2 * Copyright 2010 INRIA Saclay
4 * Use of this software is governed by the MIT license
6 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
7 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
12 #include <isl_ctx_private.h>
13 #include <isl_map_private.h>
14 #include <isl_factorization.h>
15 #include <isl_lp_private.h>
17 #include <isl_union_map_private.h>
18 #include <isl_constraint_private.h>
19 #include <isl_polynomial_private.h>
20 #include <isl_point_private.h>
21 #include <isl_space_private.h>
22 #include <isl_mat_private.h>
23 #include <isl_vec_private.h>
24 #include <isl_range.h>
25 #include <isl_local.h>
26 #include <isl_local_space_private.h>
27 #include <isl_aff_private.h>
28 #include <isl_val_private.h>
29 #include <isl_config.h>
32 #define EL_BASE pw_qpolynomial
34 #include <isl_list_templ.c>
36 static unsigned pos(__isl_keep isl_space
*dim
, enum isl_dim_type type
)
39 case isl_dim_param
: return 0;
40 case isl_dim_in
: return dim
->nparam
;
41 case isl_dim_out
: return dim
->nparam
+ dim
->n_in
;
46 isl_bool
isl_poly_is_cst(__isl_keep isl_poly
*poly
)
49 return isl_bool_error
;
51 return isl_bool_ok(poly
->var
< 0);
54 __isl_keep isl_poly_cst
*isl_poly_as_cst(__isl_keep isl_poly
*poly
)
59 isl_assert(poly
->ctx
, poly
->var
< 0, return NULL
);
61 return (isl_poly_cst
*) poly
;
64 __isl_keep isl_poly_rec
*isl_poly_as_rec(__isl_keep isl_poly
*poly
)
69 isl_assert(poly
->ctx
, poly
->var
>= 0, return NULL
);
71 return (isl_poly_rec
*) poly
;
74 /* Compare two polynomials.
76 * Return -1 if "poly1" is "smaller" than "poly2", 1 if "poly1" is "greater"
77 * than "poly2" and 0 if they are equal.
79 static int isl_poly_plain_cmp(__isl_keep isl_poly
*poly1
,
80 __isl_keep isl_poly
*poly2
)
84 isl_poly_rec
*rec1
, *rec2
;
88 is_cst1
= isl_poly_is_cst(poly1
);
93 if (poly1
->var
!= poly2
->var
)
94 return poly1
->var
- poly2
->var
;
97 isl_poly_cst
*cst1
, *cst2
;
100 cst1
= isl_poly_as_cst(poly1
);
101 cst2
= isl_poly_as_cst(poly2
);
104 cmp
= isl_int_cmp(cst1
->n
, cst2
->n
);
107 return isl_int_cmp(cst1
->d
, cst2
->d
);
110 rec1
= isl_poly_as_rec(poly1
);
111 rec2
= isl_poly_as_rec(poly2
);
115 if (rec1
->n
!= rec2
->n
)
116 return rec1
->n
- rec2
->n
;
118 for (i
= 0; i
< rec1
->n
; ++i
) {
119 int cmp
= isl_poly_plain_cmp(rec1
->p
[i
], rec2
->p
[i
]);
127 isl_bool
isl_poly_is_equal(__isl_keep isl_poly
*poly1
,
128 __isl_keep isl_poly
*poly2
)
132 isl_poly_rec
*rec1
, *rec2
;
134 is_cst1
= isl_poly_is_cst(poly1
);
135 if (is_cst1
< 0 || !poly2
)
136 return isl_bool_error
;
138 return isl_bool_true
;
139 if (poly1
->var
!= poly2
->var
)
140 return isl_bool_false
;
142 isl_poly_cst
*cst1
, *cst2
;
144 cst1
= isl_poly_as_cst(poly1
);
145 cst2
= isl_poly_as_cst(poly2
);
147 return isl_bool_error
;
148 r
= isl_int_eq(cst1
->n
, cst2
->n
) &&
149 isl_int_eq(cst1
->d
, cst2
->d
);
150 return isl_bool_ok(r
);
153 rec1
= isl_poly_as_rec(poly1
);
154 rec2
= isl_poly_as_rec(poly2
);
156 return isl_bool_error
;
158 if (rec1
->n
!= rec2
->n
)
159 return isl_bool_false
;
161 for (i
= 0; i
< rec1
->n
; ++i
) {
162 isl_bool eq
= isl_poly_is_equal(rec1
->p
[i
], rec2
->p
[i
]);
167 return isl_bool_true
;
170 isl_bool
isl_poly_is_zero(__isl_keep isl_poly
*poly
)
175 is_cst
= isl_poly_is_cst(poly
);
176 if (is_cst
< 0 || !is_cst
)
179 cst
= isl_poly_as_cst(poly
);
181 return isl_bool_error
;
183 return isl_bool_ok(isl_int_is_zero(cst
->n
) && isl_int_is_pos(cst
->d
));
186 int isl_poly_sgn(__isl_keep isl_poly
*poly
)
191 is_cst
= isl_poly_is_cst(poly
);
192 if (is_cst
< 0 || !is_cst
)
195 cst
= isl_poly_as_cst(poly
);
199 return isl_int_sgn(cst
->n
);
202 isl_bool
isl_poly_is_nan(__isl_keep isl_poly
*poly
)
207 is_cst
= isl_poly_is_cst(poly
);
208 if (is_cst
< 0 || !is_cst
)
211 cst
= isl_poly_as_cst(poly
);
213 return isl_bool_error
;
215 return isl_bool_ok(isl_int_is_zero(cst
->n
) && isl_int_is_zero(cst
->d
));
218 isl_bool
isl_poly_is_infty(__isl_keep isl_poly
*poly
)
223 is_cst
= isl_poly_is_cst(poly
);
224 if (is_cst
< 0 || !is_cst
)
227 cst
= isl_poly_as_cst(poly
);
229 return isl_bool_error
;
231 return isl_bool_ok(isl_int_is_pos(cst
->n
) && isl_int_is_zero(cst
->d
));
234 isl_bool
isl_poly_is_neginfty(__isl_keep isl_poly
*poly
)
239 is_cst
= isl_poly_is_cst(poly
);
240 if (is_cst
< 0 || !is_cst
)
243 cst
= isl_poly_as_cst(poly
);
245 return isl_bool_error
;
247 return isl_bool_ok(isl_int_is_neg(cst
->n
) && isl_int_is_zero(cst
->d
));
250 isl_bool
isl_poly_is_one(__isl_keep isl_poly
*poly
)
256 is_cst
= isl_poly_is_cst(poly
);
257 if (is_cst
< 0 || !is_cst
)
260 cst
= isl_poly_as_cst(poly
);
262 return isl_bool_error
;
264 r
= isl_int_eq(cst
->n
, cst
->d
) && isl_int_is_pos(cst
->d
);
265 return isl_bool_ok(r
);
268 isl_bool
isl_poly_is_negone(__isl_keep isl_poly
*poly
)
273 is_cst
= isl_poly_is_cst(poly
);
274 if (is_cst
< 0 || !is_cst
)
277 cst
= isl_poly_as_cst(poly
);
279 return isl_bool_error
;
281 return isl_bool_ok(isl_int_is_negone(cst
->n
) && isl_int_is_one(cst
->d
));
284 __isl_give isl_poly_cst
*isl_poly_cst_alloc(isl_ctx
*ctx
)
288 cst
= isl_alloc_type(ctx
, struct isl_poly_cst
);
297 isl_int_init(cst
->n
);
298 isl_int_init(cst
->d
);
303 __isl_give isl_poly
*isl_poly_zero(isl_ctx
*ctx
)
307 cst
= isl_poly_cst_alloc(ctx
);
311 isl_int_set_si(cst
->n
, 0);
312 isl_int_set_si(cst
->d
, 1);
317 __isl_give isl_poly
*isl_poly_one(isl_ctx
*ctx
)
321 cst
= isl_poly_cst_alloc(ctx
);
325 isl_int_set_si(cst
->n
, 1);
326 isl_int_set_si(cst
->d
, 1);
331 __isl_give isl_poly
*isl_poly_infty(isl_ctx
*ctx
)
335 cst
= isl_poly_cst_alloc(ctx
);
339 isl_int_set_si(cst
->n
, 1);
340 isl_int_set_si(cst
->d
, 0);
345 __isl_give isl_poly
*isl_poly_neginfty(isl_ctx
*ctx
)
349 cst
= isl_poly_cst_alloc(ctx
);
353 isl_int_set_si(cst
->n
, -1);
354 isl_int_set_si(cst
->d
, 0);
359 __isl_give isl_poly
*isl_poly_nan(isl_ctx
*ctx
)
363 cst
= isl_poly_cst_alloc(ctx
);
367 isl_int_set_si(cst
->n
, 0);
368 isl_int_set_si(cst
->d
, 0);
373 __isl_give isl_poly
*isl_poly_rat_cst(isl_ctx
*ctx
, isl_int n
, isl_int d
)
377 cst
= isl_poly_cst_alloc(ctx
);
381 isl_int_set(cst
->n
, n
);
382 isl_int_set(cst
->d
, d
);
387 __isl_give isl_poly_rec
*isl_poly_alloc_rec(isl_ctx
*ctx
, int var
, int size
)
391 isl_assert(ctx
, var
>= 0, return NULL
);
392 isl_assert(ctx
, size
>= 0, return NULL
);
393 rec
= isl_calloc(ctx
, struct isl_poly_rec
,
394 sizeof(struct isl_poly_rec
) +
395 size
* sizeof(struct isl_poly
*));
410 __isl_give isl_qpolynomial
*isl_qpolynomial_reset_domain_space(
411 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*dim
)
413 qp
= isl_qpolynomial_cow(qp
);
417 isl_space_free(qp
->dim
);
422 isl_qpolynomial_free(qp
);
427 /* Reset the space of "qp". This function is called from isl_pw_templ.c
428 * and doesn't know if the space of an element object is represented
429 * directly or through its domain. It therefore passes along both.
431 __isl_give isl_qpolynomial
*isl_qpolynomial_reset_space_and_domain(
432 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*space
,
433 __isl_take isl_space
*domain
)
435 isl_space_free(space
);
436 return isl_qpolynomial_reset_domain_space(qp
, domain
);
439 isl_ctx
*isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial
*qp
)
441 return qp
? qp
->dim
->ctx
: NULL
;
444 /* Return the domain space of "qp".
446 static __isl_keep isl_space
*isl_qpolynomial_peek_domain_space(
447 __isl_keep isl_qpolynomial
*qp
)
449 return qp
? qp
->dim
: NULL
;
452 /* Return a copy of the domain space of "qp".
454 __isl_give isl_space
*isl_qpolynomial_get_domain_space(
455 __isl_keep isl_qpolynomial
*qp
)
457 return isl_space_copy(isl_qpolynomial_peek_domain_space(qp
));
460 /* Return a copy of the local space on which "qp" is defined.
462 static __isl_give isl_local_space
*isl_qpolynomial_get_domain_local_space(
463 __isl_keep isl_qpolynomial
*qp
)
470 space
= isl_qpolynomial_get_domain_space(qp
);
471 return isl_local_space_alloc_div(space
, isl_mat_copy(qp
->div
));
474 __isl_give isl_space
*isl_qpolynomial_get_space(__isl_keep isl_qpolynomial
*qp
)
479 space
= isl_space_copy(qp
->dim
);
480 space
= isl_space_from_domain(space
);
481 space
= isl_space_add_dims(space
, isl_dim_out
, 1);
485 /* Return the number of variables of the given type in the domain of "qp".
487 isl_size
isl_qpolynomial_domain_dim(__isl_keep isl_qpolynomial
*qp
,
488 enum isl_dim_type type
)
493 space
= isl_qpolynomial_peek_domain_space(qp
);
496 return isl_size_error
;
497 if (type
== isl_dim_div
)
498 return qp
->div
->n_row
;
499 dim
= isl_space_dim(space
, type
);
501 return isl_size_error
;
502 if (type
== isl_dim_all
) {
505 n_div
= isl_qpolynomial_domain_dim(qp
, isl_dim_div
);
507 return isl_size_error
;
513 /* Given the type of a dimension of an isl_qpolynomial,
514 * return the type of the corresponding dimension in its domain.
515 * This function is only called for "type" equal to isl_dim_in or
518 static enum isl_dim_type
domain_type(enum isl_dim_type type
)
520 return type
== isl_dim_in
? isl_dim_set
: type
;
523 /* Externally, an isl_qpolynomial has a map space, but internally, the
524 * ls field corresponds to the domain of that space.
526 isl_size
isl_qpolynomial_dim(__isl_keep isl_qpolynomial
*qp
,
527 enum isl_dim_type type
)
530 return isl_size_error
;
531 if (type
== isl_dim_out
)
533 type
= domain_type(type
);
534 return isl_qpolynomial_domain_dim(qp
, type
);
537 /* Return the offset of the first variable of type "type" within
538 * the variables of the domain of "qp".
540 static isl_size
isl_qpolynomial_domain_var_offset(
541 __isl_keep isl_qpolynomial
*qp
, enum isl_dim_type type
)
545 space
= isl_qpolynomial_peek_domain_space(qp
);
547 return isl_size_error
;
551 case isl_dim_set
: return isl_space_offset(space
, type
);
552 case isl_dim_div
: return isl_space_dim(space
, isl_dim_all
);
555 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
556 "invalid dimension type", return isl_size_error
);
560 /* Return the offset of the first coefficient of type "type" in
561 * the domain of "qp".
563 unsigned isl_qpolynomial_domain_offset(__isl_keep isl_qpolynomial
*qp
,
564 enum isl_dim_type type
)
572 return 1 + isl_qpolynomial_domain_var_offset(qp
, type
);
578 isl_bool
isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial
*qp
)
580 return qp
? isl_poly_is_zero(qp
->poly
) : isl_bool_error
;
583 isl_bool
isl_qpolynomial_is_one(__isl_keep isl_qpolynomial
*qp
)
585 return qp
? isl_poly_is_one(qp
->poly
) : isl_bool_error
;
588 isl_bool
isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial
*qp
)
590 return qp
? isl_poly_is_nan(qp
->poly
) : isl_bool_error
;
593 isl_bool
isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial
*qp
)
595 return qp
? isl_poly_is_infty(qp
->poly
) : isl_bool_error
;
598 isl_bool
isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial
*qp
)
600 return qp
? isl_poly_is_neginfty(qp
->poly
) : isl_bool_error
;
603 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial
*qp
)
605 return qp
? isl_poly_sgn(qp
->poly
) : 0;
608 static void poly_free_cst(__isl_take isl_poly_cst
*cst
)
610 isl_int_clear(cst
->n
);
611 isl_int_clear(cst
->d
);
614 static void poly_free_rec(__isl_take isl_poly_rec
*rec
)
618 for (i
= 0; i
< rec
->n
; ++i
)
619 isl_poly_free(rec
->p
[i
]);
622 __isl_give isl_poly
*isl_poly_copy(__isl_keep isl_poly
*poly
)
631 __isl_give isl_poly
*isl_poly_dup_cst(__isl_keep isl_poly
*poly
)
636 cst
= isl_poly_as_cst(poly
);
640 dup
= isl_poly_as_cst(isl_poly_zero(poly
->ctx
));
643 isl_int_set(dup
->n
, cst
->n
);
644 isl_int_set(dup
->d
, cst
->d
);
649 __isl_give isl_poly
*isl_poly_dup_rec(__isl_keep isl_poly
*poly
)
655 rec
= isl_poly_as_rec(poly
);
659 dup
= isl_poly_alloc_rec(poly
->ctx
, poly
->var
, rec
->n
);
663 for (i
= 0; i
< rec
->n
; ++i
) {
664 dup
->p
[i
] = isl_poly_copy(rec
->p
[i
]);
672 isl_poly_free(&dup
->poly
);
676 __isl_give isl_poly
*isl_poly_dup(__isl_keep isl_poly
*poly
)
680 is_cst
= isl_poly_is_cst(poly
);
684 return isl_poly_dup_cst(poly
);
686 return isl_poly_dup_rec(poly
);
689 __isl_give isl_poly
*isl_poly_cow(__isl_take isl_poly
*poly
)
697 return isl_poly_dup(poly
);
700 __isl_null isl_poly
*isl_poly_free(__isl_take isl_poly
*poly
)
709 poly_free_cst((isl_poly_cst
*) poly
);
711 poly_free_rec((isl_poly_rec
*) poly
);
713 isl_ctx_deref(poly
->ctx
);
718 static void isl_poly_cst_reduce(__isl_keep isl_poly_cst
*cst
)
723 isl_int_gcd(gcd
, cst
->n
, cst
->d
);
724 if (!isl_int_is_zero(gcd
) && !isl_int_is_one(gcd
)) {
725 isl_int_divexact(cst
->n
, cst
->n
, gcd
);
726 isl_int_divexact(cst
->d
, cst
->d
, gcd
);
731 __isl_give isl_poly
*isl_poly_sum_cst(__isl_take isl_poly
*poly1
,
732 __isl_take isl_poly
*poly2
)
737 poly1
= isl_poly_cow(poly1
);
738 if (!poly1
|| !poly2
)
741 cst1
= isl_poly_as_cst(poly1
);
742 cst2
= isl_poly_as_cst(poly2
);
744 if (isl_int_eq(cst1
->d
, cst2
->d
))
745 isl_int_add(cst1
->n
, cst1
->n
, cst2
->n
);
747 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->d
);
748 isl_int_addmul(cst1
->n
, cst2
->n
, cst1
->d
);
749 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
752 isl_poly_cst_reduce(cst1
);
754 isl_poly_free(poly2
);
757 isl_poly_free(poly1
);
758 isl_poly_free(poly2
);
762 static __isl_give isl_poly
*replace_by_zero(__isl_take isl_poly
*poly
)
770 return isl_poly_zero(ctx
);
773 static __isl_give isl_poly
*replace_by_constant_term(__isl_take isl_poly
*poly
)
781 rec
= isl_poly_as_rec(poly
);
784 cst
= isl_poly_copy(rec
->p
[0]);
792 __isl_give isl_poly
*isl_poly_sum(__isl_take isl_poly
*poly1
,
793 __isl_take isl_poly
*poly2
)
796 isl_bool is_zero
, is_nan
, is_cst
;
797 isl_poly_rec
*rec1
, *rec2
;
799 if (!poly1
|| !poly2
)
802 is_nan
= isl_poly_is_nan(poly1
);
806 isl_poly_free(poly2
);
810 is_nan
= isl_poly_is_nan(poly2
);
814 isl_poly_free(poly1
);
818 is_zero
= isl_poly_is_zero(poly1
);
822 isl_poly_free(poly1
);
826 is_zero
= isl_poly_is_zero(poly2
);
830 isl_poly_free(poly2
);
834 if (poly1
->var
< poly2
->var
)
835 return isl_poly_sum(poly2
, poly1
);
837 if (poly2
->var
< poly1
->var
) {
841 is_infty
= isl_poly_is_infty(poly2
);
842 if (is_infty
>= 0 && !is_infty
)
843 is_infty
= isl_poly_is_neginfty(poly2
);
847 isl_poly_free(poly1
);
850 poly1
= isl_poly_cow(poly1
);
851 rec
= isl_poly_as_rec(poly1
);
854 rec
->p
[0] = isl_poly_sum(rec
->p
[0], poly2
);
856 poly1
= replace_by_constant_term(poly1
);
860 is_cst
= isl_poly_is_cst(poly1
);
864 return isl_poly_sum_cst(poly1
, poly2
);
866 rec1
= isl_poly_as_rec(poly1
);
867 rec2
= isl_poly_as_rec(poly2
);
871 if (rec1
->n
< rec2
->n
)
872 return isl_poly_sum(poly2
, poly1
);
874 poly1
= isl_poly_cow(poly1
);
875 rec1
= isl_poly_as_rec(poly1
);
879 for (i
= rec2
->n
- 1; i
>= 0; --i
) {
882 rec1
->p
[i
] = isl_poly_sum(rec1
->p
[i
],
883 isl_poly_copy(rec2
->p
[i
]));
886 if (i
!= rec1
->n
- 1)
888 is_zero
= isl_poly_is_zero(rec1
->p
[i
]);
892 isl_poly_free(rec1
->p
[i
]);
898 poly1
= replace_by_zero(poly1
);
899 else if (rec1
->n
== 1)
900 poly1
= replace_by_constant_term(poly1
);
902 isl_poly_free(poly2
);
906 isl_poly_free(poly1
);
907 isl_poly_free(poly2
);
911 __isl_give isl_poly
*isl_poly_cst_add_isl_int(__isl_take isl_poly
*poly
,
916 poly
= isl_poly_cow(poly
);
920 cst
= isl_poly_as_cst(poly
);
922 isl_int_addmul(cst
->n
, cst
->d
, v
);
927 __isl_give isl_poly
*isl_poly_add_isl_int(__isl_take isl_poly
*poly
, isl_int v
)
932 is_cst
= isl_poly_is_cst(poly
);
934 return isl_poly_free(poly
);
936 return isl_poly_cst_add_isl_int(poly
, v
);
938 poly
= isl_poly_cow(poly
);
939 rec
= isl_poly_as_rec(poly
);
943 rec
->p
[0] = isl_poly_add_isl_int(rec
->p
[0], v
);
953 __isl_give isl_poly
*isl_poly_cst_mul_isl_int(__isl_take isl_poly
*poly
,
959 is_zero
= isl_poly_is_zero(poly
);
961 return isl_poly_free(poly
);
965 poly
= isl_poly_cow(poly
);
969 cst
= isl_poly_as_cst(poly
);
971 isl_int_mul(cst
->n
, cst
->n
, v
);
976 __isl_give isl_poly
*isl_poly_mul_isl_int(__isl_take isl_poly
*poly
, isl_int v
)
982 is_cst
= isl_poly_is_cst(poly
);
984 return isl_poly_free(poly
);
986 return isl_poly_cst_mul_isl_int(poly
, v
);
988 poly
= isl_poly_cow(poly
);
989 rec
= isl_poly_as_rec(poly
);
993 for (i
= 0; i
< rec
->n
; ++i
) {
994 rec
->p
[i
] = isl_poly_mul_isl_int(rec
->p
[i
], v
);
1001 isl_poly_free(poly
);
1005 /* Multiply the constant polynomial "poly" by "v".
1007 static __isl_give isl_poly
*isl_poly_cst_scale_val(__isl_take isl_poly
*poly
,
1008 __isl_keep isl_val
*v
)
1013 is_zero
= isl_poly_is_zero(poly
);
1015 return isl_poly_free(poly
);
1019 poly
= isl_poly_cow(poly
);
1023 cst
= isl_poly_as_cst(poly
);
1025 isl_int_mul(cst
->n
, cst
->n
, v
->n
);
1026 isl_int_mul(cst
->d
, cst
->d
, v
->d
);
1027 isl_poly_cst_reduce(cst
);
1032 /* Multiply the polynomial "poly" by "v".
1034 static __isl_give isl_poly
*isl_poly_scale_val(__isl_take isl_poly
*poly
,
1035 __isl_keep isl_val
*v
)
1041 is_cst
= isl_poly_is_cst(poly
);
1043 return isl_poly_free(poly
);
1045 return isl_poly_cst_scale_val(poly
, v
);
1047 poly
= isl_poly_cow(poly
);
1048 rec
= isl_poly_as_rec(poly
);
1052 for (i
= 0; i
< rec
->n
; ++i
) {
1053 rec
->p
[i
] = isl_poly_scale_val(rec
->p
[i
], v
);
1060 isl_poly_free(poly
);
1064 __isl_give isl_poly
*isl_poly_mul_cst(__isl_take isl_poly
*poly1
,
1065 __isl_take isl_poly
*poly2
)
1070 poly1
= isl_poly_cow(poly1
);
1071 if (!poly1
|| !poly2
)
1074 cst1
= isl_poly_as_cst(poly1
);
1075 cst2
= isl_poly_as_cst(poly2
);
1077 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->n
);
1078 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
1080 isl_poly_cst_reduce(cst1
);
1082 isl_poly_free(poly2
);
1085 isl_poly_free(poly1
);
1086 isl_poly_free(poly2
);
1090 __isl_give isl_poly
*isl_poly_mul_rec(__isl_take isl_poly
*poly1
,
1091 __isl_take isl_poly
*poly2
)
1095 isl_poly_rec
*res
= NULL
;
1099 rec1
= isl_poly_as_rec(poly1
);
1100 rec2
= isl_poly_as_rec(poly2
);
1103 size
= rec1
->n
+ rec2
->n
- 1;
1104 res
= isl_poly_alloc_rec(poly1
->ctx
, poly1
->var
, size
);
1108 for (i
= 0; i
< rec1
->n
; ++i
) {
1109 res
->p
[i
] = isl_poly_mul(isl_poly_copy(rec2
->p
[0]),
1110 isl_poly_copy(rec1
->p
[i
]));
1115 for (; i
< size
; ++i
) {
1116 res
->p
[i
] = isl_poly_zero(poly1
->ctx
);
1121 for (i
= 0; i
< rec1
->n
; ++i
) {
1122 for (j
= 1; j
< rec2
->n
; ++j
) {
1124 poly
= isl_poly_mul(isl_poly_copy(rec2
->p
[j
]),
1125 isl_poly_copy(rec1
->p
[i
]));
1126 res
->p
[i
+ j
] = isl_poly_sum(res
->p
[i
+ j
], poly
);
1132 isl_poly_free(poly1
);
1133 isl_poly_free(poly2
);
1137 isl_poly_free(poly1
);
1138 isl_poly_free(poly2
);
1139 isl_poly_free(&res
->poly
);
1143 __isl_give isl_poly
*isl_poly_mul(__isl_take isl_poly
*poly1
,
1144 __isl_take isl_poly
*poly2
)
1146 isl_bool is_zero
, is_nan
, is_one
, is_cst
;
1148 if (!poly1
|| !poly2
)
1151 is_nan
= isl_poly_is_nan(poly1
);
1155 isl_poly_free(poly2
);
1159 is_nan
= isl_poly_is_nan(poly2
);
1163 isl_poly_free(poly1
);
1167 is_zero
= isl_poly_is_zero(poly1
);
1171 isl_poly_free(poly2
);
1175 is_zero
= isl_poly_is_zero(poly2
);
1179 isl_poly_free(poly1
);
1183 is_one
= isl_poly_is_one(poly1
);
1187 isl_poly_free(poly1
);
1191 is_one
= isl_poly_is_one(poly2
);
1195 isl_poly_free(poly2
);
1199 if (poly1
->var
< poly2
->var
)
1200 return isl_poly_mul(poly2
, poly1
);
1202 if (poly2
->var
< poly1
->var
) {
1207 is_infty
= isl_poly_is_infty(poly2
);
1208 if (is_infty
>= 0 && !is_infty
)
1209 is_infty
= isl_poly_is_neginfty(poly2
);
1213 isl_ctx
*ctx
= poly1
->ctx
;
1214 isl_poly_free(poly1
);
1215 isl_poly_free(poly2
);
1216 return isl_poly_nan(ctx
);
1218 poly1
= isl_poly_cow(poly1
);
1219 rec
= isl_poly_as_rec(poly1
);
1223 for (i
= 0; i
< rec
->n
; ++i
) {
1224 rec
->p
[i
] = isl_poly_mul(rec
->p
[i
],
1225 isl_poly_copy(poly2
));
1229 isl_poly_free(poly2
);
1233 is_cst
= isl_poly_is_cst(poly1
);
1237 return isl_poly_mul_cst(poly1
, poly2
);
1239 return isl_poly_mul_rec(poly1
, poly2
);
1241 isl_poly_free(poly1
);
1242 isl_poly_free(poly2
);
1246 __isl_give isl_poly
*isl_poly_pow(__isl_take isl_poly
*poly
, unsigned power
)
1256 res
= isl_poly_copy(poly
);
1258 res
= isl_poly_one(poly
->ctx
);
1260 while (power
>>= 1) {
1261 poly
= isl_poly_mul(poly
, isl_poly_copy(poly
));
1263 res
= isl_poly_mul(res
, isl_poly_copy(poly
));
1266 isl_poly_free(poly
);
1270 __isl_give isl_qpolynomial
*isl_qpolynomial_alloc(__isl_take isl_space
*space
,
1271 unsigned n_div
, __isl_take isl_poly
*poly
)
1273 struct isl_qpolynomial
*qp
= NULL
;
1276 total
= isl_space_dim(space
, isl_dim_all
);
1277 if (total
< 0 || !poly
)
1280 if (!isl_space_is_set(space
))
1281 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
1282 "domain of polynomial should be a set", goto error
);
1284 qp
= isl_calloc_type(space
->ctx
, struct isl_qpolynomial
);
1289 qp
->div
= isl_mat_alloc(space
->ctx
, n_div
, 1 + 1 + total
+ n_div
);
1298 isl_space_free(space
);
1299 isl_poly_free(poly
);
1300 isl_qpolynomial_free(qp
);
1304 __isl_give isl_qpolynomial
*isl_qpolynomial_copy(__isl_keep isl_qpolynomial
*qp
)
1313 __isl_give isl_qpolynomial
*isl_qpolynomial_dup(__isl_keep isl_qpolynomial
*qp
)
1315 struct isl_qpolynomial
*dup
;
1320 dup
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
), qp
->div
->n_row
,
1321 isl_poly_copy(qp
->poly
));
1324 isl_mat_free(dup
->div
);
1325 dup
->div
= isl_mat_copy(qp
->div
);
1331 isl_qpolynomial_free(dup
);
1335 __isl_give isl_qpolynomial
*isl_qpolynomial_cow(__isl_take isl_qpolynomial
*qp
)
1343 return isl_qpolynomial_dup(qp
);
1346 __isl_null isl_qpolynomial
*isl_qpolynomial_free(
1347 __isl_take isl_qpolynomial
*qp
)
1355 isl_space_free(qp
->dim
);
1356 isl_mat_free(qp
->div
);
1357 isl_poly_free(qp
->poly
);
1363 __isl_give isl_poly
*isl_poly_var_pow(isl_ctx
*ctx
, int pos
, int power
)
1369 rec
= isl_poly_alloc_rec(ctx
, pos
, 1 + power
);
1372 for (i
= 0; i
< 1 + power
; ++i
) {
1373 rec
->p
[i
] = isl_poly_zero(ctx
);
1378 cst
= isl_poly_as_cst(rec
->p
[power
]);
1379 isl_int_set_si(cst
->n
, 1);
1383 isl_poly_free(&rec
->poly
);
1387 /* r array maps original positions to new positions.
1389 static __isl_give isl_poly
*reorder(__isl_take isl_poly
*poly
, int *r
)
1397 is_cst
= isl_poly_is_cst(poly
);
1399 return isl_poly_free(poly
);
1403 rec
= isl_poly_as_rec(poly
);
1407 isl_assert(poly
->ctx
, rec
->n
>= 1, goto error
);
1409 base
= isl_poly_var_pow(poly
->ctx
, r
[poly
->var
], 1);
1410 res
= reorder(isl_poly_copy(rec
->p
[rec
->n
- 1]), r
);
1412 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1413 res
= isl_poly_mul(res
, isl_poly_copy(base
));
1414 res
= isl_poly_sum(res
, reorder(isl_poly_copy(rec
->p
[i
]), r
));
1417 isl_poly_free(base
);
1418 isl_poly_free(poly
);
1422 isl_poly_free(poly
);
1426 static isl_bool
compatible_divs(__isl_keep isl_mat
*div1
,
1427 __isl_keep isl_mat
*div2
)
1432 isl_assert(div1
->ctx
, div1
->n_row
>= div2
->n_row
&&
1433 div1
->n_col
>= div2
->n_col
,
1434 return isl_bool_error
);
1436 if (div1
->n_row
== div2
->n_row
)
1437 return isl_mat_is_equal(div1
, div2
);
1439 n_row
= div1
->n_row
;
1440 n_col
= div1
->n_col
;
1441 div1
->n_row
= div2
->n_row
;
1442 div1
->n_col
= div2
->n_col
;
1444 equal
= isl_mat_is_equal(div1
, div2
);
1446 div1
->n_row
= n_row
;
1447 div1
->n_col
= n_col
;
1452 static int cmp_row(__isl_keep isl_mat
*div
, int i
, int j
)
1456 li
= isl_seq_last_non_zero(div
->row
[i
], div
->n_col
);
1457 lj
= isl_seq_last_non_zero(div
->row
[j
], div
->n_col
);
1462 return isl_seq_cmp(div
->row
[i
], div
->row
[j
], div
->n_col
);
1465 struct isl_div_sort_info
{
1470 static int div_sort_cmp(const void *p1
, const void *p2
)
1472 const struct isl_div_sort_info
*i1
, *i2
;
1473 i1
= (const struct isl_div_sort_info
*) p1
;
1474 i2
= (const struct isl_div_sort_info
*) p2
;
1476 return cmp_row(i1
->div
, i1
->row
, i2
->row
);
1479 /* Sort divs and remove duplicates.
1481 static __isl_give isl_qpolynomial
*sort_divs(__isl_take isl_qpolynomial
*qp
)
1486 struct isl_div_sort_info
*array
= NULL
;
1487 int *pos
= NULL
, *at
= NULL
;
1488 int *reordering
= NULL
;
1493 if (qp
->div
->n_row
<= 1)
1496 div_pos
= isl_qpolynomial_domain_var_offset(qp
, isl_dim_div
);
1498 return isl_qpolynomial_free(qp
);
1500 array
= isl_alloc_array(qp
->div
->ctx
, struct isl_div_sort_info
,
1502 pos
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1503 at
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1504 len
= qp
->div
->n_col
- 2;
1505 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
1506 if (!array
|| !pos
|| !at
|| !reordering
)
1509 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1510 array
[i
].div
= qp
->div
;
1516 qsort(array
, qp
->div
->n_row
, sizeof(struct isl_div_sort_info
),
1519 for (i
= 0; i
< div_pos
; ++i
)
1522 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1523 if (pos
[array
[i
].row
] == i
)
1525 qp
->div
= isl_mat_swap_rows(qp
->div
, i
, pos
[array
[i
].row
]);
1526 pos
[at
[i
]] = pos
[array
[i
].row
];
1527 at
[pos
[array
[i
].row
]] = at
[i
];
1528 at
[i
] = array
[i
].row
;
1529 pos
[array
[i
].row
] = i
;
1533 for (i
= 0; i
< len
- div_pos
; ++i
) {
1535 isl_seq_eq(qp
->div
->row
[i
- skip
- 1],
1536 qp
->div
->row
[i
- skip
], qp
->div
->n_col
)) {
1537 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
1538 isl_mat_col_add(qp
->div
, 2 + div_pos
+ i
- skip
- 1,
1539 2 + div_pos
+ i
- skip
);
1540 qp
->div
= isl_mat_drop_cols(qp
->div
,
1541 2 + div_pos
+ i
- skip
, 1);
1544 reordering
[div_pos
+ array
[i
].row
] = div_pos
+ i
- skip
;
1547 qp
->poly
= reorder(qp
->poly
, reordering
);
1549 if (!qp
->poly
|| !qp
->div
)
1563 isl_qpolynomial_free(qp
);
1567 static __isl_give isl_poly
*expand(__isl_take isl_poly
*poly
, int *exp
,
1574 is_cst
= isl_poly_is_cst(poly
);
1576 return isl_poly_free(poly
);
1580 if (poly
->var
< first
)
1583 if (exp
[poly
->var
- first
] == poly
->var
- first
)
1586 poly
= isl_poly_cow(poly
);
1590 poly
->var
= exp
[poly
->var
- first
] + first
;
1592 rec
= isl_poly_as_rec(poly
);
1596 for (i
= 0; i
< rec
->n
; ++i
) {
1597 rec
->p
[i
] = expand(rec
->p
[i
], exp
, first
);
1604 isl_poly_free(poly
);
1608 static __isl_give isl_qpolynomial
*with_merged_divs(
1609 __isl_give isl_qpolynomial
*(*fn
)(__isl_take isl_qpolynomial
*qp1
,
1610 __isl_take isl_qpolynomial
*qp2
),
1611 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
1615 isl_mat
*div
= NULL
;
1618 qp1
= isl_qpolynomial_cow(qp1
);
1619 qp2
= isl_qpolynomial_cow(qp2
);
1624 isl_assert(qp1
->div
->ctx
, qp1
->div
->n_row
>= qp2
->div
->n_row
&&
1625 qp1
->div
->n_col
>= qp2
->div
->n_col
, goto error
);
1627 n_div1
= qp1
->div
->n_row
;
1628 n_div2
= qp2
->div
->n_row
;
1629 exp1
= isl_alloc_array(qp1
->div
->ctx
, int, n_div1
);
1630 exp2
= isl_alloc_array(qp2
->div
->ctx
, int, n_div2
);
1631 if ((n_div1
&& !exp1
) || (n_div2
&& !exp2
))
1634 div
= isl_merge_divs(qp1
->div
, qp2
->div
, exp1
, exp2
);
1638 isl_mat_free(qp1
->div
);
1639 qp1
->div
= isl_mat_copy(div
);
1640 isl_mat_free(qp2
->div
);
1641 qp2
->div
= isl_mat_copy(div
);
1643 qp1
->poly
= expand(qp1
->poly
, exp1
, div
->n_col
- div
->n_row
- 2);
1644 qp2
->poly
= expand(qp2
->poly
, exp2
, div
->n_col
- div
->n_row
- 2);
1646 if (!qp1
->poly
|| !qp2
->poly
)
1653 return fn(qp1
, qp2
);
1658 isl_qpolynomial_free(qp1
);
1659 isl_qpolynomial_free(qp2
);
1663 __isl_give isl_qpolynomial
*isl_qpolynomial_add(__isl_take isl_qpolynomial
*qp1
,
1664 __isl_take isl_qpolynomial
*qp2
)
1666 isl_bool compatible
;
1668 qp1
= isl_qpolynomial_cow(qp1
);
1673 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1674 return isl_qpolynomial_add(qp2
, qp1
);
1676 isl_assert(qp1
->dim
->ctx
, isl_space_is_equal(qp1
->dim
, qp2
->dim
), goto error
);
1677 compatible
= compatible_divs(qp1
->div
, qp2
->div
);
1681 return with_merged_divs(isl_qpolynomial_add
, qp1
, qp2
);
1683 qp1
->poly
= isl_poly_sum(qp1
->poly
, isl_poly_copy(qp2
->poly
));
1687 isl_qpolynomial_free(qp2
);
1691 isl_qpolynomial_free(qp1
);
1692 isl_qpolynomial_free(qp2
);
1696 __isl_give isl_qpolynomial
*isl_qpolynomial_add_on_domain(
1697 __isl_keep isl_set
*dom
,
1698 __isl_take isl_qpolynomial
*qp1
,
1699 __isl_take isl_qpolynomial
*qp2
)
1701 qp1
= isl_qpolynomial_add(qp1
, qp2
);
1702 qp1
= isl_qpolynomial_gist(qp1
, isl_set_copy(dom
));
1706 __isl_give isl_qpolynomial
*isl_qpolynomial_sub(__isl_take isl_qpolynomial
*qp1
,
1707 __isl_take isl_qpolynomial
*qp2
)
1709 return isl_qpolynomial_add(qp1
, isl_qpolynomial_neg(qp2
));
1712 __isl_give isl_qpolynomial
*isl_qpolynomial_add_isl_int(
1713 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1715 if (isl_int_is_zero(v
))
1718 qp
= isl_qpolynomial_cow(qp
);
1722 qp
->poly
= isl_poly_add_isl_int(qp
->poly
, v
);
1728 isl_qpolynomial_free(qp
);
1733 __isl_give isl_qpolynomial
*isl_qpolynomial_neg(__isl_take isl_qpolynomial
*qp
)
1738 return isl_qpolynomial_mul_isl_int(qp
, qp
->dim
->ctx
->negone
);
1741 __isl_give isl_qpolynomial
*isl_qpolynomial_mul_isl_int(
1742 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1744 if (isl_int_is_one(v
))
1747 if (qp
&& isl_int_is_zero(v
)) {
1748 isl_qpolynomial
*zero
;
1749 zero
= isl_qpolynomial_zero_on_domain(isl_space_copy(qp
->dim
));
1750 isl_qpolynomial_free(qp
);
1754 qp
= isl_qpolynomial_cow(qp
);
1758 qp
->poly
= isl_poly_mul_isl_int(qp
->poly
, v
);
1764 isl_qpolynomial_free(qp
);
1768 __isl_give isl_qpolynomial
*isl_qpolynomial_scale(
1769 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1771 return isl_qpolynomial_mul_isl_int(qp
, v
);
1774 /* Multiply "qp" by "v".
1776 __isl_give isl_qpolynomial
*isl_qpolynomial_scale_val(
1777 __isl_take isl_qpolynomial
*qp
, __isl_take isl_val
*v
)
1782 if (!isl_val_is_rat(v
))
1783 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
1784 "expecting rational factor", goto error
);
1786 if (isl_val_is_one(v
)) {
1791 if (isl_val_is_zero(v
)) {
1794 space
= isl_qpolynomial_get_domain_space(qp
);
1795 isl_qpolynomial_free(qp
);
1797 return isl_qpolynomial_zero_on_domain(space
);
1800 qp
= isl_qpolynomial_cow(qp
);
1804 qp
->poly
= isl_poly_scale_val(qp
->poly
, v
);
1806 qp
= isl_qpolynomial_free(qp
);
1812 isl_qpolynomial_free(qp
);
1816 /* Divide "qp" by "v".
1818 __isl_give isl_qpolynomial
*isl_qpolynomial_scale_down_val(
1819 __isl_take isl_qpolynomial
*qp
, __isl_take isl_val
*v
)
1824 if (!isl_val_is_rat(v
))
1825 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
1826 "expecting rational factor", goto error
);
1827 if (isl_val_is_zero(v
))
1828 isl_die(isl_val_get_ctx(v
), isl_error_invalid
,
1829 "cannot scale down by zero", goto error
);
1831 return isl_qpolynomial_scale_val(qp
, isl_val_inv(v
));
1834 isl_qpolynomial_free(qp
);
1838 __isl_give isl_qpolynomial
*isl_qpolynomial_mul(__isl_take isl_qpolynomial
*qp1
,
1839 __isl_take isl_qpolynomial
*qp2
)
1841 isl_bool compatible
;
1843 qp1
= isl_qpolynomial_cow(qp1
);
1848 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1849 return isl_qpolynomial_mul(qp2
, qp1
);
1851 isl_assert(qp1
->dim
->ctx
, isl_space_is_equal(qp1
->dim
, qp2
->dim
), goto error
);
1852 compatible
= compatible_divs(qp1
->div
, qp2
->div
);
1856 return with_merged_divs(isl_qpolynomial_mul
, qp1
, qp2
);
1858 qp1
->poly
= isl_poly_mul(qp1
->poly
, isl_poly_copy(qp2
->poly
));
1862 isl_qpolynomial_free(qp2
);
1866 isl_qpolynomial_free(qp1
);
1867 isl_qpolynomial_free(qp2
);
1871 __isl_give isl_qpolynomial
*isl_qpolynomial_pow(__isl_take isl_qpolynomial
*qp
,
1874 qp
= isl_qpolynomial_cow(qp
);
1879 qp
->poly
= isl_poly_pow(qp
->poly
, power
);
1885 isl_qpolynomial_free(qp
);
1889 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_pow(
1890 __isl_take isl_pw_qpolynomial
*pwqp
, unsigned power
)
1897 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
1901 for (i
= 0; i
< pwqp
->n
; ++i
) {
1902 pwqp
->p
[i
].qp
= isl_qpolynomial_pow(pwqp
->p
[i
].qp
, power
);
1904 return isl_pw_qpolynomial_free(pwqp
);
1910 __isl_give isl_qpolynomial
*isl_qpolynomial_zero_on_domain(
1911 __isl_take isl_space
*domain
)
1915 return isl_qpolynomial_alloc(domain
, 0, isl_poly_zero(domain
->ctx
));
1918 __isl_give isl_qpolynomial
*isl_qpolynomial_one_on_domain(
1919 __isl_take isl_space
*domain
)
1923 return isl_qpolynomial_alloc(domain
, 0, isl_poly_one(domain
->ctx
));
1926 __isl_give isl_qpolynomial
*isl_qpolynomial_infty_on_domain(
1927 __isl_take isl_space
*domain
)
1931 return isl_qpolynomial_alloc(domain
, 0, isl_poly_infty(domain
->ctx
));
1934 __isl_give isl_qpolynomial
*isl_qpolynomial_neginfty_on_domain(
1935 __isl_take isl_space
*domain
)
1939 return isl_qpolynomial_alloc(domain
, 0, isl_poly_neginfty(domain
->ctx
));
1942 __isl_give isl_qpolynomial
*isl_qpolynomial_nan_on_domain(
1943 __isl_take isl_space
*domain
)
1947 return isl_qpolynomial_alloc(domain
, 0, isl_poly_nan(domain
->ctx
));
1950 __isl_give isl_qpolynomial
*isl_qpolynomial_cst_on_domain(
1951 __isl_take isl_space
*domain
,
1954 struct isl_qpolynomial
*qp
;
1957 qp
= isl_qpolynomial_zero_on_domain(domain
);
1961 cst
= isl_poly_as_cst(qp
->poly
);
1962 isl_int_set(cst
->n
, v
);
1967 isl_bool
isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial
*qp
,
1968 isl_int
*n
, isl_int
*d
)
1974 return isl_bool_error
;
1976 is_cst
= isl_poly_is_cst(qp
->poly
);
1977 if (is_cst
< 0 || !is_cst
)
1980 cst
= isl_poly_as_cst(qp
->poly
);
1982 return isl_bool_error
;
1985 isl_int_set(*n
, cst
->n
);
1987 isl_int_set(*d
, cst
->d
);
1989 return isl_bool_true
;
1992 /* Return the constant term of "poly".
1994 static __isl_give isl_val
*isl_poly_get_constant_val(__isl_keep isl_poly
*poly
)
2002 while ((is_cst
= isl_poly_is_cst(poly
)) == isl_bool_false
) {
2005 rec
= isl_poly_as_rec(poly
);
2013 cst
= isl_poly_as_cst(poly
);
2016 return isl_val_rat_from_isl_int(cst
->poly
.ctx
, cst
->n
, cst
->d
);
2019 /* Return the constant term of "qp".
2021 __isl_give isl_val
*isl_qpolynomial_get_constant_val(
2022 __isl_keep isl_qpolynomial
*qp
)
2027 return isl_poly_get_constant_val(qp
->poly
);
2030 isl_bool
isl_poly_is_affine(__isl_keep isl_poly
*poly
)
2036 return isl_bool_error
;
2039 return isl_bool_true
;
2041 rec
= isl_poly_as_rec(poly
);
2043 return isl_bool_error
;
2046 return isl_bool_false
;
2048 isl_assert(poly
->ctx
, rec
->n
> 1, return isl_bool_error
);
2050 is_cst
= isl_poly_is_cst(rec
->p
[1]);
2051 if (is_cst
< 0 || !is_cst
)
2054 return isl_poly_is_affine(rec
->p
[0]);
2057 isl_bool
isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial
*qp
)
2060 return isl_bool_error
;
2062 if (qp
->div
->n_row
> 0)
2063 return isl_bool_false
;
2065 return isl_poly_is_affine(qp
->poly
);
2068 static void update_coeff(__isl_keep isl_vec
*aff
,
2069 __isl_keep isl_poly_cst
*cst
, int pos
)
2074 if (isl_int_is_zero(cst
->n
))
2079 isl_int_gcd(gcd
, cst
->d
, aff
->el
[0]);
2080 isl_int_divexact(f
, cst
->d
, gcd
);
2081 isl_int_divexact(gcd
, aff
->el
[0], gcd
);
2082 isl_seq_scale(aff
->el
, aff
->el
, f
, aff
->size
);
2083 isl_int_mul(aff
->el
[1 + pos
], gcd
, cst
->n
);
2088 int isl_poly_update_affine(__isl_keep isl_poly
*poly
, __isl_keep isl_vec
*aff
)
2096 if (poly
->var
< 0) {
2099 cst
= isl_poly_as_cst(poly
);
2102 update_coeff(aff
, cst
, 0);
2106 rec
= isl_poly_as_rec(poly
);
2109 isl_assert(poly
->ctx
, rec
->n
== 2, return -1);
2111 cst
= isl_poly_as_cst(rec
->p
[1]);
2114 update_coeff(aff
, cst
, 1 + poly
->var
);
2116 return isl_poly_update_affine(rec
->p
[0], aff
);
2119 __isl_give isl_vec
*isl_qpolynomial_extract_affine(
2120 __isl_keep isl_qpolynomial
*qp
)
2125 d
= isl_qpolynomial_domain_dim(qp
, isl_dim_all
);
2129 aff
= isl_vec_alloc(qp
->div
->ctx
, 2 + d
);
2133 isl_seq_clr(aff
->el
+ 1, 1 + d
);
2134 isl_int_set_si(aff
->el
[0], 1);
2136 if (isl_poly_update_affine(qp
->poly
, aff
) < 0)
2145 /* Compare two quasi-polynomials.
2147 * Return -1 if "qp1" is "smaller" than "qp2", 1 if "qp1" is "greater"
2148 * than "qp2" and 0 if they are equal.
2150 int isl_qpolynomial_plain_cmp(__isl_keep isl_qpolynomial
*qp1
,
2151 __isl_keep isl_qpolynomial
*qp2
)
2162 cmp
= isl_space_cmp(qp1
->dim
, qp2
->dim
);
2166 cmp
= isl_local_cmp(qp1
->div
, qp2
->div
);
2170 return isl_poly_plain_cmp(qp1
->poly
, qp2
->poly
);
2173 /* Is "qp1" obviously equal to "qp2"?
2175 * NaN is not equal to anything, not even to another NaN.
2177 isl_bool
isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial
*qp1
,
2178 __isl_keep isl_qpolynomial
*qp2
)
2183 return isl_bool_error
;
2185 if (isl_qpolynomial_is_nan(qp1
) || isl_qpolynomial_is_nan(qp2
))
2186 return isl_bool_false
;
2188 equal
= isl_space_is_equal(qp1
->dim
, qp2
->dim
);
2189 if (equal
< 0 || !equal
)
2192 equal
= isl_mat_is_equal(qp1
->div
, qp2
->div
);
2193 if (equal
< 0 || !equal
)
2196 return isl_poly_is_equal(qp1
->poly
, qp2
->poly
);
2199 static isl_stat
poly_update_den(__isl_keep isl_poly
*poly
, isl_int
*d
)
2205 is_cst
= isl_poly_is_cst(poly
);
2207 return isl_stat_error
;
2210 cst
= isl_poly_as_cst(poly
);
2212 return isl_stat_error
;
2213 isl_int_lcm(*d
, *d
, cst
->d
);
2217 rec
= isl_poly_as_rec(poly
);
2219 return isl_stat_error
;
2221 for (i
= 0; i
< rec
->n
; ++i
)
2222 poly_update_den(rec
->p
[i
], d
);
2227 __isl_give isl_val
*isl_qpolynomial_get_den(__isl_keep isl_qpolynomial
*qp
)
2233 d
= isl_val_one(isl_qpolynomial_get_ctx(qp
));
2236 if (poly_update_den(qp
->poly
, &d
->n
) < 0)
2237 return isl_val_free(d
);
2241 __isl_give isl_qpolynomial
*isl_qpolynomial_var_pow_on_domain(
2242 __isl_take isl_space
*domain
, int pos
, int power
)
2244 struct isl_ctx
*ctx
;
2251 return isl_qpolynomial_alloc(domain
, 0,
2252 isl_poly_var_pow(ctx
, pos
, power
));
2255 __isl_give isl_qpolynomial
*isl_qpolynomial_var_on_domain(
2256 __isl_take isl_space
*domain
, enum isl_dim_type type
, unsigned pos
)
2258 if (isl_space_check_is_set(domain
) < 0)
2260 if (isl_space_check_range(domain
, type
, pos
, 1) < 0)
2263 pos
+= isl_space_offset(domain
, type
);
2265 return isl_qpolynomial_var_pow_on_domain(domain
, pos
, 1);
2267 isl_space_free(domain
);
2271 __isl_give isl_poly
*isl_poly_subs(__isl_take isl_poly
*poly
,
2272 unsigned first
, unsigned n
, __isl_keep isl_poly
**subs
)
2277 isl_poly
*base
, *res
;
2279 is_cst
= isl_poly_is_cst(poly
);
2281 return isl_poly_free(poly
);
2285 if (poly
->var
< first
)
2288 rec
= isl_poly_as_rec(poly
);
2292 isl_assert(poly
->ctx
, rec
->n
>= 1, goto error
);
2294 if (poly
->var
>= first
+ n
)
2295 base
= isl_poly_var_pow(poly
->ctx
, poly
->var
, 1);
2297 base
= isl_poly_copy(subs
[poly
->var
- first
]);
2299 res
= isl_poly_subs(isl_poly_copy(rec
->p
[rec
->n
- 1]), first
, n
, subs
);
2300 for (i
= rec
->n
- 2; i
>= 0; --i
) {
2302 t
= isl_poly_subs(isl_poly_copy(rec
->p
[i
]), first
, n
, subs
);
2303 res
= isl_poly_mul(res
, isl_poly_copy(base
));
2304 res
= isl_poly_sum(res
, t
);
2307 isl_poly_free(base
);
2308 isl_poly_free(poly
);
2312 isl_poly_free(poly
);
2316 __isl_give isl_poly
*isl_poly_from_affine(isl_ctx
*ctx
, isl_int
*f
,
2317 isl_int denom
, unsigned len
)
2322 isl_assert(ctx
, len
>= 1, return NULL
);
2324 poly
= isl_poly_rat_cst(ctx
, f
[0], denom
);
2325 for (i
= 0; i
< len
- 1; ++i
) {
2329 if (isl_int_is_zero(f
[1 + i
]))
2332 c
= isl_poly_rat_cst(ctx
, f
[1 + i
], denom
);
2333 t
= isl_poly_var_pow(ctx
, i
, 1);
2334 t
= isl_poly_mul(c
, t
);
2335 poly
= isl_poly_sum(poly
, t
);
2341 /* Remove common factor of non-constant terms and denominator.
2343 static void normalize_div(__isl_keep isl_qpolynomial
*qp
, int div
)
2345 isl_ctx
*ctx
= qp
->div
->ctx
;
2346 unsigned total
= qp
->div
->n_col
- 2;
2348 isl_seq_gcd(qp
->div
->row
[div
] + 2, total
, &ctx
->normalize_gcd
);
2349 isl_int_gcd(ctx
->normalize_gcd
,
2350 ctx
->normalize_gcd
, qp
->div
->row
[div
][0]);
2351 if (isl_int_is_one(ctx
->normalize_gcd
))
2354 isl_seq_scale_down(qp
->div
->row
[div
] + 2, qp
->div
->row
[div
] + 2,
2355 ctx
->normalize_gcd
, total
);
2356 isl_int_divexact(qp
->div
->row
[div
][0], qp
->div
->row
[div
][0],
2357 ctx
->normalize_gcd
);
2358 isl_int_fdiv_q(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1],
2359 ctx
->normalize_gcd
);
2362 /* Replace the integer division identified by "div" by the polynomial "s".
2363 * The integer division is assumed not to appear in the definition
2364 * of any other integer divisions.
2366 static __isl_give isl_qpolynomial
*substitute_div(
2367 __isl_take isl_qpolynomial
*qp
, int div
, __isl_take isl_poly
*s
)
2377 qp
= isl_qpolynomial_cow(qp
);
2381 div_pos
= isl_qpolynomial_domain_var_offset(qp
, isl_dim_div
);
2384 qp
->poly
= isl_poly_subs(qp
->poly
, div_pos
+ div
, 1, &s
);
2388 ctx
= isl_qpolynomial_get_ctx(qp
);
2389 reordering
= isl_alloc_array(ctx
, int, div_pos
+ qp
->div
->n_row
);
2392 for (i
= 0; i
< div_pos
+ div
; ++i
)
2394 for (i
= div_pos
+ div
+ 1; i
< div_pos
+ qp
->div
->n_row
; ++i
)
2395 reordering
[i
] = i
- 1;
2396 qp
->div
= isl_mat_drop_rows(qp
->div
, div
, 1);
2397 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + div_pos
+ div
, 1);
2398 qp
->poly
= reorder(qp
->poly
, reordering
);
2401 if (!qp
->poly
|| !qp
->div
)
2407 isl_qpolynomial_free(qp
);
2412 /* Replace all integer divisions [e/d] that turn out to not actually be integer
2413 * divisions because d is equal to 1 by their definition, i.e., e.
2415 static __isl_give isl_qpolynomial
*substitute_non_divs(
2416 __isl_take isl_qpolynomial
*qp
)
2422 div_pos
= isl_qpolynomial_domain_var_offset(qp
, isl_dim_div
);
2424 return isl_qpolynomial_free(qp
);
2426 for (i
= 0; qp
&& i
< qp
->div
->n_row
; ++i
) {
2427 if (!isl_int_is_one(qp
->div
->row
[i
][0]))
2429 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
2430 if (isl_int_is_zero(qp
->div
->row
[j
][2 + div_pos
+ i
]))
2432 isl_seq_combine(qp
->div
->row
[j
] + 1,
2433 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
2434 qp
->div
->row
[j
][2 + div_pos
+ i
],
2435 qp
->div
->row
[i
] + 1, 1 + div_pos
+ i
);
2436 isl_int_set_si(qp
->div
->row
[j
][2 + div_pos
+ i
], 0);
2437 normalize_div(qp
, j
);
2439 s
= isl_poly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
2440 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
2441 qp
= substitute_div(qp
, i
, s
);
2448 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
2449 * with d the denominator. When replacing the coefficient e of x by
2450 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
2451 * inside the division, so we need to add floor(e/d) * x outside.
2452 * That is, we replace q by q' + floor(e/d) * x and we therefore need
2453 * to adjust the coefficient of x in each later div that depends on the
2454 * current div "div" and also in the affine expressions in the rows of "mat"
2455 * (if they too depend on "div").
2457 static void reduce_div(__isl_keep isl_qpolynomial
*qp
, int div
,
2458 __isl_keep isl_mat
**mat
)
2462 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
2465 for (i
= 0; i
< 1 + total
+ div
; ++i
) {
2466 if (isl_int_is_nonneg(qp
->div
->row
[div
][1 + i
]) &&
2467 isl_int_lt(qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]))
2469 isl_int_fdiv_q(v
, qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
2470 isl_int_fdiv_r(qp
->div
->row
[div
][1 + i
],
2471 qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
2472 *mat
= isl_mat_col_addmul(*mat
, i
, v
, 1 + total
+ div
);
2473 for (j
= div
+ 1; j
< qp
->div
->n_row
; ++j
) {
2474 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ div
]))
2476 isl_int_addmul(qp
->div
->row
[j
][1 + i
],
2477 v
, qp
->div
->row
[j
][2 + total
+ div
]);
2483 /* Check if the last non-zero coefficient is bigger that half of the
2484 * denominator. If so, we will invert the div to further reduce the number
2485 * of distinct divs that may appear.
2486 * If the last non-zero coefficient is exactly half the denominator,
2487 * then we continue looking for earlier coefficients that are bigger
2488 * than half the denominator.
2490 static int needs_invert(__isl_keep isl_mat
*div
, int row
)
2495 for (i
= div
->n_col
- 1; i
>= 1; --i
) {
2496 if (isl_int_is_zero(div
->row
[row
][i
]))
2498 isl_int_mul_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
2499 cmp
= isl_int_cmp(div
->row
[row
][i
], div
->row
[row
][0]);
2500 isl_int_divexact_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
2510 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
2511 * We only invert the coefficients of e (and the coefficient of q in
2512 * later divs and in the rows of "mat"). After calling this function, the
2513 * coefficients of e should be reduced again.
2515 static void invert_div(__isl_keep isl_qpolynomial
*qp
, int div
,
2516 __isl_keep isl_mat
**mat
)
2518 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
2520 isl_seq_neg(qp
->div
->row
[div
] + 1,
2521 qp
->div
->row
[div
] + 1, qp
->div
->n_col
- 1);
2522 isl_int_sub_ui(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1], 1);
2523 isl_int_add(qp
->div
->row
[div
][1],
2524 qp
->div
->row
[div
][1], qp
->div
->row
[div
][0]);
2525 *mat
= isl_mat_col_neg(*mat
, 1 + total
+ div
);
2526 isl_mat_col_mul(qp
->div
, 2 + total
+ div
,
2527 qp
->div
->ctx
->negone
, 2 + total
+ div
);
2530 /* Reduce all divs of "qp" to have coefficients
2531 * in the interval [0, d-1], with d the denominator and such that the
2532 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2533 * The modifications to the integer divisions need to be reflected
2534 * in the factors of the polynomial that refer to the original
2535 * integer divisions. To this end, the modifications are collected
2536 * as a set of affine expressions and then plugged into the polynomial.
2538 * After the reduction, some divs may have become redundant or identical,
2539 * so we call substitute_non_divs and sort_divs. If these functions
2540 * eliminate divs or merge two or more divs into one, the coefficients
2541 * of the enclosing divs may have to be reduced again, so we call
2542 * ourselves recursively if the number of divs decreases.
2544 static __isl_give isl_qpolynomial
*reduce_divs(__isl_take isl_qpolynomial
*qp
)
2551 isl_size n_div
, total
, new_n_div
;
2553 total
= isl_qpolynomial_domain_dim(qp
, isl_dim_all
);
2554 n_div
= isl_qpolynomial_domain_dim(qp
, isl_dim_div
);
2555 o_div
= isl_qpolynomial_domain_offset(qp
, isl_dim_div
);
2556 if (total
< 0 || n_div
< 0)
2557 return isl_qpolynomial_free(qp
);
2558 ctx
= isl_qpolynomial_get_ctx(qp
);
2559 mat
= isl_mat_zero(ctx
, n_div
, 1 + total
);
2561 for (i
= 0; i
< n_div
; ++i
)
2562 mat
= isl_mat_set_element_si(mat
, i
, o_div
+ i
, 1);
2564 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2565 normalize_div(qp
, i
);
2566 reduce_div(qp
, i
, &mat
);
2567 if (needs_invert(qp
->div
, i
)) {
2568 invert_div(qp
, i
, &mat
);
2569 reduce_div(qp
, i
, &mat
);
2575 s
= isl_alloc_array(ctx
, struct isl_poly
*, n_div
);
2578 for (i
= 0; i
< n_div
; ++i
)
2579 s
[i
] = isl_poly_from_affine(ctx
, mat
->row
[i
], ctx
->one
,
2581 qp
->poly
= isl_poly_subs(qp
->poly
, o_div
- 1, n_div
, s
);
2582 for (i
= 0; i
< n_div
; ++i
)
2583 isl_poly_free(s
[i
]);
2590 qp
= substitute_non_divs(qp
);
2592 new_n_div
= isl_qpolynomial_domain_dim(qp
, isl_dim_div
);
2594 return isl_qpolynomial_free(qp
);
2595 if (new_n_div
< n_div
)
2596 return reduce_divs(qp
);
2600 isl_qpolynomial_free(qp
);
2605 __isl_give isl_qpolynomial
*isl_qpolynomial_rat_cst_on_domain(
2606 __isl_take isl_space
*domain
, const isl_int n
, const isl_int d
)
2608 struct isl_qpolynomial
*qp
;
2611 qp
= isl_qpolynomial_zero_on_domain(domain
);
2615 cst
= isl_poly_as_cst(qp
->poly
);
2616 isl_int_set(cst
->n
, n
);
2617 isl_int_set(cst
->d
, d
);
2622 /* Return an isl_qpolynomial that is equal to "val" on domain space "domain".
2624 __isl_give isl_qpolynomial
*isl_qpolynomial_val_on_domain(
2625 __isl_take isl_space
*domain
, __isl_take isl_val
*val
)
2627 isl_qpolynomial
*qp
;
2630 qp
= isl_qpolynomial_zero_on_domain(domain
);
2634 cst
= isl_poly_as_cst(qp
->poly
);
2635 isl_int_set(cst
->n
, val
->n
);
2636 isl_int_set(cst
->d
, val
->d
);
2642 isl_qpolynomial_free(qp
);
2646 static isl_stat
poly_set_active(__isl_keep isl_poly
*poly
, int *active
, int d
)
2652 is_cst
= isl_poly_is_cst(poly
);
2654 return isl_stat_error
;
2659 active
[poly
->var
] = 1;
2661 rec
= isl_poly_as_rec(poly
);
2662 for (i
= 0; i
< rec
->n
; ++i
)
2663 if (poly_set_active(rec
->p
[i
], active
, d
) < 0)
2664 return isl_stat_error
;
2669 static isl_stat
set_active(__isl_keep isl_qpolynomial
*qp
, int *active
)
2675 space
= isl_qpolynomial_peek_domain_space(qp
);
2676 d
= isl_space_dim(space
, isl_dim_all
);
2677 if (d
< 0 || !active
)
2678 return isl_stat_error
;
2680 for (i
= 0; i
< d
; ++i
)
2681 for (j
= 0; j
< qp
->div
->n_row
; ++j
) {
2682 if (isl_int_is_zero(qp
->div
->row
[j
][2 + i
]))
2688 return poly_set_active(qp
->poly
, active
, d
);
2692 #define TYPE isl_qpolynomial
2694 #include "check_type_range_templ.c"
2696 isl_bool
isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial
*qp
,
2697 enum isl_dim_type type
, unsigned first
, unsigned n
)
2701 isl_bool involves
= isl_bool_false
;
2707 return isl_bool_error
;
2709 return isl_bool_false
;
2711 if (isl_qpolynomial_check_range(qp
, type
, first
, n
) < 0)
2712 return isl_bool_error
;
2713 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2714 type
== isl_dim_in
, return isl_bool_error
);
2716 space
= isl_qpolynomial_peek_domain_space(qp
);
2717 d
= isl_space_dim(space
, isl_dim_all
);
2719 return isl_bool_error
;
2720 active
= isl_calloc_array(qp
->dim
->ctx
, int, d
);
2721 if (set_active(qp
, active
) < 0)
2724 offset
= isl_qpolynomial_domain_var_offset(qp
, domain_type(type
));
2728 for (i
= 0; i
< n
; ++i
)
2729 if (active
[first
+ i
]) {
2730 involves
= isl_bool_true
;
2739 return isl_bool_error
;
2742 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2743 * of the divs that do appear in the quasi-polynomial.
2745 static __isl_give isl_qpolynomial
*remove_redundant_divs(
2746 __isl_take isl_qpolynomial
*qp
)
2753 int *reordering
= NULL
;
2760 if (qp
->div
->n_row
== 0)
2763 div_pos
= isl_qpolynomial_domain_var_offset(qp
, isl_dim_div
);
2765 return isl_qpolynomial_free(qp
);
2766 len
= qp
->div
->n_col
- 2;
2767 ctx
= isl_qpolynomial_get_ctx(qp
);
2768 active
= isl_calloc_array(ctx
, int, len
);
2772 if (poly_set_active(qp
->poly
, active
, len
) < 0)
2775 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
2776 if (!active
[div_pos
+ i
]) {
2780 for (j
= 0; j
< i
; ++j
) {
2781 if (isl_int_is_zero(qp
->div
->row
[i
][2 + div_pos
+ j
]))
2783 active
[div_pos
+ j
] = 1;
2793 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
2797 for (i
= 0; i
< div_pos
; ++i
)
2801 n_div
= qp
->div
->n_row
;
2802 for (i
= 0; i
< n_div
; ++i
) {
2803 if (!active
[div_pos
+ i
]) {
2804 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
2805 qp
->div
= isl_mat_drop_cols(qp
->div
,
2806 2 + div_pos
+ i
- skip
, 1);
2809 reordering
[div_pos
+ i
] = div_pos
+ i
- skip
;
2812 qp
->poly
= reorder(qp
->poly
, reordering
);
2814 if (!qp
->poly
|| !qp
->div
)
2824 isl_qpolynomial_free(qp
);
2828 __isl_give isl_poly
*isl_poly_drop(__isl_take isl_poly
*poly
,
2829 unsigned first
, unsigned n
)
2836 if (n
== 0 || poly
->var
< 0 || poly
->var
< first
)
2838 if (poly
->var
< first
+ n
) {
2839 poly
= replace_by_constant_term(poly
);
2840 return isl_poly_drop(poly
, first
, n
);
2842 poly
= isl_poly_cow(poly
);
2846 rec
= isl_poly_as_rec(poly
);
2850 for (i
= 0; i
< rec
->n
; ++i
) {
2851 rec
->p
[i
] = isl_poly_drop(rec
->p
[i
], first
, n
);
2858 isl_poly_free(poly
);
2862 __isl_give isl_qpolynomial
*isl_qpolynomial_set_dim_name(
2863 __isl_take isl_qpolynomial
*qp
,
2864 enum isl_dim_type type
, unsigned pos
, const char *s
)
2866 qp
= isl_qpolynomial_cow(qp
);
2869 if (type
== isl_dim_out
)
2870 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
2871 "cannot set name of output/set dimension",
2872 return isl_qpolynomial_free(qp
));
2873 type
= domain_type(type
);
2874 qp
->dim
= isl_space_set_dim_name(qp
->dim
, type
, pos
, s
);
2879 isl_qpolynomial_free(qp
);
2883 __isl_give isl_qpolynomial
*isl_qpolynomial_drop_dims(
2884 __isl_take isl_qpolynomial
*qp
,
2885 enum isl_dim_type type
, unsigned first
, unsigned n
)
2891 if (type
== isl_dim_out
)
2892 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
2893 "cannot drop output/set dimension",
2895 if (isl_qpolynomial_check_range(qp
, type
, first
, n
) < 0)
2896 return isl_qpolynomial_free(qp
);
2897 type
= domain_type(type
);
2898 if (n
== 0 && !isl_space_is_named_or_nested(qp
->dim
, type
))
2901 qp
= isl_qpolynomial_cow(qp
);
2905 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2906 type
== isl_dim_set
, goto error
);
2908 qp
->dim
= isl_space_drop_dims(qp
->dim
, type
, first
, n
);
2912 offset
= isl_qpolynomial_domain_var_offset(qp
, type
);
2917 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + first
, n
);
2921 qp
->poly
= isl_poly_drop(qp
->poly
, first
, n
);
2927 isl_qpolynomial_free(qp
);
2931 /* Project the domain of the quasi-polynomial onto its parameter space.
2932 * The quasi-polynomial may not involve any of the domain dimensions.
2934 __isl_give isl_qpolynomial
*isl_qpolynomial_project_domain_on_params(
2935 __isl_take isl_qpolynomial
*qp
)
2941 n
= isl_qpolynomial_dim(qp
, isl_dim_in
);
2943 return isl_qpolynomial_free(qp
);
2944 involves
= isl_qpolynomial_involves_dims(qp
, isl_dim_in
, 0, n
);
2946 return isl_qpolynomial_free(qp
);
2948 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
2949 "polynomial involves some of the domain dimensions",
2950 return isl_qpolynomial_free(qp
));
2951 qp
= isl_qpolynomial_drop_dims(qp
, isl_dim_in
, 0, n
);
2952 space
= isl_qpolynomial_get_domain_space(qp
);
2953 space
= isl_space_params(space
);
2954 qp
= isl_qpolynomial_reset_domain_space(qp
, space
);
2958 static __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities_lifted(
2959 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2969 if (eq
->n_eq
== 0) {
2970 isl_basic_set_free(eq
);
2974 qp
= isl_qpolynomial_cow(qp
);
2977 qp
->div
= isl_mat_cow(qp
->div
);
2981 total
= isl_basic_set_offset(eq
, isl_dim_div
);
2983 isl_int_init(denom
);
2984 for (i
= 0; i
< eq
->n_eq
; ++i
) {
2985 j
= isl_seq_last_non_zero(eq
->eq
[i
], total
+ n_div
);
2986 if (j
< 0 || j
== 0 || j
>= total
)
2989 for (k
= 0; k
< qp
->div
->n_row
; ++k
) {
2990 if (isl_int_is_zero(qp
->div
->row
[k
][1 + j
]))
2992 isl_seq_elim(qp
->div
->row
[k
] + 1, eq
->eq
[i
], j
, total
,
2993 &qp
->div
->row
[k
][0]);
2994 normalize_div(qp
, k
);
2997 if (isl_int_is_pos(eq
->eq
[i
][j
]))
2998 isl_seq_neg(eq
->eq
[i
], eq
->eq
[i
], total
);
2999 isl_int_abs(denom
, eq
->eq
[i
][j
]);
3000 isl_int_set_si(eq
->eq
[i
][j
], 0);
3002 poly
= isl_poly_from_affine(qp
->dim
->ctx
,
3003 eq
->eq
[i
], denom
, total
);
3004 qp
->poly
= isl_poly_subs(qp
->poly
, j
- 1, 1, &poly
);
3005 isl_poly_free(poly
);
3007 isl_int_clear(denom
);
3012 isl_basic_set_free(eq
);
3014 qp
= substitute_non_divs(qp
);
3019 isl_basic_set_free(eq
);
3020 isl_qpolynomial_free(qp
);
3024 /* Exploit the equalities in "eq" to simplify the quasi-polynomial.
3026 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities(
3027 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
3031 if (qp
->div
->n_row
> 0)
3032 eq
= isl_basic_set_add_dims(eq
, isl_dim_set
, qp
->div
->n_row
);
3033 return isl_qpolynomial_substitute_equalities_lifted(qp
, eq
);
3035 isl_basic_set_free(eq
);
3036 isl_qpolynomial_free(qp
);
3040 /* Look for equalities among the variables shared by context and qp
3041 * and the integer divisions of qp, if any.
3042 * The equalities are then used to eliminate variables and/or integer
3043 * divisions from qp.
3045 __isl_give isl_qpolynomial
*isl_qpolynomial_gist(
3046 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
3048 isl_local_space
*ls
;
3051 ls
= isl_qpolynomial_get_domain_local_space(qp
);
3052 context
= isl_local_space_lift_set(ls
, context
);
3054 aff
= isl_set_affine_hull(context
);
3055 return isl_qpolynomial_substitute_equalities_lifted(qp
, aff
);
3058 __isl_give isl_qpolynomial
*isl_qpolynomial_gist_params(
3059 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
3061 isl_space
*space
= isl_qpolynomial_get_domain_space(qp
);
3062 isl_set
*dom_context
= isl_set_universe(space
);
3063 dom_context
= isl_set_intersect_params(dom_context
, context
);
3064 return isl_qpolynomial_gist(qp
, dom_context
);
3067 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_from_qpolynomial(
3068 __isl_take isl_qpolynomial
*qp
)
3074 if (isl_qpolynomial_is_zero(qp
)) {
3075 isl_space
*dim
= isl_qpolynomial_get_space(qp
);
3076 isl_qpolynomial_free(qp
);
3077 return isl_pw_qpolynomial_zero(dim
);
3080 dom
= isl_set_universe(isl_qpolynomial_get_domain_space(qp
));
3081 return isl_pw_qpolynomial_alloc(dom
, qp
);
3084 #define isl_qpolynomial_involves_nan isl_qpolynomial_is_nan
3087 #define PW isl_pw_qpolynomial
3089 #define EL isl_qpolynomial
3091 #define EL_IS_ZERO is_zero
3095 #define IS_ZERO is_zero
3098 #undef DEFAULT_IS_ZERO
3099 #define DEFAULT_IS_ZERO 1
3103 #include <isl_pw_templ.c>
3104 #include <isl_pw_eval.c>
3107 #define BASE pw_qpolynomial
3109 #include <isl_union_single.c>
3110 #include <isl_union_eval.c>
3111 #include <isl_union_neg.c>
3113 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial
*pwqp
)
3121 if (!isl_set_plain_is_universe(pwqp
->p
[0].set
))
3124 return isl_qpolynomial_is_one(pwqp
->p
[0].qp
);
3127 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add(
3128 __isl_take isl_pw_qpolynomial
*pwqp1
,
3129 __isl_take isl_pw_qpolynomial
*pwqp2
)
3131 return isl_pw_qpolynomial_union_add_(pwqp1
, pwqp2
);
3134 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_mul(
3135 __isl_take isl_pw_qpolynomial
*pwqp1
,
3136 __isl_take isl_pw_qpolynomial
*pwqp2
)
3139 struct isl_pw_qpolynomial
*res
;
3141 if (!pwqp1
|| !pwqp2
)
3144 isl_assert(pwqp1
->dim
->ctx
, isl_space_is_equal(pwqp1
->dim
, pwqp2
->dim
),
3147 if (isl_pw_qpolynomial_is_zero(pwqp1
)) {
3148 isl_pw_qpolynomial_free(pwqp2
);
3152 if (isl_pw_qpolynomial_is_zero(pwqp2
)) {
3153 isl_pw_qpolynomial_free(pwqp1
);
3157 if (isl_pw_qpolynomial_is_one(pwqp1
)) {
3158 isl_pw_qpolynomial_free(pwqp1
);
3162 if (isl_pw_qpolynomial_is_one(pwqp2
)) {
3163 isl_pw_qpolynomial_free(pwqp2
);
3167 n
= pwqp1
->n
* pwqp2
->n
;
3168 res
= isl_pw_qpolynomial_alloc_size(isl_space_copy(pwqp1
->dim
), n
);
3170 for (i
= 0; i
< pwqp1
->n
; ++i
) {
3171 for (j
= 0; j
< pwqp2
->n
; ++j
) {
3172 struct isl_set
*common
;
3173 struct isl_qpolynomial
*prod
;
3174 common
= isl_set_intersect(isl_set_copy(pwqp1
->p
[i
].set
),
3175 isl_set_copy(pwqp2
->p
[j
].set
));
3176 if (isl_set_plain_is_empty(common
)) {
3177 isl_set_free(common
);
3181 prod
= isl_qpolynomial_mul(
3182 isl_qpolynomial_copy(pwqp1
->p
[i
].qp
),
3183 isl_qpolynomial_copy(pwqp2
->p
[j
].qp
));
3185 res
= isl_pw_qpolynomial_add_piece(res
, common
, prod
);
3189 isl_pw_qpolynomial_free(pwqp1
);
3190 isl_pw_qpolynomial_free(pwqp2
);
3194 isl_pw_qpolynomial_free(pwqp1
);
3195 isl_pw_qpolynomial_free(pwqp2
);
3199 __isl_give isl_val
*isl_poly_eval(__isl_take isl_poly
*poly
,
3200 __isl_take isl_vec
*vec
)
3208 is_cst
= isl_poly_is_cst(poly
);
3213 res
= isl_poly_get_constant_val(poly
);
3214 isl_poly_free(poly
);
3218 rec
= isl_poly_as_rec(poly
);
3222 isl_assert(poly
->ctx
, rec
->n
>= 1, goto error
);
3224 base
= isl_val_rat_from_isl_int(poly
->ctx
,
3225 vec
->el
[1 + poly
->var
], vec
->el
[0]);
3227 res
= isl_poly_eval(isl_poly_copy(rec
->p
[rec
->n
- 1]),
3230 for (i
= rec
->n
- 2; i
>= 0; --i
) {
3231 res
= isl_val_mul(res
, isl_val_copy(base
));
3232 res
= isl_val_add(res
, isl_poly_eval(isl_poly_copy(rec
->p
[i
]),
3233 isl_vec_copy(vec
)));
3237 isl_poly_free(poly
);
3241 isl_poly_free(poly
);
3246 /* Evaluate "qp" in the void point "pnt".
3247 * In particular, return the value NaN.
3249 static __isl_give isl_val
*eval_void(__isl_take isl_qpolynomial
*qp
,
3250 __isl_take isl_point
*pnt
)
3254 ctx
= isl_point_get_ctx(pnt
);
3255 isl_qpolynomial_free(qp
);
3256 isl_point_free(pnt
);
3257 return isl_val_nan(ctx
);
3260 __isl_give isl_val
*isl_qpolynomial_eval(__isl_take isl_qpolynomial
*qp
,
3261 __isl_take isl_point
*pnt
)
3269 isl_assert(pnt
->dim
->ctx
, isl_space_is_equal(pnt
->dim
, qp
->dim
), goto error
);
3270 is_void
= isl_point_is_void(pnt
);
3274 return eval_void(qp
, pnt
);
3276 ext
= isl_local_extend_point_vec(qp
->div
, isl_vec_copy(pnt
->vec
));
3278 v
= isl_poly_eval(isl_poly_copy(qp
->poly
), ext
);
3280 isl_qpolynomial_free(qp
);
3281 isl_point_free(pnt
);
3285 isl_qpolynomial_free(qp
);
3286 isl_point_free(pnt
);
3290 int isl_poly_cmp(__isl_keep isl_poly_cst
*cst1
, __isl_keep isl_poly_cst
*cst2
)
3295 isl_int_mul(t
, cst1
->n
, cst2
->d
);
3296 isl_int_submul(t
, cst2
->n
, cst1
->d
);
3297 cmp
= isl_int_sgn(t
);
3302 __isl_give isl_qpolynomial
*isl_qpolynomial_insert_dims(
3303 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
,
3304 unsigned first
, unsigned n
)
3312 if (type
== isl_dim_out
)
3313 isl_die(qp
->div
->ctx
, isl_error_invalid
,
3314 "cannot insert output/set dimensions",
3316 if (isl_qpolynomial_check_range(qp
, type
, first
, 0) < 0)
3317 return isl_qpolynomial_free(qp
);
3318 type
= domain_type(type
);
3319 if (n
== 0 && !isl_space_is_named_or_nested(qp
->dim
, type
))
3322 qp
= isl_qpolynomial_cow(qp
);
3326 g_pos
= pos(qp
->dim
, type
) + first
;
3328 qp
->div
= isl_mat_insert_zero_cols(qp
->div
, 2 + g_pos
, n
);
3332 total
= qp
->div
->n_col
- 2;
3333 if (total
> g_pos
) {
3335 exp
= isl_alloc_array(qp
->div
->ctx
, int, total
- g_pos
);
3338 for (i
= 0; i
< total
- g_pos
; ++i
)
3340 qp
->poly
= expand(qp
->poly
, exp
, g_pos
);
3346 qp
->dim
= isl_space_insert_dims(qp
->dim
, type
, first
, n
);
3352 isl_qpolynomial_free(qp
);
3356 __isl_give isl_qpolynomial
*isl_qpolynomial_add_dims(
3357 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
, unsigned n
)
3361 pos
= isl_qpolynomial_dim(qp
, type
);
3363 return isl_qpolynomial_free(qp
);
3365 return isl_qpolynomial_insert_dims(qp
, type
, pos
, n
);
3368 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add_dims(
3369 __isl_take isl_pw_qpolynomial
*pwqp
,
3370 enum isl_dim_type type
, unsigned n
)
3374 pos
= isl_pw_qpolynomial_dim(pwqp
, type
);
3376 return isl_pw_qpolynomial_free(pwqp
);
3378 return isl_pw_qpolynomial_insert_dims(pwqp
, type
, pos
, n
);
3381 static int *reordering_move(isl_ctx
*ctx
,
3382 unsigned len
, unsigned dst
, unsigned src
, unsigned n
)
3387 reordering
= isl_alloc_array(ctx
, int, len
);
3392 for (i
= 0; i
< dst
; ++i
)
3394 for (i
= 0; i
< n
; ++i
)
3395 reordering
[src
+ i
] = dst
+ i
;
3396 for (i
= 0; i
< src
- dst
; ++i
)
3397 reordering
[dst
+ i
] = dst
+ n
+ i
;
3398 for (i
= 0; i
< len
- src
- n
; ++i
)
3399 reordering
[src
+ n
+ i
] = src
+ n
+ i
;
3401 for (i
= 0; i
< src
; ++i
)
3403 for (i
= 0; i
< n
; ++i
)
3404 reordering
[src
+ i
] = dst
+ i
;
3405 for (i
= 0; i
< dst
- src
; ++i
)
3406 reordering
[src
+ n
+ i
] = src
+ i
;
3407 for (i
= 0; i
< len
- dst
- n
; ++i
)
3408 reordering
[dst
+ n
+ i
] = dst
+ n
+ i
;
3414 __isl_give isl_qpolynomial
*isl_qpolynomial_move_dims(
3415 __isl_take isl_qpolynomial
*qp
,
3416 enum isl_dim_type dst_type
, unsigned dst_pos
,
3417 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
3426 if (dst_type
== isl_dim_out
|| src_type
== isl_dim_out
)
3427 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
3428 "cannot move output/set dimension",
3430 if (isl_qpolynomial_check_range(qp
, src_type
, src_pos
, n
) < 0)
3431 return isl_qpolynomial_free(qp
);
3432 if (dst_type
== isl_dim_in
)
3433 dst_type
= isl_dim_set
;
3434 if (src_type
== isl_dim_in
)
3435 src_type
= isl_dim_set
;
3438 !isl_space_is_named_or_nested(qp
->dim
, src_type
) &&
3439 !isl_space_is_named_or_nested(qp
->dim
, dst_type
))
3442 qp
= isl_qpolynomial_cow(qp
);
3446 g_dst_pos
= pos(qp
->dim
, dst_type
) + dst_pos
;
3447 g_src_pos
= pos(qp
->dim
, src_type
) + src_pos
;
3448 if (dst_type
> src_type
)
3451 qp
->div
= isl_mat_move_cols(qp
->div
, 2 + g_dst_pos
, 2 + g_src_pos
, n
);
3458 reordering
= reordering_move(qp
->dim
->ctx
,
3459 qp
->div
->n_col
- 2, g_dst_pos
, g_src_pos
, n
);
3463 qp
->poly
= reorder(qp
->poly
, reordering
);
3468 qp
->dim
= isl_space_move_dims(qp
->dim
, dst_type
, dst_pos
, src_type
, src_pos
, n
);
3474 isl_qpolynomial_free(qp
);
3478 __isl_give isl_qpolynomial
*isl_qpolynomial_from_affine(
3479 __isl_take isl_space
*space
, isl_int
*f
, isl_int denom
)
3484 space
= isl_space_domain(space
);
3488 d
= isl_space_dim(space
, isl_dim_all
);
3489 poly
= d
< 0 ? NULL
: isl_poly_from_affine(space
->ctx
, f
, denom
, 1 + d
);
3491 return isl_qpolynomial_alloc(space
, 0, poly
);
3494 __isl_give isl_qpolynomial
*isl_qpolynomial_from_aff(__isl_take isl_aff
*aff
)
3498 isl_qpolynomial
*qp
;
3503 ctx
= isl_aff_get_ctx(aff
);
3504 poly
= isl_poly_from_affine(ctx
, aff
->v
->el
+ 1, aff
->v
->el
[0],
3507 qp
= isl_qpolynomial_alloc(isl_aff_get_domain_space(aff
),
3508 aff
->ls
->div
->n_row
, poly
);
3512 isl_mat_free(qp
->div
);
3513 qp
->div
= isl_mat_copy(aff
->ls
->div
);
3514 qp
->div
= isl_mat_cow(qp
->div
);
3519 qp
= reduce_divs(qp
);
3520 qp
= remove_redundant_divs(qp
);
3524 return isl_qpolynomial_free(qp
);
3527 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_from_pw_aff(
3528 __isl_take isl_pw_aff
*pwaff
)
3531 isl_pw_qpolynomial
*pwqp
;
3536 pwqp
= isl_pw_qpolynomial_alloc_size(isl_pw_aff_get_space(pwaff
),
3539 for (i
= 0; i
< pwaff
->n
; ++i
) {
3541 isl_qpolynomial
*qp
;
3543 dom
= isl_set_copy(pwaff
->p
[i
].set
);
3544 qp
= isl_qpolynomial_from_aff(isl_aff_copy(pwaff
->p
[i
].aff
));
3545 pwqp
= isl_pw_qpolynomial_add_piece(pwqp
, dom
, qp
);
3548 isl_pw_aff_free(pwaff
);
3552 __isl_give isl_qpolynomial
*isl_qpolynomial_from_constraint(
3553 __isl_take isl_constraint
*c
, enum isl_dim_type type
, unsigned pos
)
3557 aff
= isl_constraint_get_bound(c
, type
, pos
);
3558 isl_constraint_free(c
);
3559 return isl_qpolynomial_from_aff(aff
);
3562 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3563 * in "qp" by subs[i].
3565 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute(
3566 __isl_take isl_qpolynomial
*qp
,
3567 enum isl_dim_type type
, unsigned first
, unsigned n
,
3568 __isl_keep isl_qpolynomial
**subs
)
3576 qp
= isl_qpolynomial_cow(qp
);
3580 if (type
== isl_dim_out
)
3581 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
3582 "cannot substitute output/set dimension",
3584 if (isl_qpolynomial_check_range(qp
, type
, first
, n
) < 0)
3585 return isl_qpolynomial_free(qp
);
3586 type
= domain_type(type
);
3588 for (i
= 0; i
< n
; ++i
)
3592 for (i
= 0; i
< n
; ++i
)
3593 isl_assert(qp
->dim
->ctx
, isl_space_is_equal(qp
->dim
, subs
[i
]->dim
),
3596 isl_assert(qp
->dim
->ctx
, qp
->div
->n_row
== 0, goto error
);
3597 for (i
= 0; i
< n
; ++i
)
3598 isl_assert(qp
->dim
->ctx
, subs
[i
]->div
->n_row
== 0, goto error
);
3600 first
+= pos(qp
->dim
, type
);
3602 polys
= isl_alloc_array(qp
->dim
->ctx
, struct isl_poly
*, n
);
3605 for (i
= 0; i
< n
; ++i
)
3606 polys
[i
] = subs
[i
]->poly
;
3608 qp
->poly
= isl_poly_subs(qp
->poly
, first
, n
, polys
);
3617 isl_qpolynomial_free(qp
);
3621 /* Extend "bset" with extra set dimensions for each integer division
3622 * in "qp" and then call "fn" with the extended bset and the polynomial
3623 * that results from replacing each of the integer divisions by the
3624 * corresponding extra set dimension.
3626 isl_stat
isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial
*qp
,
3627 __isl_keep isl_basic_set
*bset
,
3628 isl_stat (*fn
)(__isl_take isl_basic_set
*bset
,
3629 __isl_take isl_qpolynomial
*poly
, void *user
), void *user
)
3632 isl_local_space
*ls
;
3633 isl_qpolynomial
*poly
;
3636 return isl_stat_error
;
3637 if (qp
->div
->n_row
== 0)
3638 return fn(isl_basic_set_copy(bset
), isl_qpolynomial_copy(qp
),
3641 space
= isl_space_copy(qp
->dim
);
3642 space
= isl_space_add_dims(space
, isl_dim_set
, qp
->div
->n_row
);
3643 poly
= isl_qpolynomial_alloc(space
, 0, isl_poly_copy(qp
->poly
));
3644 bset
= isl_basic_set_copy(bset
);
3645 ls
= isl_qpolynomial_get_domain_local_space(qp
);
3646 bset
= isl_local_space_lift_basic_set(ls
, bset
);
3648 return fn(bset
, poly
, user
);
3651 /* Return total degree in variables first (inclusive) up to last (exclusive).
3653 int isl_poly_degree(__isl_keep isl_poly
*poly
, int first
, int last
)
3657 isl_bool is_zero
, is_cst
;
3660 is_zero
= isl_poly_is_zero(poly
);
3665 is_cst
= isl_poly_is_cst(poly
);
3668 if (is_cst
|| poly
->var
< first
)
3671 rec
= isl_poly_as_rec(poly
);
3675 for (i
= 0; i
< rec
->n
; ++i
) {
3678 is_zero
= isl_poly_is_zero(rec
->p
[i
]);
3683 d
= isl_poly_degree(rec
->p
[i
], first
, last
);
3684 if (poly
->var
< last
)
3693 /* Return total degree in set variables.
3695 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial
*poly
)
3703 ovar
= isl_space_offset(poly
->dim
, isl_dim_set
);
3704 nvar
= isl_space_dim(poly
->dim
, isl_dim_set
);
3707 return isl_poly_degree(poly
->poly
, ovar
, ovar
+ nvar
);
3710 __isl_give isl_poly
*isl_poly_coeff(__isl_keep isl_poly
*poly
,
3711 unsigned pos
, int deg
)
3717 is_cst
= isl_poly_is_cst(poly
);
3720 if (is_cst
|| poly
->var
< pos
) {
3722 return isl_poly_copy(poly
);
3724 return isl_poly_zero(poly
->ctx
);
3727 rec
= isl_poly_as_rec(poly
);
3731 if (poly
->var
== pos
) {
3733 return isl_poly_copy(rec
->p
[deg
]);
3735 return isl_poly_zero(poly
->ctx
);
3738 poly
= isl_poly_copy(poly
);
3739 poly
= isl_poly_cow(poly
);
3740 rec
= isl_poly_as_rec(poly
);
3744 for (i
= 0; i
< rec
->n
; ++i
) {
3746 t
= isl_poly_coeff(rec
->p
[i
], pos
, deg
);
3749 isl_poly_free(rec
->p
[i
]);
3755 isl_poly_free(poly
);
3759 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3761 __isl_give isl_qpolynomial
*isl_qpolynomial_coeff(
3762 __isl_keep isl_qpolynomial
*qp
,
3763 enum isl_dim_type type
, unsigned t_pos
, int deg
)
3772 if (type
== isl_dim_out
)
3773 isl_die(qp
->div
->ctx
, isl_error_invalid
,
3774 "output/set dimension does not have a coefficient",
3776 if (isl_qpolynomial_check_range(qp
, type
, t_pos
, 1) < 0)
3778 type
= domain_type(type
);
3780 g_pos
= pos(qp
->dim
, type
) + t_pos
;
3781 poly
= isl_poly_coeff(qp
->poly
, g_pos
, deg
);
3783 c
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
),
3784 qp
->div
->n_row
, poly
);
3787 isl_mat_free(c
->div
);
3788 c
->div
= isl_mat_copy(qp
->div
);
3793 isl_qpolynomial_free(c
);
3797 /* Homogenize the polynomial in the variables first (inclusive) up to
3798 * last (exclusive) by inserting powers of variable first.
3799 * Variable first is assumed not to appear in the input.
3801 __isl_give isl_poly
*isl_poly_homogenize(__isl_take isl_poly
*poly
, int deg
,
3802 int target
, int first
, int last
)
3805 isl_bool is_zero
, is_cst
;
3808 is_zero
= isl_poly_is_zero(poly
);
3810 return isl_poly_free(poly
);
3815 is_cst
= isl_poly_is_cst(poly
);
3817 return isl_poly_free(poly
);
3818 if (is_cst
|| poly
->var
< first
) {
3821 hom
= isl_poly_var_pow(poly
->ctx
, first
, target
- deg
);
3824 rec
= isl_poly_as_rec(hom
);
3825 rec
->p
[target
- deg
] = isl_poly_mul(rec
->p
[target
- deg
], poly
);
3830 poly
= isl_poly_cow(poly
);
3831 rec
= isl_poly_as_rec(poly
);
3835 for (i
= 0; i
< rec
->n
; ++i
) {
3836 is_zero
= isl_poly_is_zero(rec
->p
[i
]);
3838 return isl_poly_free(poly
);
3841 rec
->p
[i
] = isl_poly_homogenize(rec
->p
[i
],
3842 poly
->var
< last
? deg
+ i
: i
, target
,
3850 isl_poly_free(poly
);
3854 /* Homogenize the polynomial in the set variables by introducing
3855 * powers of an extra set variable at position 0.
3857 __isl_give isl_qpolynomial
*isl_qpolynomial_homogenize(
3858 __isl_take isl_qpolynomial
*poly
)
3862 int deg
= isl_qpolynomial_degree(poly
);
3867 poly
= isl_qpolynomial_insert_dims(poly
, isl_dim_in
, 0, 1);
3868 poly
= isl_qpolynomial_cow(poly
);
3872 ovar
= isl_space_offset(poly
->dim
, isl_dim_set
);
3873 nvar
= isl_space_dim(poly
->dim
, isl_dim_set
);
3875 return isl_qpolynomial_free(poly
);
3876 poly
->poly
= isl_poly_homogenize(poly
->poly
, 0, deg
, ovar
, ovar
+ nvar
);
3882 isl_qpolynomial_free(poly
);
3886 __isl_give isl_term
*isl_term_alloc(__isl_take isl_space
*space
,
3887 __isl_take isl_mat
*div
)
3893 d
= isl_space_dim(space
, isl_dim_all
);
3899 term
= isl_calloc(space
->ctx
, struct isl_term
,
3900 sizeof(struct isl_term
) + (n
- 1) * sizeof(int));
3907 isl_int_init(term
->n
);
3908 isl_int_init(term
->d
);
3912 isl_space_free(space
);
3917 __isl_give isl_term
*isl_term_copy(__isl_keep isl_term
*term
)
3926 __isl_give isl_term
*isl_term_dup(__isl_keep isl_term
*term
)
3932 total
= isl_term_dim(term
, isl_dim_all
);
3936 dup
= isl_term_alloc(isl_space_copy(term
->dim
), isl_mat_copy(term
->div
));
3940 isl_int_set(dup
->n
, term
->n
);
3941 isl_int_set(dup
->d
, term
->d
);
3943 for (i
= 0; i
< total
; ++i
)
3944 dup
->pow
[i
] = term
->pow
[i
];
3949 __isl_give isl_term
*isl_term_cow(__isl_take isl_term
*term
)
3957 return isl_term_dup(term
);
3960 __isl_null isl_term
*isl_term_free(__isl_take isl_term
*term
)
3965 if (--term
->ref
> 0)
3968 isl_space_free(term
->dim
);
3969 isl_mat_free(term
->div
);
3970 isl_int_clear(term
->n
);
3971 isl_int_clear(term
->d
);
3977 isl_size
isl_term_dim(__isl_keep isl_term
*term
, enum isl_dim_type type
)
3982 return isl_size_error
;
3987 case isl_dim_out
: return isl_space_dim(term
->dim
, type
);
3988 case isl_dim_div
: return term
->div
->n_row
;
3989 case isl_dim_all
: dim
= isl_space_dim(term
->dim
, isl_dim_all
);
3991 return isl_size_error
;
3992 return dim
+ term
->div
->n_row
;
3993 default: return isl_size_error
;
3997 /* Return the space of "term".
3999 static __isl_keep isl_space
*isl_term_peek_space(__isl_keep isl_term
*term
)
4001 return term
? term
->dim
: NULL
;
4004 /* Return the offset of the first variable of type "type" within
4005 * the variables of "term".
4007 static isl_size
isl_term_offset(__isl_keep isl_term
*term
,
4008 enum isl_dim_type type
)
4012 space
= isl_term_peek_space(term
);
4014 return isl_size_error
;
4018 case isl_dim_set
: return isl_space_offset(space
, type
);
4019 case isl_dim_div
: return isl_space_dim(space
, isl_dim_all
);
4021 isl_die(isl_term_get_ctx(term
), isl_error_invalid
,
4022 "invalid dimension type", return isl_size_error
);
4026 isl_ctx
*isl_term_get_ctx(__isl_keep isl_term
*term
)
4028 return term
? term
->dim
->ctx
: NULL
;
4031 void isl_term_get_num(__isl_keep isl_term
*term
, isl_int
*n
)
4035 isl_int_set(*n
, term
->n
);
4038 /* Return the coefficient of the term "term".
4040 __isl_give isl_val
*isl_term_get_coefficient_val(__isl_keep isl_term
*term
)
4045 return isl_val_rat_from_isl_int(isl_term_get_ctx(term
),
4050 #define TYPE isl_term
4052 #include "check_type_range_templ.c"
4054 isl_size
isl_term_get_exp(__isl_keep isl_term
*term
,
4055 enum isl_dim_type type
, unsigned pos
)
4059 if (isl_term_check_range(term
, type
, pos
, 1) < 0)
4060 return isl_size_error
;
4061 offset
= isl_term_offset(term
, type
);
4063 return isl_size_error
;
4065 return term
->pow
[offset
+ pos
];
4068 __isl_give isl_aff
*isl_term_get_div(__isl_keep isl_term
*term
, unsigned pos
)
4070 isl_local_space
*ls
;
4073 if (isl_term_check_range(term
, isl_dim_div
, pos
, 1) < 0)
4076 ls
= isl_local_space_alloc_div(isl_space_copy(term
->dim
),
4077 isl_mat_copy(term
->div
));
4078 aff
= isl_aff_alloc(ls
);
4082 isl_seq_cpy(aff
->v
->el
, term
->div
->row
[pos
], aff
->v
->size
);
4084 aff
= isl_aff_normalize(aff
);
4089 __isl_give isl_term
*isl_poly_foreach_term(__isl_keep isl_poly
*poly
,
4090 isl_stat (*fn
)(__isl_take isl_term
*term
, void *user
),
4091 __isl_take isl_term
*term
, void *user
)
4094 isl_bool is_zero
, is_bad
, is_cst
;
4097 is_zero
= isl_poly_is_zero(poly
);
4098 if (is_zero
< 0 || !term
)
4104 is_cst
= isl_poly_is_cst(poly
);
4105 is_bad
= isl_poly_is_nan(poly
);
4106 if (is_bad
>= 0 && !is_bad
)
4107 is_bad
= isl_poly_is_infty(poly
);
4108 if (is_bad
>= 0 && !is_bad
)
4109 is_bad
= isl_poly_is_neginfty(poly
);
4110 if (is_cst
< 0 || is_bad
< 0)
4111 return isl_term_free(term
);
4113 isl_die(isl_term_get_ctx(term
), isl_error_invalid
,
4114 "cannot handle NaN/infty polynomial",
4115 return isl_term_free(term
));
4119 cst
= isl_poly_as_cst(poly
);
4122 term
= isl_term_cow(term
);
4125 isl_int_set(term
->n
, cst
->n
);
4126 isl_int_set(term
->d
, cst
->d
);
4127 if (fn(isl_term_copy(term
), user
) < 0)
4132 rec
= isl_poly_as_rec(poly
);
4136 for (i
= 0; i
< rec
->n
; ++i
) {
4137 term
= isl_term_cow(term
);
4140 term
->pow
[poly
->var
] = i
;
4141 term
= isl_poly_foreach_term(rec
->p
[i
], fn
, term
, user
);
4145 term
->pow
[poly
->var
] = 0;
4149 isl_term_free(term
);
4153 isl_stat
isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial
*qp
,
4154 isl_stat (*fn
)(__isl_take isl_term
*term
, void *user
), void *user
)
4159 return isl_stat_error
;
4161 term
= isl_term_alloc(isl_space_copy(qp
->dim
), isl_mat_copy(qp
->div
));
4163 return isl_stat_error
;
4165 term
= isl_poly_foreach_term(qp
->poly
, fn
, term
, user
);
4167 isl_term_free(term
);
4169 return term
? isl_stat_ok
: isl_stat_error
;
4172 __isl_give isl_qpolynomial
*isl_qpolynomial_from_term(__isl_take isl_term
*term
)
4175 isl_qpolynomial
*qp
;
4179 n
= isl_term_dim(term
, isl_dim_all
);
4181 term
= isl_term_free(term
);
4185 poly
= isl_poly_rat_cst(term
->dim
->ctx
, term
->n
, term
->d
);
4186 for (i
= 0; i
< n
; ++i
) {
4189 poly
= isl_poly_mul(poly
,
4190 isl_poly_var_pow(term
->dim
->ctx
, i
, term
->pow
[i
]));
4193 qp
= isl_qpolynomial_alloc(isl_space_copy(term
->dim
),
4194 term
->div
->n_row
, poly
);
4197 isl_mat_free(qp
->div
);
4198 qp
->div
= isl_mat_copy(term
->div
);
4202 isl_term_free(term
);
4205 isl_qpolynomial_free(qp
);
4206 isl_term_free(term
);
4210 __isl_give isl_qpolynomial
*isl_qpolynomial_lift(__isl_take isl_qpolynomial
*qp
,
4211 __isl_take isl_space
*space
)
4215 isl_size total
, d_set
, d_qp
;
4220 if (isl_space_is_equal(qp
->dim
, space
)) {
4221 isl_space_free(space
);
4225 qp
= isl_qpolynomial_cow(qp
);
4229 d_set
= isl_space_dim(space
, isl_dim_set
);
4230 d_qp
= isl_qpolynomial_domain_dim(qp
, isl_dim_set
);
4231 extra
= d_set
- d_qp
;
4232 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4233 if (d_set
< 0 || d_qp
< 0 || total
< 0)
4235 if (qp
->div
->n_row
) {
4238 exp
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
4241 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4243 qp
->poly
= expand(qp
->poly
, exp
, total
);
4248 qp
->div
= isl_mat_insert_cols(qp
->div
, 2 + total
, extra
);
4251 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4252 isl_seq_clr(qp
->div
->row
[i
] + 2 + total
, extra
);
4254 isl_space_free(qp
->dim
);
4259 isl_space_free(space
);
4260 isl_qpolynomial_free(qp
);
4264 /* For each parameter or variable that does not appear in qp,
4265 * first eliminate the variable from all constraints and then set it to zero.
4267 static __isl_give isl_set
*fix_inactive(__isl_take isl_set
*set
,
4268 __isl_keep isl_qpolynomial
*qp
)
4276 d
= isl_set_dim(set
, isl_dim_all
);
4280 active
= isl_calloc_array(set
->ctx
, int, d
);
4281 if (set_active(qp
, active
) < 0)
4284 for (i
= 0; i
< d
; ++i
)
4293 nparam
= isl_set_dim(set
, isl_dim_param
);
4294 nvar
= isl_set_dim(set
, isl_dim_set
);
4295 if (nparam
< 0 || nvar
< 0)
4297 for (i
= 0; i
< nparam
; ++i
) {
4300 set
= isl_set_eliminate(set
, isl_dim_param
, i
, 1);
4301 set
= isl_set_fix_si(set
, isl_dim_param
, i
, 0);
4303 for (i
= 0; i
< nvar
; ++i
) {
4304 if (active
[nparam
+ i
])
4306 set
= isl_set_eliminate(set
, isl_dim_set
, i
, 1);
4307 set
= isl_set_fix_si(set
, isl_dim_set
, i
, 0);
4319 struct isl_opt_data
{
4320 isl_qpolynomial
*qp
;
4326 static isl_stat
opt_fn(__isl_take isl_point
*pnt
, void *user
)
4328 struct isl_opt_data
*data
= (struct isl_opt_data
*)user
;
4331 val
= isl_qpolynomial_eval(isl_qpolynomial_copy(data
->qp
), pnt
);
4335 } else if (data
->max
) {
4336 data
->opt
= isl_val_max(data
->opt
, val
);
4338 data
->opt
= isl_val_min(data
->opt
, val
);
4344 __isl_give isl_val
*isl_qpolynomial_opt_on_domain(
4345 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*set
, int max
)
4347 struct isl_opt_data data
= { NULL
, 1, NULL
, max
};
4353 is_cst
= isl_poly_is_cst(qp
->poly
);
4358 data
.opt
= isl_qpolynomial_get_constant_val(qp
);
4359 isl_qpolynomial_free(qp
);
4363 set
= fix_inactive(set
, qp
);
4366 if (isl_set_foreach_point(set
, opt_fn
, &data
) < 0)
4370 data
.opt
= isl_val_zero(isl_set_get_ctx(set
));
4373 isl_qpolynomial_free(qp
);
4377 isl_qpolynomial_free(qp
);
4378 isl_val_free(data
.opt
);
4382 __isl_give isl_qpolynomial
*isl_qpolynomial_morph_domain(
4383 __isl_take isl_qpolynomial
*qp
, __isl_take isl_morph
*morph
)
4389 isl_mat
*mat
, *diag
;
4391 qp
= isl_qpolynomial_cow(qp
);
4396 isl_assert(ctx
, isl_space_is_equal(qp
->dim
, morph
->dom
->dim
), goto error
);
4398 n_sub
= morph
->inv
->n_row
- 1;
4399 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
4400 n_sub
+= qp
->div
->n_row
;
4401 subs
= isl_calloc_array(ctx
, struct isl_poly
*, n_sub
);
4405 for (i
= 0; 1 + i
< morph
->inv
->n_row
; ++i
)
4406 subs
[i
] = isl_poly_from_affine(ctx
, morph
->inv
->row
[1 + i
],
4407 morph
->inv
->row
[0][0], morph
->inv
->n_col
);
4408 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
4409 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4410 subs
[morph
->inv
->n_row
- 1 + i
] =
4411 isl_poly_var_pow(ctx
, morph
->inv
->n_col
- 1 + i
, 1);
4413 qp
->poly
= isl_poly_subs(qp
->poly
, 0, n_sub
, subs
);
4415 for (i
= 0; i
< n_sub
; ++i
)
4416 isl_poly_free(subs
[i
]);
4419 diag
= isl_mat_diag(ctx
, 1, morph
->inv
->row
[0][0]);
4420 mat
= isl_mat_diagonal(diag
, isl_mat_copy(morph
->inv
));
4421 diag
= isl_mat_diag(ctx
, qp
->div
->n_row
, morph
->inv
->row
[0][0]);
4422 mat
= isl_mat_diagonal(mat
, diag
);
4423 qp
->div
= isl_mat_product(qp
->div
, mat
);
4424 isl_space_free(qp
->dim
);
4425 qp
->dim
= isl_space_copy(morph
->ran
->dim
);
4427 if (!qp
->poly
|| !qp
->div
|| !qp
->dim
)
4430 isl_morph_free(morph
);
4434 isl_qpolynomial_free(qp
);
4435 isl_morph_free(morph
);
4439 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_mul(
4440 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
4441 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
4443 return isl_union_pw_qpolynomial_match_bin_op(upwqp1
, upwqp2
,
4444 &isl_pw_qpolynomial_mul
);
4447 /* Reorder the dimension of "qp" according to the given reordering.
4449 __isl_give isl_qpolynomial
*isl_qpolynomial_realign_domain(
4450 __isl_take isl_qpolynomial
*qp
, __isl_take isl_reordering
*r
)
4454 qp
= isl_qpolynomial_cow(qp
);
4458 r
= isl_reordering_extend(r
, qp
->div
->n_row
);
4462 qp
->div
= isl_local_reorder(qp
->div
, isl_reordering_copy(r
));
4466 qp
->poly
= reorder(qp
->poly
, r
->pos
);
4470 space
= isl_reordering_get_space(r
);
4471 qp
= isl_qpolynomial_reset_domain_space(qp
, space
);
4473 isl_reordering_free(r
);
4476 isl_qpolynomial_free(qp
);
4477 isl_reordering_free(r
);
4481 __isl_give isl_qpolynomial
*isl_qpolynomial_align_params(
4482 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*model
)
4484 isl_bool equal_params
;
4489 equal_params
= isl_space_has_equal_params(qp
->dim
, model
);
4490 if (equal_params
< 0)
4492 if (!equal_params
) {
4493 isl_reordering
*exp
;
4495 exp
= isl_parameter_alignment_reordering(qp
->dim
, model
);
4496 exp
= isl_reordering_extend_space(exp
,
4497 isl_qpolynomial_get_domain_space(qp
));
4498 qp
= isl_qpolynomial_realign_domain(qp
, exp
);
4501 isl_space_free(model
);
4504 isl_space_free(model
);
4505 isl_qpolynomial_free(qp
);
4509 struct isl_split_periods_data
{
4511 isl_pw_qpolynomial
*res
;
4514 /* Create a slice where the integer division "div" has the fixed value "v".
4515 * In particular, if "div" refers to floor(f/m), then create a slice
4517 * m v <= f <= m v + (m - 1)
4522 * -f + m v + (m - 1) >= 0
4524 static __isl_give isl_set
*set_div_slice(__isl_take isl_space
*space
,
4525 __isl_keep isl_qpolynomial
*qp
, int div
, isl_int v
)
4528 isl_basic_set
*bset
= NULL
;
4531 total
= isl_space_dim(space
, isl_dim_all
);
4532 if (total
< 0 || !qp
)
4535 bset
= isl_basic_set_alloc_space(isl_space_copy(space
), 0, 0, 2);
4537 k
= isl_basic_set_alloc_inequality(bset
);
4540 isl_seq_cpy(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4541 isl_int_submul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4543 k
= isl_basic_set_alloc_inequality(bset
);
4546 isl_seq_neg(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4547 isl_int_addmul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4548 isl_int_add(bset
->ineq
[k
][0], bset
->ineq
[k
][0], qp
->div
->row
[div
][0]);
4549 isl_int_sub_ui(bset
->ineq
[k
][0], bset
->ineq
[k
][0], 1);
4551 isl_space_free(space
);
4552 return isl_set_from_basic_set(bset
);
4554 isl_basic_set_free(bset
);
4555 isl_space_free(space
);
4559 static isl_stat
split_periods(__isl_take isl_set
*set
,
4560 __isl_take isl_qpolynomial
*qp
, void *user
);
4562 /* Create a slice of the domain "set" such that integer division "div"
4563 * has the fixed value "v" and add the results to data->res,
4564 * replacing the integer division by "v" in "qp".
4566 static isl_stat
set_div(__isl_take isl_set
*set
,
4567 __isl_take isl_qpolynomial
*qp
, int div
, isl_int v
,
4568 struct isl_split_periods_data
*data
)
4575 slice
= set_div_slice(isl_set_get_space(set
), qp
, div
, v
);
4576 set
= isl_set_intersect(set
, slice
);
4578 div_pos
= isl_qpolynomial_domain_var_offset(qp
, isl_dim_div
);
4582 for (i
= div
+ 1; i
< qp
->div
->n_row
; ++i
) {
4583 if (isl_int_is_zero(qp
->div
->row
[i
][2 + div_pos
+ div
]))
4585 isl_int_addmul(qp
->div
->row
[i
][1],
4586 qp
->div
->row
[i
][2 + div_pos
+ div
], v
);
4587 isl_int_set_si(qp
->div
->row
[i
][2 + div_pos
+ div
], 0);
4590 cst
= isl_poly_rat_cst(qp
->dim
->ctx
, v
, qp
->dim
->ctx
->one
);
4591 qp
= substitute_div(qp
, div
, cst
);
4593 return split_periods(set
, qp
, data
);
4596 isl_qpolynomial_free(qp
);
4597 return isl_stat_error
;
4600 /* Split the domain "set" such that integer division "div"
4601 * has a fixed value (ranging from "min" to "max") on each slice
4602 * and add the results to data->res.
4604 static isl_stat
split_div(__isl_take isl_set
*set
,
4605 __isl_take isl_qpolynomial
*qp
, int div
, isl_int min
, isl_int max
,
4606 struct isl_split_periods_data
*data
)
4608 for (; isl_int_le(min
, max
); isl_int_add_ui(min
, min
, 1)) {
4609 isl_set
*set_i
= isl_set_copy(set
);
4610 isl_qpolynomial
*qp_i
= isl_qpolynomial_copy(qp
);
4612 if (set_div(set_i
, qp_i
, div
, min
, data
) < 0)
4616 isl_qpolynomial_free(qp
);
4620 isl_qpolynomial_free(qp
);
4621 return isl_stat_error
;
4624 /* If "qp" refers to any integer division
4625 * that can only attain "max_periods" distinct values on "set"
4626 * then split the domain along those distinct values.
4627 * Add the results (or the original if no splitting occurs)
4630 static isl_stat
split_periods(__isl_take isl_set
*set
,
4631 __isl_take isl_qpolynomial
*qp
, void *user
)
4634 isl_pw_qpolynomial
*pwqp
;
4635 struct isl_split_periods_data
*data
;
4638 isl_stat r
= isl_stat_ok
;
4640 data
= (struct isl_split_periods_data
*)user
;
4645 if (qp
->div
->n_row
== 0) {
4646 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4647 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4651 div_pos
= isl_qpolynomial_domain_var_offset(qp
, isl_dim_div
);
4657 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4658 enum isl_lp_result lp_res
;
4660 if (isl_seq_first_non_zero(qp
->div
->row
[i
] + 2 + div_pos
,
4661 qp
->div
->n_row
) != -1)
4664 lp_res
= isl_set_solve_lp(set
, 0, qp
->div
->row
[i
] + 1,
4665 set
->ctx
->one
, &min
, NULL
, NULL
);
4666 if (lp_res
== isl_lp_error
)
4668 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4670 isl_int_fdiv_q(min
, min
, qp
->div
->row
[i
][0]);
4672 lp_res
= isl_set_solve_lp(set
, 1, qp
->div
->row
[i
] + 1,
4673 set
->ctx
->one
, &max
, NULL
, NULL
);
4674 if (lp_res
== isl_lp_error
)
4676 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4678 isl_int_fdiv_q(max
, max
, qp
->div
->row
[i
][0]);
4680 isl_int_sub(max
, max
, min
);
4681 if (isl_int_cmp_si(max
, data
->max_periods
) < 0) {
4682 isl_int_add(max
, max
, min
);
4687 if (i
< qp
->div
->n_row
) {
4688 r
= split_div(set
, qp
, i
, min
, max
, data
);
4690 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4691 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4703 isl_qpolynomial_free(qp
);
4704 return isl_stat_error
;
4707 /* If any quasi-polynomial in pwqp refers to any integer division
4708 * that can only attain "max_periods" distinct values on its domain
4709 * then split the domain along those distinct values.
4711 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_split_periods(
4712 __isl_take isl_pw_qpolynomial
*pwqp
, int max_periods
)
4714 struct isl_split_periods_data data
;
4716 data
.max_periods
= max_periods
;
4717 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp
));
4719 if (isl_pw_qpolynomial_foreach_piece(pwqp
, &split_periods
, &data
) < 0)
4722 isl_pw_qpolynomial_free(pwqp
);
4726 isl_pw_qpolynomial_free(data
.res
);
4727 isl_pw_qpolynomial_free(pwqp
);
4731 /* Construct a piecewise quasipolynomial that is constant on the given
4732 * domain. In particular, it is
4735 * infinity if cst == -1
4737 * If cst == -1, then explicitly check whether the domain is empty and,
4738 * if so, return 0 instead.
4740 static __isl_give isl_pw_qpolynomial
*constant_on_domain(
4741 __isl_take isl_basic_set
*bset
, int cst
)
4744 isl_qpolynomial
*qp
;
4746 if (cst
< 0 && isl_basic_set_is_empty(bset
) == isl_bool_true
)
4751 bset
= isl_basic_set_params(bset
);
4752 dim
= isl_basic_set_get_space(bset
);
4754 qp
= isl_qpolynomial_infty_on_domain(dim
);
4756 qp
= isl_qpolynomial_zero_on_domain(dim
);
4758 qp
= isl_qpolynomial_one_on_domain(dim
);
4759 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset
), qp
);
4762 /* Factor bset, call fn on each of the factors and return the product.
4764 * If no factors can be found, simply call fn on the input.
4765 * Otherwise, construct the factors based on the factorizer,
4766 * call fn on each factor and compute the product.
4768 static __isl_give isl_pw_qpolynomial
*compressed_multiplicative_call(
4769 __isl_take isl_basic_set
*bset
,
4770 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4776 isl_qpolynomial
*qp
;
4777 isl_pw_qpolynomial
*pwqp
;
4781 f
= isl_basic_set_factorizer(bset
);
4784 if (f
->n_group
== 0) {
4785 isl_factorizer_free(f
);
4789 nparam
= isl_basic_set_dim(bset
, isl_dim_param
);
4790 nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
4791 if (nparam
< 0 || nvar
< 0)
4792 bset
= isl_basic_set_free(bset
);
4794 space
= isl_basic_set_get_space(bset
);
4795 space
= isl_space_params(space
);
4796 set
= isl_set_universe(isl_space_copy(space
));
4797 qp
= isl_qpolynomial_one_on_domain(space
);
4798 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4800 bset
= isl_morph_basic_set(isl_morph_copy(f
->morph
), bset
);
4802 for (i
= 0, n
= 0; i
< f
->n_group
; ++i
) {
4803 isl_basic_set
*bset_i
;
4804 isl_pw_qpolynomial
*pwqp_i
;
4806 bset_i
= isl_basic_set_copy(bset
);
4807 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4808 nparam
+ n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4809 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4811 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
,
4812 n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4813 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
, 0, n
);
4815 pwqp_i
= fn(bset_i
);
4816 pwqp
= isl_pw_qpolynomial_mul(pwqp
, pwqp_i
);
4821 isl_basic_set_free(bset
);
4822 isl_factorizer_free(f
);
4826 isl_basic_set_free(bset
);
4830 /* Factor bset, call fn on each of the factors and return the product.
4831 * The function is assumed to evaluate to zero on empty domains,
4832 * to one on zero-dimensional domains and to infinity on unbounded domains
4833 * and will not be called explicitly on zero-dimensional or unbounded domains.
4835 * We first check for some special cases and remove all equalities.
4836 * Then we hand over control to compressed_multiplicative_call.
4838 __isl_give isl_pw_qpolynomial
*isl_basic_set_multiplicative_call(
4839 __isl_take isl_basic_set
*bset
,
4840 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4845 isl_pw_qpolynomial
*pwqp
;
4850 if (isl_basic_set_plain_is_empty(bset
))
4851 return constant_on_domain(bset
, 0);
4853 dim
= isl_basic_set_dim(bset
, isl_dim_set
);
4857 return constant_on_domain(bset
, 1);
4859 bounded
= isl_basic_set_is_bounded(bset
);
4863 return constant_on_domain(bset
, -1);
4865 if (bset
->n_eq
== 0)
4866 return compressed_multiplicative_call(bset
, fn
);
4868 morph
= isl_basic_set_full_compression(bset
);
4869 bset
= isl_morph_basic_set(isl_morph_copy(morph
), bset
);
4871 pwqp
= compressed_multiplicative_call(bset
, fn
);
4873 morph
= isl_morph_dom_params(morph
);
4874 morph
= isl_morph_ran_params(morph
);
4875 morph
= isl_morph_inverse(morph
);
4877 pwqp
= isl_pw_qpolynomial_morph_domain(pwqp
, morph
);
4881 isl_basic_set_free(bset
);
4885 /* Drop all floors in "qp", turning each integer division [a/m] into
4886 * a rational division a/m. If "down" is set, then the integer division
4887 * is replaced by (a-(m-1))/m instead.
4889 static __isl_give isl_qpolynomial
*qp_drop_floors(
4890 __isl_take isl_qpolynomial
*qp
, int down
)
4897 if (qp
->div
->n_row
== 0)
4900 qp
= isl_qpolynomial_cow(qp
);
4904 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
4906 isl_int_sub(qp
->div
->row
[i
][1],
4907 qp
->div
->row
[i
][1], qp
->div
->row
[i
][0]);
4908 isl_int_add_ui(qp
->div
->row
[i
][1],
4909 qp
->div
->row
[i
][1], 1);
4911 s
= isl_poly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
4912 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
4913 qp
= substitute_div(qp
, i
, s
);
4921 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4922 * a rational division a/m.
4924 static __isl_give isl_pw_qpolynomial
*pwqp_drop_floors(
4925 __isl_take isl_pw_qpolynomial
*pwqp
)
4932 if (isl_pw_qpolynomial_is_zero(pwqp
))
4935 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
4939 for (i
= 0; i
< pwqp
->n
; ++i
) {
4940 pwqp
->p
[i
].qp
= qp_drop_floors(pwqp
->p
[i
].qp
, 0);
4947 isl_pw_qpolynomial_free(pwqp
);
4951 /* Adjust all the integer divisions in "qp" such that they are at least
4952 * one over the given orthant (identified by "signs"). This ensures
4953 * that they will still be non-negative even after subtracting (m-1)/m.
4955 * In particular, f is replaced by f' + v, changing f = [a/m]
4956 * to f' = [(a - m v)/m].
4957 * If the constant term k in a is smaller than m,
4958 * the constant term of v is set to floor(k/m) - 1.
4959 * For any other term, if the coefficient c and the variable x have
4960 * the same sign, then no changes are needed.
4961 * Otherwise, if the variable is positive (and c is negative),
4962 * then the coefficient of x in v is set to floor(c/m).
4963 * If the variable is negative (and c is positive),
4964 * then the coefficient of x in v is set to ceil(c/m).
4966 static __isl_give isl_qpolynomial
*make_divs_pos(__isl_take isl_qpolynomial
*qp
,
4974 qp
= isl_qpolynomial_cow(qp
);
4975 div_pos
= isl_qpolynomial_domain_var_offset(qp
, isl_dim_div
);
4977 return isl_qpolynomial_free(qp
);
4978 qp
->div
= isl_mat_cow(qp
->div
);
4982 v
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
4984 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4985 isl_int
*row
= qp
->div
->row
[i
];
4989 if (isl_int_lt(row
[1], row
[0])) {
4990 isl_int_fdiv_q(v
->el
[0], row
[1], row
[0]);
4991 isl_int_sub_ui(v
->el
[0], v
->el
[0], 1);
4992 isl_int_submul(row
[1], row
[0], v
->el
[0]);
4994 for (j
= 0; j
< div_pos
; ++j
) {
4995 if (isl_int_sgn(row
[2 + j
]) * signs
[j
] >= 0)
4998 isl_int_cdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
5000 isl_int_fdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
5001 isl_int_submul(row
[2 + j
], row
[0], v
->el
[1 + j
]);
5003 for (j
= 0; j
< i
; ++j
) {
5004 if (isl_int_sgn(row
[2 + div_pos
+ j
]) >= 0)
5006 isl_int_fdiv_q(v
->el
[1 + div_pos
+ j
],
5007 row
[2 + div_pos
+ j
], row
[0]);
5008 isl_int_submul(row
[2 + div_pos
+ j
],
5009 row
[0], v
->el
[1 + div_pos
+ j
]);
5011 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
5012 if (isl_int_is_zero(qp
->div
->row
[j
][2 + div_pos
+ i
]))
5014 isl_seq_combine(qp
->div
->row
[j
] + 1,
5015 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
5016 qp
->div
->row
[j
][2 + div_pos
+ i
], v
->el
,
5019 isl_int_set_si(v
->el
[1 + div_pos
+ i
], 1);
5020 s
= isl_poly_from_affine(qp
->dim
->ctx
, v
->el
,
5021 qp
->div
->ctx
->one
, v
->size
);
5022 qp
->poly
= isl_poly_subs(qp
->poly
, div_pos
+ i
, 1, &s
);
5032 isl_qpolynomial_free(qp
);
5036 struct isl_to_poly_data
{
5038 isl_pw_qpolynomial
*res
;
5039 isl_qpolynomial
*qp
;
5042 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
5043 * We first make all integer divisions positive and then split the
5044 * quasipolynomials into terms with sign data->sign (the direction
5045 * of the requested approximation) and terms with the opposite sign.
5046 * In the first set of terms, each integer division [a/m] is
5047 * overapproximated by a/m, while in the second it is underapproximated
5050 static isl_stat
to_polynomial_on_orthant(__isl_take isl_set
*orthant
,
5051 int *signs
, void *user
)
5053 struct isl_to_poly_data
*data
= user
;
5054 isl_pw_qpolynomial
*t
;
5055 isl_qpolynomial
*qp
, *up
, *down
;
5057 qp
= isl_qpolynomial_copy(data
->qp
);
5058 qp
= make_divs_pos(qp
, signs
);
5060 up
= isl_qpolynomial_terms_of_sign(qp
, signs
, data
->sign
);
5061 up
= qp_drop_floors(up
, 0);
5062 down
= isl_qpolynomial_terms_of_sign(qp
, signs
, -data
->sign
);
5063 down
= qp_drop_floors(down
, 1);
5065 isl_qpolynomial_free(qp
);
5066 qp
= isl_qpolynomial_add(up
, down
);
5068 t
= isl_pw_qpolynomial_alloc(orthant
, qp
);
5069 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, t
);
5074 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
5075 * the polynomial will be an overapproximation. If "sign" is negative,
5076 * it will be an underapproximation. If "sign" is zero, the approximation
5077 * will lie somewhere in between.
5079 * In particular, is sign == 0, we simply drop the floors, turning
5080 * the integer divisions into rational divisions.
5081 * Otherwise, we split the domains into orthants, make all integer divisions
5082 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
5083 * depending on the requested sign and the sign of the term in which
5084 * the integer division appears.
5086 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_to_polynomial(
5087 __isl_take isl_pw_qpolynomial
*pwqp
, int sign
)
5090 struct isl_to_poly_data data
;
5093 return pwqp_drop_floors(pwqp
);
5099 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp
));
5101 for (i
= 0; i
< pwqp
->n
; ++i
) {
5102 if (pwqp
->p
[i
].qp
->div
->n_row
== 0) {
5103 isl_pw_qpolynomial
*t
;
5104 t
= isl_pw_qpolynomial_alloc(
5105 isl_set_copy(pwqp
->p
[i
].set
),
5106 isl_qpolynomial_copy(pwqp
->p
[i
].qp
));
5107 data
.res
= isl_pw_qpolynomial_add_disjoint(data
.res
, t
);
5110 data
.qp
= pwqp
->p
[i
].qp
;
5111 if (isl_set_foreach_orthant(pwqp
->p
[i
].set
,
5112 &to_polynomial_on_orthant
, &data
) < 0)
5116 isl_pw_qpolynomial_free(pwqp
);
5120 isl_pw_qpolynomial_free(pwqp
);
5121 isl_pw_qpolynomial_free(data
.res
);
5125 static __isl_give isl_pw_qpolynomial
*poly_entry(
5126 __isl_take isl_pw_qpolynomial
*pwqp
, void *user
)
5130 return isl_pw_qpolynomial_to_polynomial(pwqp
, *sign
);
5133 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_to_polynomial(
5134 __isl_take isl_union_pw_qpolynomial
*upwqp
, int sign
)
5136 return isl_union_pw_qpolynomial_transform_inplace(upwqp
,
5137 &poly_entry
, &sign
);
5140 __isl_give isl_basic_map
*isl_basic_map_from_qpolynomial(
5141 __isl_take isl_qpolynomial
*qp
)
5145 isl_vec
*aff
= NULL
;
5146 isl_basic_map
*bmap
= NULL
;
5153 is_affine
= isl_poly_is_affine(qp
->poly
);
5157 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
5158 "input quasi-polynomial not affine", goto error
);
5159 aff
= isl_qpolynomial_extract_affine(qp
);
5162 dim
= isl_qpolynomial_get_space(qp
);
5163 pos
= 1 + isl_space_offset(dim
, isl_dim_out
);
5164 n_div
= qp
->div
->n_row
;
5165 bmap
= isl_basic_map_alloc_space(dim
, n_div
, 1, 2 * n_div
);
5167 for (i
= 0; i
< n_div
; ++i
) {
5168 k
= isl_basic_map_alloc_div(bmap
);
5171 isl_seq_cpy(bmap
->div
[k
], qp
->div
->row
[i
], qp
->div
->n_col
);
5172 isl_int_set_si(bmap
->div
[k
][qp
->div
->n_col
], 0);
5173 bmap
= isl_basic_map_add_div_constraints(bmap
, k
);
5175 k
= isl_basic_map_alloc_equality(bmap
);
5178 isl_int_neg(bmap
->eq
[k
][pos
], aff
->el
[0]);
5179 isl_seq_cpy(bmap
->eq
[k
], aff
->el
+ 1, pos
);
5180 isl_seq_cpy(bmap
->eq
[k
] + pos
+ 1, aff
->el
+ 1 + pos
, n_div
);
5183 isl_qpolynomial_free(qp
);
5184 bmap
= isl_basic_map_finalize(bmap
);
5188 isl_qpolynomial_free(qp
);
5189 isl_basic_map_free(bmap
);