 isl_basic_map
*bmap
= NULL
;
5190 is_affine
= isl_poly_is_affine(qp
->poly
);
5194 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
5195 "input quasi-polynomial not affine", goto error
);
5196 aff
= isl_qpolynomial_extract_affine(qp
);
5199 space
= isl_qpolynomial_get_space(qp
);
5200 pos
= 1 + isl_space_offset(space
, isl_dim_out
);
5201 n_div
= qp
->div
->n_row
;
5202 bmap
= isl_basic_map_alloc_space(space
, n_div
, 1, 2 * n_div
);
5204 for (i
= 0; i
< n_div
; ++i
) {
5205 k
= isl_basic_map_alloc_div(bmap
);
5208 isl_seq_cpy(bmap
->div
[k
], qp
->div
->row
[i
], qp
->div
->n_col
);
5209 isl_int_set_si(bmap
->div
[k
][qp
->div
->n_col
], 0);
5210 bmap
= isl_basic_map_add_div_constraints(bmap
, k
);
5212 k
= isl_basic_map_alloc_equality(bmap
);
5215 isl_int_neg(bmap
->eq
[k
][pos
], aff
->el
[0]);
5216 isl_seq_cpy(bmap
->eq
[k
], aff
->el
+ 1, pos
);
5217 isl_seq_cpy(bmap
->eq
[k
] + pos
+ 1, aff
->el
+ 1 + pos
, n_div
);
5220 isl_qpolynomial_free(qp
);
5221 bmap
= isl_basic_map_finalize(bmap
);
5225 isl_qpolynomial_free(qp
);
5226 isl_basic_map_free(bmap
);