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_upoly_is_cst(__isl_keep
struct isl_upoly
*up
)
54 __isl_keep
struct isl_upoly_cst
*isl_upoly_as_cst(__isl_keep
struct isl_upoly
*up
)
59 isl_assert(up
->ctx
, up
->var
< 0, return NULL
);
61 return (struct isl_upoly_cst
*)up
;
64 __isl_keep
struct isl_upoly_rec
*isl_upoly_as_rec(__isl_keep
struct isl_upoly
*up
)
69 isl_assert(up
->ctx
, up
->var
>= 0, return NULL
);
71 return (struct isl_upoly_rec
*)up
;
74 /* Compare two polynomials.
76 * Return -1 if "up1" is "smaller" than "up2", 1 if "up1" is "greater"
77 * than "up2" and 0 if they are equal.
79 static int isl_upoly_plain_cmp(__isl_keep
struct isl_upoly
*up1
,
80 __isl_keep
struct isl_upoly
*up2
)
83 struct isl_upoly_rec
*rec1
, *rec2
;
91 if (up1
->var
!= up2
->var
)
92 return up1
->var
- up2
->var
;
94 if (isl_upoly_is_cst(up1
)) {
95 struct isl_upoly_cst
*cst1
, *cst2
;
98 cst1
= isl_upoly_as_cst(up1
);
99 cst2
= isl_upoly_as_cst(up2
);
102 cmp
= isl_int_cmp(cst1
->n
, cst2
->n
);
105 return isl_int_cmp(cst1
->d
, cst2
->d
);
108 rec1
= isl_upoly_as_rec(up1
);
109 rec2
= isl_upoly_as_rec(up2
);
113 if (rec1
->n
!= rec2
->n
)
114 return rec1
->n
- rec2
->n
;
116 for (i
= 0; i
< rec1
->n
; ++i
) {
117 int cmp
= isl_upoly_plain_cmp(rec1
->p
[i
], rec2
->p
[i
]);
125 isl_bool
isl_upoly_is_equal(__isl_keep
struct isl_upoly
*up1
,
126 __isl_keep
struct isl_upoly
*up2
)
129 struct isl_upoly_rec
*rec1
, *rec2
;
132 return isl_bool_error
;
134 return isl_bool_true
;
135 if (up1
->var
!= up2
->var
)
136 return isl_bool_false
;
137 if (isl_upoly_is_cst(up1
)) {
138 struct isl_upoly_cst
*cst1
, *cst2
;
139 cst1
= isl_upoly_as_cst(up1
);
140 cst2
= isl_upoly_as_cst(up2
);
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_upoly_as_rec(up1
);
148 rec2
= isl_upoly_as_rec(up2
);
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_upoly_is_equal(rec1
->p
[i
], rec2
->p
[i
]);
161 return isl_bool_true
;
164 int isl_upoly_is_zero(__isl_keep
struct isl_upoly
*up
)
166 struct isl_upoly_cst
*cst
;
170 if (!isl_upoly_is_cst(up
))
173 cst
= isl_upoly_as_cst(up
);
177 return isl_int_is_zero(cst
->n
) && isl_int_is_pos(cst
->d
);
180 int isl_upoly_sgn(__isl_keep
struct isl_upoly
*up
)
182 struct isl_upoly_cst
*cst
;
186 if (!isl_upoly_is_cst(up
))
189 cst
= isl_upoly_as_cst(up
);
193 return isl_int_sgn(cst
->n
);
196 int isl_upoly_is_nan(__isl_keep
struct isl_upoly
*up
)
198 struct isl_upoly_cst
*cst
;
202 if (!isl_upoly_is_cst(up
))
205 cst
= isl_upoly_as_cst(up
);
209 return isl_int_is_zero(cst
->n
) && isl_int_is_zero(cst
->d
);
212 int isl_upoly_is_infty(__isl_keep
struct isl_upoly
*up
)
214 struct isl_upoly_cst
*cst
;
218 if (!isl_upoly_is_cst(up
))
221 cst
= isl_upoly_as_cst(up
);
225 return isl_int_is_pos(cst
->n
) && isl_int_is_zero(cst
->d
);
228 int isl_upoly_is_neginfty(__isl_keep
struct isl_upoly
*up
)
230 struct isl_upoly_cst
*cst
;
234 if (!isl_upoly_is_cst(up
))
237 cst
= isl_upoly_as_cst(up
);
241 return isl_int_is_neg(cst
->n
) && isl_int_is_zero(cst
->d
);
244 int isl_upoly_is_one(__isl_keep
struct isl_upoly
*up
)
246 struct isl_upoly_cst
*cst
;
250 if (!isl_upoly_is_cst(up
))
253 cst
= isl_upoly_as_cst(up
);
257 return isl_int_eq(cst
->n
, cst
->d
) && isl_int_is_pos(cst
->d
);
260 int isl_upoly_is_negone(__isl_keep
struct isl_upoly
*up
)
262 struct isl_upoly_cst
*cst
;
266 if (!isl_upoly_is_cst(up
))
269 cst
= isl_upoly_as_cst(up
);
273 return isl_int_is_negone(cst
->n
) && isl_int_is_one(cst
->d
);
276 __isl_give
struct isl_upoly_cst
*isl_upoly_cst_alloc(struct isl_ctx
*ctx
)
278 struct isl_upoly_cst
*cst
;
280 cst
= isl_alloc_type(ctx
, struct isl_upoly_cst
);
289 isl_int_init(cst
->n
);
290 isl_int_init(cst
->d
);
295 __isl_give
struct isl_upoly
*isl_upoly_zero(struct isl_ctx
*ctx
)
297 struct isl_upoly_cst
*cst
;
299 cst
= isl_upoly_cst_alloc(ctx
);
303 isl_int_set_si(cst
->n
, 0);
304 isl_int_set_si(cst
->d
, 1);
309 __isl_give
struct isl_upoly
*isl_upoly_one(struct isl_ctx
*ctx
)
311 struct isl_upoly_cst
*cst
;
313 cst
= isl_upoly_cst_alloc(ctx
);
317 isl_int_set_si(cst
->n
, 1);
318 isl_int_set_si(cst
->d
, 1);
323 __isl_give
struct isl_upoly
*isl_upoly_infty(struct isl_ctx
*ctx
)
325 struct isl_upoly_cst
*cst
;
327 cst
= isl_upoly_cst_alloc(ctx
);
331 isl_int_set_si(cst
->n
, 1);
332 isl_int_set_si(cst
->d
, 0);
337 __isl_give
struct isl_upoly
*isl_upoly_neginfty(struct isl_ctx
*ctx
)
339 struct isl_upoly_cst
*cst
;
341 cst
= isl_upoly_cst_alloc(ctx
);
345 isl_int_set_si(cst
->n
, -1);
346 isl_int_set_si(cst
->d
, 0);
351 __isl_give
struct isl_upoly
*isl_upoly_nan(struct isl_ctx
*ctx
)
353 struct isl_upoly_cst
*cst
;
355 cst
= isl_upoly_cst_alloc(ctx
);
359 isl_int_set_si(cst
->n
, 0);
360 isl_int_set_si(cst
->d
, 0);
365 __isl_give
struct isl_upoly
*isl_upoly_rat_cst(struct isl_ctx
*ctx
,
366 isl_int n
, isl_int d
)
368 struct isl_upoly_cst
*cst
;
370 cst
= isl_upoly_cst_alloc(ctx
);
374 isl_int_set(cst
->n
, n
);
375 isl_int_set(cst
->d
, d
);
380 __isl_give
struct isl_upoly_rec
*isl_upoly_alloc_rec(struct isl_ctx
*ctx
,
383 struct isl_upoly_rec
*rec
;
385 isl_assert(ctx
, var
>= 0, return NULL
);
386 isl_assert(ctx
, size
>= 0, return NULL
);
387 rec
= isl_calloc(ctx
, struct isl_upoly_rec
,
388 sizeof(struct isl_upoly_rec
) +
389 size
* sizeof(struct isl_upoly
*));
404 __isl_give isl_qpolynomial
*isl_qpolynomial_reset_domain_space(
405 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*dim
)
407 qp
= isl_qpolynomial_cow(qp
);
411 isl_space_free(qp
->dim
);
416 isl_qpolynomial_free(qp
);
421 /* Reset the space of "qp". This function is called from isl_pw_templ.c
422 * and doesn't know if the space of an element object is represented
423 * directly or through its domain. It therefore passes along both.
425 __isl_give isl_qpolynomial
*isl_qpolynomial_reset_space_and_domain(
426 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*space
,
427 __isl_take isl_space
*domain
)
429 isl_space_free(space
);
430 return isl_qpolynomial_reset_domain_space(qp
, domain
);
433 isl_ctx
*isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial
*qp
)
435 return qp
? qp
->dim
->ctx
: NULL
;
438 __isl_give isl_space
*isl_qpolynomial_get_domain_space(
439 __isl_keep isl_qpolynomial
*qp
)
441 return qp
? isl_space_copy(qp
->dim
) : NULL
;
444 /* Return a copy of the local space on which "qp" is defined.
446 static __isl_give isl_local_space
*isl_qpolynomial_get_domain_local_space(
447 __isl_keep isl_qpolynomial
*qp
)
454 space
= isl_qpolynomial_get_domain_space(qp
);
455 return isl_local_space_alloc_div(space
, isl_mat_copy(qp
->div
));
458 __isl_give isl_space
*isl_qpolynomial_get_space(__isl_keep isl_qpolynomial
*qp
)
463 space
= isl_space_copy(qp
->dim
);
464 space
= isl_space_from_domain(space
);
465 space
= isl_space_add_dims(space
, isl_dim_out
, 1);
469 /* Return the number of variables of the given type in the domain of "qp".
471 unsigned isl_qpolynomial_domain_dim(__isl_keep isl_qpolynomial
*qp
,
472 enum isl_dim_type type
)
476 if (type
== isl_dim_div
)
477 return qp
->div
->n_row
;
478 if (type
== isl_dim_all
)
479 return isl_space_dim(qp
->dim
, isl_dim_all
) +
480 isl_qpolynomial_domain_dim(qp
, isl_dim_div
);
481 return isl_space_dim(qp
->dim
, type
);
484 /* Given the type of a dimension of an isl_qpolynomial,
485 * return the type of the corresponding dimension in its domain.
486 * This function is only called for "type" equal to isl_dim_in or
489 static enum isl_dim_type
domain_type(enum isl_dim_type type
)
491 return type
== isl_dim_in
? isl_dim_set
: type
;
494 /* Externally, an isl_qpolynomial has a map space, but internally, the
495 * ls field corresponds to the domain of that space.
497 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial
*qp
,
498 enum isl_dim_type type
)
502 if (type
== isl_dim_out
)
504 type
= domain_type(type
);
505 return isl_qpolynomial_domain_dim(qp
, type
);
508 /* Return the offset of the first coefficient of type "type" in
509 * the domain of "qp".
511 unsigned isl_qpolynomial_domain_offset(__isl_keep isl_qpolynomial
*qp
,
512 enum isl_dim_type type
)
521 return 1 + isl_space_offset(qp
->dim
, type
);
523 return 1 + isl_space_dim(qp
->dim
, isl_dim_all
);
529 isl_bool
isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial
*qp
)
531 return qp
? isl_upoly_is_zero(qp
->upoly
) : isl_bool_error
;
534 isl_bool
isl_qpolynomial_is_one(__isl_keep isl_qpolynomial
*qp
)
536 return qp
? isl_upoly_is_one(qp
->upoly
) : isl_bool_error
;
539 isl_bool
isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial
*qp
)
541 return qp
? isl_upoly_is_nan(qp
->upoly
) : isl_bool_error
;
544 isl_bool
isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial
*qp
)
546 return qp
? isl_upoly_is_infty(qp
->upoly
) : isl_bool_error
;
549 isl_bool
isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial
*qp
)
551 return qp
? isl_upoly_is_neginfty(qp
->upoly
) : isl_bool_error
;
554 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial
*qp
)
556 return qp
? isl_upoly_sgn(qp
->upoly
) : 0;
559 static void upoly_free_cst(__isl_take
struct isl_upoly_cst
*cst
)
561 isl_int_clear(cst
->n
);
562 isl_int_clear(cst
->d
);
565 static void upoly_free_rec(__isl_take
struct isl_upoly_rec
*rec
)
569 for (i
= 0; i
< rec
->n
; ++i
)
570 isl_upoly_free(rec
->p
[i
]);
573 __isl_give
struct isl_upoly
*isl_upoly_copy(__isl_keep
struct isl_upoly
*up
)
582 __isl_give
struct isl_upoly
*isl_upoly_dup_cst(__isl_keep
struct isl_upoly
*up
)
584 struct isl_upoly_cst
*cst
;
585 struct isl_upoly_cst
*dup
;
587 cst
= isl_upoly_as_cst(up
);
591 dup
= isl_upoly_as_cst(isl_upoly_zero(up
->ctx
));
594 isl_int_set(dup
->n
, cst
->n
);
595 isl_int_set(dup
->d
, cst
->d
);
600 __isl_give
struct isl_upoly
*isl_upoly_dup_rec(__isl_keep
struct isl_upoly
*up
)
603 struct isl_upoly_rec
*rec
;
604 struct isl_upoly_rec
*dup
;
606 rec
= isl_upoly_as_rec(up
);
610 dup
= isl_upoly_alloc_rec(up
->ctx
, up
->var
, rec
->n
);
614 for (i
= 0; i
< rec
->n
; ++i
) {
615 dup
->p
[i
] = isl_upoly_copy(rec
->p
[i
]);
623 isl_upoly_free(&dup
->up
);
627 __isl_give
struct isl_upoly
*isl_upoly_dup(__isl_keep
struct isl_upoly
*up
)
632 if (isl_upoly_is_cst(up
))
633 return isl_upoly_dup_cst(up
);
635 return isl_upoly_dup_rec(up
);
638 __isl_give
struct isl_upoly
*isl_upoly_cow(__isl_take
struct isl_upoly
*up
)
646 return isl_upoly_dup(up
);
649 __isl_null
struct isl_upoly
*isl_upoly_free(__isl_take
struct isl_upoly
*up
)
658 upoly_free_cst((struct isl_upoly_cst
*)up
);
660 upoly_free_rec((struct isl_upoly_rec
*)up
);
662 isl_ctx_deref(up
->ctx
);
667 static void isl_upoly_cst_reduce(__isl_keep
struct isl_upoly_cst
*cst
)
672 isl_int_gcd(gcd
, cst
->n
, cst
->d
);
673 if (!isl_int_is_zero(gcd
) && !isl_int_is_one(gcd
)) {
674 isl_int_divexact(cst
->n
, cst
->n
, gcd
);
675 isl_int_divexact(cst
->d
, cst
->d
, gcd
);
680 __isl_give
struct isl_upoly
*isl_upoly_sum_cst(__isl_take
struct isl_upoly
*up1
,
681 __isl_take
struct isl_upoly
*up2
)
683 struct isl_upoly_cst
*cst1
;
684 struct isl_upoly_cst
*cst2
;
686 up1
= isl_upoly_cow(up1
);
690 cst1
= isl_upoly_as_cst(up1
);
691 cst2
= isl_upoly_as_cst(up2
);
693 if (isl_int_eq(cst1
->d
, cst2
->d
))
694 isl_int_add(cst1
->n
, cst1
->n
, cst2
->n
);
696 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->d
);
697 isl_int_addmul(cst1
->n
, cst2
->n
, cst1
->d
);
698 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
701 isl_upoly_cst_reduce(cst1
);
711 static __isl_give
struct isl_upoly
*replace_by_zero(
712 __isl_take
struct isl_upoly
*up
)
720 return isl_upoly_zero(ctx
);
723 static __isl_give
struct isl_upoly
*replace_by_constant_term(
724 __isl_take
struct isl_upoly
*up
)
726 struct isl_upoly_rec
*rec
;
727 struct isl_upoly
*cst
;
732 rec
= isl_upoly_as_rec(up
);
735 cst
= isl_upoly_copy(rec
->p
[0]);
743 __isl_give
struct isl_upoly
*isl_upoly_sum(__isl_take
struct isl_upoly
*up1
,
744 __isl_take
struct isl_upoly
*up2
)
747 struct isl_upoly_rec
*rec1
, *rec2
;
752 if (isl_upoly_is_nan(up1
)) {
757 if (isl_upoly_is_nan(up2
)) {
762 if (isl_upoly_is_zero(up1
)) {
767 if (isl_upoly_is_zero(up2
)) {
772 if (up1
->var
< up2
->var
)
773 return isl_upoly_sum(up2
, up1
);
775 if (up2
->var
< up1
->var
) {
776 struct isl_upoly_rec
*rec
;
777 if (isl_upoly_is_infty(up2
) || isl_upoly_is_neginfty(up2
)) {
781 up1
= isl_upoly_cow(up1
);
782 rec
= isl_upoly_as_rec(up1
);
785 rec
->p
[0] = isl_upoly_sum(rec
->p
[0], up2
);
787 up1
= replace_by_constant_term(up1
);
791 if (isl_upoly_is_cst(up1
))
792 return isl_upoly_sum_cst(up1
, up2
);
794 rec1
= isl_upoly_as_rec(up1
);
795 rec2
= isl_upoly_as_rec(up2
);
799 if (rec1
->n
< rec2
->n
)
800 return isl_upoly_sum(up2
, up1
);
802 up1
= isl_upoly_cow(up1
);
803 rec1
= isl_upoly_as_rec(up1
);
807 for (i
= rec2
->n
- 1; i
>= 0; --i
) {
808 rec1
->p
[i
] = isl_upoly_sum(rec1
->p
[i
],
809 isl_upoly_copy(rec2
->p
[i
]));
812 if (i
== rec1
->n
- 1 && isl_upoly_is_zero(rec1
->p
[i
])) {
813 isl_upoly_free(rec1
->p
[i
]);
819 up1
= replace_by_zero(up1
);
820 else if (rec1
->n
== 1)
821 up1
= replace_by_constant_term(up1
);
832 __isl_give
struct isl_upoly
*isl_upoly_cst_add_isl_int(
833 __isl_take
struct isl_upoly
*up
, isl_int v
)
835 struct isl_upoly_cst
*cst
;
837 up
= isl_upoly_cow(up
);
841 cst
= isl_upoly_as_cst(up
);
843 isl_int_addmul(cst
->n
, cst
->d
, v
);
848 __isl_give
struct isl_upoly
*isl_upoly_add_isl_int(
849 __isl_take
struct isl_upoly
*up
, isl_int v
)
851 struct isl_upoly_rec
*rec
;
856 if (isl_upoly_is_cst(up
))
857 return isl_upoly_cst_add_isl_int(up
, v
);
859 up
= isl_upoly_cow(up
);
860 rec
= isl_upoly_as_rec(up
);
864 rec
->p
[0] = isl_upoly_add_isl_int(rec
->p
[0], v
);
874 __isl_give
struct isl_upoly
*isl_upoly_cst_mul_isl_int(
875 __isl_take
struct isl_upoly
*up
, isl_int v
)
877 struct isl_upoly_cst
*cst
;
879 if (isl_upoly_is_zero(up
))
882 up
= isl_upoly_cow(up
);
886 cst
= isl_upoly_as_cst(up
);
888 isl_int_mul(cst
->n
, cst
->n
, v
);
893 __isl_give
struct isl_upoly
*isl_upoly_mul_isl_int(
894 __isl_take
struct isl_upoly
*up
, isl_int v
)
897 struct isl_upoly_rec
*rec
;
902 if (isl_upoly_is_cst(up
))
903 return isl_upoly_cst_mul_isl_int(up
, v
);
905 up
= isl_upoly_cow(up
);
906 rec
= isl_upoly_as_rec(up
);
910 for (i
= 0; i
< rec
->n
; ++i
) {
911 rec
->p
[i
] = isl_upoly_mul_isl_int(rec
->p
[i
], v
);
922 /* Multiply the constant polynomial "up" by "v".
924 static __isl_give
struct isl_upoly
*isl_upoly_cst_scale_val(
925 __isl_take
struct isl_upoly
*up
, __isl_keep isl_val
*v
)
927 struct isl_upoly_cst
*cst
;
929 if (isl_upoly_is_zero(up
))
932 up
= isl_upoly_cow(up
);
936 cst
= isl_upoly_as_cst(up
);
938 isl_int_mul(cst
->n
, cst
->n
, v
->n
);
939 isl_int_mul(cst
->d
, cst
->d
, v
->d
);
940 isl_upoly_cst_reduce(cst
);
945 /* Multiply the polynomial "up" by "v".
947 static __isl_give
struct isl_upoly
*isl_upoly_scale_val(
948 __isl_take
struct isl_upoly
*up
, __isl_keep isl_val
*v
)
951 struct isl_upoly_rec
*rec
;
956 if (isl_upoly_is_cst(up
))
957 return isl_upoly_cst_scale_val(up
, v
);
959 up
= isl_upoly_cow(up
);
960 rec
= isl_upoly_as_rec(up
);
964 for (i
= 0; i
< rec
->n
; ++i
) {
965 rec
->p
[i
] = isl_upoly_scale_val(rec
->p
[i
], v
);
976 __isl_give
struct isl_upoly
*isl_upoly_mul_cst(__isl_take
struct isl_upoly
*up1
,
977 __isl_take
struct isl_upoly
*up2
)
979 struct isl_upoly_cst
*cst1
;
980 struct isl_upoly_cst
*cst2
;
982 up1
= isl_upoly_cow(up1
);
986 cst1
= isl_upoly_as_cst(up1
);
987 cst2
= isl_upoly_as_cst(up2
);
989 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->n
);
990 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
992 isl_upoly_cst_reduce(cst1
);
1002 __isl_give
struct isl_upoly
*isl_upoly_mul_rec(__isl_take
struct isl_upoly
*up1
,
1003 __isl_take
struct isl_upoly
*up2
)
1005 struct isl_upoly_rec
*rec1
;
1006 struct isl_upoly_rec
*rec2
;
1007 struct isl_upoly_rec
*res
= NULL
;
1011 rec1
= isl_upoly_as_rec(up1
);
1012 rec2
= isl_upoly_as_rec(up2
);
1015 size
= rec1
->n
+ rec2
->n
- 1;
1016 res
= isl_upoly_alloc_rec(up1
->ctx
, up1
->var
, size
);
1020 for (i
= 0; i
< rec1
->n
; ++i
) {
1021 res
->p
[i
] = isl_upoly_mul(isl_upoly_copy(rec2
->p
[0]),
1022 isl_upoly_copy(rec1
->p
[i
]));
1027 for (; i
< size
; ++i
) {
1028 res
->p
[i
] = isl_upoly_zero(up1
->ctx
);
1033 for (i
= 0; i
< rec1
->n
; ++i
) {
1034 for (j
= 1; j
< rec2
->n
; ++j
) {
1035 struct isl_upoly
*up
;
1036 up
= isl_upoly_mul(isl_upoly_copy(rec2
->p
[j
]),
1037 isl_upoly_copy(rec1
->p
[i
]));
1038 res
->p
[i
+ j
] = isl_upoly_sum(res
->p
[i
+ j
], up
);
1044 isl_upoly_free(up1
);
1045 isl_upoly_free(up2
);
1049 isl_upoly_free(up1
);
1050 isl_upoly_free(up2
);
1051 isl_upoly_free(&res
->up
);
1055 __isl_give
struct isl_upoly
*isl_upoly_mul(__isl_take
struct isl_upoly
*up1
,
1056 __isl_take
struct isl_upoly
*up2
)
1061 if (isl_upoly_is_nan(up1
)) {
1062 isl_upoly_free(up2
);
1066 if (isl_upoly_is_nan(up2
)) {
1067 isl_upoly_free(up1
);
1071 if (isl_upoly_is_zero(up1
)) {
1072 isl_upoly_free(up2
);
1076 if (isl_upoly_is_zero(up2
)) {
1077 isl_upoly_free(up1
);
1081 if (isl_upoly_is_one(up1
)) {
1082 isl_upoly_free(up1
);
1086 if (isl_upoly_is_one(up2
)) {
1087 isl_upoly_free(up2
);
1091 if (up1
->var
< up2
->var
)
1092 return isl_upoly_mul(up2
, up1
);
1094 if (up2
->var
< up1
->var
) {
1096 struct isl_upoly_rec
*rec
;
1097 if (isl_upoly_is_infty(up2
) || isl_upoly_is_neginfty(up2
)) {
1098 isl_ctx
*ctx
= up1
->ctx
;
1099 isl_upoly_free(up1
);
1100 isl_upoly_free(up2
);
1101 return isl_upoly_nan(ctx
);
1103 up1
= isl_upoly_cow(up1
);
1104 rec
= isl_upoly_as_rec(up1
);
1108 for (i
= 0; i
< rec
->n
; ++i
) {
1109 rec
->p
[i
] = isl_upoly_mul(rec
->p
[i
],
1110 isl_upoly_copy(up2
));
1114 isl_upoly_free(up2
);
1118 if (isl_upoly_is_cst(up1
))
1119 return isl_upoly_mul_cst(up1
, up2
);
1121 return isl_upoly_mul_rec(up1
, up2
);
1123 isl_upoly_free(up1
);
1124 isl_upoly_free(up2
);
1128 __isl_give
struct isl_upoly
*isl_upoly_pow(__isl_take
struct isl_upoly
*up
,
1131 struct isl_upoly
*res
;
1139 res
= isl_upoly_copy(up
);
1141 res
= isl_upoly_one(up
->ctx
);
1143 while (power
>>= 1) {
1144 up
= isl_upoly_mul(up
, isl_upoly_copy(up
));
1146 res
= isl_upoly_mul(res
, isl_upoly_copy(up
));
1153 __isl_give isl_qpolynomial
*isl_qpolynomial_alloc(__isl_take isl_space
*space
,
1154 unsigned n_div
, __isl_take
struct isl_upoly
*up
)
1156 struct isl_qpolynomial
*qp
= NULL
;
1162 if (!isl_space_is_set(space
))
1163 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
1164 "domain of polynomial should be a set", goto error
);
1166 total
= isl_space_dim(space
, isl_dim_all
);
1168 qp
= isl_calloc_type(space
->ctx
, struct isl_qpolynomial
);
1173 qp
->div
= isl_mat_alloc(space
->ctx
, n_div
, 1 + 1 + total
+ n_div
);
1182 isl_space_free(space
);
1184 isl_qpolynomial_free(qp
);
1188 __isl_give isl_qpolynomial
*isl_qpolynomial_copy(__isl_keep isl_qpolynomial
*qp
)
1197 __isl_give isl_qpolynomial
*isl_qpolynomial_dup(__isl_keep isl_qpolynomial
*qp
)
1199 struct isl_qpolynomial
*dup
;
1204 dup
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
), qp
->div
->n_row
,
1205 isl_upoly_copy(qp
->upoly
));
1208 isl_mat_free(dup
->div
);
1209 dup
->div
= isl_mat_copy(qp
->div
);
1215 isl_qpolynomial_free(dup
);
1219 __isl_give isl_qpolynomial
*isl_qpolynomial_cow(__isl_take isl_qpolynomial
*qp
)
1227 return isl_qpolynomial_dup(qp
);
1230 __isl_null isl_qpolynomial
*isl_qpolynomial_free(
1231 __isl_take isl_qpolynomial
*qp
)
1239 isl_space_free(qp
->dim
);
1240 isl_mat_free(qp
->div
);
1241 isl_upoly_free(qp
->upoly
);
1247 __isl_give
struct isl_upoly
*isl_upoly_var_pow(isl_ctx
*ctx
, int pos
, int power
)
1250 struct isl_upoly_rec
*rec
;
1251 struct isl_upoly_cst
*cst
;
1253 rec
= isl_upoly_alloc_rec(ctx
, pos
, 1 + power
);
1256 for (i
= 0; i
< 1 + power
; ++i
) {
1257 rec
->p
[i
] = isl_upoly_zero(ctx
);
1262 cst
= isl_upoly_as_cst(rec
->p
[power
]);
1263 isl_int_set_si(cst
->n
, 1);
1267 isl_upoly_free(&rec
->up
);
1271 /* r array maps original positions to new positions.
1273 static __isl_give
struct isl_upoly
*reorder(__isl_take
struct isl_upoly
*up
,
1277 struct isl_upoly_rec
*rec
;
1278 struct isl_upoly
*base
;
1279 struct isl_upoly
*res
;
1281 if (isl_upoly_is_cst(up
))
1284 rec
= isl_upoly_as_rec(up
);
1288 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
1290 base
= isl_upoly_var_pow(up
->ctx
, r
[up
->var
], 1);
1291 res
= reorder(isl_upoly_copy(rec
->p
[rec
->n
- 1]), r
);
1293 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1294 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
1295 res
= isl_upoly_sum(res
, reorder(isl_upoly_copy(rec
->p
[i
]), r
));
1298 isl_upoly_free(base
);
1307 static isl_bool
compatible_divs(__isl_keep isl_mat
*div1
,
1308 __isl_keep isl_mat
*div2
)
1313 isl_assert(div1
->ctx
, div1
->n_row
>= div2
->n_row
&&
1314 div1
->n_col
>= div2
->n_col
,
1315 return isl_bool_error
);
1317 if (div1
->n_row
== div2
->n_row
)
1318 return isl_mat_is_equal(div1
, div2
);
1320 n_row
= div1
->n_row
;
1321 n_col
= div1
->n_col
;
1322 div1
->n_row
= div2
->n_row
;
1323 div1
->n_col
= div2
->n_col
;
1325 equal
= isl_mat_is_equal(div1
, div2
);
1327 div1
->n_row
= n_row
;
1328 div1
->n_col
= n_col
;
1333 static int cmp_row(__isl_keep isl_mat
*div
, int i
, int j
)
1337 li
= isl_seq_last_non_zero(div
->row
[i
], div
->n_col
);
1338 lj
= isl_seq_last_non_zero(div
->row
[j
], div
->n_col
);
1343 return isl_seq_cmp(div
->row
[i
], div
->row
[j
], div
->n_col
);
1346 struct isl_div_sort_info
{
1351 static int div_sort_cmp(const void *p1
, const void *p2
)
1353 const struct isl_div_sort_info
*i1
, *i2
;
1354 i1
= (const struct isl_div_sort_info
*) p1
;
1355 i2
= (const struct isl_div_sort_info
*) p2
;
1357 return cmp_row(i1
->div
, i1
->row
, i2
->row
);
1360 /* Sort divs and remove duplicates.
1362 static __isl_give isl_qpolynomial
*sort_divs(__isl_take isl_qpolynomial
*qp
)
1367 struct isl_div_sort_info
*array
= NULL
;
1368 int *pos
= NULL
, *at
= NULL
;
1369 int *reordering
= NULL
;
1374 if (qp
->div
->n_row
<= 1)
1377 div_pos
= isl_space_dim(qp
->dim
, isl_dim_all
);
1379 array
= isl_alloc_array(qp
->div
->ctx
, struct isl_div_sort_info
,
1381 pos
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1382 at
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1383 len
= qp
->div
->n_col
- 2;
1384 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
1385 if (!array
|| !pos
|| !at
|| !reordering
)
1388 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1389 array
[i
].div
= qp
->div
;
1395 qsort(array
, qp
->div
->n_row
, sizeof(struct isl_div_sort_info
),
1398 for (i
= 0; i
< div_pos
; ++i
)
1401 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1402 if (pos
[array
[i
].row
] == i
)
1404 qp
->div
= isl_mat_swap_rows(qp
->div
, i
, pos
[array
[i
].row
]);
1405 pos
[at
[i
]] = pos
[array
[i
].row
];
1406 at
[pos
[array
[i
].row
]] = at
[i
];
1407 at
[i
] = array
[i
].row
;
1408 pos
[array
[i
].row
] = i
;
1412 for (i
= 0; i
< len
- div_pos
; ++i
) {
1414 isl_seq_eq(qp
->div
->row
[i
- skip
- 1],
1415 qp
->div
->row
[i
- skip
], qp
->div
->n_col
)) {
1416 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
1417 isl_mat_col_add(qp
->div
, 2 + div_pos
+ i
- skip
- 1,
1418 2 + div_pos
+ i
- skip
);
1419 qp
->div
= isl_mat_drop_cols(qp
->div
,
1420 2 + div_pos
+ i
- skip
, 1);
1423 reordering
[div_pos
+ array
[i
].row
] = div_pos
+ i
- skip
;
1426 qp
->upoly
= reorder(qp
->upoly
, reordering
);
1428 if (!qp
->upoly
|| !qp
->div
)
1442 isl_qpolynomial_free(qp
);
1446 static __isl_give
struct isl_upoly
*expand(__isl_take
struct isl_upoly
*up
,
1447 int *exp
, int first
)
1450 struct isl_upoly_rec
*rec
;
1452 if (isl_upoly_is_cst(up
))
1455 if (up
->var
< first
)
1458 if (exp
[up
->var
- first
] == up
->var
- first
)
1461 up
= isl_upoly_cow(up
);
1465 up
->var
= exp
[up
->var
- first
] + first
;
1467 rec
= isl_upoly_as_rec(up
);
1471 for (i
= 0; i
< rec
->n
; ++i
) {
1472 rec
->p
[i
] = expand(rec
->p
[i
], exp
, first
);
1483 static __isl_give isl_qpolynomial
*with_merged_divs(
1484 __isl_give isl_qpolynomial
*(*fn
)(__isl_take isl_qpolynomial
*qp1
,
1485 __isl_take isl_qpolynomial
*qp2
),
1486 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
1490 isl_mat
*div
= NULL
;
1493 qp1
= isl_qpolynomial_cow(qp1
);
1494 qp2
= isl_qpolynomial_cow(qp2
);
1499 isl_assert(qp1
->div
->ctx
, qp1
->div
->n_row
>= qp2
->div
->n_row
&&
1500 qp1
->div
->n_col
>= qp2
->div
->n_col
, goto error
);
1502 n_div1
= qp1
->div
->n_row
;
1503 n_div2
= qp2
->div
->n_row
;
1504 exp1
= isl_alloc_array(qp1
->div
->ctx
, int, n_div1
);
1505 exp2
= isl_alloc_array(qp2
->div
->ctx
, int, n_div2
);
1506 if ((n_div1
&& !exp1
) || (n_div2
&& !exp2
))
1509 div
= isl_merge_divs(qp1
->div
, qp2
->div
, exp1
, exp2
);
1513 isl_mat_free(qp1
->div
);
1514 qp1
->div
= isl_mat_copy(div
);
1515 isl_mat_free(qp2
->div
);
1516 qp2
->div
= isl_mat_copy(div
);
1518 qp1
->upoly
= expand(qp1
->upoly
, exp1
, div
->n_col
- div
->n_row
- 2);
1519 qp2
->upoly
= expand(qp2
->upoly
, exp2
, div
->n_col
- div
->n_row
- 2);
1521 if (!qp1
->upoly
|| !qp2
->upoly
)
1528 return fn(qp1
, qp2
);
1533 isl_qpolynomial_free(qp1
);
1534 isl_qpolynomial_free(qp2
);
1538 __isl_give isl_qpolynomial
*isl_qpolynomial_add(__isl_take isl_qpolynomial
*qp1
,
1539 __isl_take isl_qpolynomial
*qp2
)
1541 isl_bool compatible
;
1543 qp1
= isl_qpolynomial_cow(qp1
);
1548 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1549 return isl_qpolynomial_add(qp2
, qp1
);
1551 isl_assert(qp1
->dim
->ctx
, isl_space_is_equal(qp1
->dim
, qp2
->dim
), goto error
);
1552 compatible
= compatible_divs(qp1
->div
, qp2
->div
);
1556 return with_merged_divs(isl_qpolynomial_add
, qp1
, qp2
);
1558 qp1
->upoly
= isl_upoly_sum(qp1
->upoly
, isl_upoly_copy(qp2
->upoly
));
1562 isl_qpolynomial_free(qp2
);
1566 isl_qpolynomial_free(qp1
);
1567 isl_qpolynomial_free(qp2
);
1571 __isl_give isl_qpolynomial
*isl_qpolynomial_add_on_domain(
1572 __isl_keep isl_set
*dom
,
1573 __isl_take isl_qpolynomial
*qp1
,
1574 __isl_take isl_qpolynomial
*qp2
)
1576 qp1
= isl_qpolynomial_add(qp1
, qp2
);
1577 qp1
= isl_qpolynomial_gist(qp1
, isl_set_copy(dom
));
1581 __isl_give isl_qpolynomial
*isl_qpolynomial_sub(__isl_take isl_qpolynomial
*qp1
,
1582 __isl_take isl_qpolynomial
*qp2
)
1584 return isl_qpolynomial_add(qp1
, isl_qpolynomial_neg(qp2
));
1587 __isl_give isl_qpolynomial
*isl_qpolynomial_add_isl_int(
1588 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1590 if (isl_int_is_zero(v
))
1593 qp
= isl_qpolynomial_cow(qp
);
1597 qp
->upoly
= isl_upoly_add_isl_int(qp
->upoly
, v
);
1603 isl_qpolynomial_free(qp
);
1608 __isl_give isl_qpolynomial
*isl_qpolynomial_neg(__isl_take isl_qpolynomial
*qp
)
1613 return isl_qpolynomial_mul_isl_int(qp
, qp
->dim
->ctx
->negone
);
1616 __isl_give isl_qpolynomial
*isl_qpolynomial_mul_isl_int(
1617 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1619 if (isl_int_is_one(v
))
1622 if (qp
&& isl_int_is_zero(v
)) {
1623 isl_qpolynomial
*zero
;
1624 zero
= isl_qpolynomial_zero_on_domain(isl_space_copy(qp
->dim
));
1625 isl_qpolynomial_free(qp
);
1629 qp
= isl_qpolynomial_cow(qp
);
1633 qp
->upoly
= isl_upoly_mul_isl_int(qp
->upoly
, v
);
1639 isl_qpolynomial_free(qp
);
1643 __isl_give isl_qpolynomial
*isl_qpolynomial_scale(
1644 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1646 return isl_qpolynomial_mul_isl_int(qp
, v
);
1649 /* Multiply "qp" by "v".
1651 __isl_give isl_qpolynomial
*isl_qpolynomial_scale_val(
1652 __isl_take isl_qpolynomial
*qp
, __isl_take isl_val
*v
)
1657 if (!isl_val_is_rat(v
))
1658 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
1659 "expecting rational factor", goto error
);
1661 if (isl_val_is_one(v
)) {
1666 if (isl_val_is_zero(v
)) {
1669 space
= isl_qpolynomial_get_domain_space(qp
);
1670 isl_qpolynomial_free(qp
);
1672 return isl_qpolynomial_zero_on_domain(space
);
1675 qp
= isl_qpolynomial_cow(qp
);
1679 qp
->upoly
= isl_upoly_scale_val(qp
->upoly
, v
);
1681 qp
= isl_qpolynomial_free(qp
);
1687 isl_qpolynomial_free(qp
);
1691 /* Divide "qp" by "v".
1693 __isl_give isl_qpolynomial
*isl_qpolynomial_scale_down_val(
1694 __isl_take isl_qpolynomial
*qp
, __isl_take isl_val
*v
)
1699 if (!isl_val_is_rat(v
))
1700 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
1701 "expecting rational factor", goto error
);
1702 if (isl_val_is_zero(v
))
1703 isl_die(isl_val_get_ctx(v
), isl_error_invalid
,
1704 "cannot scale down by zero", goto error
);
1706 return isl_qpolynomial_scale_val(qp
, isl_val_inv(v
));
1709 isl_qpolynomial_free(qp
);
1713 __isl_give isl_qpolynomial
*isl_qpolynomial_mul(__isl_take isl_qpolynomial
*qp1
,
1714 __isl_take isl_qpolynomial
*qp2
)
1716 isl_bool compatible
;
1718 qp1
= isl_qpolynomial_cow(qp1
);
1723 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1724 return isl_qpolynomial_mul(qp2
, qp1
);
1726 isl_assert(qp1
->dim
->ctx
, isl_space_is_equal(qp1
->dim
, qp2
->dim
), goto error
);
1727 compatible
= compatible_divs(qp1
->div
, qp2
->div
);
1731 return with_merged_divs(isl_qpolynomial_mul
, qp1
, qp2
);
1733 qp1
->upoly
= isl_upoly_mul(qp1
->upoly
, isl_upoly_copy(qp2
->upoly
));
1737 isl_qpolynomial_free(qp2
);
1741 isl_qpolynomial_free(qp1
);
1742 isl_qpolynomial_free(qp2
);
1746 __isl_give isl_qpolynomial
*isl_qpolynomial_pow(__isl_take isl_qpolynomial
*qp
,
1749 qp
= isl_qpolynomial_cow(qp
);
1754 qp
->upoly
= isl_upoly_pow(qp
->upoly
, power
);
1760 isl_qpolynomial_free(qp
);
1764 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_pow(
1765 __isl_take isl_pw_qpolynomial
*pwqp
, unsigned power
)
1772 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
1776 for (i
= 0; i
< pwqp
->n
; ++i
) {
1777 pwqp
->p
[i
].qp
= isl_qpolynomial_pow(pwqp
->p
[i
].qp
, power
);
1779 return isl_pw_qpolynomial_free(pwqp
);
1785 __isl_give isl_qpolynomial
*isl_qpolynomial_zero_on_domain(
1786 __isl_take isl_space
*domain
)
1790 return isl_qpolynomial_alloc(domain
, 0, isl_upoly_zero(domain
->ctx
));
1793 __isl_give isl_qpolynomial
*isl_qpolynomial_one_on_domain(
1794 __isl_take isl_space
*domain
)
1798 return isl_qpolynomial_alloc(domain
, 0, isl_upoly_one(domain
->ctx
));
1801 __isl_give isl_qpolynomial
*isl_qpolynomial_infty_on_domain(
1802 __isl_take isl_space
*domain
)
1806 return isl_qpolynomial_alloc(domain
, 0, isl_upoly_infty(domain
->ctx
));
1809 __isl_give isl_qpolynomial
*isl_qpolynomial_neginfty_on_domain(
1810 __isl_take isl_space
*domain
)
1814 return isl_qpolynomial_alloc(domain
, 0,
1815 isl_upoly_neginfty(domain
->ctx
));
1818 __isl_give isl_qpolynomial
*isl_qpolynomial_nan_on_domain(
1819 __isl_take isl_space
*domain
)
1823 return isl_qpolynomial_alloc(domain
, 0, isl_upoly_nan(domain
->ctx
));
1826 __isl_give isl_qpolynomial
*isl_qpolynomial_cst_on_domain(
1827 __isl_take isl_space
*domain
,
1830 struct isl_qpolynomial
*qp
;
1831 struct isl_upoly_cst
*cst
;
1836 qp
= isl_qpolynomial_alloc(domain
, 0, isl_upoly_zero(domain
->ctx
));
1840 cst
= isl_upoly_as_cst(qp
->upoly
);
1841 isl_int_set(cst
->n
, v
);
1846 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial
*qp
,
1847 isl_int
*n
, isl_int
*d
)
1849 struct isl_upoly_cst
*cst
;
1854 if (!isl_upoly_is_cst(qp
->upoly
))
1857 cst
= isl_upoly_as_cst(qp
->upoly
);
1862 isl_int_set(*n
, cst
->n
);
1864 isl_int_set(*d
, cst
->d
);
1869 /* Return the constant term of "up".
1871 static __isl_give isl_val
*isl_upoly_get_constant_val(
1872 __isl_keep
struct isl_upoly
*up
)
1874 struct isl_upoly_cst
*cst
;
1879 while (!isl_upoly_is_cst(up
)) {
1880 struct isl_upoly_rec
*rec
;
1882 rec
= isl_upoly_as_rec(up
);
1888 cst
= isl_upoly_as_cst(up
);
1891 return isl_val_rat_from_isl_int(cst
->up
.ctx
, cst
->n
, cst
->d
);
1894 /* Return the constant term of "qp".
1896 __isl_give isl_val
*isl_qpolynomial_get_constant_val(
1897 __isl_keep isl_qpolynomial
*qp
)
1902 return isl_upoly_get_constant_val(qp
->upoly
);
1905 int isl_upoly_is_affine(__isl_keep
struct isl_upoly
*up
)
1908 struct isl_upoly_rec
*rec
;
1916 rec
= isl_upoly_as_rec(up
);
1923 isl_assert(up
->ctx
, rec
->n
> 1, return -1);
1925 is_cst
= isl_upoly_is_cst(rec
->p
[1]);
1931 return isl_upoly_is_affine(rec
->p
[0]);
1934 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial
*qp
)
1939 if (qp
->div
->n_row
> 0)
1942 return isl_upoly_is_affine(qp
->upoly
);
1945 static void update_coeff(__isl_keep isl_vec
*aff
,
1946 __isl_keep
struct isl_upoly_cst
*cst
, int pos
)
1951 if (isl_int_is_zero(cst
->n
))
1956 isl_int_gcd(gcd
, cst
->d
, aff
->el
[0]);
1957 isl_int_divexact(f
, cst
->d
, gcd
);
1958 isl_int_divexact(gcd
, aff
->el
[0], gcd
);
1959 isl_seq_scale(aff
->el
, aff
->el
, f
, aff
->size
);
1960 isl_int_mul(aff
->el
[1 + pos
], gcd
, cst
->n
);
1965 int isl_upoly_update_affine(__isl_keep
struct isl_upoly
*up
,
1966 __isl_keep isl_vec
*aff
)
1968 struct isl_upoly_cst
*cst
;
1969 struct isl_upoly_rec
*rec
;
1975 struct isl_upoly_cst
*cst
;
1977 cst
= isl_upoly_as_cst(up
);
1980 update_coeff(aff
, cst
, 0);
1984 rec
= isl_upoly_as_rec(up
);
1987 isl_assert(up
->ctx
, rec
->n
== 2, return -1);
1989 cst
= isl_upoly_as_cst(rec
->p
[1]);
1992 update_coeff(aff
, cst
, 1 + up
->var
);
1994 return isl_upoly_update_affine(rec
->p
[0], aff
);
1997 __isl_give isl_vec
*isl_qpolynomial_extract_affine(
1998 __isl_keep isl_qpolynomial
*qp
)
2006 d
= isl_space_dim(qp
->dim
, isl_dim_all
);
2007 aff
= isl_vec_alloc(qp
->div
->ctx
, 2 + d
+ qp
->div
->n_row
);
2011 isl_seq_clr(aff
->el
+ 1, 1 + d
+ qp
->div
->n_row
);
2012 isl_int_set_si(aff
->el
[0], 1);
2014 if (isl_upoly_update_affine(qp
->upoly
, aff
) < 0)
2023 /* Compare two quasi-polynomials.
2025 * Return -1 if "qp1" is "smaller" than "qp2", 1 if "qp1" is "greater"
2026 * than "qp2" and 0 if they are equal.
2028 int isl_qpolynomial_plain_cmp(__isl_keep isl_qpolynomial
*qp1
,
2029 __isl_keep isl_qpolynomial
*qp2
)
2040 cmp
= isl_space_cmp(qp1
->dim
, qp2
->dim
);
2044 cmp
= isl_local_cmp(qp1
->div
, qp2
->div
);
2048 return isl_upoly_plain_cmp(qp1
->upoly
, qp2
->upoly
);
2051 /* Is "qp1" obviously equal to "qp2"?
2053 * NaN is not equal to anything, not even to another NaN.
2055 isl_bool
isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial
*qp1
,
2056 __isl_keep isl_qpolynomial
*qp2
)
2061 return isl_bool_error
;
2063 if (isl_qpolynomial_is_nan(qp1
) || isl_qpolynomial_is_nan(qp2
))
2064 return isl_bool_false
;
2066 equal
= isl_space_is_equal(qp1
->dim
, qp2
->dim
);
2067 if (equal
< 0 || !equal
)
2070 equal
= isl_mat_is_equal(qp1
->div
, qp2
->div
);
2071 if (equal
< 0 || !equal
)
2074 return isl_upoly_is_equal(qp1
->upoly
, qp2
->upoly
);
2077 static void upoly_update_den(__isl_keep
struct isl_upoly
*up
, isl_int
*d
)
2080 struct isl_upoly_rec
*rec
;
2082 if (isl_upoly_is_cst(up
)) {
2083 struct isl_upoly_cst
*cst
;
2084 cst
= isl_upoly_as_cst(up
);
2087 isl_int_lcm(*d
, *d
, cst
->d
);
2091 rec
= isl_upoly_as_rec(up
);
2095 for (i
= 0; i
< rec
->n
; ++i
)
2096 upoly_update_den(rec
->p
[i
], d
);
2099 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial
*qp
, isl_int
*d
)
2101 isl_int_set_si(*d
, 1);
2104 upoly_update_den(qp
->upoly
, d
);
2107 __isl_give isl_qpolynomial
*isl_qpolynomial_var_pow_on_domain(
2108 __isl_take isl_space
*domain
, int pos
, int power
)
2110 struct isl_ctx
*ctx
;
2117 return isl_qpolynomial_alloc(domain
, 0,
2118 isl_upoly_var_pow(ctx
, pos
, power
));
2121 __isl_give isl_qpolynomial
*isl_qpolynomial_var_on_domain(
2122 __isl_take isl_space
*domain
, enum isl_dim_type type
, unsigned pos
)
2124 if (isl_space_check_is_set(domain
) < 0)
2126 isl_assert(domain
->ctx
, pos
< isl_space_dim(domain
, type
), goto error
);
2128 if (type
== isl_dim_set
)
2129 pos
+= isl_space_dim(domain
, isl_dim_param
);
2131 return isl_qpolynomial_var_pow_on_domain(domain
, pos
, 1);
2133 isl_space_free(domain
);
2137 __isl_give
struct isl_upoly
*isl_upoly_subs(__isl_take
struct isl_upoly
*up
,
2138 unsigned first
, unsigned n
, __isl_keep
struct isl_upoly
**subs
)
2141 struct isl_upoly_rec
*rec
;
2142 struct isl_upoly
*base
, *res
;
2147 if (isl_upoly_is_cst(up
))
2150 if (up
->var
< first
)
2153 rec
= isl_upoly_as_rec(up
);
2157 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
2159 if (up
->var
>= first
+ n
)
2160 base
= isl_upoly_var_pow(up
->ctx
, up
->var
, 1);
2162 base
= isl_upoly_copy(subs
[up
->var
- first
]);
2164 res
= isl_upoly_subs(isl_upoly_copy(rec
->p
[rec
->n
- 1]), first
, n
, subs
);
2165 for (i
= rec
->n
- 2; i
>= 0; --i
) {
2166 struct isl_upoly
*t
;
2167 t
= isl_upoly_subs(isl_upoly_copy(rec
->p
[i
]), first
, n
, subs
);
2168 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
2169 res
= isl_upoly_sum(res
, t
);
2172 isl_upoly_free(base
);
2181 __isl_give
struct isl_upoly
*isl_upoly_from_affine(isl_ctx
*ctx
, isl_int
*f
,
2182 isl_int denom
, unsigned len
)
2185 struct isl_upoly
*up
;
2187 isl_assert(ctx
, len
>= 1, return NULL
);
2189 up
= isl_upoly_rat_cst(ctx
, f
[0], denom
);
2190 for (i
= 0; i
< len
- 1; ++i
) {
2191 struct isl_upoly
*t
;
2192 struct isl_upoly
*c
;
2194 if (isl_int_is_zero(f
[1 + i
]))
2197 c
= isl_upoly_rat_cst(ctx
, f
[1 + i
], denom
);
2198 t
= isl_upoly_var_pow(ctx
, i
, 1);
2199 t
= isl_upoly_mul(c
, t
);
2200 up
= isl_upoly_sum(up
, t
);
2206 /* Remove common factor of non-constant terms and denominator.
2208 static void normalize_div(__isl_keep isl_qpolynomial
*qp
, int div
)
2210 isl_ctx
*ctx
= qp
->div
->ctx
;
2211 unsigned total
= qp
->div
->n_col
- 2;
2213 isl_seq_gcd(qp
->div
->row
[div
] + 2, total
, &ctx
->normalize_gcd
);
2214 isl_int_gcd(ctx
->normalize_gcd
,
2215 ctx
->normalize_gcd
, qp
->div
->row
[div
][0]);
2216 if (isl_int_is_one(ctx
->normalize_gcd
))
2219 isl_seq_scale_down(qp
->div
->row
[div
] + 2, qp
->div
->row
[div
] + 2,
2220 ctx
->normalize_gcd
, total
);
2221 isl_int_divexact(qp
->div
->row
[div
][0], qp
->div
->row
[div
][0],
2222 ctx
->normalize_gcd
);
2223 isl_int_fdiv_q(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1],
2224 ctx
->normalize_gcd
);
2227 /* Replace the integer division identified by "div" by the polynomial "s".
2228 * The integer division is assumed not to appear in the definition
2229 * of any other integer divisions.
2231 static __isl_give isl_qpolynomial
*substitute_div(
2232 __isl_take isl_qpolynomial
*qp
,
2233 int div
, __isl_take
struct isl_upoly
*s
)
2242 qp
= isl_qpolynomial_cow(qp
);
2246 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
2247 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ div
, 1, &s
);
2251 reordering
= isl_alloc_array(qp
->dim
->ctx
, int, total
+ qp
->div
->n_row
);
2254 for (i
= 0; i
< total
+ div
; ++i
)
2256 for (i
= total
+ div
+ 1; i
< total
+ qp
->div
->n_row
; ++i
)
2257 reordering
[i
] = i
- 1;
2258 qp
->div
= isl_mat_drop_rows(qp
->div
, div
, 1);
2259 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + total
+ div
, 1);
2260 qp
->upoly
= reorder(qp
->upoly
, reordering
);
2263 if (!qp
->upoly
|| !qp
->div
)
2269 isl_qpolynomial_free(qp
);
2274 /* Replace all integer divisions [e/d] that turn out to not actually be integer
2275 * divisions because d is equal to 1 by their definition, i.e., e.
2277 static __isl_give isl_qpolynomial
*substitute_non_divs(
2278 __isl_take isl_qpolynomial
*qp
)
2282 struct isl_upoly
*s
;
2287 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
2288 for (i
= 0; qp
&& i
< qp
->div
->n_row
; ++i
) {
2289 if (!isl_int_is_one(qp
->div
->row
[i
][0]))
2291 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
2292 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
2294 isl_seq_combine(qp
->div
->row
[j
] + 1,
2295 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
2296 qp
->div
->row
[j
][2 + total
+ i
],
2297 qp
->div
->row
[i
] + 1, 1 + total
+ i
);
2298 isl_int_set_si(qp
->div
->row
[j
][2 + total
+ i
], 0);
2299 normalize_div(qp
, j
);
2301 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
2302 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
2303 qp
= substitute_div(qp
, i
, s
);
2310 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
2311 * with d the denominator. When replacing the coefficient e of x by
2312 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
2313 * inside the division, so we need to add floor(e/d) * x outside.
2314 * That is, we replace q by q' + floor(e/d) * x and we therefore need
2315 * to adjust the coefficient of x in each later div that depends on the
2316 * current div "div" and also in the affine expressions in the rows of "mat"
2317 * (if they too depend on "div").
2319 static void reduce_div(__isl_keep isl_qpolynomial
*qp
, int div
,
2320 __isl_keep isl_mat
**mat
)
2324 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
2327 for (i
= 0; i
< 1 + total
+ div
; ++i
) {
2328 if (isl_int_is_nonneg(qp
->div
->row
[div
][1 + i
]) &&
2329 isl_int_lt(qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]))
2331 isl_int_fdiv_q(v
, qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
2332 isl_int_fdiv_r(qp
->div
->row
[div
][1 + i
],
2333 qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
2334 *mat
= isl_mat_col_addmul(*mat
, i
, v
, 1 + total
+ div
);
2335 for (j
= div
+ 1; j
< qp
->div
->n_row
; ++j
) {
2336 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ div
]))
2338 isl_int_addmul(qp
->div
->row
[j
][1 + i
],
2339 v
, qp
->div
->row
[j
][2 + total
+ div
]);
2345 /* Check if the last non-zero coefficient is bigger that half of the
2346 * denominator. If so, we will invert the div to further reduce the number
2347 * of distinct divs that may appear.
2348 * If the last non-zero coefficient is exactly half the denominator,
2349 * then we continue looking for earlier coefficients that are bigger
2350 * than half the denominator.
2352 static int needs_invert(__isl_keep isl_mat
*div
, int row
)
2357 for (i
= div
->n_col
- 1; i
>= 1; --i
) {
2358 if (isl_int_is_zero(div
->row
[row
][i
]))
2360 isl_int_mul_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
2361 cmp
= isl_int_cmp(div
->row
[row
][i
], div
->row
[row
][0]);
2362 isl_int_divexact_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
2372 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
2373 * We only invert the coefficients of e (and the coefficient of q in
2374 * later divs and in the rows of "mat"). After calling this function, the
2375 * coefficients of e should be reduced again.
2377 static void invert_div(__isl_keep isl_qpolynomial
*qp
, int div
,
2378 __isl_keep isl_mat
**mat
)
2380 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
2382 isl_seq_neg(qp
->div
->row
[div
] + 1,
2383 qp
->div
->row
[div
] + 1, qp
->div
->n_col
- 1);
2384 isl_int_sub_ui(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1], 1);
2385 isl_int_add(qp
->div
->row
[div
][1],
2386 qp
->div
->row
[div
][1], qp
->div
->row
[div
][0]);
2387 *mat
= isl_mat_col_neg(*mat
, 1 + total
+ div
);
2388 isl_mat_col_mul(qp
->div
, 2 + total
+ div
,
2389 qp
->div
->ctx
->negone
, 2 + total
+ div
);
2392 /* Reduce all divs of "qp" to have coefficients
2393 * in the interval [0, d-1], with d the denominator and such that the
2394 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2395 * The modifications to the integer divisions need to be reflected
2396 * in the factors of the polynomial that refer to the original
2397 * integer divisions. To this end, the modifications are collected
2398 * as a set of affine expressions and then plugged into the polynomial.
2400 * After the reduction, some divs may have become redundant or identical,
2401 * so we call substitute_non_divs and sort_divs. If these functions
2402 * eliminate divs or merge two or more divs into one, the coefficients
2403 * of the enclosing divs may have to be reduced again, so we call
2404 * ourselves recursively if the number of divs decreases.
2406 static __isl_give isl_qpolynomial
*reduce_divs(__isl_take isl_qpolynomial
*qp
)
2411 struct isl_upoly
**s
;
2412 unsigned o_div
, n_div
, total
;
2417 total
= isl_qpolynomial_domain_dim(qp
, isl_dim_all
);
2418 n_div
= isl_qpolynomial_domain_dim(qp
, isl_dim_div
);
2419 o_div
= isl_qpolynomial_domain_offset(qp
, isl_dim_div
);
2420 ctx
= isl_qpolynomial_get_ctx(qp
);
2421 mat
= isl_mat_zero(ctx
, n_div
, 1 + total
);
2423 for (i
= 0; i
< n_div
; ++i
)
2424 mat
= isl_mat_set_element_si(mat
, i
, o_div
+ i
, 1);
2426 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2427 normalize_div(qp
, i
);
2428 reduce_div(qp
, i
, &mat
);
2429 if (needs_invert(qp
->div
, i
)) {
2430 invert_div(qp
, i
, &mat
);
2431 reduce_div(qp
, i
, &mat
);
2437 s
= isl_alloc_array(ctx
, struct isl_upoly
*, n_div
);
2440 for (i
= 0; i
< n_div
; ++i
)
2441 s
[i
] = isl_upoly_from_affine(ctx
, mat
->row
[i
], ctx
->one
,
2443 qp
->upoly
= isl_upoly_subs(qp
->upoly
, o_div
- 1, n_div
, s
);
2444 for (i
= 0; i
< n_div
; ++i
)
2445 isl_upoly_free(s
[i
]);
2452 qp
= substitute_non_divs(qp
);
2454 if (qp
&& isl_qpolynomial_domain_dim(qp
, isl_dim_div
) < n_div
)
2455 return reduce_divs(qp
);
2459 isl_qpolynomial_free(qp
);
2464 __isl_give isl_qpolynomial
*isl_qpolynomial_rat_cst_on_domain(
2465 __isl_take isl_space
*domain
, const isl_int n
, const isl_int d
)
2467 struct isl_qpolynomial
*qp
;
2468 struct isl_upoly_cst
*cst
;
2470 qp
= isl_qpolynomial_zero_on_domain(domain
);
2474 cst
= isl_upoly_as_cst(qp
->upoly
);
2475 isl_int_set(cst
->n
, n
);
2476 isl_int_set(cst
->d
, d
);
2481 /* Return an isl_qpolynomial that is equal to "val" on domain space "domain".
2483 __isl_give isl_qpolynomial
*isl_qpolynomial_val_on_domain(
2484 __isl_take isl_space
*domain
, __isl_take isl_val
*val
)
2486 isl_qpolynomial
*qp
;
2487 struct isl_upoly_cst
*cst
;
2489 if (!domain
|| !val
)
2492 qp
= isl_qpolynomial_alloc(isl_space_copy(domain
), 0,
2493 isl_upoly_zero(domain
->ctx
));
2497 cst
= isl_upoly_as_cst(qp
->upoly
);
2498 isl_int_set(cst
->n
, val
->n
);
2499 isl_int_set(cst
->d
, val
->d
);
2501 isl_space_free(domain
);
2505 isl_space_free(domain
);
2510 static int up_set_active(__isl_keep
struct isl_upoly
*up
, int *active
, int d
)
2512 struct isl_upoly_rec
*rec
;
2518 if (isl_upoly_is_cst(up
))
2522 active
[up
->var
] = 1;
2524 rec
= isl_upoly_as_rec(up
);
2525 for (i
= 0; i
< rec
->n
; ++i
)
2526 if (up_set_active(rec
->p
[i
], active
, d
) < 0)
2532 static int set_active(__isl_keep isl_qpolynomial
*qp
, int *active
)
2535 int d
= isl_space_dim(qp
->dim
, isl_dim_all
);
2540 for (i
= 0; i
< d
; ++i
)
2541 for (j
= 0; j
< qp
->div
->n_row
; ++j
) {
2542 if (isl_int_is_zero(qp
->div
->row
[j
][2 + i
]))
2548 return up_set_active(qp
->upoly
, active
, d
);
2551 isl_bool
isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial
*qp
,
2552 enum isl_dim_type type
, unsigned first
, unsigned n
)
2556 isl_bool involves
= isl_bool_false
;
2559 return isl_bool_error
;
2561 return isl_bool_false
;
2563 isl_assert(qp
->dim
->ctx
,
2564 first
+ n
<= isl_qpolynomial_dim(qp
, type
),
2565 return isl_bool_error
);
2566 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2567 type
== isl_dim_in
, return isl_bool_error
);
2569 active
= isl_calloc_array(qp
->dim
->ctx
, int,
2570 isl_space_dim(qp
->dim
, isl_dim_all
));
2571 if (set_active(qp
, active
) < 0)
2574 if (type
== isl_dim_in
)
2575 first
+= isl_space_dim(qp
->dim
, isl_dim_param
);
2576 for (i
= 0; i
< n
; ++i
)
2577 if (active
[first
+ i
]) {
2578 involves
= isl_bool_true
;
2587 return isl_bool_error
;
2590 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2591 * of the divs that do appear in the quasi-polynomial.
2593 static __isl_give isl_qpolynomial
*remove_redundant_divs(
2594 __isl_take isl_qpolynomial
*qp
)
2601 int *reordering
= NULL
;
2608 if (qp
->div
->n_row
== 0)
2611 d
= isl_space_dim(qp
->dim
, isl_dim_all
);
2612 len
= qp
->div
->n_col
- 2;
2613 ctx
= isl_qpolynomial_get_ctx(qp
);
2614 active
= isl_calloc_array(ctx
, int, len
);
2618 if (up_set_active(qp
->upoly
, active
, len
) < 0)
2621 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
2622 if (!active
[d
+ i
]) {
2626 for (j
= 0; j
< i
; ++j
) {
2627 if (isl_int_is_zero(qp
->div
->row
[i
][2 + d
+ j
]))
2639 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
2643 for (i
= 0; i
< d
; ++i
)
2647 n_div
= qp
->div
->n_row
;
2648 for (i
= 0; i
< n_div
; ++i
) {
2649 if (!active
[d
+ i
]) {
2650 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
2651 qp
->div
= isl_mat_drop_cols(qp
->div
,
2652 2 + d
+ i
- skip
, 1);
2655 reordering
[d
+ i
] = d
+ i
- skip
;
2658 qp
->upoly
= reorder(qp
->upoly
, reordering
);
2660 if (!qp
->upoly
|| !qp
->div
)
2670 isl_qpolynomial_free(qp
);
2674 __isl_give
struct isl_upoly
*isl_upoly_drop(__isl_take
struct isl_upoly
*up
,
2675 unsigned first
, unsigned n
)
2678 struct isl_upoly_rec
*rec
;
2682 if (n
== 0 || up
->var
< 0 || up
->var
< first
)
2684 if (up
->var
< first
+ n
) {
2685 up
= replace_by_constant_term(up
);
2686 return isl_upoly_drop(up
, first
, n
);
2688 up
= isl_upoly_cow(up
);
2692 rec
= isl_upoly_as_rec(up
);
2696 for (i
= 0; i
< rec
->n
; ++i
) {
2697 rec
->p
[i
] = isl_upoly_drop(rec
->p
[i
], first
, n
);
2708 __isl_give isl_qpolynomial
*isl_qpolynomial_set_dim_name(
2709 __isl_take isl_qpolynomial
*qp
,
2710 enum isl_dim_type type
, unsigned pos
, const char *s
)
2712 qp
= isl_qpolynomial_cow(qp
);
2715 if (type
== isl_dim_out
)
2716 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
2717 "cannot set name of output/set dimension",
2718 return isl_qpolynomial_free(qp
));
2719 type
= domain_type(type
);
2720 qp
->dim
= isl_space_set_dim_name(qp
->dim
, type
, pos
, s
);
2725 isl_qpolynomial_free(qp
);
2729 __isl_give isl_qpolynomial
*isl_qpolynomial_drop_dims(
2730 __isl_take isl_qpolynomial
*qp
,
2731 enum isl_dim_type type
, unsigned first
, unsigned n
)
2735 if (type
== isl_dim_out
)
2736 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
2737 "cannot drop output/set dimension",
2739 type
= domain_type(type
);
2740 if (n
== 0 && !isl_space_is_named_or_nested(qp
->dim
, type
))
2743 qp
= isl_qpolynomial_cow(qp
);
2747 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_space_dim(qp
->dim
, type
),
2749 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2750 type
== isl_dim_set
, goto error
);
2752 qp
->dim
= isl_space_drop_dims(qp
->dim
, type
, first
, n
);
2756 if (type
== isl_dim_set
)
2757 first
+= isl_space_dim(qp
->dim
, isl_dim_param
);
2759 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + first
, n
);
2763 qp
->upoly
= isl_upoly_drop(qp
->upoly
, first
, n
);
2769 isl_qpolynomial_free(qp
);
2773 /* Project the domain of the quasi-polynomial onto its parameter space.
2774 * The quasi-polynomial may not involve any of the domain dimensions.
2776 __isl_give isl_qpolynomial
*isl_qpolynomial_project_domain_on_params(
2777 __isl_take isl_qpolynomial
*qp
)
2783 n
= isl_qpolynomial_dim(qp
, isl_dim_in
);
2784 involves
= isl_qpolynomial_involves_dims(qp
, isl_dim_in
, 0, n
);
2786 return isl_qpolynomial_free(qp
);
2788 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
2789 "polynomial involves some of the domain dimensions",
2790 return isl_qpolynomial_free(qp
));
2791 qp
= isl_qpolynomial_drop_dims(qp
, isl_dim_in
, 0, n
);
2792 space
= isl_qpolynomial_get_domain_space(qp
);
2793 space
= isl_space_params(space
);
2794 qp
= isl_qpolynomial_reset_domain_space(qp
, space
);
2798 static __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities_lifted(
2799 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2805 struct isl_upoly
*up
;
2809 if (eq
->n_eq
== 0) {
2810 isl_basic_set_free(eq
);
2814 qp
= isl_qpolynomial_cow(qp
);
2817 qp
->div
= isl_mat_cow(qp
->div
);
2821 total
= 1 + isl_space_dim(eq
->dim
, isl_dim_all
);
2823 isl_int_init(denom
);
2824 for (i
= 0; i
< eq
->n_eq
; ++i
) {
2825 j
= isl_seq_last_non_zero(eq
->eq
[i
], total
+ n_div
);
2826 if (j
< 0 || j
== 0 || j
>= total
)
2829 for (k
= 0; k
< qp
->div
->n_row
; ++k
) {
2830 if (isl_int_is_zero(qp
->div
->row
[k
][1 + j
]))
2832 isl_seq_elim(qp
->div
->row
[k
] + 1, eq
->eq
[i
], j
, total
,
2833 &qp
->div
->row
[k
][0]);
2834 normalize_div(qp
, k
);
2837 if (isl_int_is_pos(eq
->eq
[i
][j
]))
2838 isl_seq_neg(eq
->eq
[i
], eq
->eq
[i
], total
);
2839 isl_int_abs(denom
, eq
->eq
[i
][j
]);
2840 isl_int_set_si(eq
->eq
[i
][j
], 0);
2842 up
= isl_upoly_from_affine(qp
->dim
->ctx
,
2843 eq
->eq
[i
], denom
, total
);
2844 qp
->upoly
= isl_upoly_subs(qp
->upoly
, j
- 1, 1, &up
);
2847 isl_int_clear(denom
);
2852 isl_basic_set_free(eq
);
2854 qp
= substitute_non_divs(qp
);
2859 isl_basic_set_free(eq
);
2860 isl_qpolynomial_free(qp
);
2864 /* Exploit the equalities in "eq" to simplify the quasi-polynomial.
2866 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities(
2867 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2871 if (qp
->div
->n_row
> 0)
2872 eq
= isl_basic_set_add_dims(eq
, isl_dim_set
, qp
->div
->n_row
);
2873 return isl_qpolynomial_substitute_equalities_lifted(qp
, eq
);
2875 isl_basic_set_free(eq
);
2876 isl_qpolynomial_free(qp
);
2880 /* Look for equalities among the variables shared by context and qp
2881 * and the integer divisions of qp, if any.
2882 * The equalities are then used to eliminate variables and/or integer
2883 * divisions from qp.
2885 __isl_give isl_qpolynomial
*isl_qpolynomial_gist(
2886 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
2888 isl_local_space
*ls
;
2891 ls
= isl_qpolynomial_get_domain_local_space(qp
);
2892 context
= isl_local_space_lift_set(ls
, context
);
2894 aff
= isl_set_affine_hull(context
);
2895 return isl_qpolynomial_substitute_equalities_lifted(qp
, aff
);
2898 __isl_give isl_qpolynomial
*isl_qpolynomial_gist_params(
2899 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
2901 isl_space
*space
= isl_qpolynomial_get_domain_space(qp
);
2902 isl_set
*dom_context
= isl_set_universe(space
);
2903 dom_context
= isl_set_intersect_params(dom_context
, context
);
2904 return isl_qpolynomial_gist(qp
, dom_context
);
2907 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_from_qpolynomial(
2908 __isl_take isl_qpolynomial
*qp
)
2914 if (isl_qpolynomial_is_zero(qp
)) {
2915 isl_space
*dim
= isl_qpolynomial_get_space(qp
);
2916 isl_qpolynomial_free(qp
);
2917 return isl_pw_qpolynomial_zero(dim
);
2920 dom
= isl_set_universe(isl_qpolynomial_get_domain_space(qp
));
2921 return isl_pw_qpolynomial_alloc(dom
, qp
);
2924 #define isl_qpolynomial_involves_nan isl_qpolynomial_is_nan
2927 #define PW isl_pw_qpolynomial
2929 #define EL isl_qpolynomial
2931 #define EL_IS_ZERO is_zero
2935 #define IS_ZERO is_zero
2938 #undef DEFAULT_IS_ZERO
2939 #define DEFAULT_IS_ZERO 1
2943 #include <isl_pw_templ.c>
2944 #include <isl_pw_eval.c>
2947 #define BASE pw_qpolynomial
2949 #include <isl_union_single.c>
2950 #include <isl_union_eval.c>
2951 #include <isl_union_neg.c>
2953 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial
*pwqp
)
2961 if (!isl_set_plain_is_universe(pwqp
->p
[0].set
))
2964 return isl_qpolynomial_is_one(pwqp
->p
[0].qp
);
2967 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add(
2968 __isl_take isl_pw_qpolynomial
*pwqp1
,
2969 __isl_take isl_pw_qpolynomial
*pwqp2
)
2971 return isl_pw_qpolynomial_union_add_(pwqp1
, pwqp2
);
2974 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_mul(
2975 __isl_take isl_pw_qpolynomial
*pwqp1
,
2976 __isl_take isl_pw_qpolynomial
*pwqp2
)
2979 struct isl_pw_qpolynomial
*res
;
2981 if (!pwqp1
|| !pwqp2
)
2984 isl_assert(pwqp1
->dim
->ctx
, isl_space_is_equal(pwqp1
->dim
, pwqp2
->dim
),
2987 if (isl_pw_qpolynomial_is_zero(pwqp1
)) {
2988 isl_pw_qpolynomial_free(pwqp2
);
2992 if (isl_pw_qpolynomial_is_zero(pwqp2
)) {
2993 isl_pw_qpolynomial_free(pwqp1
);
2997 if (isl_pw_qpolynomial_is_one(pwqp1
)) {
2998 isl_pw_qpolynomial_free(pwqp1
);
3002 if (isl_pw_qpolynomial_is_one(pwqp2
)) {
3003 isl_pw_qpolynomial_free(pwqp2
);
3007 n
= pwqp1
->n
* pwqp2
->n
;
3008 res
= isl_pw_qpolynomial_alloc_size(isl_space_copy(pwqp1
->dim
), n
);
3010 for (i
= 0; i
< pwqp1
->n
; ++i
) {
3011 for (j
= 0; j
< pwqp2
->n
; ++j
) {
3012 struct isl_set
*common
;
3013 struct isl_qpolynomial
*prod
;
3014 common
= isl_set_intersect(isl_set_copy(pwqp1
->p
[i
].set
),
3015 isl_set_copy(pwqp2
->p
[j
].set
));
3016 if (isl_set_plain_is_empty(common
)) {
3017 isl_set_free(common
);
3021 prod
= isl_qpolynomial_mul(
3022 isl_qpolynomial_copy(pwqp1
->p
[i
].qp
),
3023 isl_qpolynomial_copy(pwqp2
->p
[j
].qp
));
3025 res
= isl_pw_qpolynomial_add_piece(res
, common
, prod
);
3029 isl_pw_qpolynomial_free(pwqp1
);
3030 isl_pw_qpolynomial_free(pwqp2
);
3034 isl_pw_qpolynomial_free(pwqp1
);
3035 isl_pw_qpolynomial_free(pwqp2
);
3039 __isl_give isl_val
*isl_upoly_eval(__isl_take
struct isl_upoly
*up
,
3040 __isl_take isl_vec
*vec
)
3043 struct isl_upoly_rec
*rec
;
3047 if (isl_upoly_is_cst(up
)) {
3049 res
= isl_upoly_get_constant_val(up
);
3054 rec
= isl_upoly_as_rec(up
);
3058 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
3060 base
= isl_val_rat_from_isl_int(up
->ctx
,
3061 vec
->el
[1 + up
->var
], vec
->el
[0]);
3063 res
= isl_upoly_eval(isl_upoly_copy(rec
->p
[rec
->n
- 1]),
3066 for (i
= rec
->n
- 2; i
>= 0; --i
) {
3067 res
= isl_val_mul(res
, isl_val_copy(base
));
3068 res
= isl_val_add(res
,
3069 isl_upoly_eval(isl_upoly_copy(rec
->p
[i
]),
3070 isl_vec_copy(vec
)));
3083 /* Evaluate "qp" in the void point "pnt".
3084 * In particular, return the value NaN.
3086 static __isl_give isl_val
*eval_void(__isl_take isl_qpolynomial
*qp
,
3087 __isl_take isl_point
*pnt
)
3091 ctx
= isl_point_get_ctx(pnt
);
3092 isl_qpolynomial_free(qp
);
3093 isl_point_free(pnt
);
3094 return isl_val_nan(ctx
);
3097 __isl_give isl_val
*isl_qpolynomial_eval(__isl_take isl_qpolynomial
*qp
,
3098 __isl_take isl_point
*pnt
)
3106 isl_assert(pnt
->dim
->ctx
, isl_space_is_equal(pnt
->dim
, qp
->dim
), goto error
);
3107 is_void
= isl_point_is_void(pnt
);
3111 return eval_void(qp
, pnt
);
3113 ext
= isl_local_extend_point_vec(qp
->div
, isl_vec_copy(pnt
->vec
));
3115 v
= isl_upoly_eval(isl_upoly_copy(qp
->upoly
), ext
);
3117 isl_qpolynomial_free(qp
);
3118 isl_point_free(pnt
);
3122 isl_qpolynomial_free(qp
);
3123 isl_point_free(pnt
);
3127 int isl_upoly_cmp(__isl_keep
struct isl_upoly_cst
*cst1
,
3128 __isl_keep
struct isl_upoly_cst
*cst2
)
3133 isl_int_mul(t
, cst1
->n
, cst2
->d
);
3134 isl_int_submul(t
, cst2
->n
, cst1
->d
);
3135 cmp
= isl_int_sgn(t
);
3140 __isl_give isl_qpolynomial
*isl_qpolynomial_insert_dims(
3141 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
,
3142 unsigned first
, unsigned n
)
3150 if (type
== isl_dim_out
)
3151 isl_die(qp
->div
->ctx
, isl_error_invalid
,
3152 "cannot insert output/set dimensions",
3154 type
= domain_type(type
);
3155 if (n
== 0 && !isl_space_is_named_or_nested(qp
->dim
, type
))
3158 qp
= isl_qpolynomial_cow(qp
);
3162 isl_assert(qp
->div
->ctx
, first
<= isl_space_dim(qp
->dim
, type
),
3165 g_pos
= pos(qp
->dim
, type
) + first
;
3167 qp
->div
= isl_mat_insert_zero_cols(qp
->div
, 2 + g_pos
, n
);
3171 total
= qp
->div
->n_col
- 2;
3172 if (total
> g_pos
) {
3174 exp
= isl_alloc_array(qp
->div
->ctx
, int, total
- g_pos
);
3177 for (i
= 0; i
< total
- g_pos
; ++i
)
3179 qp
->upoly
= expand(qp
->upoly
, exp
, g_pos
);
3185 qp
->dim
= isl_space_insert_dims(qp
->dim
, type
, first
, n
);
3191 isl_qpolynomial_free(qp
);
3195 __isl_give isl_qpolynomial
*isl_qpolynomial_add_dims(
3196 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
, unsigned n
)
3200 pos
= isl_qpolynomial_dim(qp
, type
);
3202 return isl_qpolynomial_insert_dims(qp
, type
, pos
, n
);
3205 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add_dims(
3206 __isl_take isl_pw_qpolynomial
*pwqp
,
3207 enum isl_dim_type type
, unsigned n
)
3211 pos
= isl_pw_qpolynomial_dim(pwqp
, type
);
3213 return isl_pw_qpolynomial_insert_dims(pwqp
, type
, pos
, n
);
3216 static int *reordering_move(isl_ctx
*ctx
,
3217 unsigned len
, unsigned dst
, unsigned src
, unsigned n
)
3222 reordering
= isl_alloc_array(ctx
, int, len
);
3227 for (i
= 0; i
< dst
; ++i
)
3229 for (i
= 0; i
< n
; ++i
)
3230 reordering
[src
+ i
] = dst
+ i
;
3231 for (i
= 0; i
< src
- dst
; ++i
)
3232 reordering
[dst
+ i
] = dst
+ n
+ i
;
3233 for (i
= 0; i
< len
- src
- n
; ++i
)
3234 reordering
[src
+ n
+ i
] = src
+ n
+ i
;
3236 for (i
= 0; i
< src
; ++i
)
3238 for (i
= 0; i
< n
; ++i
)
3239 reordering
[src
+ i
] = dst
+ i
;
3240 for (i
= 0; i
< dst
- src
; ++i
)
3241 reordering
[src
+ n
+ i
] = src
+ i
;
3242 for (i
= 0; i
< len
- dst
- n
; ++i
)
3243 reordering
[dst
+ n
+ i
] = dst
+ n
+ i
;
3249 __isl_give isl_qpolynomial
*isl_qpolynomial_move_dims(
3250 __isl_take isl_qpolynomial
*qp
,
3251 enum isl_dim_type dst_type
, unsigned dst_pos
,
3252 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
3261 if (dst_type
== isl_dim_out
|| src_type
== isl_dim_out
)
3262 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
3263 "cannot move output/set dimension",
3265 if (dst_type
== isl_dim_in
)
3266 dst_type
= isl_dim_set
;
3267 if (src_type
== isl_dim_in
)
3268 src_type
= isl_dim_set
;
3271 !isl_space_is_named_or_nested(qp
->dim
, src_type
) &&
3272 !isl_space_is_named_or_nested(qp
->dim
, dst_type
))
3275 qp
= isl_qpolynomial_cow(qp
);
3279 isl_assert(qp
->dim
->ctx
, src_pos
+ n
<= isl_space_dim(qp
->dim
, src_type
),
3282 g_dst_pos
= pos(qp
->dim
, dst_type
) + dst_pos
;
3283 g_src_pos
= pos(qp
->dim
, src_type
) + src_pos
;
3284 if (dst_type
> src_type
)
3287 qp
->div
= isl_mat_move_cols(qp
->div
, 2 + g_dst_pos
, 2 + g_src_pos
, n
);
3294 reordering
= reordering_move(qp
->dim
->ctx
,
3295 qp
->div
->n_col
- 2, g_dst_pos
, g_src_pos
, n
);
3299 qp
->upoly
= reorder(qp
->upoly
, reordering
);
3304 qp
->dim
= isl_space_move_dims(qp
->dim
, dst_type
, dst_pos
, src_type
, src_pos
, n
);
3310 isl_qpolynomial_free(qp
);
3314 __isl_give isl_qpolynomial
*isl_qpolynomial_from_affine(
3315 __isl_take isl_space
*space
, isl_int
*f
, isl_int denom
)
3317 struct isl_upoly
*up
;
3319 space
= isl_space_domain(space
);
3323 up
= isl_upoly_from_affine(space
->ctx
, f
, denom
,
3324 1 + isl_space_dim(space
, isl_dim_all
));
3326 return isl_qpolynomial_alloc(space
, 0, up
);
3329 __isl_give isl_qpolynomial
*isl_qpolynomial_from_aff(__isl_take isl_aff
*aff
)
3332 struct isl_upoly
*up
;
3333 isl_qpolynomial
*qp
;
3338 ctx
= isl_aff_get_ctx(aff
);
3339 up
= isl_upoly_from_affine(ctx
, aff
->v
->el
+ 1, aff
->v
->el
[0],
3342 qp
= isl_qpolynomial_alloc(isl_aff_get_domain_space(aff
),
3343 aff
->ls
->div
->n_row
, up
);
3347 isl_mat_free(qp
->div
);
3348 qp
->div
= isl_mat_copy(aff
->ls
->div
);
3349 qp
->div
= isl_mat_cow(qp
->div
);
3354 qp
= reduce_divs(qp
);
3355 qp
= remove_redundant_divs(qp
);
3359 return isl_qpolynomial_free(qp
);
3362 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_from_pw_aff(
3363 __isl_take isl_pw_aff
*pwaff
)
3366 isl_pw_qpolynomial
*pwqp
;
3371 pwqp
= isl_pw_qpolynomial_alloc_size(isl_pw_aff_get_space(pwaff
),
3374 for (i
= 0; i
< pwaff
->n
; ++i
) {
3376 isl_qpolynomial
*qp
;
3378 dom
= isl_set_copy(pwaff
->p
[i
].set
);
3379 qp
= isl_qpolynomial_from_aff(isl_aff_copy(pwaff
->p
[i
].aff
));
3380 pwqp
= isl_pw_qpolynomial_add_piece(pwqp
, dom
, qp
);
3383 isl_pw_aff_free(pwaff
);
3387 __isl_give isl_qpolynomial
*isl_qpolynomial_from_constraint(
3388 __isl_take isl_constraint
*c
, enum isl_dim_type type
, unsigned pos
)
3392 aff
= isl_constraint_get_bound(c
, type
, pos
);
3393 isl_constraint_free(c
);
3394 return isl_qpolynomial_from_aff(aff
);
3397 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3398 * in "qp" by subs[i].
3400 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute(
3401 __isl_take isl_qpolynomial
*qp
,
3402 enum isl_dim_type type
, unsigned first
, unsigned n
,
3403 __isl_keep isl_qpolynomial
**subs
)
3406 struct isl_upoly
**ups
;
3411 qp
= isl_qpolynomial_cow(qp
);
3415 if (type
== isl_dim_out
)
3416 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
3417 "cannot substitute output/set dimension",
3419 type
= domain_type(type
);
3421 for (i
= 0; i
< n
; ++i
)
3425 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_space_dim(qp
->dim
, type
),
3428 for (i
= 0; i
< n
; ++i
)
3429 isl_assert(qp
->dim
->ctx
, isl_space_is_equal(qp
->dim
, subs
[i
]->dim
),
3432 isl_assert(qp
->dim
->ctx
, qp
->div
->n_row
== 0, goto error
);
3433 for (i
= 0; i
< n
; ++i
)
3434 isl_assert(qp
->dim
->ctx
, subs
[i
]->div
->n_row
== 0, goto error
);
3436 first
+= pos(qp
->dim
, type
);
3438 ups
= isl_alloc_array(qp
->dim
->ctx
, struct isl_upoly
*, n
);
3441 for (i
= 0; i
< n
; ++i
)
3442 ups
[i
] = subs
[i
]->upoly
;
3444 qp
->upoly
= isl_upoly_subs(qp
->upoly
, first
, n
, ups
);
3453 isl_qpolynomial_free(qp
);
3457 /* Extend "bset" with extra set dimensions for each integer division
3458 * in "qp" and then call "fn" with the extended bset and the polynomial
3459 * that results from replacing each of the integer divisions by the
3460 * corresponding extra set dimension.
3462 isl_stat
isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial
*qp
,
3463 __isl_keep isl_basic_set
*bset
,
3464 isl_stat (*fn
)(__isl_take isl_basic_set
*bset
,
3465 __isl_take isl_qpolynomial
*poly
, void *user
), void *user
)
3468 isl_local_space
*ls
;
3469 isl_qpolynomial
*poly
;
3472 return isl_stat_error
;
3473 if (qp
->div
->n_row
== 0)
3474 return fn(isl_basic_set_copy(bset
), isl_qpolynomial_copy(qp
),
3477 space
= isl_space_copy(qp
->dim
);
3478 space
= isl_space_add_dims(space
, isl_dim_set
, qp
->div
->n_row
);
3479 poly
= isl_qpolynomial_alloc(space
, 0, isl_upoly_copy(qp
->upoly
));
3480 bset
= isl_basic_set_copy(bset
);
3481 ls
= isl_qpolynomial_get_domain_local_space(qp
);
3482 bset
= isl_local_space_lift_basic_set(ls
, bset
);
3484 return fn(bset
, poly
, user
);
3487 /* Return total degree in variables first (inclusive) up to last (exclusive).
3489 int isl_upoly_degree(__isl_keep
struct isl_upoly
*up
, int first
, int last
)
3493 struct isl_upoly_rec
*rec
;
3497 if (isl_upoly_is_zero(up
))
3499 if (isl_upoly_is_cst(up
) || up
->var
< first
)
3502 rec
= isl_upoly_as_rec(up
);
3506 for (i
= 0; i
< rec
->n
; ++i
) {
3509 if (isl_upoly_is_zero(rec
->p
[i
]))
3511 d
= isl_upoly_degree(rec
->p
[i
], first
, last
);
3521 /* Return total degree in set variables.
3523 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial
*poly
)
3531 ovar
= isl_space_offset(poly
->dim
, isl_dim_set
);
3532 nvar
= isl_space_dim(poly
->dim
, isl_dim_set
);
3533 return isl_upoly_degree(poly
->upoly
, ovar
, ovar
+ nvar
);
3536 __isl_give
struct isl_upoly
*isl_upoly_coeff(__isl_keep
struct isl_upoly
*up
,
3537 unsigned pos
, int deg
)
3540 struct isl_upoly_rec
*rec
;
3545 if (isl_upoly_is_cst(up
) || up
->var
< pos
) {
3547 return isl_upoly_copy(up
);
3549 return isl_upoly_zero(up
->ctx
);
3552 rec
= isl_upoly_as_rec(up
);
3556 if (up
->var
== pos
) {
3558 return isl_upoly_copy(rec
->p
[deg
]);
3560 return isl_upoly_zero(up
->ctx
);
3563 up
= isl_upoly_copy(up
);
3564 up
= isl_upoly_cow(up
);
3565 rec
= isl_upoly_as_rec(up
);
3569 for (i
= 0; i
< rec
->n
; ++i
) {
3570 struct isl_upoly
*t
;
3571 t
= isl_upoly_coeff(rec
->p
[i
], pos
, deg
);
3574 isl_upoly_free(rec
->p
[i
]);
3584 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3586 __isl_give isl_qpolynomial
*isl_qpolynomial_coeff(
3587 __isl_keep isl_qpolynomial
*qp
,
3588 enum isl_dim_type type
, unsigned t_pos
, int deg
)
3591 struct isl_upoly
*up
;
3597 if (type
== isl_dim_out
)
3598 isl_die(qp
->div
->ctx
, isl_error_invalid
,
3599 "output/set dimension does not have a coefficient",
3601 type
= domain_type(type
);
3603 isl_assert(qp
->div
->ctx
, t_pos
< isl_space_dim(qp
->dim
, type
),
3606 g_pos
= pos(qp
->dim
, type
) + t_pos
;
3607 up
= isl_upoly_coeff(qp
->upoly
, g_pos
, deg
);
3609 c
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
), qp
->div
->n_row
, up
);
3612 isl_mat_free(c
->div
);
3613 c
->div
= isl_mat_copy(qp
->div
);
3618 isl_qpolynomial_free(c
);
3622 /* Homogenize the polynomial in the variables first (inclusive) up to
3623 * last (exclusive) by inserting powers of variable first.
3624 * Variable first is assumed not to appear in the input.
3626 __isl_give
struct isl_upoly
*isl_upoly_homogenize(
3627 __isl_take
struct isl_upoly
*up
, int deg
, int target
,
3628 int first
, int last
)
3631 struct isl_upoly_rec
*rec
;
3635 if (isl_upoly_is_zero(up
))
3639 if (isl_upoly_is_cst(up
) || up
->var
< first
) {
3640 struct isl_upoly
*hom
;
3642 hom
= isl_upoly_var_pow(up
->ctx
, first
, target
- deg
);
3645 rec
= isl_upoly_as_rec(hom
);
3646 rec
->p
[target
- deg
] = isl_upoly_mul(rec
->p
[target
- deg
], up
);
3651 up
= isl_upoly_cow(up
);
3652 rec
= isl_upoly_as_rec(up
);
3656 for (i
= 0; i
< rec
->n
; ++i
) {
3657 if (isl_upoly_is_zero(rec
->p
[i
]))
3659 rec
->p
[i
] = isl_upoly_homogenize(rec
->p
[i
],
3660 up
->var
< last
? deg
+ i
: i
, target
,
3672 /* Homogenize the polynomial in the set variables by introducing
3673 * powers of an extra set variable at position 0.
3675 __isl_give isl_qpolynomial
*isl_qpolynomial_homogenize(
3676 __isl_take isl_qpolynomial
*poly
)
3680 int deg
= isl_qpolynomial_degree(poly
);
3685 poly
= isl_qpolynomial_insert_dims(poly
, isl_dim_in
, 0, 1);
3686 poly
= isl_qpolynomial_cow(poly
);
3690 ovar
= isl_space_offset(poly
->dim
, isl_dim_set
);
3691 nvar
= isl_space_dim(poly
->dim
, isl_dim_set
);
3692 poly
->upoly
= isl_upoly_homogenize(poly
->upoly
, 0, deg
,
3699 isl_qpolynomial_free(poly
);
3703 __isl_give isl_term
*isl_term_alloc(__isl_take isl_space
*space
,
3704 __isl_take isl_mat
*div
)
3712 n
= isl_space_dim(space
, isl_dim_all
) + div
->n_row
;
3714 term
= isl_calloc(space
->ctx
, struct isl_term
,
3715 sizeof(struct isl_term
) + (n
- 1) * sizeof(int));
3722 isl_int_init(term
->n
);
3723 isl_int_init(term
->d
);
3727 isl_space_free(space
);
3732 __isl_give isl_term
*isl_term_copy(__isl_keep isl_term
*term
)
3741 __isl_give isl_term
*isl_term_dup(__isl_keep isl_term
*term
)
3750 total
= isl_space_dim(term
->dim
, isl_dim_all
) + term
->div
->n_row
;
3752 dup
= isl_term_alloc(isl_space_copy(term
->dim
), isl_mat_copy(term
->div
));
3756 isl_int_set(dup
->n
, term
->n
);
3757 isl_int_set(dup
->d
, term
->d
);
3759 for (i
= 0; i
< total
; ++i
)
3760 dup
->pow
[i
] = term
->pow
[i
];
3765 __isl_give isl_term
*isl_term_cow(__isl_take isl_term
*term
)
3773 return isl_term_dup(term
);
3776 __isl_null isl_term
*isl_term_free(__isl_take isl_term
*term
)
3781 if (--term
->ref
> 0)
3784 isl_space_free(term
->dim
);
3785 isl_mat_free(term
->div
);
3786 isl_int_clear(term
->n
);
3787 isl_int_clear(term
->d
);
3793 unsigned isl_term_dim(__isl_keep isl_term
*term
, enum isl_dim_type type
)
3801 case isl_dim_out
: return isl_space_dim(term
->dim
, type
);
3802 case isl_dim_div
: return term
->div
->n_row
;
3803 case isl_dim_all
: return isl_space_dim(term
->dim
, isl_dim_all
) +
3809 isl_ctx
*isl_term_get_ctx(__isl_keep isl_term
*term
)
3811 return term
? term
->dim
->ctx
: NULL
;
3814 void isl_term_get_num(__isl_keep isl_term
*term
, isl_int
*n
)
3818 isl_int_set(*n
, term
->n
);
3821 /* Return the coefficient of the term "term".
3823 __isl_give isl_val
*isl_term_get_coefficient_val(__isl_keep isl_term
*term
)
3828 return isl_val_rat_from_isl_int(isl_term_get_ctx(term
),
3832 int isl_term_get_exp(__isl_keep isl_term
*term
,
3833 enum isl_dim_type type
, unsigned pos
)
3838 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, type
), return -1);
3840 if (type
>= isl_dim_set
)
3841 pos
+= isl_space_dim(term
->dim
, isl_dim_param
);
3842 if (type
>= isl_dim_div
)
3843 pos
+= isl_space_dim(term
->dim
, isl_dim_set
);
3845 return term
->pow
[pos
];
3848 __isl_give isl_aff
*isl_term_get_div(__isl_keep isl_term
*term
, unsigned pos
)
3850 isl_local_space
*ls
;
3856 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, isl_dim_div
),
3859 ls
= isl_local_space_alloc_div(isl_space_copy(term
->dim
),
3860 isl_mat_copy(term
->div
));
3861 aff
= isl_aff_alloc(ls
);
3865 isl_seq_cpy(aff
->v
->el
, term
->div
->row
[pos
], aff
->v
->size
);
3867 aff
= isl_aff_normalize(aff
);
3872 __isl_give isl_term
*isl_upoly_foreach_term(__isl_keep
struct isl_upoly
*up
,
3873 isl_stat (*fn
)(__isl_take isl_term
*term
, void *user
),
3874 __isl_take isl_term
*term
, void *user
)
3877 struct isl_upoly_rec
*rec
;
3882 if (isl_upoly_is_zero(up
))
3885 isl_assert(up
->ctx
, !isl_upoly_is_nan(up
), goto error
);
3886 isl_assert(up
->ctx
, !isl_upoly_is_infty(up
), goto error
);
3887 isl_assert(up
->ctx
, !isl_upoly_is_neginfty(up
), goto error
);
3889 if (isl_upoly_is_cst(up
)) {
3890 struct isl_upoly_cst
*cst
;
3891 cst
= isl_upoly_as_cst(up
);
3894 term
= isl_term_cow(term
);
3897 isl_int_set(term
->n
, cst
->n
);
3898 isl_int_set(term
->d
, cst
->d
);
3899 if (fn(isl_term_copy(term
), user
) < 0)
3904 rec
= isl_upoly_as_rec(up
);
3908 for (i
= 0; i
< rec
->n
; ++i
) {
3909 term
= isl_term_cow(term
);
3912 term
->pow
[up
->var
] = i
;
3913 term
= isl_upoly_foreach_term(rec
->p
[i
], fn
, term
, user
);
3917 term
->pow
[up
->var
] = 0;
3921 isl_term_free(term
);
3925 isl_stat
isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial
*qp
,
3926 isl_stat (*fn
)(__isl_take isl_term
*term
, void *user
), void *user
)
3931 return isl_stat_error
;
3933 term
= isl_term_alloc(isl_space_copy(qp
->dim
), isl_mat_copy(qp
->div
));
3935 return isl_stat_error
;
3937 term
= isl_upoly_foreach_term(qp
->upoly
, fn
, term
, user
);
3939 isl_term_free(term
);
3941 return term
? isl_stat_ok
: isl_stat_error
;
3944 __isl_give isl_qpolynomial
*isl_qpolynomial_from_term(__isl_take isl_term
*term
)
3946 struct isl_upoly
*up
;
3947 isl_qpolynomial
*qp
;
3953 n
= isl_space_dim(term
->dim
, isl_dim_all
) + term
->div
->n_row
;
3955 up
= isl_upoly_rat_cst(term
->dim
->ctx
, term
->n
, term
->d
);
3956 for (i
= 0; i
< n
; ++i
) {
3959 up
= isl_upoly_mul(up
,
3960 isl_upoly_var_pow(term
->dim
->ctx
, i
, term
->pow
[i
]));
3963 qp
= isl_qpolynomial_alloc(isl_space_copy(term
->dim
), term
->div
->n_row
, up
);
3966 isl_mat_free(qp
->div
);
3967 qp
->div
= isl_mat_copy(term
->div
);
3971 isl_term_free(term
);
3974 isl_qpolynomial_free(qp
);
3975 isl_term_free(term
);
3979 __isl_give isl_qpolynomial
*isl_qpolynomial_lift(__isl_take isl_qpolynomial
*qp
,
3980 __isl_take isl_space
*space
)
3989 if (isl_space_is_equal(qp
->dim
, space
)) {
3990 isl_space_free(space
);
3994 qp
= isl_qpolynomial_cow(qp
);
3998 extra
= isl_space_dim(space
, isl_dim_set
) -
3999 isl_space_dim(qp
->dim
, isl_dim_set
);
4000 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4001 if (qp
->div
->n_row
) {
4004 exp
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
4007 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4009 qp
->upoly
= expand(qp
->upoly
, exp
, total
);
4014 qp
->div
= isl_mat_insert_cols(qp
->div
, 2 + total
, extra
);
4017 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4018 isl_seq_clr(qp
->div
->row
[i
] + 2 + total
, extra
);
4020 isl_space_free(qp
->dim
);
4025 isl_space_free(space
);
4026 isl_qpolynomial_free(qp
);
4030 /* For each parameter or variable that does not appear in qp,
4031 * first eliminate the variable from all constraints and then set it to zero.
4033 static __isl_give isl_set
*fix_inactive(__isl_take isl_set
*set
,
4034 __isl_keep isl_qpolynomial
*qp
)
4045 d
= isl_space_dim(set
->dim
, isl_dim_all
);
4046 active
= isl_calloc_array(set
->ctx
, int, d
);
4047 if (set_active(qp
, active
) < 0)
4050 for (i
= 0; i
< d
; ++i
)
4059 nparam
= isl_space_dim(set
->dim
, isl_dim_param
);
4060 nvar
= isl_space_dim(set
->dim
, isl_dim_set
);
4061 for (i
= 0; i
< nparam
; ++i
) {
4064 set
= isl_set_eliminate(set
, isl_dim_param
, i
, 1);
4065 set
= isl_set_fix_si(set
, isl_dim_param
, i
, 0);
4067 for (i
= 0; i
< nvar
; ++i
) {
4068 if (active
[nparam
+ i
])
4070 set
= isl_set_eliminate(set
, isl_dim_set
, i
, 1);
4071 set
= isl_set_fix_si(set
, isl_dim_set
, i
, 0);
4083 struct isl_opt_data
{
4084 isl_qpolynomial
*qp
;
4090 static isl_stat
opt_fn(__isl_take isl_point
*pnt
, void *user
)
4092 struct isl_opt_data
*data
= (struct isl_opt_data
*)user
;
4095 val
= isl_qpolynomial_eval(isl_qpolynomial_copy(data
->qp
), pnt
);
4099 } else if (data
->max
) {
4100 data
->opt
= isl_val_max(data
->opt
, val
);
4102 data
->opt
= isl_val_min(data
->opt
, val
);
4108 __isl_give isl_val
*isl_qpolynomial_opt_on_domain(
4109 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*set
, int max
)
4111 struct isl_opt_data data
= { NULL
, 1, NULL
, max
};
4116 if (isl_upoly_is_cst(qp
->upoly
)) {
4118 data
.opt
= isl_qpolynomial_get_constant_val(qp
);
4119 isl_qpolynomial_free(qp
);
4123 set
= fix_inactive(set
, qp
);
4126 if (isl_set_foreach_point(set
, opt_fn
, &data
) < 0)
4130 data
.opt
= isl_val_zero(isl_set_get_ctx(set
));
4133 isl_qpolynomial_free(qp
);
4137 isl_qpolynomial_free(qp
);
4138 isl_val_free(data
.opt
);
4142 __isl_give isl_qpolynomial
*isl_qpolynomial_morph_domain(
4143 __isl_take isl_qpolynomial
*qp
, __isl_take isl_morph
*morph
)
4148 struct isl_upoly
**subs
;
4149 isl_mat
*mat
, *diag
;
4151 qp
= isl_qpolynomial_cow(qp
);
4156 isl_assert(ctx
, isl_space_is_equal(qp
->dim
, morph
->dom
->dim
), goto error
);
4158 n_sub
= morph
->inv
->n_row
- 1;
4159 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
4160 n_sub
+= qp
->div
->n_row
;
4161 subs
= isl_calloc_array(ctx
, struct isl_upoly
*, n_sub
);
4165 for (i
= 0; 1 + i
< morph
->inv
->n_row
; ++i
)
4166 subs
[i
] = isl_upoly_from_affine(ctx
, morph
->inv
->row
[1 + i
],
4167 morph
->inv
->row
[0][0], morph
->inv
->n_col
);
4168 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
4169 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4170 subs
[morph
->inv
->n_row
- 1 + i
] =
4171 isl_upoly_var_pow(ctx
, morph
->inv
->n_col
- 1 + i
, 1);
4173 qp
->upoly
= isl_upoly_subs(qp
->upoly
, 0, n_sub
, subs
);
4175 for (i
= 0; i
< n_sub
; ++i
)
4176 isl_upoly_free(subs
[i
]);
4179 diag
= isl_mat_diag(ctx
, 1, morph
->inv
->row
[0][0]);
4180 mat
= isl_mat_diagonal(diag
, isl_mat_copy(morph
->inv
));
4181 diag
= isl_mat_diag(ctx
, qp
->div
->n_row
, morph
->inv
->row
[0][0]);
4182 mat
= isl_mat_diagonal(mat
, diag
);
4183 qp
->div
= isl_mat_product(qp
->div
, mat
);
4184 isl_space_free(qp
->dim
);
4185 qp
->dim
= isl_space_copy(morph
->ran
->dim
);
4187 if (!qp
->upoly
|| !qp
->div
|| !qp
->dim
)
4190 isl_morph_free(morph
);
4194 isl_qpolynomial_free(qp
);
4195 isl_morph_free(morph
);
4199 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_mul(
4200 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
4201 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
4203 return isl_union_pw_qpolynomial_match_bin_op(upwqp1
, upwqp2
,
4204 &isl_pw_qpolynomial_mul
);
4207 /* Reorder the dimension of "qp" according to the given reordering.
4209 __isl_give isl_qpolynomial
*isl_qpolynomial_realign_domain(
4210 __isl_take isl_qpolynomial
*qp
, __isl_take isl_reordering
*r
)
4214 qp
= isl_qpolynomial_cow(qp
);
4218 r
= isl_reordering_extend(r
, qp
->div
->n_row
);
4222 qp
->div
= isl_local_reorder(qp
->div
, isl_reordering_copy(r
));
4226 qp
->upoly
= reorder(qp
->upoly
, r
->pos
);
4230 space
= isl_reordering_get_space(r
);
4231 qp
= isl_qpolynomial_reset_domain_space(qp
, space
);
4233 isl_reordering_free(r
);
4236 isl_qpolynomial_free(qp
);
4237 isl_reordering_free(r
);
4241 __isl_give isl_qpolynomial
*isl_qpolynomial_align_params(
4242 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*model
)
4244 isl_bool equal_params
;
4249 equal_params
= isl_space_has_equal_params(qp
->dim
, model
);
4250 if (equal_params
< 0)
4252 if (!equal_params
) {
4253 isl_reordering
*exp
;
4255 exp
= isl_parameter_alignment_reordering(qp
->dim
, model
);
4256 exp
= isl_reordering_extend_space(exp
,
4257 isl_qpolynomial_get_domain_space(qp
));
4258 qp
= isl_qpolynomial_realign_domain(qp
, exp
);
4261 isl_space_free(model
);
4264 isl_space_free(model
);
4265 isl_qpolynomial_free(qp
);
4269 struct isl_split_periods_data
{
4271 isl_pw_qpolynomial
*res
;
4274 /* Create a slice where the integer division "div" has the fixed value "v".
4275 * In particular, if "div" refers to floor(f/m), then create a slice
4277 * m v <= f <= m v + (m - 1)
4282 * -f + m v + (m - 1) >= 0
4284 static __isl_give isl_set
*set_div_slice(__isl_take isl_space
*space
,
4285 __isl_keep isl_qpolynomial
*qp
, int div
, isl_int v
)
4288 isl_basic_set
*bset
= NULL
;
4294 total
= isl_space_dim(space
, isl_dim_all
);
4295 bset
= isl_basic_set_alloc_space(isl_space_copy(space
), 0, 0, 2);
4297 k
= isl_basic_set_alloc_inequality(bset
);
4300 isl_seq_cpy(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4301 isl_int_submul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4303 k
= isl_basic_set_alloc_inequality(bset
);
4306 isl_seq_neg(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4307 isl_int_addmul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4308 isl_int_add(bset
->ineq
[k
][0], bset
->ineq
[k
][0], qp
->div
->row
[div
][0]);
4309 isl_int_sub_ui(bset
->ineq
[k
][0], bset
->ineq
[k
][0], 1);
4311 isl_space_free(space
);
4312 return isl_set_from_basic_set(bset
);
4314 isl_basic_set_free(bset
);
4315 isl_space_free(space
);
4319 static isl_stat
split_periods(__isl_take isl_set
*set
,
4320 __isl_take isl_qpolynomial
*qp
, void *user
);
4322 /* Create a slice of the domain "set" such that integer division "div"
4323 * has the fixed value "v" and add the results to data->res,
4324 * replacing the integer division by "v" in "qp".
4326 static isl_stat
set_div(__isl_take isl_set
*set
,
4327 __isl_take isl_qpolynomial
*qp
, int div
, isl_int v
,
4328 struct isl_split_periods_data
*data
)
4333 struct isl_upoly
*cst
;
4335 slice
= set_div_slice(isl_set_get_space(set
), qp
, div
, v
);
4336 set
= isl_set_intersect(set
, slice
);
4341 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4343 for (i
= div
+ 1; i
< qp
->div
->n_row
; ++i
) {
4344 if (isl_int_is_zero(qp
->div
->row
[i
][2 + total
+ div
]))
4346 isl_int_addmul(qp
->div
->row
[i
][1],
4347 qp
->div
->row
[i
][2 + total
+ div
], v
);
4348 isl_int_set_si(qp
->div
->row
[i
][2 + total
+ div
], 0);
4351 cst
= isl_upoly_rat_cst(qp
->dim
->ctx
, v
, qp
->dim
->ctx
->one
);
4352 qp
= substitute_div(qp
, div
, cst
);
4354 return split_periods(set
, qp
, data
);
4357 isl_qpolynomial_free(qp
);
4358 return isl_stat_error
;
4361 /* Split the domain "set" such that integer division "div"
4362 * has a fixed value (ranging from "min" to "max") on each slice
4363 * and add the results to data->res.
4365 static isl_stat
split_div(__isl_take isl_set
*set
,
4366 __isl_take isl_qpolynomial
*qp
, int div
, isl_int min
, isl_int max
,
4367 struct isl_split_periods_data
*data
)
4369 for (; isl_int_le(min
, max
); isl_int_add_ui(min
, min
, 1)) {
4370 isl_set
*set_i
= isl_set_copy(set
);
4371 isl_qpolynomial
*qp_i
= isl_qpolynomial_copy(qp
);
4373 if (set_div(set_i
, qp_i
, div
, min
, data
) < 0)
4377 isl_qpolynomial_free(qp
);
4381 isl_qpolynomial_free(qp
);
4382 return isl_stat_error
;
4385 /* If "qp" refers to any integer division
4386 * that can only attain "max_periods" distinct values on "set"
4387 * then split the domain along those distinct values.
4388 * Add the results (or the original if no splitting occurs)
4391 static isl_stat
split_periods(__isl_take isl_set
*set
,
4392 __isl_take isl_qpolynomial
*qp
, void *user
)
4395 isl_pw_qpolynomial
*pwqp
;
4396 struct isl_split_periods_data
*data
;
4399 isl_stat r
= isl_stat_ok
;
4401 data
= (struct isl_split_periods_data
*)user
;
4406 if (qp
->div
->n_row
== 0) {
4407 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4408 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4414 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4415 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4416 enum isl_lp_result lp_res
;
4418 if (isl_seq_first_non_zero(qp
->div
->row
[i
] + 2 + total
,
4419 qp
->div
->n_row
) != -1)
4422 lp_res
= isl_set_solve_lp(set
, 0, qp
->div
->row
[i
] + 1,
4423 set
->ctx
->one
, &min
, NULL
, NULL
);
4424 if (lp_res
== isl_lp_error
)
4426 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4428 isl_int_fdiv_q(min
, min
, qp
->div
->row
[i
][0]);
4430 lp_res
= isl_set_solve_lp(set
, 1, qp
->div
->row
[i
] + 1,
4431 set
->ctx
->one
, &max
, NULL
, NULL
);
4432 if (lp_res
== isl_lp_error
)
4434 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4436 isl_int_fdiv_q(max
, max
, qp
->div
->row
[i
][0]);
4438 isl_int_sub(max
, max
, min
);
4439 if (isl_int_cmp_si(max
, data
->max_periods
) < 0) {
4440 isl_int_add(max
, max
, min
);
4445 if (i
< qp
->div
->n_row
) {
4446 r
= split_div(set
, qp
, i
, min
, max
, data
);
4448 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4449 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4461 isl_qpolynomial_free(qp
);
4462 return isl_stat_error
;
4465 /* If any quasi-polynomial in pwqp refers to any integer division
4466 * that can only attain "max_periods" distinct values on its domain
4467 * then split the domain along those distinct values.
4469 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_split_periods(
4470 __isl_take isl_pw_qpolynomial
*pwqp
, int max_periods
)
4472 struct isl_split_periods_data data
;
4474 data
.max_periods
= max_periods
;
4475 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp
));
4477 if (isl_pw_qpolynomial_foreach_piece(pwqp
, &split_periods
, &data
) < 0)
4480 isl_pw_qpolynomial_free(pwqp
);
4484 isl_pw_qpolynomial_free(data
.res
);
4485 isl_pw_qpolynomial_free(pwqp
);
4489 /* Construct a piecewise quasipolynomial that is constant on the given
4490 * domain. In particular, it is
4493 * infinity if cst == -1
4495 * If cst == -1, then explicitly check whether the domain is empty and,
4496 * if so, return 0 instead.
4498 static __isl_give isl_pw_qpolynomial
*constant_on_domain(
4499 __isl_take isl_basic_set
*bset
, int cst
)
4502 isl_qpolynomial
*qp
;
4504 if (cst
< 0 && isl_basic_set_is_empty(bset
) == isl_bool_true
)
4509 bset
= isl_basic_set_params(bset
);
4510 dim
= isl_basic_set_get_space(bset
);
4512 qp
= isl_qpolynomial_infty_on_domain(dim
);
4514 qp
= isl_qpolynomial_zero_on_domain(dim
);
4516 qp
= isl_qpolynomial_one_on_domain(dim
);
4517 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset
), qp
);
4520 /* Factor bset, call fn on each of the factors and return the product.
4522 * If no factors can be found, simply call fn on the input.
4523 * Otherwise, construct the factors based on the factorizer,
4524 * call fn on each factor and compute the product.
4526 static __isl_give isl_pw_qpolynomial
*compressed_multiplicative_call(
4527 __isl_take isl_basic_set
*bset
,
4528 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4534 isl_qpolynomial
*qp
;
4535 isl_pw_qpolynomial
*pwqp
;
4539 f
= isl_basic_set_factorizer(bset
);
4542 if (f
->n_group
== 0) {
4543 isl_factorizer_free(f
);
4547 nparam
= isl_basic_set_dim(bset
, isl_dim_param
);
4548 nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
4550 space
= isl_basic_set_get_space(bset
);
4551 space
= isl_space_params(space
);
4552 set
= isl_set_universe(isl_space_copy(space
));
4553 qp
= isl_qpolynomial_one_on_domain(space
);
4554 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4556 bset
= isl_morph_basic_set(isl_morph_copy(f
->morph
), bset
);
4558 for (i
= 0, n
= 0; i
< f
->n_group
; ++i
) {
4559 isl_basic_set
*bset_i
;
4560 isl_pw_qpolynomial
*pwqp_i
;
4562 bset_i
= isl_basic_set_copy(bset
);
4563 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4564 nparam
+ n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4565 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4567 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
,
4568 n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4569 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
, 0, n
);
4571 pwqp_i
= fn(bset_i
);
4572 pwqp
= isl_pw_qpolynomial_mul(pwqp
, pwqp_i
);
4577 isl_basic_set_free(bset
);
4578 isl_factorizer_free(f
);
4582 isl_basic_set_free(bset
);
4586 /* Factor bset, call fn on each of the factors and return the product.
4587 * The function is assumed to evaluate to zero on empty domains,
4588 * to one on zero-dimensional domains and to infinity on unbounded domains
4589 * and will not be called explicitly on zero-dimensional or unbounded domains.
4591 * We first check for some special cases and remove all equalities.
4592 * Then we hand over control to compressed_multiplicative_call.
4594 __isl_give isl_pw_qpolynomial
*isl_basic_set_multiplicative_call(
4595 __isl_take isl_basic_set
*bset
,
4596 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4600 isl_pw_qpolynomial
*pwqp
;
4605 if (isl_basic_set_plain_is_empty(bset
))
4606 return constant_on_domain(bset
, 0);
4608 if (isl_basic_set_dim(bset
, isl_dim_set
) == 0)
4609 return constant_on_domain(bset
, 1);
4611 bounded
= isl_basic_set_is_bounded(bset
);
4615 return constant_on_domain(bset
, -1);
4617 if (bset
->n_eq
== 0)
4618 return compressed_multiplicative_call(bset
, fn
);
4620 morph
= isl_basic_set_full_compression(bset
);
4621 bset
= isl_morph_basic_set(isl_morph_copy(morph
), bset
);
4623 pwqp
= compressed_multiplicative_call(bset
, fn
);
4625 morph
= isl_morph_dom_params(morph
);
4626 morph
= isl_morph_ran_params(morph
);
4627 morph
= isl_morph_inverse(morph
);
4629 pwqp
= isl_pw_qpolynomial_morph_domain(pwqp
, morph
);
4633 isl_basic_set_free(bset
);
4637 /* Drop all floors in "qp", turning each integer division [a/m] into
4638 * a rational division a/m. If "down" is set, then the integer division
4639 * is replaced by (a-(m-1))/m instead.
4641 static __isl_give isl_qpolynomial
*qp_drop_floors(
4642 __isl_take isl_qpolynomial
*qp
, int down
)
4645 struct isl_upoly
*s
;
4649 if (qp
->div
->n_row
== 0)
4652 qp
= isl_qpolynomial_cow(qp
);
4656 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
4658 isl_int_sub(qp
->div
->row
[i
][1],
4659 qp
->div
->row
[i
][1], qp
->div
->row
[i
][0]);
4660 isl_int_add_ui(qp
->div
->row
[i
][1],
4661 qp
->div
->row
[i
][1], 1);
4663 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
4664 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
4665 qp
= substitute_div(qp
, i
, s
);
4673 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4674 * a rational division a/m.
4676 static __isl_give isl_pw_qpolynomial
*pwqp_drop_floors(
4677 __isl_take isl_pw_qpolynomial
*pwqp
)
4684 if (isl_pw_qpolynomial_is_zero(pwqp
))
4687 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
4691 for (i
= 0; i
< pwqp
->n
; ++i
) {
4692 pwqp
->p
[i
].qp
= qp_drop_floors(pwqp
->p
[i
].qp
, 0);
4699 isl_pw_qpolynomial_free(pwqp
);
4703 /* Adjust all the integer divisions in "qp" such that they are at least
4704 * one over the given orthant (identified by "signs"). This ensures
4705 * that they will still be non-negative even after subtracting (m-1)/m.
4707 * In particular, f is replaced by f' + v, changing f = [a/m]
4708 * to f' = [(a - m v)/m].
4709 * If the constant term k in a is smaller than m,
4710 * the constant term of v is set to floor(k/m) - 1.
4711 * For any other term, if the coefficient c and the variable x have
4712 * the same sign, then no changes are needed.
4713 * Otherwise, if the variable is positive (and c is negative),
4714 * then the coefficient of x in v is set to floor(c/m).
4715 * If the variable is negative (and c is positive),
4716 * then the coefficient of x in v is set to ceil(c/m).
4718 static __isl_give isl_qpolynomial
*make_divs_pos(__isl_take isl_qpolynomial
*qp
,
4724 struct isl_upoly
*s
;
4726 qp
= isl_qpolynomial_cow(qp
);
4729 qp
->div
= isl_mat_cow(qp
->div
);
4733 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4734 v
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
4736 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4737 isl_int
*row
= qp
->div
->row
[i
];
4741 if (isl_int_lt(row
[1], row
[0])) {
4742 isl_int_fdiv_q(v
->el
[0], row
[1], row
[0]);
4743 isl_int_sub_ui(v
->el
[0], v
->el
[0], 1);
4744 isl_int_submul(row
[1], row
[0], v
->el
[0]);
4746 for (j
= 0; j
< total
; ++j
) {
4747 if (isl_int_sgn(row
[2 + j
]) * signs
[j
] >= 0)
4750 isl_int_cdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4752 isl_int_fdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4753 isl_int_submul(row
[2 + j
], row
[0], v
->el
[1 + j
]);
4755 for (j
= 0; j
< i
; ++j
) {
4756 if (isl_int_sgn(row
[2 + total
+ j
]) >= 0)
4758 isl_int_fdiv_q(v
->el
[1 + total
+ j
],
4759 row
[2 + total
+ j
], row
[0]);
4760 isl_int_submul(row
[2 + total
+ j
],
4761 row
[0], v
->el
[1 + total
+ j
]);
4763 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
4764 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
4766 isl_seq_combine(qp
->div
->row
[j
] + 1,
4767 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
4768 qp
->div
->row
[j
][2 + total
+ i
], v
->el
, v
->size
);
4770 isl_int_set_si(v
->el
[1 + total
+ i
], 1);
4771 s
= isl_upoly_from_affine(qp
->dim
->ctx
, v
->el
,
4772 qp
->div
->ctx
->one
, v
->size
);
4773 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ i
, 1, &s
);
4783 isl_qpolynomial_free(qp
);
4787 struct isl_to_poly_data
{
4789 isl_pw_qpolynomial
*res
;
4790 isl_qpolynomial
*qp
;
4793 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4794 * We first make all integer divisions positive and then split the
4795 * quasipolynomials into terms with sign data->sign (the direction
4796 * of the requested approximation) and terms with the opposite sign.
4797 * In the first set of terms, each integer division [a/m] is
4798 * overapproximated by a/m, while in the second it is underapproximated
4801 static isl_stat
to_polynomial_on_orthant(__isl_take isl_set
*orthant
,
4802 int *signs
, void *user
)
4804 struct isl_to_poly_data
*data
= user
;
4805 isl_pw_qpolynomial
*t
;
4806 isl_qpolynomial
*qp
, *up
, *down
;
4808 qp
= isl_qpolynomial_copy(data
->qp
);
4809 qp
= make_divs_pos(qp
, signs
);
4811 up
= isl_qpolynomial_terms_of_sign(qp
, signs
, data
->sign
);
4812 up
= qp_drop_floors(up
, 0);
4813 down
= isl_qpolynomial_terms_of_sign(qp
, signs
, -data
->sign
);
4814 down
= qp_drop_floors(down
, 1);
4816 isl_qpolynomial_free(qp
);
4817 qp
= isl_qpolynomial_add(up
, down
);
4819 t
= isl_pw_qpolynomial_alloc(orthant
, qp
);
4820 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, t
);
4825 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4826 * the polynomial will be an overapproximation. If "sign" is negative,
4827 * it will be an underapproximation. If "sign" is zero, the approximation
4828 * will lie somewhere in between.
4830 * In particular, is sign == 0, we simply drop the floors, turning
4831 * the integer divisions into rational divisions.
4832 * Otherwise, we split the domains into orthants, make all integer divisions
4833 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4834 * depending on the requested sign and the sign of the term in which
4835 * the integer division appears.
4837 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_to_polynomial(
4838 __isl_take isl_pw_qpolynomial
*pwqp
, int sign
)
4841 struct isl_to_poly_data data
;
4844 return pwqp_drop_floors(pwqp
);
4850 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp
));
4852 for (i
= 0; i
< pwqp
->n
; ++i
) {
4853 if (pwqp
->p
[i
].qp
->div
->n_row
== 0) {
4854 isl_pw_qpolynomial
*t
;
4855 t
= isl_pw_qpolynomial_alloc(
4856 isl_set_copy(pwqp
->p
[i
].set
),
4857 isl_qpolynomial_copy(pwqp
->p
[i
].qp
));
4858 data
.res
= isl_pw_qpolynomial_add_disjoint(data
.res
, t
);
4861 data
.qp
= pwqp
->p
[i
].qp
;
4862 if (isl_set_foreach_orthant(pwqp
->p
[i
].set
,
4863 &to_polynomial_on_orthant
, &data
) < 0)
4867 isl_pw_qpolynomial_free(pwqp
);
4871 isl_pw_qpolynomial_free(pwqp
);
4872 isl_pw_qpolynomial_free(data
.res
);
4876 static __isl_give isl_pw_qpolynomial
*poly_entry(
4877 __isl_take isl_pw_qpolynomial
*pwqp
, void *user
)
4881 return isl_pw_qpolynomial_to_polynomial(pwqp
, *sign
);
4884 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_to_polynomial(
4885 __isl_take isl_union_pw_qpolynomial
*upwqp
, int sign
)
4887 return isl_union_pw_qpolynomial_transform_inplace(upwqp
,
4888 &poly_entry
, &sign
);
4891 __isl_give isl_basic_map
*isl_basic_map_from_qpolynomial(
4892 __isl_take isl_qpolynomial
*qp
)
4896 isl_vec
*aff
= NULL
;
4897 isl_basic_map
*bmap
= NULL
;
4903 if (!isl_upoly_is_affine(qp
->upoly
))
4904 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
4905 "input quasi-polynomial not affine", goto error
);
4906 aff
= isl_qpolynomial_extract_affine(qp
);
4909 dim
= isl_qpolynomial_get_space(qp
);
4910 pos
= 1 + isl_space_offset(dim
, isl_dim_out
);
4911 n_div
= qp
->div
->n_row
;
4912 bmap
= isl_basic_map_alloc_space(dim
, n_div
, 1, 2 * n_div
);
4914 for (i
= 0; i
< n_div
; ++i
) {
4915 k
= isl_basic_map_alloc_div(bmap
);
4918 isl_seq_cpy(bmap
->div
[k
], qp
->div
->row
[i
], qp
->div
->n_col
);
4919 isl_int_set_si(bmap
->div
[k
][qp
->div
->n_col
], 0);
4920 if (isl_basic_map_add_div_constraints(bmap
, k
) < 0)
4923 k
= isl_basic_map_alloc_equality(bmap
);
4926 isl_int_neg(bmap
->eq
[k
][pos
], aff
->el
[0]);
4927 isl_seq_cpy(bmap
->eq
[k
], aff
->el
+ 1, pos
);
4928 isl_seq_cpy(bmap
->eq
[k
] + pos
+ 1, aff
->el
+ 1 + pos
, n_div
);
4931 isl_qpolynomial_free(qp
);
4932 bmap
= isl_basic_map_finalize(bmap
);
4936 isl_qpolynomial_free(qp
);
4937 isl_basic_map_free(bmap
);