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 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 int isl_poly_is_cst(__isl_keep isl_poly
*poly
)
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
)
83 isl_poly_rec
*rec1
, *rec2
;
91 if (poly1
->var
!= poly2
->var
)
92 return poly1
->var
- poly2
->var
;
94 if (isl_poly_is_cst(poly1
)) {
95 isl_poly_cst
*cst1
, *cst2
;
98 cst1
= isl_poly_as_cst(poly1
);
99 cst2
= isl_poly_as_cst(poly2
);
102 cmp
= isl_int_cmp(cst1
->n
, cst2
->n
);
105 return isl_int_cmp(cst1
->d
, cst2
->d
);
108 rec1
= isl_poly_as_rec(poly1
);
109 rec2
= isl_poly_as_rec(poly2
);
113 if (rec1
->n
!= rec2
->n
)
114 return rec1
->n
- rec2
->n
;
116 for (i
= 0; i
< rec1
->n
; ++i
) {
117 int cmp
= isl_poly_plain_cmp(rec1
->p
[i
], rec2
->p
[i
]);
125 isl_bool
isl_poly_is_equal(__isl_keep isl_poly
*poly1
,
126 __isl_keep isl_poly
*poly2
)
129 isl_poly_rec
*rec1
, *rec2
;
131 if (!poly1
|| !poly2
)
132 return isl_bool_error
;
134 return isl_bool_true
;
135 if (poly1
->var
!= poly2
->var
)
136 return isl_bool_false
;
137 if (isl_poly_is_cst(poly1
)) {
138 isl_poly_cst
*cst1
, *cst2
;
139 cst1
= isl_poly_as_cst(poly1
);
140 cst2
= isl_poly_as_cst(poly2
);
142 return isl_bool_error
;
143 return isl_int_eq(cst1
->n
, cst2
->n
) &&
144 isl_int_eq(cst1
->d
, cst2
->d
);
147 rec1
= isl_poly_as_rec(poly1
);
148 rec2
= isl_poly_as_rec(poly2
);
150 return isl_bool_error
;
152 if (rec1
->n
!= rec2
->n
)
153 return isl_bool_false
;
155 for (i
= 0; i
< rec1
->n
; ++i
) {
156 isl_bool eq
= isl_poly_is_equal(rec1
->p
[i
], rec2
->p
[i
]);
161 return isl_bool_true
;
164 isl_bool
isl_poly_is_zero(__isl_keep isl_poly
*poly
)
169 return isl_bool_error
;
170 if (!isl_poly_is_cst(poly
))
171 return isl_bool_false
;
173 cst
= isl_poly_as_cst(poly
);
175 return isl_bool_error
;
177 return isl_int_is_zero(cst
->n
) && isl_int_is_pos(cst
->d
);
180 int isl_poly_sgn(__isl_keep isl_poly
*poly
)
186 if (!isl_poly_is_cst(poly
))
189 cst
= isl_poly_as_cst(poly
);
193 return isl_int_sgn(cst
->n
);
196 isl_bool
isl_poly_is_nan(__isl_keep isl_poly
*poly
)
201 return isl_bool_error
;
202 if (!isl_poly_is_cst(poly
))
203 return isl_bool_false
;
205 cst
= isl_poly_as_cst(poly
);
207 return isl_bool_error
;
209 return isl_int_is_zero(cst
->n
) && isl_int_is_zero(cst
->d
);
212 isl_bool
isl_poly_is_infty(__isl_keep isl_poly
*poly
)
217 return isl_bool_error
;
218 if (!isl_poly_is_cst(poly
))
219 return isl_bool_false
;
221 cst
= isl_poly_as_cst(poly
);
223 return isl_bool_error
;
225 return isl_int_is_pos(cst
->n
) && isl_int_is_zero(cst
->d
);
228 isl_bool
isl_poly_is_neginfty(__isl_keep isl_poly
*poly
)
233 return isl_bool_error
;
234 if (!isl_poly_is_cst(poly
))
235 return isl_bool_false
;
237 cst
= isl_poly_as_cst(poly
);
239 return isl_bool_error
;
241 return isl_int_is_neg(cst
->n
) && isl_int_is_zero(cst
->d
);
244 isl_bool
isl_poly_is_one(__isl_keep isl_poly
*poly
)
249 return isl_bool_error
;
250 if (!isl_poly_is_cst(poly
))
251 return isl_bool_false
;
253 cst
= isl_poly_as_cst(poly
);
255 return isl_bool_error
;
257 return isl_int_eq(cst
->n
, cst
->d
) && isl_int_is_pos(cst
->d
);
260 isl_bool
isl_poly_is_negone(__isl_keep isl_poly
*poly
)
265 return isl_bool_error
;
266 if (!isl_poly_is_cst(poly
))
267 return isl_bool_false
;
269 cst
= isl_poly_as_cst(poly
);
271 return isl_bool_error
;
273 return isl_int_is_negone(cst
->n
) && isl_int_is_one(cst
->d
);
276 __isl_give isl_poly_cst
*isl_poly_cst_alloc(isl_ctx
*ctx
)
280 cst
= isl_alloc_type(ctx
, struct isl_poly_cst
);
289 isl_int_init(cst
->n
);
290 isl_int_init(cst
->d
);
295 __isl_give isl_poly
*isl_poly_zero(isl_ctx
*ctx
)
299 cst
= isl_poly_cst_alloc(ctx
);
303 isl_int_set_si(cst
->n
, 0);
304 isl_int_set_si(cst
->d
, 1);
309 __isl_give isl_poly
*isl_poly_one(isl_ctx
*ctx
)
313 cst
= isl_poly_cst_alloc(ctx
);
317 isl_int_set_si(cst
->n
, 1);
318 isl_int_set_si(cst
->d
, 1);
323 __isl_give isl_poly
*isl_poly_infty(isl_ctx
*ctx
)
327 cst
= isl_poly_cst_alloc(ctx
);
331 isl_int_set_si(cst
->n
, 1);
332 isl_int_set_si(cst
->d
, 0);
337 __isl_give isl_poly
*isl_poly_neginfty(isl_ctx
*ctx
)
341 cst
= isl_poly_cst_alloc(ctx
);
345 isl_int_set_si(cst
->n
, -1);
346 isl_int_set_si(cst
->d
, 0);
351 __isl_give isl_poly
*isl_poly_nan(isl_ctx
*ctx
)
355 cst
= isl_poly_cst_alloc(ctx
);
359 isl_int_set_si(cst
->n
, 0);
360 isl_int_set_si(cst
->d
, 0);
365 __isl_give isl_poly
*isl_poly_rat_cst(isl_ctx
*ctx
, isl_int n
, isl_int d
)
369 cst
= isl_poly_cst_alloc(ctx
);
373 isl_int_set(cst
->n
, n
);
374 isl_int_set(cst
->d
, d
);
379 __isl_give isl_poly_rec
*isl_poly_alloc_rec(isl_ctx
*ctx
, int var
, int size
)
383 isl_assert(ctx
, var
>= 0, return NULL
);
384 isl_assert(ctx
, size
>= 0, return NULL
);
385 rec
= isl_calloc(ctx
, struct isl_poly_rec
,
386 sizeof(struct isl_poly_rec
) +
387 size
* sizeof(struct isl_poly
*));
402 __isl_give isl_qpolynomial
*isl_qpolynomial_reset_domain_space(
403 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*dim
)
405 qp
= isl_qpolynomial_cow(qp
);
409 isl_space_free(qp
->dim
);
414 isl_qpolynomial_free(qp
);
419 /* Reset the space of "qp". This function is called from isl_pw_templ.c
420 * and doesn't know if the space of an element object is represented
421 * directly or through its domain. It therefore passes along both.
423 __isl_give isl_qpolynomial
*isl_qpolynomial_reset_space_and_domain(
424 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*space
,
425 __isl_take isl_space
*domain
)
427 isl_space_free(space
);
428 return isl_qpolynomial_reset_domain_space(qp
, domain
);
431 isl_ctx
*isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial
*qp
)
433 return qp
? qp
->dim
->ctx
: NULL
;
436 __isl_give isl_space
*isl_qpolynomial_get_domain_space(
437 __isl_keep isl_qpolynomial
*qp
)
439 return qp
? isl_space_copy(qp
->dim
) : NULL
;
442 /* Return a copy of the local space on which "qp" is defined.
444 static __isl_give isl_local_space
*isl_qpolynomial_get_domain_local_space(
445 __isl_keep isl_qpolynomial
*qp
)
452 space
= isl_qpolynomial_get_domain_space(qp
);
453 return isl_local_space_alloc_div(space
, isl_mat_copy(qp
->div
));
456 __isl_give isl_space
*isl_qpolynomial_get_space(__isl_keep isl_qpolynomial
*qp
)
461 space
= isl_space_copy(qp
->dim
);
462 space
= isl_space_from_domain(space
);
463 space
= isl_space_add_dims(space
, isl_dim_out
, 1);
467 /* Return the number of variables of the given type in the domain of "qp".
469 unsigned isl_qpolynomial_domain_dim(__isl_keep isl_qpolynomial
*qp
,
470 enum isl_dim_type type
)
474 if (type
== isl_dim_div
)
475 return qp
->div
->n_row
;
476 if (type
== isl_dim_all
)
477 return isl_space_dim(qp
->dim
, isl_dim_all
) +
478 isl_qpolynomial_domain_dim(qp
, isl_dim_div
);
479 return isl_space_dim(qp
->dim
, type
);
482 /* Given the type of a dimension of an isl_qpolynomial,
483 * return the type of the corresponding dimension in its domain.
484 * This function is only called for "type" equal to isl_dim_in or
487 static enum isl_dim_type
domain_type(enum isl_dim_type type
)
489 return type
== isl_dim_in
? isl_dim_set
: type
;
492 /* Externally, an isl_qpolynomial has a map space, but internally, the
493 * ls field corresponds to the domain of that space.
495 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial
*qp
,
496 enum isl_dim_type type
)
500 if (type
== isl_dim_out
)
502 type
= domain_type(type
);
503 return isl_qpolynomial_domain_dim(qp
, type
);
506 /* Return the offset of the first coefficient of type "type" in
507 * the domain of "qp".
509 unsigned isl_qpolynomial_domain_offset(__isl_keep isl_qpolynomial
*qp
,
510 enum isl_dim_type type
)
519 return 1 + isl_space_offset(qp
->dim
, type
);
521 return 1 + isl_space_dim(qp
->dim
, isl_dim_all
);
527 isl_bool
isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial
*qp
)
529 return qp
? isl_poly_is_zero(qp
->poly
) : isl_bool_error
;
532 isl_bool
isl_qpolynomial_is_one(__isl_keep isl_qpolynomial
*qp
)
534 return qp
? isl_poly_is_one(qp
->poly
) : isl_bool_error
;
537 isl_bool
isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial
*qp
)
539 return qp
? isl_poly_is_nan(qp
->poly
) : isl_bool_error
;
542 isl_bool
isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial
*qp
)
544 return qp
? isl_poly_is_infty(qp
->poly
) : isl_bool_error
;
547 isl_bool
isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial
*qp
)
549 return qp
? isl_poly_is_neginfty(qp
->poly
) : isl_bool_error
;
552 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial
*qp
)
554 return qp
? isl_poly_sgn(qp
->poly
) : 0;
557 static void poly_free_cst(__isl_take isl_poly_cst
*cst
)
559 isl_int_clear(cst
->n
);
560 isl_int_clear(cst
->d
);
563 static void poly_free_rec(__isl_take isl_poly_rec
*rec
)
567 for (i
= 0; i
< rec
->n
; ++i
)
568 isl_poly_free(rec
->p
[i
]);
571 __isl_give isl_poly
*isl_poly_copy(__isl_keep isl_poly
*poly
)
580 __isl_give isl_poly
*isl_poly_dup_cst(__isl_keep isl_poly
*poly
)
585 cst
= isl_poly_as_cst(poly
);
589 dup
= isl_poly_as_cst(isl_poly_zero(poly
->ctx
));
592 isl_int_set(dup
->n
, cst
->n
);
593 isl_int_set(dup
->d
, cst
->d
);
598 __isl_give isl_poly
*isl_poly_dup_rec(__isl_keep isl_poly
*poly
)
604 rec
= isl_poly_as_rec(poly
);
608 dup
= isl_poly_alloc_rec(poly
->ctx
, poly
->var
, rec
->n
);
612 for (i
= 0; i
< rec
->n
; ++i
) {
613 dup
->p
[i
] = isl_poly_copy(rec
->p
[i
]);
621 isl_poly_free(&dup
->poly
);
625 __isl_give isl_poly
*isl_poly_dup(__isl_keep isl_poly
*poly
)
630 if (isl_poly_is_cst(poly
))
631 return isl_poly_dup_cst(poly
);
633 return isl_poly_dup_rec(poly
);
636 __isl_give isl_poly
*isl_poly_cow(__isl_take isl_poly
*poly
)
644 return isl_poly_dup(poly
);
647 __isl_null isl_poly
*isl_poly_free(__isl_take isl_poly
*poly
)
656 poly_free_cst((isl_poly_cst
*) poly
);
658 poly_free_rec((isl_poly_rec
*) poly
);
660 isl_ctx_deref(poly
->ctx
);
665 static void isl_poly_cst_reduce(__isl_keep isl_poly_cst
*cst
)
670 isl_int_gcd(gcd
, cst
->n
, cst
->d
);
671 if (!isl_int_is_zero(gcd
) && !isl_int_is_one(gcd
)) {
672 isl_int_divexact(cst
->n
, cst
->n
, gcd
);
673 isl_int_divexact(cst
->d
, cst
->d
, gcd
);
678 __isl_give isl_poly
*isl_poly_sum_cst(__isl_take isl_poly
*poly1
,
679 __isl_take isl_poly
*poly2
)
684 poly1
= isl_poly_cow(poly1
);
685 if (!poly1
|| !poly2
)
688 cst1
= isl_poly_as_cst(poly1
);
689 cst2
= isl_poly_as_cst(poly2
);
691 if (isl_int_eq(cst1
->d
, cst2
->d
))
692 isl_int_add(cst1
->n
, cst1
->n
, cst2
->n
);
694 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->d
);
695 isl_int_addmul(cst1
->n
, cst2
->n
, cst1
->d
);
696 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
699 isl_poly_cst_reduce(cst1
);
701 isl_poly_free(poly2
);
704 isl_poly_free(poly1
);
705 isl_poly_free(poly2
);
709 static __isl_give isl_poly
*replace_by_zero(__isl_take isl_poly
*poly
)
717 return isl_poly_zero(ctx
);
720 static __isl_give isl_poly
*replace_by_constant_term(__isl_take isl_poly
*poly
)
728 rec
= isl_poly_as_rec(poly
);
731 cst
= isl_poly_copy(rec
->p
[0]);
739 __isl_give isl_poly
*isl_poly_sum(__isl_take isl_poly
*poly1
,
740 __isl_take isl_poly
*poly2
)
743 isl_bool is_zero
, is_nan
;
744 isl_poly_rec
*rec1
, *rec2
;
746 if (!poly1
|| !poly2
)
749 is_nan
= isl_poly_is_nan(poly1
);
753 isl_poly_free(poly2
);
757 is_nan
= isl_poly_is_nan(poly2
);
761 isl_poly_free(poly1
);
765 is_zero
= isl_poly_is_zero(poly1
);
769 isl_poly_free(poly1
);
773 is_zero
= isl_poly_is_zero(poly2
);
777 isl_poly_free(poly2
);
781 if (poly1
->var
< poly2
->var
)
782 return isl_poly_sum(poly2
, poly1
);
784 if (poly2
->var
< poly1
->var
) {
788 is_infty
= isl_poly_is_infty(poly2
);
789 if (is_infty
>= 0 && !is_infty
)
790 is_infty
= isl_poly_is_neginfty(poly2
);
794 isl_poly_free(poly1
);
797 poly1
= isl_poly_cow(poly1
);
798 rec
= isl_poly_as_rec(poly1
);
801 rec
->p
[0] = isl_poly_sum(rec
->p
[0], poly2
);
803 poly1
= replace_by_constant_term(poly1
);
807 if (isl_poly_is_cst(poly1
))
808 return isl_poly_sum_cst(poly1
, poly2
);
810 rec1
= isl_poly_as_rec(poly1
);
811 rec2
= isl_poly_as_rec(poly2
);
815 if (rec1
->n
< rec2
->n
)
816 return isl_poly_sum(poly2
, poly1
);
818 poly1
= isl_poly_cow(poly1
);
819 rec1
= isl_poly_as_rec(poly1
);
823 for (i
= rec2
->n
- 1; i
>= 0; --i
) {
826 rec1
->p
[i
] = isl_poly_sum(rec1
->p
[i
],
827 isl_poly_copy(rec2
->p
[i
]));
830 if (i
!= rec1
->n
- 1)
832 is_zero
= isl_poly_is_zero(rec1
->p
[i
]);
836 isl_poly_free(rec1
->p
[i
]);
842 poly1
= replace_by_zero(poly1
);
843 else if (rec1
->n
== 1)
844 poly1
= replace_by_constant_term(poly1
);
846 isl_poly_free(poly2
);
850 isl_poly_free(poly1
);
851 isl_poly_free(poly2
);
855 __isl_give isl_poly
*isl_poly_cst_add_isl_int(__isl_take isl_poly
*poly
,
860 poly
= isl_poly_cow(poly
);
864 cst
= isl_poly_as_cst(poly
);
866 isl_int_addmul(cst
->n
, cst
->d
, v
);
871 __isl_give isl_poly
*isl_poly_add_isl_int(__isl_take isl_poly
*poly
, isl_int v
)
878 if (isl_poly_is_cst(poly
))
879 return isl_poly_cst_add_isl_int(poly
, v
);
881 poly
= isl_poly_cow(poly
);
882 rec
= isl_poly_as_rec(poly
);
886 rec
->p
[0] = isl_poly_add_isl_int(rec
->p
[0], v
);
896 __isl_give isl_poly
*isl_poly_cst_mul_isl_int(__isl_take isl_poly
*poly
,
902 is_zero
= isl_poly_is_zero(poly
);
904 return isl_poly_free(poly
);
908 poly
= isl_poly_cow(poly
);
912 cst
= isl_poly_as_cst(poly
);
914 isl_int_mul(cst
->n
, cst
->n
, v
);
919 __isl_give isl_poly
*isl_poly_mul_isl_int(__isl_take isl_poly
*poly
, isl_int v
)
927 if (isl_poly_is_cst(poly
))
928 return isl_poly_cst_mul_isl_int(poly
, v
);
930 poly
= isl_poly_cow(poly
);
931 rec
= isl_poly_as_rec(poly
);
935 for (i
= 0; i
< rec
->n
; ++i
) {
936 rec
->p
[i
] = isl_poly_mul_isl_int(rec
->p
[i
], v
);
947 /* Multiply the constant polynomial "poly" by "v".
949 static __isl_give isl_poly
*isl_poly_cst_scale_val(__isl_take isl_poly
*poly
,
950 __isl_keep isl_val
*v
)
955 is_zero
= isl_poly_is_zero(poly
);
957 return isl_poly_free(poly
);
961 poly
= isl_poly_cow(poly
);
965 cst
= isl_poly_as_cst(poly
);
967 isl_int_mul(cst
->n
, cst
->n
, v
->n
);
968 isl_int_mul(cst
->d
, cst
->d
, v
->d
);
969 isl_poly_cst_reduce(cst
);
974 /* Multiply the polynomial "poly" by "v".
976 static __isl_give isl_poly
*isl_poly_scale_val(__isl_take isl_poly
*poly
,
977 __isl_keep isl_val
*v
)
985 if (isl_poly_is_cst(poly
))
986 return isl_poly_cst_scale_val(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_scale_val(rec
->p
[i
], v
);
1001 isl_poly_free(poly
);
1005 __isl_give isl_poly
*isl_poly_mul_cst(__isl_take isl_poly
*poly1
,
1006 __isl_take isl_poly
*poly2
)
1011 poly1
= isl_poly_cow(poly1
);
1012 if (!poly1
|| !poly2
)
1015 cst1
= isl_poly_as_cst(poly1
);
1016 cst2
= isl_poly_as_cst(poly2
);
1018 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->n
);
1019 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
1021 isl_poly_cst_reduce(cst1
);
1023 isl_poly_free(poly2
);
1026 isl_poly_free(poly1
);
1027 isl_poly_free(poly2
);
1031 __isl_give isl_poly
*isl_poly_mul_rec(__isl_take isl_poly
*poly1
,
1032 __isl_take isl_poly
*poly2
)
1036 isl_poly_rec
*res
= NULL
;
1040 rec1
= isl_poly_as_rec(poly1
);
1041 rec2
= isl_poly_as_rec(poly2
);
1044 size
= rec1
->n
+ rec2
->n
- 1;
1045 res
= isl_poly_alloc_rec(poly1
->ctx
, poly1
->var
, size
);
1049 for (i
= 0; i
< rec1
->n
; ++i
) {
1050 res
->p
[i
] = isl_poly_mul(isl_poly_copy(rec2
->p
[0]),
1051 isl_poly_copy(rec1
->p
[i
]));
1056 for (; i
< size
; ++i
) {
1057 res
->p
[i
] = isl_poly_zero(poly1
->ctx
);
1062 for (i
= 0; i
< rec1
->n
; ++i
) {
1063 for (j
= 1; j
< rec2
->n
; ++j
) {
1065 poly
= isl_poly_mul(isl_poly_copy(rec2
->p
[j
]),
1066 isl_poly_copy(rec1
->p
[i
]));
1067 res
->p
[i
+ j
] = isl_poly_sum(res
->p
[i
+ j
], poly
);
1073 isl_poly_free(poly1
);
1074 isl_poly_free(poly2
);
1078 isl_poly_free(poly1
);
1079 isl_poly_free(poly2
);
1080 isl_poly_free(&res
->poly
);
1084 __isl_give isl_poly
*isl_poly_mul(__isl_take isl_poly
*poly1
,
1085 __isl_take isl_poly
*poly2
)
1087 isl_bool is_zero
, is_nan
, is_one
;
1089 if (!poly1
|| !poly2
)
1092 is_nan
= isl_poly_is_nan(poly1
);
1096 isl_poly_free(poly2
);
1100 is_nan
= isl_poly_is_nan(poly2
);
1104 isl_poly_free(poly1
);
1108 is_zero
= isl_poly_is_zero(poly1
);
1112 isl_poly_free(poly2
);
1116 is_zero
= isl_poly_is_zero(poly2
);
1120 isl_poly_free(poly1
);
1124 is_one
= isl_poly_is_one(poly1
);
1128 isl_poly_free(poly1
);
1132 is_one
= isl_poly_is_one(poly2
);
1136 isl_poly_free(poly2
);
1140 if (poly1
->var
< poly2
->var
)
1141 return isl_poly_mul(poly2
, poly1
);
1143 if (poly2
->var
< poly1
->var
) {
1148 is_infty
= isl_poly_is_infty(poly2
);
1149 if (is_infty
>= 0 && !is_infty
)
1150 is_infty
= isl_poly_is_neginfty(poly2
);
1154 isl_ctx
*ctx
= poly1
->ctx
;
1155 isl_poly_free(poly1
);
1156 isl_poly_free(poly2
);
1157 return isl_poly_nan(ctx
);
1159 poly1
= isl_poly_cow(poly1
);
1160 rec
= isl_poly_as_rec(poly1
);
1164 for (i
= 0; i
< rec
->n
; ++i
) {
1165 rec
->p
[i
] = isl_poly_mul(rec
->p
[i
],
1166 isl_poly_copy(poly2
));
1170 isl_poly_free(poly2
);
1174 if (isl_poly_is_cst(poly1
))
1175 return isl_poly_mul_cst(poly1
, poly2
);
1177 return isl_poly_mul_rec(poly1
, poly2
);
1179 isl_poly_free(poly1
);
1180 isl_poly_free(poly2
);
1184 __isl_give isl_poly
*isl_poly_pow(__isl_take isl_poly
*poly
, unsigned power
)
1194 res
= isl_poly_copy(poly
);
1196 res
= isl_poly_one(poly
->ctx
);
1198 while (power
>>= 1) {
1199 poly
= isl_poly_mul(poly
, isl_poly_copy(poly
));
1201 res
= isl_poly_mul(res
, isl_poly_copy(poly
));
1204 isl_poly_free(poly
);
1208 __isl_give isl_qpolynomial
*isl_qpolynomial_alloc(__isl_take isl_space
*space
,
1209 unsigned n_div
, __isl_take isl_poly
*poly
)
1211 struct isl_qpolynomial
*qp
= NULL
;
1214 if (!space
|| !poly
)
1217 if (!isl_space_is_set(space
))
1218 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
1219 "domain of polynomial should be a set", goto error
);
1221 total
= isl_space_dim(space
, isl_dim_all
);
1223 qp
= isl_calloc_type(space
->ctx
, struct isl_qpolynomial
);
1228 qp
->div
= isl_mat_alloc(space
->ctx
, n_div
, 1 + 1 + total
+ n_div
);
1237 isl_space_free(space
);
1238 isl_poly_free(poly
);
1239 isl_qpolynomial_free(qp
);
1243 __isl_give isl_qpolynomial
*isl_qpolynomial_copy(__isl_keep isl_qpolynomial
*qp
)
1252 __isl_give isl_qpolynomial
*isl_qpolynomial_dup(__isl_keep isl_qpolynomial
*qp
)
1254 struct isl_qpolynomial
*dup
;
1259 dup
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
), qp
->div
->n_row
,
1260 isl_poly_copy(qp
->poly
));
1263 isl_mat_free(dup
->div
);
1264 dup
->div
= isl_mat_copy(qp
->div
);
1270 isl_qpolynomial_free(dup
);
1274 __isl_give isl_qpolynomial
*isl_qpolynomial_cow(__isl_take isl_qpolynomial
*qp
)
1282 return isl_qpolynomial_dup(qp
);
1285 __isl_null isl_qpolynomial
*isl_qpolynomial_free(
1286 __isl_take isl_qpolynomial
*qp
)
1294 isl_space_free(qp
->dim
);
1295 isl_mat_free(qp
->div
);
1296 isl_poly_free(qp
->poly
);
1302 __isl_give isl_poly
*isl_poly_var_pow(isl_ctx
*ctx
, int pos
, int power
)
1308 rec
= isl_poly_alloc_rec(ctx
, pos
, 1 + power
);
1311 for (i
= 0; i
< 1 + power
; ++i
) {
1312 rec
->p
[i
] = isl_poly_zero(ctx
);
1317 cst
= isl_poly_as_cst(rec
->p
[power
]);
1318 isl_int_set_si(cst
->n
, 1);
1322 isl_poly_free(&rec
->poly
);
1326 /* r array maps original positions to new positions.
1328 static __isl_give isl_poly
*reorder(__isl_take isl_poly
*poly
, int *r
)
1335 if (isl_poly_is_cst(poly
))
1338 rec
= isl_poly_as_rec(poly
);
1342 isl_assert(poly
->ctx
, rec
->n
>= 1, goto error
);
1344 base
= isl_poly_var_pow(poly
->ctx
, r
[poly
->var
], 1);
1345 res
= reorder(isl_poly_copy(rec
->p
[rec
->n
- 1]), r
);
1347 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1348 res
= isl_poly_mul(res
, isl_poly_copy(base
));
1349 res
= isl_poly_sum(res
, reorder(isl_poly_copy(rec
->p
[i
]), r
));
1352 isl_poly_free(base
);
1353 isl_poly_free(poly
);
1357 isl_poly_free(poly
);
1361 static isl_bool
compatible_divs(__isl_keep isl_mat
*div1
,
1362 __isl_keep isl_mat
*div2
)
1367 isl_assert(div1
->ctx
, div1
->n_row
>= div2
->n_row
&&
1368 div1
->n_col
>= div2
->n_col
,
1369 return isl_bool_error
);
1371 if (div1
->n_row
== div2
->n_row
)
1372 return isl_mat_is_equal(div1
, div2
);
1374 n_row
= div1
->n_row
;
1375 n_col
= div1
->n_col
;
1376 div1
->n_row
= div2
->n_row
;
1377 div1
->n_col
= div2
->n_col
;
1379 equal
= isl_mat_is_equal(div1
, div2
);
1381 div1
->n_row
= n_row
;
1382 div1
->n_col
= n_col
;
1387 static int cmp_row(__isl_keep isl_mat
*div
, int i
, int j
)
1391 li
= isl_seq_last_non_zero(div
->row
[i
], div
->n_col
);
1392 lj
= isl_seq_last_non_zero(div
->row
[j
], div
->n_col
);
1397 return isl_seq_cmp(div
->row
[i
], div
->row
[j
], div
->n_col
);
1400 struct isl_div_sort_info
{
1405 static int div_sort_cmp(const void *p1
, const void *p2
)
1407 const struct isl_div_sort_info
*i1
, *i2
;
1408 i1
= (const struct isl_div_sort_info
*) p1
;
1409 i2
= (const struct isl_div_sort_info
*) p2
;
1411 return cmp_row(i1
->div
, i1
->row
, i2
->row
);
1414 /* Sort divs and remove duplicates.
1416 static __isl_give isl_qpolynomial
*sort_divs(__isl_take isl_qpolynomial
*qp
)
1421 struct isl_div_sort_info
*array
= NULL
;
1422 int *pos
= NULL
, *at
= NULL
;
1423 int *reordering
= NULL
;
1428 if (qp
->div
->n_row
<= 1)
1431 div_pos
= isl_space_dim(qp
->dim
, isl_dim_all
);
1433 array
= isl_alloc_array(qp
->div
->ctx
, struct isl_div_sort_info
,
1435 pos
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1436 at
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1437 len
= qp
->div
->n_col
- 2;
1438 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
1439 if (!array
|| !pos
|| !at
|| !reordering
)
1442 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1443 array
[i
].div
= qp
->div
;
1449 qsort(array
, qp
->div
->n_row
, sizeof(struct isl_div_sort_info
),
1452 for (i
= 0; i
< div_pos
; ++i
)
1455 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1456 if (pos
[array
[i
].row
] == i
)
1458 qp
->div
= isl_mat_swap_rows(qp
->div
, i
, pos
[array
[i
].row
]);
1459 pos
[at
[i
]] = pos
[array
[i
].row
];
1460 at
[pos
[array
[i
].row
]] = at
[i
];
1461 at
[i
] = array
[i
].row
;
1462 pos
[array
[i
].row
] = i
;
1466 for (i
= 0; i
< len
- div_pos
; ++i
) {
1468 isl_seq_eq(qp
->div
->row
[i
- skip
- 1],
1469 qp
->div
->row
[i
- skip
], qp
->div
->n_col
)) {
1470 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
1471 isl_mat_col_add(qp
->div
, 2 + div_pos
+ i
- skip
- 1,
1472 2 + div_pos
+ i
- skip
);
1473 qp
->div
= isl_mat_drop_cols(qp
->div
,
1474 2 + div_pos
+ i
- skip
, 1);
1477 reordering
[div_pos
+ array
[i
].row
] = div_pos
+ i
- skip
;
1480 qp
->poly
= reorder(qp
->poly
, reordering
);
1482 if (!qp
->poly
|| !qp
->div
)
1496 isl_qpolynomial_free(qp
);
1500 static __isl_give isl_poly
*expand(__isl_take isl_poly
*poly
, int *exp
,
1506 if (isl_poly_is_cst(poly
))
1509 if (poly
->var
< first
)
1512 if (exp
[poly
->var
- first
] == poly
->var
- first
)
1515 poly
= isl_poly_cow(poly
);
1519 poly
->var
= exp
[poly
->var
- first
] + first
;
1521 rec
= isl_poly_as_rec(poly
);
1525 for (i
= 0; i
< rec
->n
; ++i
) {
1526 rec
->p
[i
] = expand(rec
->p
[i
], exp
, first
);
1533 isl_poly_free(poly
);
1537 static __isl_give isl_qpolynomial
*with_merged_divs(
1538 __isl_give isl_qpolynomial
*(*fn
)(__isl_take isl_qpolynomial
*qp1
,
1539 __isl_take isl_qpolynomial
*qp2
),
1540 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
1544 isl_mat
*div
= NULL
;
1547 qp1
= isl_qpolynomial_cow(qp1
);
1548 qp2
= isl_qpolynomial_cow(qp2
);
1553 isl_assert(qp1
->div
->ctx
, qp1
->div
->n_row
>= qp2
->div
->n_row
&&
1554 qp1
->div
->n_col
>= qp2
->div
->n_col
, goto error
);
1556 n_div1
= qp1
->div
->n_row
;
1557 n_div2
= qp2
->div
->n_row
;
1558 exp1
= isl_alloc_array(qp1
->div
->ctx
, int, n_div1
);
1559 exp2
= isl_alloc_array(qp2
->div
->ctx
, int, n_div2
);
1560 if ((n_div1
&& !exp1
) || (n_div2
&& !exp2
))
1563 div
= isl_merge_divs(qp1
->div
, qp2
->div
, exp1
, exp2
);
1567 isl_mat_free(qp1
->div
);
1568 qp1
->div
= isl_mat_copy(div
);
1569 isl_mat_free(qp2
->div
);
1570 qp2
->div
= isl_mat_copy(div
);
1572 qp1
->poly
= expand(qp1
->poly
, exp1
, div
->n_col
- div
->n_row
- 2);
1573 qp2
->poly
= expand(qp2
->poly
, exp2
, div
->n_col
- div
->n_row
- 2);
1575 if (!qp1
->poly
|| !qp2
->poly
)
1582 return fn(qp1
, qp2
);
1587 isl_qpolynomial_free(qp1
);
1588 isl_qpolynomial_free(qp2
);
1592 __isl_give isl_qpolynomial
*isl_qpolynomial_add(__isl_take isl_qpolynomial
*qp1
,
1593 __isl_take isl_qpolynomial
*qp2
)
1595 isl_bool compatible
;
1597 qp1
= isl_qpolynomial_cow(qp1
);
1602 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1603 return isl_qpolynomial_add(qp2
, qp1
);
1605 isl_assert(qp1
->dim
->ctx
, isl_space_is_equal(qp1
->dim
, qp2
->dim
), goto error
);
1606 compatible
= compatible_divs(qp1
->div
, qp2
->div
);
1610 return with_merged_divs(isl_qpolynomial_add
, qp1
, qp2
);
1612 qp1
->poly
= isl_poly_sum(qp1
->poly
, isl_poly_copy(qp2
->poly
));
1616 isl_qpolynomial_free(qp2
);
1620 isl_qpolynomial_free(qp1
);
1621 isl_qpolynomial_free(qp2
);
1625 __isl_give isl_qpolynomial
*isl_qpolynomial_add_on_domain(
1626 __isl_keep isl_set
*dom
,
1627 __isl_take isl_qpolynomial
*qp1
,
1628 __isl_take isl_qpolynomial
*qp2
)
1630 qp1
= isl_qpolynomial_add(qp1
, qp2
);
1631 qp1
= isl_qpolynomial_gist(qp1
, isl_set_copy(dom
));
1635 __isl_give isl_qpolynomial
*isl_qpolynomial_sub(__isl_take isl_qpolynomial
*qp1
,
1636 __isl_take isl_qpolynomial
*qp2
)
1638 return isl_qpolynomial_add(qp1
, isl_qpolynomial_neg(qp2
));
1641 __isl_give isl_qpolynomial
*isl_qpolynomial_add_isl_int(
1642 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1644 if (isl_int_is_zero(v
))
1647 qp
= isl_qpolynomial_cow(qp
);
1651 qp
->poly
= isl_poly_add_isl_int(qp
->poly
, v
);
1657 isl_qpolynomial_free(qp
);
1662 __isl_give isl_qpolynomial
*isl_qpolynomial_neg(__isl_take isl_qpolynomial
*qp
)
1667 return isl_qpolynomial_mul_isl_int(qp
, qp
->dim
->ctx
->negone
);
1670 __isl_give isl_qpolynomial
*isl_qpolynomial_mul_isl_int(
1671 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1673 if (isl_int_is_one(v
))
1676 if (qp
&& isl_int_is_zero(v
)) {
1677 isl_qpolynomial
*zero
;
1678 zero
= isl_qpolynomial_zero_on_domain(isl_space_copy(qp
->dim
));
1679 isl_qpolynomial_free(qp
);
1683 qp
= isl_qpolynomial_cow(qp
);
1687 qp
->poly
= isl_poly_mul_isl_int(qp
->poly
, v
);
1693 isl_qpolynomial_free(qp
);
1697 __isl_give isl_qpolynomial
*isl_qpolynomial_scale(
1698 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1700 return isl_qpolynomial_mul_isl_int(qp
, v
);
1703 /* Multiply "qp" by "v".
1705 __isl_give isl_qpolynomial
*isl_qpolynomial_scale_val(
1706 __isl_take isl_qpolynomial
*qp
, __isl_take isl_val
*v
)
1711 if (!isl_val_is_rat(v
))
1712 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
1713 "expecting rational factor", goto error
);
1715 if (isl_val_is_one(v
)) {
1720 if (isl_val_is_zero(v
)) {
1723 space
= isl_qpolynomial_get_domain_space(qp
);
1724 isl_qpolynomial_free(qp
);
1726 return isl_qpolynomial_zero_on_domain(space
);
1729 qp
= isl_qpolynomial_cow(qp
);
1733 qp
->poly
= isl_poly_scale_val(qp
->poly
, v
);
1735 qp
= isl_qpolynomial_free(qp
);
1741 isl_qpolynomial_free(qp
);
1745 /* Divide "qp" by "v".
1747 __isl_give isl_qpolynomial
*isl_qpolynomial_scale_down_val(
1748 __isl_take isl_qpolynomial
*qp
, __isl_take isl_val
*v
)
1753 if (!isl_val_is_rat(v
))
1754 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
1755 "expecting rational factor", goto error
);
1756 if (isl_val_is_zero(v
))
1757 isl_die(isl_val_get_ctx(v
), isl_error_invalid
,
1758 "cannot scale down by zero", goto error
);
1760 return isl_qpolynomial_scale_val(qp
, isl_val_inv(v
));
1763 isl_qpolynomial_free(qp
);
1767 __isl_give isl_qpolynomial
*isl_qpolynomial_mul(__isl_take isl_qpolynomial
*qp1
,
1768 __isl_take isl_qpolynomial
*qp2
)
1770 isl_bool compatible
;
1772 qp1
= isl_qpolynomial_cow(qp1
);
1777 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1778 return isl_qpolynomial_mul(qp2
, qp1
);
1780 isl_assert(qp1
->dim
->ctx
, isl_space_is_equal(qp1
->dim
, qp2
->dim
), goto error
);
1781 compatible
= compatible_divs(qp1
->div
, qp2
->div
);
1785 return with_merged_divs(isl_qpolynomial_mul
, qp1
, qp2
);
1787 qp1
->poly
= isl_poly_mul(qp1
->poly
, isl_poly_copy(qp2
->poly
));
1791 isl_qpolynomial_free(qp2
);
1795 isl_qpolynomial_free(qp1
);
1796 isl_qpolynomial_free(qp2
);
1800 __isl_give isl_qpolynomial
*isl_qpolynomial_pow(__isl_take isl_qpolynomial
*qp
,
1803 qp
= isl_qpolynomial_cow(qp
);
1808 qp
->poly
= isl_poly_pow(qp
->poly
, power
);
1814 isl_qpolynomial_free(qp
);
1818 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_pow(
1819 __isl_take isl_pw_qpolynomial
*pwqp
, unsigned power
)
1826 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
1830 for (i
= 0; i
< pwqp
->n
; ++i
) {
1831 pwqp
->p
[i
].qp
= isl_qpolynomial_pow(pwqp
->p
[i
].qp
, power
);
1833 return isl_pw_qpolynomial_free(pwqp
);
1839 __isl_give isl_qpolynomial
*isl_qpolynomial_zero_on_domain(
1840 __isl_take isl_space
*domain
)
1844 return isl_qpolynomial_alloc(domain
, 0, isl_poly_zero(domain
->ctx
));
1847 __isl_give isl_qpolynomial
*isl_qpolynomial_one_on_domain(
1848 __isl_take isl_space
*domain
)
1852 return isl_qpolynomial_alloc(domain
, 0, isl_poly_one(domain
->ctx
));
1855 __isl_give isl_qpolynomial
*isl_qpolynomial_infty_on_domain(
1856 __isl_take isl_space
*domain
)
1860 return isl_qpolynomial_alloc(domain
, 0, isl_poly_infty(domain
->ctx
));
1863 __isl_give isl_qpolynomial
*isl_qpolynomial_neginfty_on_domain(
1864 __isl_take isl_space
*domain
)
1868 return isl_qpolynomial_alloc(domain
, 0, isl_poly_neginfty(domain
->ctx
));
1871 __isl_give isl_qpolynomial
*isl_qpolynomial_nan_on_domain(
1872 __isl_take isl_space
*domain
)
1876 return isl_qpolynomial_alloc(domain
, 0, isl_poly_nan(domain
->ctx
));
1879 __isl_give isl_qpolynomial
*isl_qpolynomial_cst_on_domain(
1880 __isl_take isl_space
*domain
,
1883 struct isl_qpolynomial
*qp
;
1886 qp
= isl_qpolynomial_zero_on_domain(domain
);
1890 cst
= isl_poly_as_cst(qp
->poly
);
1891 isl_int_set(cst
->n
, v
);
1896 isl_bool
isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial
*qp
,
1897 isl_int
*n
, isl_int
*d
)
1902 return isl_bool_error
;
1904 if (!isl_poly_is_cst(qp
->poly
))
1905 return isl_bool_false
;
1907 cst
= isl_poly_as_cst(qp
->poly
);
1909 return isl_bool_error
;
1912 isl_int_set(*n
, cst
->n
);
1914 isl_int_set(*d
, cst
->d
);
1916 return isl_bool_true
;
1919 /* Return the constant term of "poly".
1921 static __isl_give isl_val
*isl_poly_get_constant_val(__isl_keep isl_poly
*poly
)
1928 while (!isl_poly_is_cst(poly
)) {
1931 rec
= isl_poly_as_rec(poly
);
1937 cst
= isl_poly_as_cst(poly
);
1940 return isl_val_rat_from_isl_int(cst
->poly
.ctx
, cst
->n
, cst
->d
);
1943 /* Return the constant term of "qp".
1945 __isl_give isl_val
*isl_qpolynomial_get_constant_val(
1946 __isl_keep isl_qpolynomial
*qp
)
1951 return isl_poly_get_constant_val(qp
->poly
);
1954 isl_bool
isl_poly_is_affine(__isl_keep isl_poly
*poly
)
1960 return isl_bool_error
;
1963 return isl_bool_true
;
1965 rec
= isl_poly_as_rec(poly
);
1967 return isl_bool_error
;
1970 return isl_bool_false
;
1972 isl_assert(poly
->ctx
, rec
->n
> 1, return isl_bool_error
);
1974 is_cst
= isl_poly_is_cst(rec
->p
[1]);
1976 return isl_bool_error
;
1978 return isl_bool_false
;
1980 return isl_poly_is_affine(rec
->p
[0]);
1983 isl_bool
isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial
*qp
)
1986 return isl_bool_error
;
1988 if (qp
->div
->n_row
> 0)
1989 return isl_bool_false
;
1991 return isl_poly_is_affine(qp
->poly
);
1994 static void update_coeff(__isl_keep isl_vec
*aff
,
1995 __isl_keep isl_poly_cst
*cst
, int pos
)
2000 if (isl_int_is_zero(cst
->n
))
2005 isl_int_gcd(gcd
, cst
->d
, aff
->el
[0]);
2006 isl_int_divexact(f
, cst
->d
, gcd
);
2007 isl_int_divexact(gcd
, aff
->el
[0], gcd
);
2008 isl_seq_scale(aff
->el
, aff
->el
, f
, aff
->size
);
2009 isl_int_mul(aff
->el
[1 + pos
], gcd
, cst
->n
);
2014 int isl_poly_update_affine(__isl_keep isl_poly
*poly
, __isl_keep isl_vec
*aff
)
2022 if (poly
->var
< 0) {
2025 cst
= isl_poly_as_cst(poly
);
2028 update_coeff(aff
, cst
, 0);
2032 rec
= isl_poly_as_rec(poly
);
2035 isl_assert(poly
->ctx
, rec
->n
== 2, return -1);
2037 cst
= isl_poly_as_cst(rec
->p
[1]);
2040 update_coeff(aff
, cst
, 1 + poly
->var
);
2042 return isl_poly_update_affine(rec
->p
[0], aff
);
2045 __isl_give isl_vec
*isl_qpolynomial_extract_affine(
2046 __isl_keep isl_qpolynomial
*qp
)
2054 d
= isl_space_dim(qp
->dim
, isl_dim_all
);
2055 aff
= isl_vec_alloc(qp
->div
->ctx
, 2 + d
+ qp
->div
->n_row
);
2059 isl_seq_clr(aff
->el
+ 1, 1 + d
+ qp
->div
->n_row
);
2060 isl_int_set_si(aff
->el
[0], 1);
2062 if (isl_poly_update_affine(qp
->poly
, aff
) < 0)
2071 /* Compare two quasi-polynomials.
2073 * Return -1 if "qp1" is "smaller" than "qp2", 1 if "qp1" is "greater"
2074 * than "qp2" and 0 if they are equal.
2076 int isl_qpolynomial_plain_cmp(__isl_keep isl_qpolynomial
*qp1
,
2077 __isl_keep isl_qpolynomial
*qp2
)
2088 cmp
= isl_space_cmp(qp1
->dim
, qp2
->dim
);
2092 cmp
= isl_local_cmp(qp1
->div
, qp2
->div
);
2096 return isl_poly_plain_cmp(qp1
->poly
, qp2
->poly
);
2099 /* Is "qp1" obviously equal to "qp2"?
2101 * NaN is not equal to anything, not even to another NaN.
2103 isl_bool
isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial
*qp1
,
2104 __isl_keep isl_qpolynomial
*qp2
)
2109 return isl_bool_error
;
2111 if (isl_qpolynomial_is_nan(qp1
) || isl_qpolynomial_is_nan(qp2
))
2112 return isl_bool_false
;
2114 equal
= isl_space_is_equal(qp1
->dim
, qp2
->dim
);
2115 if (equal
< 0 || !equal
)
2118 equal
= isl_mat_is_equal(qp1
->div
, qp2
->div
);
2119 if (equal
< 0 || !equal
)
2122 return isl_poly_is_equal(qp1
->poly
, qp2
->poly
);
2125 static isl_stat
poly_update_den(__isl_keep isl_poly
*poly
, isl_int
*d
)
2130 if (isl_poly_is_cst(poly
)) {
2132 cst
= isl_poly_as_cst(poly
);
2134 return isl_stat_error
;
2135 isl_int_lcm(*d
, *d
, cst
->d
);
2139 rec
= isl_poly_as_rec(poly
);
2141 return isl_stat_error
;
2143 for (i
= 0; i
< rec
->n
; ++i
)
2144 poly_update_den(rec
->p
[i
], d
);
2149 __isl_give isl_val
*isl_qpolynomial_get_den(__isl_keep isl_qpolynomial
*qp
)
2155 d
= isl_val_one(isl_qpolynomial_get_ctx(qp
));
2158 if (poly_update_den(qp
->poly
, &d
->n
) < 0)
2159 return isl_val_free(d
);
2163 __isl_give isl_qpolynomial
*isl_qpolynomial_var_pow_on_domain(
2164 __isl_take isl_space
*domain
, int pos
, int power
)
2166 struct isl_ctx
*ctx
;
2173 return isl_qpolynomial_alloc(domain
, 0,
2174 isl_poly_var_pow(ctx
, pos
, power
));
2177 __isl_give isl_qpolynomial
*isl_qpolynomial_var_on_domain(
2178 __isl_take isl_space
*domain
, enum isl_dim_type type
, unsigned pos
)
2180 if (isl_space_check_is_set(domain
) < 0)
2182 if (isl_space_check_range(domain
, type
, pos
, 1) < 0)
2185 if (type
== isl_dim_set
)
2186 pos
+= isl_space_dim(domain
, isl_dim_param
);
2188 return isl_qpolynomial_var_pow_on_domain(domain
, pos
, 1);
2190 isl_space_free(domain
);
2194 __isl_give isl_poly
*isl_poly_subs(__isl_take isl_poly
*poly
,
2195 unsigned first
, unsigned n
, __isl_keep isl_poly
**subs
)
2199 isl_poly
*base
, *res
;
2204 if (isl_poly_is_cst(poly
))
2207 if (poly
->var
< first
)
2210 rec
= isl_poly_as_rec(poly
);
2214 isl_assert(poly
->ctx
, rec
->n
>= 1, goto error
);
2216 if (poly
->var
>= first
+ n
)
2217 base
= isl_poly_var_pow(poly
->ctx
, poly
->var
, 1);
2219 base
= isl_poly_copy(subs
[poly
->var
- first
]);
2221 res
= isl_poly_subs(isl_poly_copy(rec
->p
[rec
->n
- 1]), first
, n
, subs
);
2222 for (i
= rec
->n
- 2; i
>= 0; --i
) {
2224 t
= isl_poly_subs(isl_poly_copy(rec
->p
[i
]), first
, n
, subs
);
2225 res
= isl_poly_mul(res
, isl_poly_copy(base
));
2226 res
= isl_poly_sum(res
, t
);
2229 isl_poly_free(base
);
2230 isl_poly_free(poly
);
2234 isl_poly_free(poly
);
2238 __isl_give isl_poly
*isl_poly_from_affine(isl_ctx
*ctx
, isl_int
*f
,
2239 isl_int denom
, unsigned len
)
2244 isl_assert(ctx
, len
>= 1, return NULL
);
2246 poly
= isl_poly_rat_cst(ctx
, f
[0], denom
);
2247 for (i
= 0; i
< len
- 1; ++i
) {
2251 if (isl_int_is_zero(f
[1 + i
]))
2254 c
= isl_poly_rat_cst(ctx
, f
[1 + i
], denom
);
2255 t
= isl_poly_var_pow(ctx
, i
, 1);
2256 t
= isl_poly_mul(c
, t
);
2257 poly
= isl_poly_sum(poly
, t
);
2263 /* Remove common factor of non-constant terms and denominator.
2265 static void normalize_div(__isl_keep isl_qpolynomial
*qp
, int div
)
2267 isl_ctx
*ctx
= qp
->div
->ctx
;
2268 unsigned total
= qp
->div
->n_col
- 2;
2270 isl_seq_gcd(qp
->div
->row
[div
] + 2, total
, &ctx
->normalize_gcd
);
2271 isl_int_gcd(ctx
->normalize_gcd
,
2272 ctx
->normalize_gcd
, qp
->div
->row
[div
][0]);
2273 if (isl_int_is_one(ctx
->normalize_gcd
))
2276 isl_seq_scale_down(qp
->div
->row
[div
] + 2, qp
->div
->row
[div
] + 2,
2277 ctx
->normalize_gcd
, total
);
2278 isl_int_divexact(qp
->div
->row
[div
][0], qp
->div
->row
[div
][0],
2279 ctx
->normalize_gcd
);
2280 isl_int_fdiv_q(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1],
2281 ctx
->normalize_gcd
);
2284 /* Replace the integer division identified by "div" by the polynomial "s".
2285 * The integer division is assumed not to appear in the definition
2286 * of any other integer divisions.
2288 static __isl_give isl_qpolynomial
*substitute_div(
2289 __isl_take isl_qpolynomial
*qp
, int div
, __isl_take isl_poly
*s
)
2298 qp
= isl_qpolynomial_cow(qp
);
2302 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
2303 qp
->poly
= isl_poly_subs(qp
->poly
, total
+ div
, 1, &s
);
2307 reordering
= isl_alloc_array(qp
->dim
->ctx
, int, total
+ qp
->div
->n_row
);
2310 for (i
= 0; i
< total
+ div
; ++i
)
2312 for (i
= total
+ div
+ 1; i
< total
+ qp
->div
->n_row
; ++i
)
2313 reordering
[i
] = i
- 1;
2314 qp
->div
= isl_mat_drop_rows(qp
->div
, div
, 1);
2315 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + total
+ div
, 1);
2316 qp
->poly
= reorder(qp
->poly
, reordering
);
2319 if (!qp
->poly
|| !qp
->div
)
2325 isl_qpolynomial_free(qp
);
2330 /* Replace all integer divisions [e/d] that turn out to not actually be integer
2331 * divisions because d is equal to 1 by their definition, i.e., e.
2333 static __isl_give isl_qpolynomial
*substitute_non_divs(
2334 __isl_take isl_qpolynomial
*qp
)
2343 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
2344 for (i
= 0; qp
&& i
< qp
->div
->n_row
; ++i
) {
2345 if (!isl_int_is_one(qp
->div
->row
[i
][0]))
2347 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
2348 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
2350 isl_seq_combine(qp
->div
->row
[j
] + 1,
2351 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
2352 qp
->div
->row
[j
][2 + total
+ i
],
2353 qp
->div
->row
[i
] + 1, 1 + total
+ i
);
2354 isl_int_set_si(qp
->div
->row
[j
][2 + total
+ i
], 0);
2355 normalize_div(qp
, j
);
2357 s
= isl_poly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
2358 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
2359 qp
= substitute_div(qp
, i
, s
);
2366 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
2367 * with d the denominator. When replacing the coefficient e of x by
2368 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
2369 * inside the division, so we need to add floor(e/d) * x outside.
2370 * That is, we replace q by q' + floor(e/d) * x and we therefore need
2371 * to adjust the coefficient of x in each later div that depends on the
2372 * current div "div" and also in the affine expressions in the rows of "mat"
2373 * (if they too depend on "div").
2375 static void reduce_div(__isl_keep isl_qpolynomial
*qp
, int div
,
2376 __isl_keep isl_mat
**mat
)
2380 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
2383 for (i
= 0; i
< 1 + total
+ div
; ++i
) {
2384 if (isl_int_is_nonneg(qp
->div
->row
[div
][1 + i
]) &&
2385 isl_int_lt(qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]))
2387 isl_int_fdiv_q(v
, qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
2388 isl_int_fdiv_r(qp
->div
->row
[div
][1 + i
],
2389 qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
2390 *mat
= isl_mat_col_addmul(*mat
, i
, v
, 1 + total
+ div
);
2391 for (j
= div
+ 1; j
< qp
->div
->n_row
; ++j
) {
2392 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ div
]))
2394 isl_int_addmul(qp
->div
->row
[j
][1 + i
],
2395 v
, qp
->div
->row
[j
][2 + total
+ div
]);
2401 /* Check if the last non-zero coefficient is bigger that half of the
2402 * denominator. If so, we will invert the div to further reduce the number
2403 * of distinct divs that may appear.
2404 * If the last non-zero coefficient is exactly half the denominator,
2405 * then we continue looking for earlier coefficients that are bigger
2406 * than half the denominator.
2408 static int needs_invert(__isl_keep isl_mat
*div
, int row
)
2413 for (i
= div
->n_col
- 1; i
>= 1; --i
) {
2414 if (isl_int_is_zero(div
->row
[row
][i
]))
2416 isl_int_mul_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
2417 cmp
= isl_int_cmp(div
->row
[row
][i
], div
->row
[row
][0]);
2418 isl_int_divexact_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
2428 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
2429 * We only invert the coefficients of e (and the coefficient of q in
2430 * later divs and in the rows of "mat"). After calling this function, the
2431 * coefficients of e should be reduced again.
2433 static void invert_div(__isl_keep isl_qpolynomial
*qp
, int div
,
2434 __isl_keep isl_mat
**mat
)
2436 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
2438 isl_seq_neg(qp
->div
->row
[div
] + 1,
2439 qp
->div
->row
[div
] + 1, qp
->div
->n_col
- 1);
2440 isl_int_sub_ui(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1], 1);
2441 isl_int_add(qp
->div
->row
[div
][1],
2442 qp
->div
->row
[div
][1], qp
->div
->row
[div
][0]);
2443 *mat
= isl_mat_col_neg(*mat
, 1 + total
+ div
);
2444 isl_mat_col_mul(qp
->div
, 2 + total
+ div
,
2445 qp
->div
->ctx
->negone
, 2 + total
+ div
);
2448 /* Reduce all divs of "qp" to have coefficients
2449 * in the interval [0, d-1], with d the denominator and such that the
2450 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2451 * The modifications to the integer divisions need to be reflected
2452 * in the factors of the polynomial that refer to the original
2453 * integer divisions. To this end, the modifications are collected
2454 * as a set of affine expressions and then plugged into the polynomial.
2456 * After the reduction, some divs may have become redundant or identical,
2457 * so we call substitute_non_divs and sort_divs. If these functions
2458 * eliminate divs or merge two or more divs into one, the coefficients
2459 * of the enclosing divs may have to be reduced again, so we call
2460 * ourselves recursively if the number of divs decreases.
2462 static __isl_give isl_qpolynomial
*reduce_divs(__isl_take isl_qpolynomial
*qp
)
2468 unsigned o_div
, n_div
, total
;
2473 total
= isl_qpolynomial_domain_dim(qp
, isl_dim_all
);
2474 n_div
= isl_qpolynomial_domain_dim(qp
, isl_dim_div
);
2475 o_div
= isl_qpolynomial_domain_offset(qp
, isl_dim_div
);
2476 ctx
= isl_qpolynomial_get_ctx(qp
);
2477 mat
= isl_mat_zero(ctx
, n_div
, 1 + total
);
2479 for (i
= 0; i
< n_div
; ++i
)
2480 mat
= isl_mat_set_element_si(mat
, i
, o_div
+ i
, 1);
2482 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2483 normalize_div(qp
, i
);
2484 reduce_div(qp
, i
, &mat
);
2485 if (needs_invert(qp
->div
, i
)) {
2486 invert_div(qp
, i
, &mat
);
2487 reduce_div(qp
, i
, &mat
);
2493 s
= isl_alloc_array(ctx
, struct isl_poly
*, n_div
);
2496 for (i
= 0; i
< n_div
; ++i
)
2497 s
[i
] = isl_poly_from_affine(ctx
, mat
->row
[i
], ctx
->one
,
2499 qp
->poly
= isl_poly_subs(qp
->poly
, o_div
- 1, n_div
, s
);
2500 for (i
= 0; i
< n_div
; ++i
)
2501 isl_poly_free(s
[i
]);
2508 qp
= substitute_non_divs(qp
);
2510 if (qp
&& isl_qpolynomial_domain_dim(qp
, isl_dim_div
) < n_div
)
2511 return reduce_divs(qp
);
2515 isl_qpolynomial_free(qp
);
2520 __isl_give isl_qpolynomial
*isl_qpolynomial_rat_cst_on_domain(
2521 __isl_take isl_space
*domain
, const isl_int n
, const isl_int d
)
2523 struct isl_qpolynomial
*qp
;
2526 qp
= isl_qpolynomial_zero_on_domain(domain
);
2530 cst
= isl_poly_as_cst(qp
->poly
);
2531 isl_int_set(cst
->n
, n
);
2532 isl_int_set(cst
->d
, d
);
2537 /* Return an isl_qpolynomial that is equal to "val" on domain space "domain".
2539 __isl_give isl_qpolynomial
*isl_qpolynomial_val_on_domain(
2540 __isl_take isl_space
*domain
, __isl_take isl_val
*val
)
2542 isl_qpolynomial
*qp
;
2545 qp
= isl_qpolynomial_zero_on_domain(domain
);
2549 cst
= isl_poly_as_cst(qp
->poly
);
2550 isl_int_set(cst
->n
, val
->n
);
2551 isl_int_set(cst
->d
, val
->d
);
2557 isl_qpolynomial_free(qp
);
2561 static isl_stat
poly_set_active(__isl_keep isl_poly
*poly
, int *active
, int d
)
2567 return isl_stat_error
;
2569 if (isl_poly_is_cst(poly
))
2573 active
[poly
->var
] = 1;
2575 rec
= isl_poly_as_rec(poly
);
2576 for (i
= 0; i
< rec
->n
; ++i
)
2577 if (poly_set_active(rec
->p
[i
], active
, d
) < 0)
2578 return isl_stat_error
;
2583 static isl_stat
set_active(__isl_keep isl_qpolynomial
*qp
, int *active
)
2586 int d
= isl_space_dim(qp
->dim
, isl_dim_all
);
2589 return isl_stat_error
;
2591 for (i
= 0; i
< d
; ++i
)
2592 for (j
= 0; j
< qp
->div
->n_row
; ++j
) {
2593 if (isl_int_is_zero(qp
->div
->row
[j
][2 + i
]))
2599 return poly_set_active(qp
->poly
, active
, d
);
2603 #define TYPE isl_qpolynomial
2605 #include "check_type_range_templ.c"
2607 isl_bool
isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial
*qp
,
2608 enum isl_dim_type type
, unsigned first
, unsigned n
)
2612 isl_bool involves
= isl_bool_false
;
2615 return isl_bool_error
;
2617 return isl_bool_false
;
2619 if (isl_qpolynomial_check_range(qp
, type
, first
, n
) < 0)
2620 return isl_bool_error
;
2621 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2622 type
== isl_dim_in
, return isl_bool_error
);
2624 active
= isl_calloc_array(qp
->dim
->ctx
, int,
2625 isl_space_dim(qp
->dim
, isl_dim_all
));
2626 if (set_active(qp
, active
) < 0)
2629 if (type
== isl_dim_in
)
2630 first
+= isl_space_dim(qp
->dim
, isl_dim_param
);
2631 for (i
= 0; i
< n
; ++i
)
2632 if (active
[first
+ i
]) {
2633 involves
= isl_bool_true
;
2642 return isl_bool_error
;
2645 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2646 * of the divs that do appear in the quasi-polynomial.
2648 static __isl_give isl_qpolynomial
*remove_redundant_divs(
2649 __isl_take isl_qpolynomial
*qp
)
2656 int *reordering
= NULL
;
2663 if (qp
->div
->n_row
== 0)
2666 d
= isl_space_dim(qp
->dim
, isl_dim_all
);
2667 len
= qp
->div
->n_col
- 2;
2668 ctx
= isl_qpolynomial_get_ctx(qp
);
2669 active
= isl_calloc_array(ctx
, int, len
);
2673 if (poly_set_active(qp
->poly
, active
, len
) < 0)
2676 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
2677 if (!active
[d
+ i
]) {
2681 for (j
= 0; j
< i
; ++j
) {
2682 if (isl_int_is_zero(qp
->div
->row
[i
][2 + d
+ j
]))
2694 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
2698 for (i
= 0; i
< d
; ++i
)
2702 n_div
= qp
->div
->n_row
;
2703 for (i
= 0; i
< n_div
; ++i
) {
2704 if (!active
[d
+ i
]) {
2705 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
2706 qp
->div
= isl_mat_drop_cols(qp
->div
,
2707 2 + d
+ i
- skip
, 1);
2710 reordering
[d
+ i
] = d
+ i
- skip
;
2713 qp
->poly
= reorder(qp
->poly
, reordering
);
2715 if (!qp
->poly
|| !qp
->div
)
2725 isl_qpolynomial_free(qp
);
2729 __isl_give isl_poly
*isl_poly_drop(__isl_take isl_poly
*poly
,
2730 unsigned first
, unsigned n
)
2737 if (n
== 0 || poly
->var
< 0 || poly
->var
< first
)
2739 if (poly
->var
< first
+ n
) {
2740 poly
= replace_by_constant_term(poly
);
2741 return isl_poly_drop(poly
, first
, n
);
2743 poly
= isl_poly_cow(poly
);
2747 rec
= isl_poly_as_rec(poly
);
2751 for (i
= 0; i
< rec
->n
; ++i
) {
2752 rec
->p
[i
] = isl_poly_drop(rec
->p
[i
], first
, n
);
2759 isl_poly_free(poly
);
2763 __isl_give isl_qpolynomial
*isl_qpolynomial_set_dim_name(
2764 __isl_take isl_qpolynomial
*qp
,
2765 enum isl_dim_type type
, unsigned pos
, const char *s
)
2767 qp
= isl_qpolynomial_cow(qp
);
2770 if (type
== isl_dim_out
)
2771 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
2772 "cannot set name of output/set dimension",
2773 return isl_qpolynomial_free(qp
));
2774 type
= domain_type(type
);
2775 qp
->dim
= isl_space_set_dim_name(qp
->dim
, type
, pos
, s
);
2780 isl_qpolynomial_free(qp
);
2784 __isl_give isl_qpolynomial
*isl_qpolynomial_drop_dims(
2785 __isl_take isl_qpolynomial
*qp
,
2786 enum isl_dim_type type
, unsigned first
, unsigned n
)
2790 if (type
== isl_dim_out
)
2791 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
2792 "cannot drop output/set dimension",
2794 if (isl_qpolynomial_check_range(qp
, type
, first
, n
) < 0)
2795 return isl_qpolynomial_free(qp
);
2796 type
= domain_type(type
);
2797 if (n
== 0 && !isl_space_is_named_or_nested(qp
->dim
, type
))
2800 qp
= isl_qpolynomial_cow(qp
);
2804 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2805 type
== isl_dim_set
, goto error
);
2807 qp
->dim
= isl_space_drop_dims(qp
->dim
, type
, first
, n
);
2811 if (type
== isl_dim_set
)
2812 first
+= isl_space_dim(qp
->dim
, isl_dim_param
);
2814 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + first
, n
);
2818 qp
->poly
= isl_poly_drop(qp
->poly
, first
, n
);
2824 isl_qpolynomial_free(qp
);
2828 /* Project the domain of the quasi-polynomial onto its parameter space.
2829 * The quasi-polynomial may not involve any of the domain dimensions.
2831 __isl_give isl_qpolynomial
*isl_qpolynomial_project_domain_on_params(
2832 __isl_take isl_qpolynomial
*qp
)
2838 n
= isl_qpolynomial_dim(qp
, isl_dim_in
);
2839 involves
= isl_qpolynomial_involves_dims(qp
, isl_dim_in
, 0, n
);
2841 return isl_qpolynomial_free(qp
);
2843 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
2844 "polynomial involves some of the domain dimensions",
2845 return isl_qpolynomial_free(qp
));
2846 qp
= isl_qpolynomial_drop_dims(qp
, isl_dim_in
, 0, n
);
2847 space
= isl_qpolynomial_get_domain_space(qp
);
2848 space
= isl_space_params(space
);
2849 qp
= isl_qpolynomial_reset_domain_space(qp
, space
);
2853 static __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities_lifted(
2854 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2864 if (eq
->n_eq
== 0) {
2865 isl_basic_set_free(eq
);
2869 qp
= isl_qpolynomial_cow(qp
);
2872 qp
->div
= isl_mat_cow(qp
->div
);
2876 total
= 1 + isl_space_dim(eq
->dim
, isl_dim_all
);
2878 isl_int_init(denom
);
2879 for (i
= 0; i
< eq
->n_eq
; ++i
) {
2880 j
= isl_seq_last_non_zero(eq
->eq
[i
], total
+ n_div
);
2881 if (j
< 0 || j
== 0 || j
>= total
)
2884 for (k
= 0; k
< qp
->div
->n_row
; ++k
) {
2885 if (isl_int_is_zero(qp
->div
->row
[k
][1 + j
]))
2887 isl_seq_elim(qp
->div
->row
[k
] + 1, eq
->eq
[i
], j
, total
,
2888 &qp
->div
->row
[k
][0]);
2889 normalize_div(qp
, k
);
2892 if (isl_int_is_pos(eq
->eq
[i
][j
]))
2893 isl_seq_neg(eq
->eq
[i
], eq
->eq
[i
], total
);
2894 isl_int_abs(denom
, eq
->eq
[i
][j
]);
2895 isl_int_set_si(eq
->eq
[i
][j
], 0);
2897 poly
= isl_poly_from_affine(qp
->dim
->ctx
,
2898 eq
->eq
[i
], denom
, total
);
2899 qp
->poly
= isl_poly_subs(qp
->poly
, j
- 1, 1, &poly
);
2900 isl_poly_free(poly
);
2902 isl_int_clear(denom
);
2907 isl_basic_set_free(eq
);
2909 qp
= substitute_non_divs(qp
);
2914 isl_basic_set_free(eq
);
2915 isl_qpolynomial_free(qp
);
2919 /* Exploit the equalities in "eq" to simplify the quasi-polynomial.
2921 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities(
2922 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2926 if (qp
->div
->n_row
> 0)
2927 eq
= isl_basic_set_add_dims(eq
, isl_dim_set
, qp
->div
->n_row
);
2928 return isl_qpolynomial_substitute_equalities_lifted(qp
, eq
);
2930 isl_basic_set_free(eq
);
2931 isl_qpolynomial_free(qp
);
2935 /* Look for equalities among the variables shared by context and qp
2936 * and the integer divisions of qp, if any.
2937 * The equalities are then used to eliminate variables and/or integer
2938 * divisions from qp.
2940 __isl_give isl_qpolynomial
*isl_qpolynomial_gist(
2941 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
2943 isl_local_space
*ls
;
2946 ls
= isl_qpolynomial_get_domain_local_space(qp
);
2947 context
= isl_local_space_lift_set(ls
, context
);
2949 aff
= isl_set_affine_hull(context
);
2950 return isl_qpolynomial_substitute_equalities_lifted(qp
, aff
);
2953 __isl_give isl_qpolynomial
*isl_qpolynomial_gist_params(
2954 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
2956 isl_space
*space
= isl_qpolynomial_get_domain_space(qp
);
2957 isl_set
*dom_context
= isl_set_universe(space
);
2958 dom_context
= isl_set_intersect_params(dom_context
, context
);
2959 return isl_qpolynomial_gist(qp
, dom_context
);
2962 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_from_qpolynomial(
2963 __isl_take isl_qpolynomial
*qp
)
2969 if (isl_qpolynomial_is_zero(qp
)) {
2970 isl_space
*dim
= isl_qpolynomial_get_space(qp
);
2971 isl_qpolynomial_free(qp
);
2972 return isl_pw_qpolynomial_zero(dim
);
2975 dom
= isl_set_universe(isl_qpolynomial_get_domain_space(qp
));
2976 return isl_pw_qpolynomial_alloc(dom
, qp
);
2979 #define isl_qpolynomial_involves_nan isl_qpolynomial_is_nan
2982 #define PW isl_pw_qpolynomial
2984 #define EL isl_qpolynomial
2986 #define EL_IS_ZERO is_zero
2990 #define IS_ZERO is_zero
2993 #undef DEFAULT_IS_ZERO
2994 #define DEFAULT_IS_ZERO 1
2998 #include <isl_pw_templ.c>
2999 #include <isl_pw_eval.c>
3002 #define BASE pw_qpolynomial
3004 #include <isl_union_single.c>
3005 #include <isl_union_eval.c>
3006 #include <isl_union_neg.c>
3008 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial
*pwqp
)
3016 if (!isl_set_plain_is_universe(pwqp
->p
[0].set
))
3019 return isl_qpolynomial_is_one(pwqp
->p
[0].qp
);
3022 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add(
3023 __isl_take isl_pw_qpolynomial
*pwqp1
,
3024 __isl_take isl_pw_qpolynomial
*pwqp2
)
3026 return isl_pw_qpolynomial_union_add_(pwqp1
, pwqp2
);
3029 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_mul(
3030 __isl_take isl_pw_qpolynomial
*pwqp1
,
3031 __isl_take isl_pw_qpolynomial
*pwqp2
)
3034 struct isl_pw_qpolynomial
*res
;
3036 if (!pwqp1
|| !pwqp2
)
3039 isl_assert(pwqp1
->dim
->ctx
, isl_space_is_equal(pwqp1
->dim
, pwqp2
->dim
),
3042 if (isl_pw_qpolynomial_is_zero(pwqp1
)) {
3043 isl_pw_qpolynomial_free(pwqp2
);
3047 if (isl_pw_qpolynomial_is_zero(pwqp2
)) {
3048 isl_pw_qpolynomial_free(pwqp1
);
3052 if (isl_pw_qpolynomial_is_one(pwqp1
)) {
3053 isl_pw_qpolynomial_free(pwqp1
);
3057 if (isl_pw_qpolynomial_is_one(pwqp2
)) {
3058 isl_pw_qpolynomial_free(pwqp2
);
3062 n
= pwqp1
->n
* pwqp2
->n
;
3063 res
= isl_pw_qpolynomial_alloc_size(isl_space_copy(pwqp1
->dim
), n
);
3065 for (i
= 0; i
< pwqp1
->n
; ++i
) {
3066 for (j
= 0; j
< pwqp2
->n
; ++j
) {
3067 struct isl_set
*common
;
3068 struct isl_qpolynomial
*prod
;
3069 common
= isl_set_intersect(isl_set_copy(pwqp1
->p
[i
].set
),
3070 isl_set_copy(pwqp2
->p
[j
].set
));
3071 if (isl_set_plain_is_empty(common
)) {
3072 isl_set_free(common
);
3076 prod
= isl_qpolynomial_mul(
3077 isl_qpolynomial_copy(pwqp1
->p
[i
].qp
),
3078 isl_qpolynomial_copy(pwqp2
->p
[j
].qp
));
3080 res
= isl_pw_qpolynomial_add_piece(res
, common
, prod
);
3084 isl_pw_qpolynomial_free(pwqp1
);
3085 isl_pw_qpolynomial_free(pwqp2
);
3089 isl_pw_qpolynomial_free(pwqp1
);
3090 isl_pw_qpolynomial_free(pwqp2
);
3094 __isl_give isl_val
*isl_poly_eval(__isl_take isl_poly
*poly
,
3095 __isl_take isl_vec
*vec
)
3102 if (isl_poly_is_cst(poly
)) {
3104 res
= isl_poly_get_constant_val(poly
);
3105 isl_poly_free(poly
);
3109 rec
= isl_poly_as_rec(poly
);
3113 isl_assert(poly
->ctx
, rec
->n
>= 1, goto error
);
3115 base
= isl_val_rat_from_isl_int(poly
->ctx
,
3116 vec
->el
[1 + poly
->var
], vec
->el
[0]);
3118 res
= isl_poly_eval(isl_poly_copy(rec
->p
[rec
->n
- 1]),
3121 for (i
= rec
->n
- 2; i
>= 0; --i
) {
3122 res
= isl_val_mul(res
, isl_val_copy(base
));
3123 res
= isl_val_add(res
, isl_poly_eval(isl_poly_copy(rec
->p
[i
]),
3124 isl_vec_copy(vec
)));
3128 isl_poly_free(poly
);
3132 isl_poly_free(poly
);
3137 /* Evaluate "qp" in the void point "pnt".
3138 * In particular, return the value NaN.
3140 static __isl_give isl_val
*eval_void(__isl_take isl_qpolynomial
*qp
,
3141 __isl_take isl_point
*pnt
)
3145 ctx
= isl_point_get_ctx(pnt
);
3146 isl_qpolynomial_free(qp
);
3147 isl_point_free(pnt
);
3148 return isl_val_nan(ctx
);
3151 __isl_give isl_val
*isl_qpolynomial_eval(__isl_take isl_qpolynomial
*qp
,
3152 __isl_take isl_point
*pnt
)
3160 isl_assert(pnt
->dim
->ctx
, isl_space_is_equal(pnt
->dim
, qp
->dim
), goto error
);
3161 is_void
= isl_point_is_void(pnt
);
3165 return eval_void(qp
, pnt
);
3167 ext
= isl_local_extend_point_vec(qp
->div
, isl_vec_copy(pnt
->vec
));
3169 v
= isl_poly_eval(isl_poly_copy(qp
->poly
), ext
);
3171 isl_qpolynomial_free(qp
);
3172 isl_point_free(pnt
);
3176 isl_qpolynomial_free(qp
);
3177 isl_point_free(pnt
);
3181 int isl_poly_cmp(__isl_keep isl_poly_cst
*cst1
, __isl_keep isl_poly_cst
*cst2
)
3186 isl_int_mul(t
, cst1
->n
, cst2
->d
);
3187 isl_int_submul(t
, cst2
->n
, cst1
->d
);
3188 cmp
= isl_int_sgn(t
);
3193 __isl_give isl_qpolynomial
*isl_qpolynomial_insert_dims(
3194 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
,
3195 unsigned first
, unsigned n
)
3203 if (type
== isl_dim_out
)
3204 isl_die(qp
->div
->ctx
, isl_error_invalid
,
3205 "cannot insert output/set dimensions",
3207 if (isl_qpolynomial_check_range(qp
, type
, first
, 0) < 0)
3208 return isl_qpolynomial_free(qp
);
3209 type
= domain_type(type
);
3210 if (n
== 0 && !isl_space_is_named_or_nested(qp
->dim
, type
))
3213 qp
= isl_qpolynomial_cow(qp
);
3217 g_pos
= pos(qp
->dim
, type
) + first
;
3219 qp
->div
= isl_mat_insert_zero_cols(qp
->div
, 2 + g_pos
, n
);
3223 total
= qp
->div
->n_col
- 2;
3224 if (total
> g_pos
) {
3226 exp
= isl_alloc_array(qp
->div
->ctx
, int, total
- g_pos
);
3229 for (i
= 0; i
< total
- g_pos
; ++i
)
3231 qp
->poly
= expand(qp
->poly
, exp
, g_pos
);
3237 qp
->dim
= isl_space_insert_dims(qp
->dim
, type
, first
, n
);
3243 isl_qpolynomial_free(qp
);
3247 __isl_give isl_qpolynomial
*isl_qpolynomial_add_dims(
3248 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
, unsigned n
)
3252 pos
= isl_qpolynomial_dim(qp
, type
);
3254 return isl_qpolynomial_insert_dims(qp
, type
, pos
, n
);
3257 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add_dims(
3258 __isl_take isl_pw_qpolynomial
*pwqp
,
3259 enum isl_dim_type type
, unsigned n
)
3263 pos
= isl_pw_qpolynomial_dim(pwqp
, type
);
3265 return isl_pw_qpolynomial_insert_dims(pwqp
, type
, pos
, n
);
3268 static int *reordering_move(isl_ctx
*ctx
,
3269 unsigned len
, unsigned dst
, unsigned src
, unsigned n
)
3274 reordering
= isl_alloc_array(ctx
, int, len
);
3279 for (i
= 0; i
< dst
; ++i
)
3281 for (i
= 0; i
< n
; ++i
)
3282 reordering
[src
+ i
] = dst
+ i
;
3283 for (i
= 0; i
< src
- dst
; ++i
)
3284 reordering
[dst
+ i
] = dst
+ n
+ i
;
3285 for (i
= 0; i
< len
- src
- n
; ++i
)
3286 reordering
[src
+ n
+ i
] = src
+ n
+ i
;
3288 for (i
= 0; i
< src
; ++i
)
3290 for (i
= 0; i
< n
; ++i
)
3291 reordering
[src
+ i
] = dst
+ i
;
3292 for (i
= 0; i
< dst
- src
; ++i
)
3293 reordering
[src
+ n
+ i
] = src
+ i
;
3294 for (i
= 0; i
< len
- dst
- n
; ++i
)
3295 reordering
[dst
+ n
+ i
] = dst
+ n
+ i
;
3301 __isl_give isl_qpolynomial
*isl_qpolynomial_move_dims(
3302 __isl_take isl_qpolynomial
*qp
,
3303 enum isl_dim_type dst_type
, unsigned dst_pos
,
3304 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
3313 if (dst_type
== isl_dim_out
|| src_type
== isl_dim_out
)
3314 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
3315 "cannot move output/set dimension",
3317 if (isl_qpolynomial_check_range(qp
, src_type
, src_pos
, n
) < 0)
3318 return isl_qpolynomial_free(qp
);
3319 if (dst_type
== isl_dim_in
)
3320 dst_type
= isl_dim_set
;
3321 if (src_type
== isl_dim_in
)
3322 src_type
= isl_dim_set
;
3325 !isl_space_is_named_or_nested(qp
->dim
, src_type
) &&
3326 !isl_space_is_named_or_nested(qp
->dim
, dst_type
))
3329 qp
= isl_qpolynomial_cow(qp
);
3333 g_dst_pos
= pos(qp
->dim
, dst_type
) + dst_pos
;
3334 g_src_pos
= pos(qp
->dim
, src_type
) + src_pos
;
3335 if (dst_type
> src_type
)
3338 qp
->div
= isl_mat_move_cols(qp
->div
, 2 + g_dst_pos
, 2 + g_src_pos
, n
);
3345 reordering
= reordering_move(qp
->dim
->ctx
,
3346 qp
->div
->n_col
- 2, g_dst_pos
, g_src_pos
, n
);
3350 qp
->poly
= reorder(qp
->poly
, reordering
);
3355 qp
->dim
= isl_space_move_dims(qp
->dim
, dst_type
, dst_pos
, src_type
, src_pos
, n
);
3361 isl_qpolynomial_free(qp
);
3365 __isl_give isl_qpolynomial
*isl_qpolynomial_from_affine(
3366 __isl_take isl_space
*space
, isl_int
*f
, isl_int denom
)
3370 space
= isl_space_domain(space
);
3374 poly
= isl_poly_from_affine(space
->ctx
, f
, denom
,
3375 1 + isl_space_dim(space
, isl_dim_all
));
3377 return isl_qpolynomial_alloc(space
, 0, poly
);
3380 __isl_give isl_qpolynomial
*isl_qpolynomial_from_aff(__isl_take isl_aff
*aff
)
3384 isl_qpolynomial
*qp
;
3389 ctx
= isl_aff_get_ctx(aff
);
3390 poly
= isl_poly_from_affine(ctx
, aff
->v
->el
+ 1, aff
->v
->el
[0],
3393 qp
= isl_qpolynomial_alloc(isl_aff_get_domain_space(aff
),
3394 aff
->ls
->div
->n_row
, poly
);
3398 isl_mat_free(qp
->div
);
3399 qp
->div
= isl_mat_copy(aff
->ls
->div
);
3400 qp
->div
= isl_mat_cow(qp
->div
);
3405 qp
= reduce_divs(qp
);
3406 qp
= remove_redundant_divs(qp
);
3410 return isl_qpolynomial_free(qp
);
3413 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_from_pw_aff(
3414 __isl_take isl_pw_aff
*pwaff
)
3417 isl_pw_qpolynomial
*pwqp
;
3422 pwqp
= isl_pw_qpolynomial_alloc_size(isl_pw_aff_get_space(pwaff
),
3425 for (i
= 0; i
< pwaff
->n
; ++i
) {
3427 isl_qpolynomial
*qp
;
3429 dom
= isl_set_copy(pwaff
->p
[i
].set
);
3430 qp
= isl_qpolynomial_from_aff(isl_aff_copy(pwaff
->p
[i
].aff
));
3431 pwqp
= isl_pw_qpolynomial_add_piece(pwqp
, dom
, qp
);
3434 isl_pw_aff_free(pwaff
);
3438 __isl_give isl_qpolynomial
*isl_qpolynomial_from_constraint(
3439 __isl_take isl_constraint
*c
, enum isl_dim_type type
, unsigned pos
)
3443 aff
= isl_constraint_get_bound(c
, type
, pos
);
3444 isl_constraint_free(c
);
3445 return isl_qpolynomial_from_aff(aff
);
3448 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3449 * in "qp" by subs[i].
3451 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute(
3452 __isl_take isl_qpolynomial
*qp
,
3453 enum isl_dim_type type
, unsigned first
, unsigned n
,
3454 __isl_keep isl_qpolynomial
**subs
)
3462 qp
= isl_qpolynomial_cow(qp
);
3466 if (type
== isl_dim_out
)
3467 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
3468 "cannot substitute output/set dimension",
3470 if (isl_qpolynomial_check_range(qp
, type
, first
, n
) < 0)
3471 return isl_qpolynomial_free(qp
);
3472 type
= domain_type(type
);
3474 for (i
= 0; i
< n
; ++i
)
3478 for (i
= 0; i
< n
; ++i
)
3479 isl_assert(qp
->dim
->ctx
, isl_space_is_equal(qp
->dim
, subs
[i
]->dim
),
3482 isl_assert(qp
->dim
->ctx
, qp
->div
->n_row
== 0, goto error
);
3483 for (i
= 0; i
< n
; ++i
)
3484 isl_assert(qp
->dim
->ctx
, subs
[i
]->div
->n_row
== 0, goto error
);
3486 first
+= pos(qp
->dim
, type
);
3488 polys
= isl_alloc_array(qp
->dim
->ctx
, struct isl_poly
*, n
);
3491 for (i
= 0; i
< n
; ++i
)
3492 polys
[i
] = subs
[i
]->poly
;
3494 qp
->poly
= isl_poly_subs(qp
->poly
, first
, n
, polys
);
3503 isl_qpolynomial_free(qp
);
3507 /* Extend "bset" with extra set dimensions for each integer division
3508 * in "qp" and then call "fn" with the extended bset and the polynomial
3509 * that results from replacing each of the integer divisions by the
3510 * corresponding extra set dimension.
3512 isl_stat
isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial
*qp
,
3513 __isl_keep isl_basic_set
*bset
,
3514 isl_stat (*fn
)(__isl_take isl_basic_set
*bset
,
3515 __isl_take isl_qpolynomial
*poly
, void *user
), void *user
)
3518 isl_local_space
*ls
;
3519 isl_qpolynomial
*poly
;
3522 return isl_stat_error
;
3523 if (qp
->div
->n_row
== 0)
3524 return fn(isl_basic_set_copy(bset
), isl_qpolynomial_copy(qp
),
3527 space
= isl_space_copy(qp
->dim
);
3528 space
= isl_space_add_dims(space
, isl_dim_set
, qp
->div
->n_row
);
3529 poly
= isl_qpolynomial_alloc(space
, 0, isl_poly_copy(qp
->poly
));
3530 bset
= isl_basic_set_copy(bset
);
3531 ls
= isl_qpolynomial_get_domain_local_space(qp
);
3532 bset
= isl_local_space_lift_basic_set(ls
, bset
);
3534 return fn(bset
, poly
, user
);
3537 /* Return total degree in variables first (inclusive) up to last (exclusive).
3539 int isl_poly_degree(__isl_keep isl_poly
*poly
, int first
, int last
)
3546 is_zero
= isl_poly_is_zero(poly
);
3551 if (isl_poly_is_cst(poly
) || poly
->var
< first
)
3554 rec
= isl_poly_as_rec(poly
);
3558 for (i
= 0; i
< rec
->n
; ++i
) {
3561 is_zero
= isl_poly_is_zero(rec
->p
[i
]);
3566 d
= isl_poly_degree(rec
->p
[i
], first
, last
);
3567 if (poly
->var
< last
)
3576 /* Return total degree in set variables.
3578 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial
*poly
)
3586 ovar
= isl_space_offset(poly
->dim
, isl_dim_set
);
3587 nvar
= isl_space_dim(poly
->dim
, isl_dim_set
);
3588 return isl_poly_degree(poly
->poly
, ovar
, ovar
+ nvar
);
3591 __isl_give isl_poly
*isl_poly_coeff(__isl_keep isl_poly
*poly
,
3592 unsigned pos
, int deg
)
3600 if (isl_poly_is_cst(poly
) || poly
->var
< pos
) {
3602 return isl_poly_copy(poly
);
3604 return isl_poly_zero(poly
->ctx
);
3607 rec
= isl_poly_as_rec(poly
);
3611 if (poly
->var
== pos
) {
3613 return isl_poly_copy(rec
->p
[deg
]);
3615 return isl_poly_zero(poly
->ctx
);
3618 poly
= isl_poly_copy(poly
);
3619 poly
= isl_poly_cow(poly
);
3620 rec
= isl_poly_as_rec(poly
);
3624 for (i
= 0; i
< rec
->n
; ++i
) {
3626 t
= isl_poly_coeff(rec
->p
[i
], pos
, deg
);
3629 isl_poly_free(rec
->p
[i
]);
3635 isl_poly_free(poly
);
3639 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3641 __isl_give isl_qpolynomial
*isl_qpolynomial_coeff(
3642 __isl_keep isl_qpolynomial
*qp
,
3643 enum isl_dim_type type
, unsigned t_pos
, int deg
)
3652 if (type
== isl_dim_out
)
3653 isl_die(qp
->div
->ctx
, isl_error_invalid
,
3654 "output/set dimension does not have a coefficient",
3656 if (isl_qpolynomial_check_range(qp
, type
, t_pos
, 1) < 0)
3658 type
= domain_type(type
);
3660 g_pos
= pos(qp
->dim
, type
) + t_pos
;
3661 poly
= isl_poly_coeff(qp
->poly
, g_pos
, deg
);
3663 c
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
),
3664 qp
->div
->n_row
, poly
);
3667 isl_mat_free(c
->div
);
3668 c
->div
= isl_mat_copy(qp
->div
);
3673 isl_qpolynomial_free(c
);
3677 /* Homogenize the polynomial in the variables first (inclusive) up to
3678 * last (exclusive) by inserting powers of variable first.
3679 * Variable first is assumed not to appear in the input.
3681 __isl_give isl_poly
*isl_poly_homogenize(__isl_take isl_poly
*poly
, int deg
,
3682 int target
, int first
, int last
)
3688 is_zero
= isl_poly_is_zero(poly
);
3690 return isl_poly_free(poly
);
3695 if (isl_poly_is_cst(poly
) || poly
->var
< first
) {
3698 hom
= isl_poly_var_pow(poly
->ctx
, first
, target
- deg
);
3701 rec
= isl_poly_as_rec(hom
);
3702 rec
->p
[target
- deg
] = isl_poly_mul(rec
->p
[target
- deg
], poly
);
3707 poly
= isl_poly_cow(poly
);
3708 rec
= isl_poly_as_rec(poly
);
3712 for (i
= 0; i
< rec
->n
; ++i
) {
3713 is_zero
= isl_poly_is_zero(rec
->p
[i
]);
3715 return isl_poly_free(poly
);
3718 rec
->p
[i
] = isl_poly_homogenize(rec
->p
[i
],
3719 poly
->var
< last
? deg
+ i
: i
, target
,
3727 isl_poly_free(poly
);
3731 /* Homogenize the polynomial in the set variables by introducing
3732 * powers of an extra set variable at position 0.
3734 __isl_give isl_qpolynomial
*isl_qpolynomial_homogenize(
3735 __isl_take isl_qpolynomial
*poly
)
3739 int deg
= isl_qpolynomial_degree(poly
);
3744 poly
= isl_qpolynomial_insert_dims(poly
, isl_dim_in
, 0, 1);
3745 poly
= isl_qpolynomial_cow(poly
);
3749 ovar
= isl_space_offset(poly
->dim
, isl_dim_set
);
3750 nvar
= isl_space_dim(poly
->dim
, isl_dim_set
);
3751 poly
->poly
= isl_poly_homogenize(poly
->poly
, 0, deg
, ovar
, ovar
+ nvar
);
3757 isl_qpolynomial_free(poly
);
3761 __isl_give isl_term
*isl_term_alloc(__isl_take isl_space
*space
,
3762 __isl_take isl_mat
*div
)
3770 n
= isl_space_dim(space
, isl_dim_all
) + div
->n_row
;
3772 term
= isl_calloc(space
->ctx
, struct isl_term
,
3773 sizeof(struct isl_term
) + (n
- 1) * sizeof(int));
3780 isl_int_init(term
->n
);
3781 isl_int_init(term
->d
);
3785 isl_space_free(space
);
3790 __isl_give isl_term
*isl_term_copy(__isl_keep isl_term
*term
)
3799 __isl_give isl_term
*isl_term_dup(__isl_keep isl_term
*term
)
3808 total
= isl_space_dim(term
->dim
, isl_dim_all
) + term
->div
->n_row
;
3810 dup
= isl_term_alloc(isl_space_copy(term
->dim
), isl_mat_copy(term
->div
));
3814 isl_int_set(dup
->n
, term
->n
);
3815 isl_int_set(dup
->d
, term
->d
);
3817 for (i
= 0; i
< total
; ++i
)
3818 dup
->pow
[i
] = term
->pow
[i
];
3823 __isl_give isl_term
*isl_term_cow(__isl_take isl_term
*term
)
3831 return isl_term_dup(term
);
3834 __isl_null isl_term
*isl_term_free(__isl_take isl_term
*term
)
3839 if (--term
->ref
> 0)
3842 isl_space_free(term
->dim
);
3843 isl_mat_free(term
->div
);
3844 isl_int_clear(term
->n
);
3845 isl_int_clear(term
->d
);
3851 unsigned isl_term_dim(__isl_keep isl_term
*term
, enum isl_dim_type type
)
3859 case isl_dim_out
: return isl_space_dim(term
->dim
, type
);
3860 case isl_dim_div
: return term
->div
->n_row
;
3861 case isl_dim_all
: return isl_space_dim(term
->dim
, isl_dim_all
) +
3867 isl_ctx
*isl_term_get_ctx(__isl_keep isl_term
*term
)
3869 return term
? term
->dim
->ctx
: NULL
;
3872 void isl_term_get_num(__isl_keep isl_term
*term
, isl_int
*n
)
3876 isl_int_set(*n
, term
->n
);
3879 /* Return the coefficient of the term "term".
3881 __isl_give isl_val
*isl_term_get_coefficient_val(__isl_keep isl_term
*term
)
3886 return isl_val_rat_from_isl_int(isl_term_get_ctx(term
),
3891 #define TYPE isl_term
3893 #include "check_type_range_templ.c"
3895 int isl_term_get_exp(__isl_keep isl_term
*term
,
3896 enum isl_dim_type type
, unsigned pos
)
3898 if (isl_term_check_range(term
, type
, pos
, 1) < 0)
3901 if (type
>= isl_dim_set
)
3902 pos
+= isl_space_dim(term
->dim
, isl_dim_param
);
3903 if (type
>= isl_dim_div
)
3904 pos
+= isl_space_dim(term
->dim
, isl_dim_set
);
3906 return term
->pow
[pos
];
3909 __isl_give isl_aff
*isl_term_get_div(__isl_keep isl_term
*term
, unsigned pos
)
3911 isl_local_space
*ls
;
3914 if (isl_term_check_range(term
, isl_dim_div
, pos
, 1) < 0)
3917 ls
= isl_local_space_alloc_div(isl_space_copy(term
->dim
),
3918 isl_mat_copy(term
->div
));
3919 aff
= isl_aff_alloc(ls
);
3923 isl_seq_cpy(aff
->v
->el
, term
->div
->row
[pos
], aff
->v
->size
);
3925 aff
= isl_aff_normalize(aff
);
3930 __isl_give isl_term
*isl_poly_foreach_term(__isl_keep isl_poly
*poly
,
3931 isl_stat (*fn
)(__isl_take isl_term
*term
, void *user
),
3932 __isl_take isl_term
*term
, void *user
)
3935 isl_bool is_zero
, is_bad
;
3938 is_zero
= isl_poly_is_zero(poly
);
3939 if (is_zero
< 0 || !term
)
3945 is_bad
= isl_poly_is_nan(poly
);
3946 if (is_bad
>= 0 && !is_bad
)
3947 is_bad
= isl_poly_is_infty(poly
);
3948 if (is_bad
>= 0 && !is_bad
)
3949 is_bad
= isl_poly_is_neginfty(poly
);
3951 return isl_term_free(term
);
3953 isl_die(isl_term_get_ctx(term
), isl_error_invalid
,
3954 "cannot handle NaN/infty polynomial",
3955 return isl_term_free(term
));
3957 if (isl_poly_is_cst(poly
)) {
3959 cst
= isl_poly_as_cst(poly
);
3962 term
= isl_term_cow(term
);
3965 isl_int_set(term
->n
, cst
->n
);
3966 isl_int_set(term
->d
, cst
->d
);
3967 if (fn(isl_term_copy(term
), user
) < 0)
3972 rec
= isl_poly_as_rec(poly
);
3976 for (i
= 0; i
< rec
->n
; ++i
) {
3977 term
= isl_term_cow(term
);
3980 term
->pow
[poly
->var
] = i
;
3981 term
= isl_poly_foreach_term(rec
->p
[i
], fn
, term
, user
);
3985 term
->pow
[poly
->var
] = 0;
3989 isl_term_free(term
);
3993 isl_stat
isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial
*qp
,
3994 isl_stat (*fn
)(__isl_take isl_term
*term
, void *user
), void *user
)
3999 return isl_stat_error
;
4001 term
= isl_term_alloc(isl_space_copy(qp
->dim
), isl_mat_copy(qp
->div
));
4003 return isl_stat_error
;
4005 term
= isl_poly_foreach_term(qp
->poly
, fn
, term
, user
);
4007 isl_term_free(term
);
4009 return term
? isl_stat_ok
: isl_stat_error
;
4012 __isl_give isl_qpolynomial
*isl_qpolynomial_from_term(__isl_take isl_term
*term
)
4015 isl_qpolynomial
*qp
;
4021 n
= isl_space_dim(term
->dim
, isl_dim_all
) + term
->div
->n_row
;
4023 poly
= isl_poly_rat_cst(term
->dim
->ctx
, term
->n
, term
->d
);
4024 for (i
= 0; i
< n
; ++i
) {
4027 poly
= isl_poly_mul(poly
,
4028 isl_poly_var_pow(term
->dim
->ctx
, i
, term
->pow
[i
]));
4031 qp
= isl_qpolynomial_alloc(isl_space_copy(term
->dim
),
4032 term
->div
->n_row
, poly
);
4035 isl_mat_free(qp
->div
);
4036 qp
->div
= isl_mat_copy(term
->div
);
4040 isl_term_free(term
);
4043 isl_qpolynomial_free(qp
);
4044 isl_term_free(term
);
4048 __isl_give isl_qpolynomial
*isl_qpolynomial_lift(__isl_take isl_qpolynomial
*qp
,
4049 __isl_take isl_space
*space
)
4058 if (isl_space_is_equal(qp
->dim
, space
)) {
4059 isl_space_free(space
);
4063 qp
= isl_qpolynomial_cow(qp
);
4067 extra
= isl_space_dim(space
, isl_dim_set
) -
4068 isl_space_dim(qp
->dim
, isl_dim_set
);
4069 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4070 if (qp
->div
->n_row
) {
4073 exp
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
4076 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4078 qp
->poly
= expand(qp
->poly
, exp
, total
);
4083 qp
->div
= isl_mat_insert_cols(qp
->div
, 2 + total
, extra
);
4086 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4087 isl_seq_clr(qp
->div
->row
[i
] + 2 + total
, extra
);
4089 isl_space_free(qp
->dim
);
4094 isl_space_free(space
);
4095 isl_qpolynomial_free(qp
);
4099 /* For each parameter or variable that does not appear in qp,
4100 * first eliminate the variable from all constraints and then set it to zero.
4102 static __isl_give isl_set
*fix_inactive(__isl_take isl_set
*set
,
4103 __isl_keep isl_qpolynomial
*qp
)
4114 d
= isl_space_dim(set
->dim
, isl_dim_all
);
4115 active
= isl_calloc_array(set
->ctx
, int, d
);
4116 if (set_active(qp
, active
) < 0)
4119 for (i
= 0; i
< d
; ++i
)
4128 nparam
= isl_space_dim(set
->dim
, isl_dim_param
);
4129 nvar
= isl_space_dim(set
->dim
, isl_dim_set
);
4130 for (i
= 0; i
< nparam
; ++i
) {
4133 set
= isl_set_eliminate(set
, isl_dim_param
, i
, 1);
4134 set
= isl_set_fix_si(set
, isl_dim_param
, i
, 0);
4136 for (i
= 0; i
< nvar
; ++i
) {
4137 if (active
[nparam
+ i
])
4139 set
= isl_set_eliminate(set
, isl_dim_set
, i
, 1);
4140 set
= isl_set_fix_si(set
, isl_dim_set
, i
, 0);
4152 struct isl_opt_data
{
4153 isl_qpolynomial
*qp
;
4159 static isl_stat
opt_fn(__isl_take isl_point
*pnt
, void *user
)
4161 struct isl_opt_data
*data
= (struct isl_opt_data
*)user
;
4164 val
= isl_qpolynomial_eval(isl_qpolynomial_copy(data
->qp
), pnt
);
4168 } else if (data
->max
) {
4169 data
->opt
= isl_val_max(data
->opt
, val
);
4171 data
->opt
= isl_val_min(data
->opt
, val
);
4177 __isl_give isl_val
*isl_qpolynomial_opt_on_domain(
4178 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*set
, int max
)
4180 struct isl_opt_data data
= { NULL
, 1, NULL
, max
};
4185 if (isl_poly_is_cst(qp
->poly
)) {
4187 data
.opt
= isl_qpolynomial_get_constant_val(qp
);
4188 isl_qpolynomial_free(qp
);
4192 set
= fix_inactive(set
, qp
);
4195 if (isl_set_foreach_point(set
, opt_fn
, &data
) < 0)
4199 data
.opt
= isl_val_zero(isl_set_get_ctx(set
));
4202 isl_qpolynomial_free(qp
);
4206 isl_qpolynomial_free(qp
);
4207 isl_val_free(data
.opt
);
4211 __isl_give isl_qpolynomial
*isl_qpolynomial_morph_domain(
4212 __isl_take isl_qpolynomial
*qp
, __isl_take isl_morph
*morph
)
4218 isl_mat
*mat
, *diag
;
4220 qp
= isl_qpolynomial_cow(qp
);
4225 isl_assert(ctx
, isl_space_is_equal(qp
->dim
, morph
->dom
->dim
), goto error
);
4227 n_sub
= morph
->inv
->n_row
- 1;
4228 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
4229 n_sub
+= qp
->div
->n_row
;
4230 subs
= isl_calloc_array(ctx
, struct isl_poly
*, n_sub
);
4234 for (i
= 0; 1 + i
< morph
->inv
->n_row
; ++i
)
4235 subs
[i
] = isl_poly_from_affine(ctx
, morph
->inv
->row
[1 + i
],
4236 morph
->inv
->row
[0][0], morph
->inv
->n_col
);
4237 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
4238 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4239 subs
[morph
->inv
->n_row
- 1 + i
] =
4240 isl_poly_var_pow(ctx
, morph
->inv
->n_col
- 1 + i
, 1);
4242 qp
->poly
= isl_poly_subs(qp
->poly
, 0, n_sub
, subs
);
4244 for (i
= 0; i
< n_sub
; ++i
)
4245 isl_poly_free(subs
[i
]);
4248 diag
= isl_mat_diag(ctx
, 1, morph
->inv
->row
[0][0]);
4249 mat
= isl_mat_diagonal(diag
, isl_mat_copy(morph
->inv
));
4250 diag
= isl_mat_diag(ctx
, qp
->div
->n_row
, morph
->inv
->row
[0][0]);
4251 mat
= isl_mat_diagonal(mat
, diag
);
4252 qp
->div
= isl_mat_product(qp
->div
, mat
);
4253 isl_space_free(qp
->dim
);
4254 qp
->dim
= isl_space_copy(morph
->ran
->dim
);
4256 if (!qp
->poly
|| !qp
->div
|| !qp
->dim
)
4259 isl_morph_free(morph
);
4263 isl_qpolynomial_free(qp
);
4264 isl_morph_free(morph
);
4268 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_mul(
4269 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
4270 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
4272 return isl_union_pw_qpolynomial_match_bin_op(upwqp1
, upwqp2
,
4273 &isl_pw_qpolynomial_mul
);
4276 /* Reorder the dimension of "qp" according to the given reordering.
4278 __isl_give isl_qpolynomial
*isl_qpolynomial_realign_domain(
4279 __isl_take isl_qpolynomial
*qp
, __isl_take isl_reordering
*r
)
4283 qp
= isl_qpolynomial_cow(qp
);
4287 r
= isl_reordering_extend(r
, qp
->div
->n_row
);
4291 qp
->div
= isl_local_reorder(qp
->div
, isl_reordering_copy(r
));
4295 qp
->poly
= reorder(qp
->poly
, r
->pos
);
4299 space
= isl_reordering_get_space(r
);
4300 qp
= isl_qpolynomial_reset_domain_space(qp
, space
);
4302 isl_reordering_free(r
);
4305 isl_qpolynomial_free(qp
);
4306 isl_reordering_free(r
);
4310 __isl_give isl_qpolynomial
*isl_qpolynomial_align_params(
4311 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*model
)
4313 isl_bool equal_params
;
4318 equal_params
= isl_space_has_equal_params(qp
->dim
, model
);
4319 if (equal_params
< 0)
4321 if (!equal_params
) {
4322 isl_reordering
*exp
;
4324 exp
= isl_parameter_alignment_reordering(qp
->dim
, model
);
4325 exp
= isl_reordering_extend_space(exp
,
4326 isl_qpolynomial_get_domain_space(qp
));
4327 qp
= isl_qpolynomial_realign_domain(qp
, exp
);
4330 isl_space_free(model
);
4333 isl_space_free(model
);
4334 isl_qpolynomial_free(qp
);
4338 struct isl_split_periods_data
{
4340 isl_pw_qpolynomial
*res
;
4343 /* Create a slice where the integer division "div" has the fixed value "v".
4344 * In particular, if "div" refers to floor(f/m), then create a slice
4346 * m v <= f <= m v + (m - 1)
4351 * -f + m v + (m - 1) >= 0
4353 static __isl_give isl_set
*set_div_slice(__isl_take isl_space
*space
,
4354 __isl_keep isl_qpolynomial
*qp
, int div
, isl_int v
)
4357 isl_basic_set
*bset
= NULL
;
4363 total
= isl_space_dim(space
, isl_dim_all
);
4364 bset
= isl_basic_set_alloc_space(isl_space_copy(space
), 0, 0, 2);
4366 k
= isl_basic_set_alloc_inequality(bset
);
4369 isl_seq_cpy(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4370 isl_int_submul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4372 k
= isl_basic_set_alloc_inequality(bset
);
4375 isl_seq_neg(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4376 isl_int_addmul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4377 isl_int_add(bset
->ineq
[k
][0], bset
->ineq
[k
][0], qp
->div
->row
[div
][0]);
4378 isl_int_sub_ui(bset
->ineq
[k
][0], bset
->ineq
[k
][0], 1);
4380 isl_space_free(space
);
4381 return isl_set_from_basic_set(bset
);
4383 isl_basic_set_free(bset
);
4384 isl_space_free(space
);
4388 static isl_stat
split_periods(__isl_take isl_set
*set
,
4389 __isl_take isl_qpolynomial
*qp
, void *user
);
4391 /* Create a slice of the domain "set" such that integer division "div"
4392 * has the fixed value "v" and add the results to data->res,
4393 * replacing the integer division by "v" in "qp".
4395 static isl_stat
set_div(__isl_take isl_set
*set
,
4396 __isl_take isl_qpolynomial
*qp
, int div
, isl_int v
,
4397 struct isl_split_periods_data
*data
)
4404 slice
= set_div_slice(isl_set_get_space(set
), qp
, div
, v
);
4405 set
= isl_set_intersect(set
, slice
);
4410 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4412 for (i
= div
+ 1; i
< qp
->div
->n_row
; ++i
) {
4413 if (isl_int_is_zero(qp
->div
->row
[i
][2 + total
+ div
]))
4415 isl_int_addmul(qp
->div
->row
[i
][1],
4416 qp
->div
->row
[i
][2 + total
+ div
], v
);
4417 isl_int_set_si(qp
->div
->row
[i
][2 + total
+ div
], 0);
4420 cst
= isl_poly_rat_cst(qp
->dim
->ctx
, v
, qp
->dim
->ctx
->one
);
4421 qp
= substitute_div(qp
, div
, cst
);
4423 return split_periods(set
, qp
, data
);
4426 isl_qpolynomial_free(qp
);
4427 return isl_stat_error
;
4430 /* Split the domain "set" such that integer division "div"
4431 * has a fixed value (ranging from "min" to "max") on each slice
4432 * and add the results to data->res.
4434 static isl_stat
split_div(__isl_take isl_set
*set
,
4435 __isl_take isl_qpolynomial
*qp
, int div
, isl_int min
, isl_int max
,
4436 struct isl_split_periods_data
*data
)
4438 for (; isl_int_le(min
, max
); isl_int_add_ui(min
, min
, 1)) {
4439 isl_set
*set_i
= isl_set_copy(set
);
4440 isl_qpolynomial
*qp_i
= isl_qpolynomial_copy(qp
);
4442 if (set_div(set_i
, qp_i
, div
, min
, data
) < 0)
4446 isl_qpolynomial_free(qp
);
4450 isl_qpolynomial_free(qp
);
4451 return isl_stat_error
;
4454 /* If "qp" refers to any integer division
4455 * that can only attain "max_periods" distinct values on "set"
4456 * then split the domain along those distinct values.
4457 * Add the results (or the original if no splitting occurs)
4460 static isl_stat
split_periods(__isl_take isl_set
*set
,
4461 __isl_take isl_qpolynomial
*qp
, void *user
)
4464 isl_pw_qpolynomial
*pwqp
;
4465 struct isl_split_periods_data
*data
;
4468 isl_stat r
= isl_stat_ok
;
4470 data
= (struct isl_split_periods_data
*)user
;
4475 if (qp
->div
->n_row
== 0) {
4476 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4477 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4483 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4484 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4485 enum isl_lp_result lp_res
;
4487 if (isl_seq_first_non_zero(qp
->div
->row
[i
] + 2 + total
,
4488 qp
->div
->n_row
) != -1)
4491 lp_res
= isl_set_solve_lp(set
, 0, qp
->div
->row
[i
] + 1,
4492 set
->ctx
->one
, &min
, NULL
, NULL
);
4493 if (lp_res
== isl_lp_error
)
4495 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4497 isl_int_fdiv_q(min
, min
, qp
->div
->row
[i
][0]);
4499 lp_res
= isl_set_solve_lp(set
, 1, qp
->div
->row
[i
] + 1,
4500 set
->ctx
->one
, &max
, NULL
, NULL
);
4501 if (lp_res
== isl_lp_error
)
4503 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4505 isl_int_fdiv_q(max
, max
, qp
->div
->row
[i
][0]);
4507 isl_int_sub(max
, max
, min
);
4508 if (isl_int_cmp_si(max
, data
->max_periods
) < 0) {
4509 isl_int_add(max
, max
, min
);
4514 if (i
< qp
->div
->n_row
) {
4515 r
= split_div(set
, qp
, i
, min
, max
, data
);
4517 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4518 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4530 isl_qpolynomial_free(qp
);
4531 return isl_stat_error
;
4534 /* If any quasi-polynomial in pwqp refers to any integer division
4535 * that can only attain "max_periods" distinct values on its domain
4536 * then split the domain along those distinct values.
4538 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_split_periods(
4539 __isl_take isl_pw_qpolynomial
*pwqp
, int max_periods
)
4541 struct isl_split_periods_data data
;
4543 data
.max_periods
= max_periods
;
4544 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp
));
4546 if (isl_pw_qpolynomial_foreach_piece(pwqp
, &split_periods
, &data
) < 0)
4549 isl_pw_qpolynomial_free(pwqp
);
4553 isl_pw_qpolynomial_free(data
.res
);
4554 isl_pw_qpolynomial_free(pwqp
);
4558 /* Construct a piecewise quasipolynomial that is constant on the given
4559 * domain. In particular, it is
4562 * infinity if cst == -1
4564 * If cst == -1, then explicitly check whether the domain is empty and,
4565 * if so, return 0 instead.
4567 static __isl_give isl_pw_qpolynomial
*constant_on_domain(
4568 __isl_take isl_basic_set
*bset
, int cst
)
4571 isl_qpolynomial
*qp
;
4573 if (cst
< 0 && isl_basic_set_is_empty(bset
) == isl_bool_true
)
4578 bset
= isl_basic_set_params(bset
);
4579 dim
= isl_basic_set_get_space(bset
);
4581 qp
= isl_qpolynomial_infty_on_domain(dim
);
4583 qp
= isl_qpolynomial_zero_on_domain(dim
);
4585 qp
= isl_qpolynomial_one_on_domain(dim
);
4586 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset
), qp
);
4589 /* Factor bset, call fn on each of the factors and return the product.
4591 * If no factors can be found, simply call fn on the input.
4592 * Otherwise, construct the factors based on the factorizer,
4593 * call fn on each factor and compute the product.
4595 static __isl_give isl_pw_qpolynomial
*compressed_multiplicative_call(
4596 __isl_take isl_basic_set
*bset
,
4597 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4603 isl_qpolynomial
*qp
;
4604 isl_pw_qpolynomial
*pwqp
;
4608 f
= isl_basic_set_factorizer(bset
);
4611 if (f
->n_group
== 0) {
4612 isl_factorizer_free(f
);
4616 nparam
= isl_basic_set_dim(bset
, isl_dim_param
);
4617 nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
4619 space
= isl_basic_set_get_space(bset
);
4620 space
= isl_space_params(space
);
4621 set
= isl_set_universe(isl_space_copy(space
));
4622 qp
= isl_qpolynomial_one_on_domain(space
);
4623 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4625 bset
= isl_morph_basic_set(isl_morph_copy(f
->morph
), bset
);
4627 for (i
= 0, n
= 0; i
< f
->n_group
; ++i
) {
4628 isl_basic_set
*bset_i
;
4629 isl_pw_qpolynomial
*pwqp_i
;
4631 bset_i
= isl_basic_set_copy(bset
);
4632 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4633 nparam
+ n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4634 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4636 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
,
4637 n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4638 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
, 0, n
);
4640 pwqp_i
= fn(bset_i
);
4641 pwqp
= isl_pw_qpolynomial_mul(pwqp
, pwqp_i
);
4646 isl_basic_set_free(bset
);
4647 isl_factorizer_free(f
);
4651 isl_basic_set_free(bset
);
4655 /* Factor bset, call fn on each of the factors and return the product.
4656 * The function is assumed to evaluate to zero on empty domains,
4657 * to one on zero-dimensional domains and to infinity on unbounded domains
4658 * and will not be called explicitly on zero-dimensional or unbounded domains.
4660 * We first check for some special cases and remove all equalities.
4661 * Then we hand over control to compressed_multiplicative_call.
4663 __isl_give isl_pw_qpolynomial
*isl_basic_set_multiplicative_call(
4664 __isl_take isl_basic_set
*bset
,
4665 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4669 isl_pw_qpolynomial
*pwqp
;
4674 if (isl_basic_set_plain_is_empty(bset
))
4675 return constant_on_domain(bset
, 0);
4677 if (isl_basic_set_dim(bset
, isl_dim_set
) == 0)
4678 return constant_on_domain(bset
, 1);
4680 bounded
= isl_basic_set_is_bounded(bset
);
4684 return constant_on_domain(bset
, -1);
4686 if (bset
->n_eq
== 0)
4687 return compressed_multiplicative_call(bset
, fn
);
4689 morph
= isl_basic_set_full_compression(bset
);
4690 bset
= isl_morph_basic_set(isl_morph_copy(morph
), bset
);
4692 pwqp
= compressed_multiplicative_call(bset
, fn
);
4694 morph
= isl_morph_dom_params(morph
);
4695 morph
= isl_morph_ran_params(morph
);
4696 morph
= isl_morph_inverse(morph
);
4698 pwqp
= isl_pw_qpolynomial_morph_domain(pwqp
, morph
);
4702 isl_basic_set_free(bset
);
4706 /* Drop all floors in "qp", turning each integer division [a/m] into
4707 * a rational division a/m. If "down" is set, then the integer division
4708 * is replaced by (a-(m-1))/m instead.
4710 static __isl_give isl_qpolynomial
*qp_drop_floors(
4711 __isl_take isl_qpolynomial
*qp
, int down
)
4718 if (qp
->div
->n_row
== 0)
4721 qp
= isl_qpolynomial_cow(qp
);
4725 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
4727 isl_int_sub(qp
->div
->row
[i
][1],
4728 qp
->div
->row
[i
][1], qp
->div
->row
[i
][0]);
4729 isl_int_add_ui(qp
->div
->row
[i
][1],
4730 qp
->div
->row
[i
][1], 1);
4732 s
= isl_poly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
4733 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
4734 qp
= substitute_div(qp
, i
, s
);
4742 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4743 * a rational division a/m.
4745 static __isl_give isl_pw_qpolynomial
*pwqp_drop_floors(
4746 __isl_take isl_pw_qpolynomial
*pwqp
)
4753 if (isl_pw_qpolynomial_is_zero(pwqp
))
4756 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
4760 for (i
= 0; i
< pwqp
->n
; ++i
) {
4761 pwqp
->p
[i
].qp
= qp_drop_floors(pwqp
->p
[i
].qp
, 0);
4768 isl_pw_qpolynomial_free(pwqp
);
4772 /* Adjust all the integer divisions in "qp" such that they are at least
4773 * one over the given orthant (identified by "signs"). This ensures
4774 * that they will still be non-negative even after subtracting (m-1)/m.
4776 * In particular, f is replaced by f' + v, changing f = [a/m]
4777 * to f' = [(a - m v)/m].
4778 * If the constant term k in a is smaller than m,
4779 * the constant term of v is set to floor(k/m) - 1.
4780 * For any other term, if the coefficient c and the variable x have
4781 * the same sign, then no changes are needed.
4782 * Otherwise, if the variable is positive (and c is negative),
4783 * then the coefficient of x in v is set to floor(c/m).
4784 * If the variable is negative (and c is positive),
4785 * then the coefficient of x in v is set to ceil(c/m).
4787 static __isl_give isl_qpolynomial
*make_divs_pos(__isl_take isl_qpolynomial
*qp
,
4795 qp
= isl_qpolynomial_cow(qp
);
4798 qp
->div
= isl_mat_cow(qp
->div
);
4802 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4803 v
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
4805 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4806 isl_int
*row
= qp
->div
->row
[i
];
4810 if (isl_int_lt(row
[1], row
[0])) {
4811 isl_int_fdiv_q(v
->el
[0], row
[1], row
[0]);
4812 isl_int_sub_ui(v
->el
[0], v
->el
[0], 1);
4813 isl_int_submul(row
[1], row
[0], v
->el
[0]);
4815 for (j
= 0; j
< total
; ++j
) {
4816 if (isl_int_sgn(row
[2 + j
]) * signs
[j
] >= 0)
4819 isl_int_cdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4821 isl_int_fdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4822 isl_int_submul(row
[2 + j
], row
[0], v
->el
[1 + j
]);
4824 for (j
= 0; j
< i
; ++j
) {
4825 if (isl_int_sgn(row
[2 + total
+ j
]) >= 0)
4827 isl_int_fdiv_q(v
->el
[1 + total
+ j
],
4828 row
[2 + total
+ j
], row
[0]);
4829 isl_int_submul(row
[2 + total
+ j
],
4830 row
[0], v
->el
[1 + total
+ j
]);
4832 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
4833 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
4835 isl_seq_combine(qp
->div
->row
[j
] + 1,
4836 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
4837 qp
->div
->row
[j
][2 + total
+ i
], v
->el
, v
->size
);
4839 isl_int_set_si(v
->el
[1 + total
+ i
], 1);
4840 s
= isl_poly_from_affine(qp
->dim
->ctx
, v
->el
,
4841 qp
->div
->ctx
->one
, v
->size
);
4842 qp
->poly
= isl_poly_subs(qp
->poly
, total
+ i
, 1, &s
);
4852 isl_qpolynomial_free(qp
);
4856 struct isl_to_poly_data
{
4858 isl_pw_qpolynomial
*res
;
4859 isl_qpolynomial
*qp
;
4862 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4863 * We first make all integer divisions positive and then split the
4864 * quasipolynomials into terms with sign data->sign (the direction
4865 * of the requested approximation) and terms with the opposite sign.
4866 * In the first set of terms, each integer division [a/m] is
4867 * overapproximated by a/m, while in the second it is underapproximated
4870 static isl_stat
to_polynomial_on_orthant(__isl_take isl_set
*orthant
,
4871 int *signs
, void *user
)
4873 struct isl_to_poly_data
*data
= user
;
4874 isl_pw_qpolynomial
*t
;
4875 isl_qpolynomial
*qp
, *up
, *down
;
4877 qp
= isl_qpolynomial_copy(data
->qp
);
4878 qp
= make_divs_pos(qp
, signs
);
4880 up
= isl_qpolynomial_terms_of_sign(qp
, signs
, data
->sign
);
4881 up
= qp_drop_floors(up
, 0);
4882 down
= isl_qpolynomial_terms_of_sign(qp
, signs
, -data
->sign
);
4883 down
= qp_drop_floors(down
, 1);
4885 isl_qpolynomial_free(qp
);
4886 qp
= isl_qpolynomial_add(up
, down
);
4888 t
= isl_pw_qpolynomial_alloc(orthant
, qp
);
4889 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, t
);
4894 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4895 * the polynomial will be an overapproximation. If "sign" is negative,
4896 * it will be an underapproximation. If "sign" is zero, the approximation
4897 * will lie somewhere in between.
4899 * In particular, is sign == 0, we simply drop the floors, turning
4900 * the integer divisions into rational divisions.
4901 * Otherwise, we split the domains into orthants, make all integer divisions
4902 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4903 * depending on the requested sign and the sign of the term in which
4904 * the integer division appears.
4906 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_to_polynomial(
4907 __isl_take isl_pw_qpolynomial
*pwqp
, int sign
)
4910 struct isl_to_poly_data data
;
4913 return pwqp_drop_floors(pwqp
);
4919 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp
));
4921 for (i
= 0; i
< pwqp
->n
; ++i
) {
4922 if (pwqp
->p
[i
].qp
->div
->n_row
== 0) {
4923 isl_pw_qpolynomial
*t
;
4924 t
= isl_pw_qpolynomial_alloc(
4925 isl_set_copy(pwqp
->p
[i
].set
),
4926 isl_qpolynomial_copy(pwqp
->p
[i
].qp
));
4927 data
.res
= isl_pw_qpolynomial_add_disjoint(data
.res
, t
);
4930 data
.qp
= pwqp
->p
[i
].qp
;
4931 if (isl_set_foreach_orthant(pwqp
->p
[i
].set
,
4932 &to_polynomial_on_orthant
, &data
) < 0)
4936 isl_pw_qpolynomial_free(pwqp
);
4940 isl_pw_qpolynomial_free(pwqp
);
4941 isl_pw_qpolynomial_free(data
.res
);
4945 static __isl_give isl_pw_qpolynomial
*poly_entry(
4946 __isl_take isl_pw_qpolynomial
*pwqp
, void *user
)
4950 return isl_pw_qpolynomial_to_polynomial(pwqp
, *sign
);
4953 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_to_polynomial(
4954 __isl_take isl_union_pw_qpolynomial
*upwqp
, int sign
)
4956 return isl_union_pw_qpolynomial_transform_inplace(upwqp
,
4957 &poly_entry
, &sign
);
4960 __isl_give isl_basic_map
*isl_basic_map_from_qpolynomial(
4961 __isl_take isl_qpolynomial
*qp
)
4965 isl_vec
*aff
= NULL
;
4966 isl_basic_map
*bmap
= NULL
;
4973 is_affine
= isl_poly_is_affine(qp
->poly
);
4977 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
4978 "input quasi-polynomial not affine", goto error
);
4979 aff
= isl_qpolynomial_extract_affine(qp
);
4982 dim
= isl_qpolynomial_get_space(qp
);
4983 pos
= 1 + isl_space_offset(dim
, isl_dim_out
);
4984 n_div
= qp
->div
->n_row
;
4985 bmap
= isl_basic_map_alloc_space(dim
, n_div
, 1, 2 * n_div
);
4987 for (i
= 0; i
< n_div
; ++i
) {
4988 k
= isl_basic_map_alloc_div(bmap
);
4991 isl_seq_cpy(bmap
->div
[k
], qp
->div
->row
[i
], qp
->div
->n_col
);
4992 isl_int_set_si(bmap
->div
[k
][qp
->div
->n_col
], 0);
4993 if (isl_basic_map_add_div_constraints(bmap
, k
) < 0)
4996 k
= isl_basic_map_alloc_equality(bmap
);
4999 isl_int_neg(bmap
->eq
[k
][pos
], aff
->el
[0]);
5000 isl_seq_cpy(bmap
->eq
[k
], aff
->el
+ 1, pos
);
5001 isl_seq_cpy(bmap
->eq
[k
] + pos
+ 1, aff
->el
+ 1 + pos
, n_div
);
5004 isl_qpolynomial_free(qp
);
5005 bmap
= isl_basic_map_finalize(bmap
);
5009 isl_qpolynomial_free(qp
);
5010 isl_basic_map_free(bmap
);