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,
13 #include <isl_ctx_private.h>
14 #include <isl_map_private.h>
15 #include <isl_factorization.h>
16 #include <isl_lp_private.h>
18 #include <isl_union_map_private.h>
19 #include <isl_constraint_private.h>
20 #include <isl_polynomial_private.h>
21 #include <isl_point_private.h>
22 #include <isl_space_private.h>
23 #include <isl_mat_private.h>
24 #include <isl_vec_private.h>
25 #include <isl_range.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>
30 #include <isl/deprecated/polynomial_int.h>
32 static unsigned pos(__isl_keep isl_space
*dim
, enum isl_dim_type type
)
35 case isl_dim_param
: return 0;
36 case isl_dim_in
: return dim
->nparam
;
37 case isl_dim_out
: return dim
->nparam
+ dim
->n_in
;
42 int isl_upoly_is_cst(__isl_keep
struct isl_upoly
*up
)
50 __isl_keep
struct isl_upoly_cst
*isl_upoly_as_cst(__isl_keep
struct isl_upoly
*up
)
55 isl_assert(up
->ctx
, up
->var
< 0, return NULL
);
57 return (struct isl_upoly_cst
*)up
;
60 __isl_keep
struct isl_upoly_rec
*isl_upoly_as_rec(__isl_keep
struct isl_upoly
*up
)
65 isl_assert(up
->ctx
, up
->var
>= 0, return NULL
);
67 return (struct isl_upoly_rec
*)up
;
70 int isl_upoly_is_equal(__isl_keep
struct isl_upoly
*up1
,
71 __isl_keep
struct isl_upoly
*up2
)
74 struct isl_upoly_rec
*rec1
, *rec2
;
80 if (up1
->var
!= up2
->var
)
82 if (isl_upoly_is_cst(up1
)) {
83 struct isl_upoly_cst
*cst1
, *cst2
;
84 cst1
= isl_upoly_as_cst(up1
);
85 cst2
= isl_upoly_as_cst(up2
);
88 return isl_int_eq(cst1
->n
, cst2
->n
) &&
89 isl_int_eq(cst1
->d
, cst2
->d
);
92 rec1
= isl_upoly_as_rec(up1
);
93 rec2
= isl_upoly_as_rec(up2
);
97 if (rec1
->n
!= rec2
->n
)
100 for (i
= 0; i
< rec1
->n
; ++i
) {
101 int eq
= isl_upoly_is_equal(rec1
->p
[i
], rec2
->p
[i
]);
109 int isl_upoly_is_zero(__isl_keep
struct isl_upoly
*up
)
111 struct isl_upoly_cst
*cst
;
115 if (!isl_upoly_is_cst(up
))
118 cst
= isl_upoly_as_cst(up
);
122 return isl_int_is_zero(cst
->n
) && isl_int_is_pos(cst
->d
);
125 int isl_upoly_sgn(__isl_keep
struct isl_upoly
*up
)
127 struct isl_upoly_cst
*cst
;
131 if (!isl_upoly_is_cst(up
))
134 cst
= isl_upoly_as_cst(up
);
138 return isl_int_sgn(cst
->n
);
141 int isl_upoly_is_nan(__isl_keep
struct isl_upoly
*up
)
143 struct isl_upoly_cst
*cst
;
147 if (!isl_upoly_is_cst(up
))
150 cst
= isl_upoly_as_cst(up
);
154 return isl_int_is_zero(cst
->n
) && isl_int_is_zero(cst
->d
);
157 int isl_upoly_is_infty(__isl_keep
struct isl_upoly
*up
)
159 struct isl_upoly_cst
*cst
;
163 if (!isl_upoly_is_cst(up
))
166 cst
= isl_upoly_as_cst(up
);
170 return isl_int_is_pos(cst
->n
) && isl_int_is_zero(cst
->d
);
173 int isl_upoly_is_neginfty(__isl_keep
struct isl_upoly
*up
)
175 struct isl_upoly_cst
*cst
;
179 if (!isl_upoly_is_cst(up
))
182 cst
= isl_upoly_as_cst(up
);
186 return isl_int_is_neg(cst
->n
) && isl_int_is_zero(cst
->d
);
189 int isl_upoly_is_one(__isl_keep
struct isl_upoly
*up
)
191 struct isl_upoly_cst
*cst
;
195 if (!isl_upoly_is_cst(up
))
198 cst
= isl_upoly_as_cst(up
);
202 return isl_int_eq(cst
->n
, cst
->d
) && isl_int_is_pos(cst
->d
);
205 int isl_upoly_is_negone(__isl_keep
struct isl_upoly
*up
)
207 struct isl_upoly_cst
*cst
;
211 if (!isl_upoly_is_cst(up
))
214 cst
= isl_upoly_as_cst(up
);
218 return isl_int_is_negone(cst
->n
) && isl_int_is_one(cst
->d
);
221 __isl_give
struct isl_upoly_cst
*isl_upoly_cst_alloc(struct isl_ctx
*ctx
)
223 struct isl_upoly_cst
*cst
;
225 cst
= isl_alloc_type(ctx
, struct isl_upoly_cst
);
234 isl_int_init(cst
->n
);
235 isl_int_init(cst
->d
);
240 __isl_give
struct isl_upoly
*isl_upoly_zero(struct isl_ctx
*ctx
)
242 struct isl_upoly_cst
*cst
;
244 cst
= isl_upoly_cst_alloc(ctx
);
248 isl_int_set_si(cst
->n
, 0);
249 isl_int_set_si(cst
->d
, 1);
254 __isl_give
struct isl_upoly
*isl_upoly_one(struct isl_ctx
*ctx
)
256 struct isl_upoly_cst
*cst
;
258 cst
= isl_upoly_cst_alloc(ctx
);
262 isl_int_set_si(cst
->n
, 1);
263 isl_int_set_si(cst
->d
, 1);
268 __isl_give
struct isl_upoly
*isl_upoly_infty(struct isl_ctx
*ctx
)
270 struct isl_upoly_cst
*cst
;
272 cst
= isl_upoly_cst_alloc(ctx
);
276 isl_int_set_si(cst
->n
, 1);
277 isl_int_set_si(cst
->d
, 0);
282 __isl_give
struct isl_upoly
*isl_upoly_neginfty(struct isl_ctx
*ctx
)
284 struct isl_upoly_cst
*cst
;
286 cst
= isl_upoly_cst_alloc(ctx
);
290 isl_int_set_si(cst
->n
, -1);
291 isl_int_set_si(cst
->d
, 0);
296 __isl_give
struct isl_upoly
*isl_upoly_nan(struct isl_ctx
*ctx
)
298 struct isl_upoly_cst
*cst
;
300 cst
= isl_upoly_cst_alloc(ctx
);
304 isl_int_set_si(cst
->n
, 0);
305 isl_int_set_si(cst
->d
, 0);
310 __isl_give
struct isl_upoly
*isl_upoly_rat_cst(struct isl_ctx
*ctx
,
311 isl_int n
, isl_int d
)
313 struct isl_upoly_cst
*cst
;
315 cst
= isl_upoly_cst_alloc(ctx
);
319 isl_int_set(cst
->n
, n
);
320 isl_int_set(cst
->d
, d
);
325 __isl_give
struct isl_upoly_rec
*isl_upoly_alloc_rec(struct isl_ctx
*ctx
,
328 struct isl_upoly_rec
*rec
;
330 isl_assert(ctx
, var
>= 0, return NULL
);
331 isl_assert(ctx
, size
>= 0, return NULL
);
332 rec
= isl_calloc(ctx
, struct isl_upoly_rec
,
333 sizeof(struct isl_upoly_rec
) +
334 size
* sizeof(struct isl_upoly
*));
349 __isl_give isl_qpolynomial
*isl_qpolynomial_reset_domain_space(
350 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*dim
)
352 qp
= isl_qpolynomial_cow(qp
);
356 isl_space_free(qp
->dim
);
361 isl_qpolynomial_free(qp
);
366 /* Reset the space of "qp". This function is called from isl_pw_templ.c
367 * and doesn't know if the space of an element object is represented
368 * directly or through its domain. It therefore passes along both.
370 __isl_give isl_qpolynomial
*isl_qpolynomial_reset_space_and_domain(
371 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*space
,
372 __isl_take isl_space
*domain
)
374 isl_space_free(space
);
375 return isl_qpolynomial_reset_domain_space(qp
, domain
);
378 isl_ctx
*isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial
*qp
)
380 return qp
? qp
->dim
->ctx
: NULL
;
383 __isl_give isl_space
*isl_qpolynomial_get_domain_space(
384 __isl_keep isl_qpolynomial
*qp
)
386 return qp
? isl_space_copy(qp
->dim
) : NULL
;
389 __isl_give isl_space
*isl_qpolynomial_get_space(__isl_keep isl_qpolynomial
*qp
)
394 space
= isl_space_copy(qp
->dim
);
395 space
= isl_space_from_domain(space
);
396 space
= isl_space_add_dims(space
, isl_dim_out
, 1);
400 /* Externally, an isl_qpolynomial has a map space, but internally, the
401 * ls field corresponds to the domain of that space.
403 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial
*qp
,
404 enum isl_dim_type type
)
408 if (type
== isl_dim_out
)
410 if (type
== isl_dim_in
)
412 return isl_space_dim(qp
->dim
, type
);
415 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial
*qp
)
417 return qp
? isl_upoly_is_zero(qp
->upoly
) : -1;
420 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial
*qp
)
422 return qp
? isl_upoly_is_one(qp
->upoly
) : -1;
425 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial
*qp
)
427 return qp
? isl_upoly_is_nan(qp
->upoly
) : -1;
430 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial
*qp
)
432 return qp
? isl_upoly_is_infty(qp
->upoly
) : -1;
435 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial
*qp
)
437 return qp
? isl_upoly_is_neginfty(qp
->upoly
) : -1;
440 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial
*qp
)
442 return qp
? isl_upoly_sgn(qp
->upoly
) : 0;
445 static void upoly_free_cst(__isl_take
struct isl_upoly_cst
*cst
)
447 isl_int_clear(cst
->n
);
448 isl_int_clear(cst
->d
);
451 static void upoly_free_rec(__isl_take
struct isl_upoly_rec
*rec
)
455 for (i
= 0; i
< rec
->n
; ++i
)
456 isl_upoly_free(rec
->p
[i
]);
459 __isl_give
struct isl_upoly
*isl_upoly_copy(__isl_keep
struct isl_upoly
*up
)
468 __isl_give
struct isl_upoly
*isl_upoly_dup_cst(__isl_keep
struct isl_upoly
*up
)
470 struct isl_upoly_cst
*cst
;
471 struct isl_upoly_cst
*dup
;
473 cst
= isl_upoly_as_cst(up
);
477 dup
= isl_upoly_as_cst(isl_upoly_zero(up
->ctx
));
480 isl_int_set(dup
->n
, cst
->n
);
481 isl_int_set(dup
->d
, cst
->d
);
486 __isl_give
struct isl_upoly
*isl_upoly_dup_rec(__isl_keep
struct isl_upoly
*up
)
489 struct isl_upoly_rec
*rec
;
490 struct isl_upoly_rec
*dup
;
492 rec
= isl_upoly_as_rec(up
);
496 dup
= isl_upoly_alloc_rec(up
->ctx
, up
->var
, rec
->n
);
500 for (i
= 0; i
< rec
->n
; ++i
) {
501 dup
->p
[i
] = isl_upoly_copy(rec
->p
[i
]);
509 isl_upoly_free(&dup
->up
);
513 __isl_give
struct isl_upoly
*isl_upoly_dup(__isl_keep
struct isl_upoly
*up
)
518 if (isl_upoly_is_cst(up
))
519 return isl_upoly_dup_cst(up
);
521 return isl_upoly_dup_rec(up
);
524 __isl_give
struct isl_upoly
*isl_upoly_cow(__isl_take
struct isl_upoly
*up
)
532 return isl_upoly_dup(up
);
535 void isl_upoly_free(__isl_take
struct isl_upoly
*up
)
544 upoly_free_cst((struct isl_upoly_cst
*)up
);
546 upoly_free_rec((struct isl_upoly_rec
*)up
);
548 isl_ctx_deref(up
->ctx
);
552 static void isl_upoly_cst_reduce(__isl_keep
struct isl_upoly_cst
*cst
)
557 isl_int_gcd(gcd
, cst
->n
, cst
->d
);
558 if (!isl_int_is_zero(gcd
) && !isl_int_is_one(gcd
)) {
559 isl_int_divexact(cst
->n
, cst
->n
, gcd
);
560 isl_int_divexact(cst
->d
, cst
->d
, gcd
);
565 __isl_give
struct isl_upoly
*isl_upoly_sum_cst(__isl_take
struct isl_upoly
*up1
,
566 __isl_take
struct isl_upoly
*up2
)
568 struct isl_upoly_cst
*cst1
;
569 struct isl_upoly_cst
*cst2
;
571 up1
= isl_upoly_cow(up1
);
575 cst1
= isl_upoly_as_cst(up1
);
576 cst2
= isl_upoly_as_cst(up2
);
578 if (isl_int_eq(cst1
->d
, cst2
->d
))
579 isl_int_add(cst1
->n
, cst1
->n
, cst2
->n
);
581 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->d
);
582 isl_int_addmul(cst1
->n
, cst2
->n
, cst1
->d
);
583 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
586 isl_upoly_cst_reduce(cst1
);
596 static __isl_give
struct isl_upoly
*replace_by_zero(
597 __isl_take
struct isl_upoly
*up
)
605 return isl_upoly_zero(ctx
);
608 static __isl_give
struct isl_upoly
*replace_by_constant_term(
609 __isl_take
struct isl_upoly
*up
)
611 struct isl_upoly_rec
*rec
;
612 struct isl_upoly
*cst
;
617 rec
= isl_upoly_as_rec(up
);
620 cst
= isl_upoly_copy(rec
->p
[0]);
628 __isl_give
struct isl_upoly
*isl_upoly_sum(__isl_take
struct isl_upoly
*up1
,
629 __isl_take
struct isl_upoly
*up2
)
632 struct isl_upoly_rec
*rec1
, *rec2
;
637 if (isl_upoly_is_nan(up1
)) {
642 if (isl_upoly_is_nan(up2
)) {
647 if (isl_upoly_is_zero(up1
)) {
652 if (isl_upoly_is_zero(up2
)) {
657 if (up1
->var
< up2
->var
)
658 return isl_upoly_sum(up2
, up1
);
660 if (up2
->var
< up1
->var
) {
661 struct isl_upoly_rec
*rec
;
662 if (isl_upoly_is_infty(up2
) || isl_upoly_is_neginfty(up2
)) {
666 up1
= isl_upoly_cow(up1
);
667 rec
= isl_upoly_as_rec(up1
);
670 rec
->p
[0] = isl_upoly_sum(rec
->p
[0], up2
);
672 up1
= replace_by_constant_term(up1
);
676 if (isl_upoly_is_cst(up1
))
677 return isl_upoly_sum_cst(up1
, up2
);
679 rec1
= isl_upoly_as_rec(up1
);
680 rec2
= isl_upoly_as_rec(up2
);
684 if (rec1
->n
< rec2
->n
)
685 return isl_upoly_sum(up2
, up1
);
687 up1
= isl_upoly_cow(up1
);
688 rec1
= isl_upoly_as_rec(up1
);
692 for (i
= rec2
->n
- 1; i
>= 0; --i
) {
693 rec1
->p
[i
] = isl_upoly_sum(rec1
->p
[i
],
694 isl_upoly_copy(rec2
->p
[i
]));
697 if (i
== rec1
->n
- 1 && isl_upoly_is_zero(rec1
->p
[i
])) {
698 isl_upoly_free(rec1
->p
[i
]);
704 up1
= replace_by_zero(up1
);
705 else if (rec1
->n
== 1)
706 up1
= replace_by_constant_term(up1
);
717 __isl_give
struct isl_upoly
*isl_upoly_cst_add_isl_int(
718 __isl_take
struct isl_upoly
*up
, isl_int v
)
720 struct isl_upoly_cst
*cst
;
722 up
= isl_upoly_cow(up
);
726 cst
= isl_upoly_as_cst(up
);
728 isl_int_addmul(cst
->n
, cst
->d
, v
);
733 __isl_give
struct isl_upoly
*isl_upoly_add_isl_int(
734 __isl_take
struct isl_upoly
*up
, isl_int v
)
736 struct isl_upoly_rec
*rec
;
741 if (isl_upoly_is_cst(up
))
742 return isl_upoly_cst_add_isl_int(up
, v
);
744 up
= isl_upoly_cow(up
);
745 rec
= isl_upoly_as_rec(up
);
749 rec
->p
[0] = isl_upoly_add_isl_int(rec
->p
[0], v
);
759 __isl_give
struct isl_upoly
*isl_upoly_cst_mul_isl_int(
760 __isl_take
struct isl_upoly
*up
, isl_int v
)
762 struct isl_upoly_cst
*cst
;
764 if (isl_upoly_is_zero(up
))
767 up
= isl_upoly_cow(up
);
771 cst
= isl_upoly_as_cst(up
);
773 isl_int_mul(cst
->n
, cst
->n
, v
);
778 __isl_give
struct isl_upoly
*isl_upoly_mul_isl_int(
779 __isl_take
struct isl_upoly
*up
, isl_int v
)
782 struct isl_upoly_rec
*rec
;
787 if (isl_upoly_is_cst(up
))
788 return isl_upoly_cst_mul_isl_int(up
, v
);
790 up
= isl_upoly_cow(up
);
791 rec
= isl_upoly_as_rec(up
);
795 for (i
= 0; i
< rec
->n
; ++i
) {
796 rec
->p
[i
] = isl_upoly_mul_isl_int(rec
->p
[i
], v
);
807 /* Multiply the constant polynomial "up" by "v".
809 static __isl_give
struct isl_upoly
*isl_upoly_cst_scale_val(
810 __isl_take
struct isl_upoly
*up
, __isl_keep isl_val
*v
)
812 struct isl_upoly_cst
*cst
;
814 if (isl_upoly_is_zero(up
))
817 up
= isl_upoly_cow(up
);
821 cst
= isl_upoly_as_cst(up
);
823 isl_int_mul(cst
->n
, cst
->n
, v
->n
);
824 isl_int_mul(cst
->d
, cst
->d
, v
->d
);
825 isl_upoly_cst_reduce(cst
);
830 /* Multiply the polynomial "up" by "v".
832 static __isl_give
struct isl_upoly
*isl_upoly_scale_val(
833 __isl_take
struct isl_upoly
*up
, __isl_keep isl_val
*v
)
836 struct isl_upoly_rec
*rec
;
841 if (isl_upoly_is_cst(up
))
842 return isl_upoly_cst_scale_val(up
, v
);
844 up
= isl_upoly_cow(up
);
845 rec
= isl_upoly_as_rec(up
);
849 for (i
= 0; i
< rec
->n
; ++i
) {
850 rec
->p
[i
] = isl_upoly_scale_val(rec
->p
[i
], v
);
861 __isl_give
struct isl_upoly
*isl_upoly_mul_cst(__isl_take
struct isl_upoly
*up1
,
862 __isl_take
struct isl_upoly
*up2
)
864 struct isl_upoly_cst
*cst1
;
865 struct isl_upoly_cst
*cst2
;
867 up1
= isl_upoly_cow(up1
);
871 cst1
= isl_upoly_as_cst(up1
);
872 cst2
= isl_upoly_as_cst(up2
);
874 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->n
);
875 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
877 isl_upoly_cst_reduce(cst1
);
887 __isl_give
struct isl_upoly
*isl_upoly_mul_rec(__isl_take
struct isl_upoly
*up1
,
888 __isl_take
struct isl_upoly
*up2
)
890 struct isl_upoly_rec
*rec1
;
891 struct isl_upoly_rec
*rec2
;
892 struct isl_upoly_rec
*res
= NULL
;
896 rec1
= isl_upoly_as_rec(up1
);
897 rec2
= isl_upoly_as_rec(up2
);
900 size
= rec1
->n
+ rec2
->n
- 1;
901 res
= isl_upoly_alloc_rec(up1
->ctx
, up1
->var
, size
);
905 for (i
= 0; i
< rec1
->n
; ++i
) {
906 res
->p
[i
] = isl_upoly_mul(isl_upoly_copy(rec2
->p
[0]),
907 isl_upoly_copy(rec1
->p
[i
]));
912 for (; i
< size
; ++i
) {
913 res
->p
[i
] = isl_upoly_zero(up1
->ctx
);
918 for (i
= 0; i
< rec1
->n
; ++i
) {
919 for (j
= 1; j
< rec2
->n
; ++j
) {
920 struct isl_upoly
*up
;
921 up
= isl_upoly_mul(isl_upoly_copy(rec2
->p
[j
]),
922 isl_upoly_copy(rec1
->p
[i
]));
923 res
->p
[i
+ j
] = isl_upoly_sum(res
->p
[i
+ j
], up
);
936 isl_upoly_free(&res
->up
);
940 __isl_give
struct isl_upoly
*isl_upoly_mul(__isl_take
struct isl_upoly
*up1
,
941 __isl_take
struct isl_upoly
*up2
)
946 if (isl_upoly_is_nan(up1
)) {
951 if (isl_upoly_is_nan(up2
)) {
956 if (isl_upoly_is_zero(up1
)) {
961 if (isl_upoly_is_zero(up2
)) {
966 if (isl_upoly_is_one(up1
)) {
971 if (isl_upoly_is_one(up2
)) {
976 if (up1
->var
< up2
->var
)
977 return isl_upoly_mul(up2
, up1
);
979 if (up2
->var
< up1
->var
) {
981 struct isl_upoly_rec
*rec
;
982 if (isl_upoly_is_infty(up2
) || isl_upoly_is_neginfty(up2
)) {
983 isl_ctx
*ctx
= up1
->ctx
;
986 return isl_upoly_nan(ctx
);
988 up1
= isl_upoly_cow(up1
);
989 rec
= isl_upoly_as_rec(up1
);
993 for (i
= 0; i
< rec
->n
; ++i
) {
994 rec
->p
[i
] = isl_upoly_mul(rec
->p
[i
],
995 isl_upoly_copy(up2
));
1003 if (isl_upoly_is_cst(up1
))
1004 return isl_upoly_mul_cst(up1
, up2
);
1006 return isl_upoly_mul_rec(up1
, up2
);
1008 isl_upoly_free(up1
);
1009 isl_upoly_free(up2
);
1013 __isl_give
struct isl_upoly
*isl_upoly_pow(__isl_take
struct isl_upoly
*up
,
1016 struct isl_upoly
*res
;
1024 res
= isl_upoly_copy(up
);
1026 res
= isl_upoly_one(up
->ctx
);
1028 while (power
>>= 1) {
1029 up
= isl_upoly_mul(up
, isl_upoly_copy(up
));
1031 res
= isl_upoly_mul(res
, isl_upoly_copy(up
));
1038 __isl_give isl_qpolynomial
*isl_qpolynomial_alloc(__isl_take isl_space
*dim
,
1039 unsigned n_div
, __isl_take
struct isl_upoly
*up
)
1041 struct isl_qpolynomial
*qp
= NULL
;
1047 if (!isl_space_is_set(dim
))
1048 isl_die(isl_space_get_ctx(dim
), isl_error_invalid
,
1049 "domain of polynomial should be a set", goto error
);
1051 total
= isl_space_dim(dim
, isl_dim_all
);
1053 qp
= isl_calloc_type(dim
->ctx
, struct isl_qpolynomial
);
1058 qp
->div
= isl_mat_alloc(dim
->ctx
, n_div
, 1 + 1 + total
+ n_div
);
1067 isl_space_free(dim
);
1069 isl_qpolynomial_free(qp
);
1073 __isl_give isl_qpolynomial
*isl_qpolynomial_copy(__isl_keep isl_qpolynomial
*qp
)
1082 __isl_give isl_qpolynomial
*isl_qpolynomial_dup(__isl_keep isl_qpolynomial
*qp
)
1084 struct isl_qpolynomial
*dup
;
1089 dup
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
), qp
->div
->n_row
,
1090 isl_upoly_copy(qp
->upoly
));
1093 isl_mat_free(dup
->div
);
1094 dup
->div
= isl_mat_copy(qp
->div
);
1100 isl_qpolynomial_free(dup
);
1104 __isl_give isl_qpolynomial
*isl_qpolynomial_cow(__isl_take isl_qpolynomial
*qp
)
1112 return isl_qpolynomial_dup(qp
);
1115 void *isl_qpolynomial_free(__isl_take isl_qpolynomial
*qp
)
1123 isl_space_free(qp
->dim
);
1124 isl_mat_free(qp
->div
);
1125 isl_upoly_free(qp
->upoly
);
1131 __isl_give
struct isl_upoly
*isl_upoly_var_pow(isl_ctx
*ctx
, int pos
, int power
)
1134 struct isl_upoly_rec
*rec
;
1135 struct isl_upoly_cst
*cst
;
1137 rec
= isl_upoly_alloc_rec(ctx
, pos
, 1 + power
);
1140 for (i
= 0; i
< 1 + power
; ++i
) {
1141 rec
->p
[i
] = isl_upoly_zero(ctx
);
1146 cst
= isl_upoly_as_cst(rec
->p
[power
]);
1147 isl_int_set_si(cst
->n
, 1);
1151 isl_upoly_free(&rec
->up
);
1155 /* r array maps original positions to new positions.
1157 static __isl_give
struct isl_upoly
*reorder(__isl_take
struct isl_upoly
*up
,
1161 struct isl_upoly_rec
*rec
;
1162 struct isl_upoly
*base
;
1163 struct isl_upoly
*res
;
1165 if (isl_upoly_is_cst(up
))
1168 rec
= isl_upoly_as_rec(up
);
1172 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
1174 base
= isl_upoly_var_pow(up
->ctx
, r
[up
->var
], 1);
1175 res
= reorder(isl_upoly_copy(rec
->p
[rec
->n
- 1]), r
);
1177 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1178 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
1179 res
= isl_upoly_sum(res
, reorder(isl_upoly_copy(rec
->p
[i
]), r
));
1182 isl_upoly_free(base
);
1191 static int compatible_divs(__isl_keep isl_mat
*div1
, __isl_keep isl_mat
*div2
)
1196 isl_assert(div1
->ctx
, div1
->n_row
>= div2
->n_row
&&
1197 div1
->n_col
>= div2
->n_col
, return -1);
1199 if (div1
->n_row
== div2
->n_row
)
1200 return isl_mat_is_equal(div1
, div2
);
1202 n_row
= div1
->n_row
;
1203 n_col
= div1
->n_col
;
1204 div1
->n_row
= div2
->n_row
;
1205 div1
->n_col
= div2
->n_col
;
1207 equal
= isl_mat_is_equal(div1
, div2
);
1209 div1
->n_row
= n_row
;
1210 div1
->n_col
= n_col
;
1215 static int cmp_row(__isl_keep isl_mat
*div
, int i
, int j
)
1219 li
= isl_seq_last_non_zero(div
->row
[i
], div
->n_col
);
1220 lj
= isl_seq_last_non_zero(div
->row
[j
], div
->n_col
);
1225 return isl_seq_cmp(div
->row
[i
], div
->row
[j
], div
->n_col
);
1228 struct isl_div_sort_info
{
1233 static int div_sort_cmp(const void *p1
, const void *p2
)
1235 const struct isl_div_sort_info
*i1
, *i2
;
1236 i1
= (const struct isl_div_sort_info
*) p1
;
1237 i2
= (const struct isl_div_sort_info
*) p2
;
1239 return cmp_row(i1
->div
, i1
->row
, i2
->row
);
1242 /* Sort divs and remove duplicates.
1244 static __isl_give isl_qpolynomial
*sort_divs(__isl_take isl_qpolynomial
*qp
)
1249 struct isl_div_sort_info
*array
= NULL
;
1250 int *pos
= NULL
, *at
= NULL
;
1251 int *reordering
= NULL
;
1256 if (qp
->div
->n_row
<= 1)
1259 div_pos
= isl_space_dim(qp
->dim
, isl_dim_all
);
1261 array
= isl_alloc_array(qp
->div
->ctx
, struct isl_div_sort_info
,
1263 pos
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1264 at
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1265 len
= qp
->div
->n_col
- 2;
1266 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
1267 if (!array
|| !pos
|| !at
|| !reordering
)
1270 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1271 array
[i
].div
= qp
->div
;
1277 qsort(array
, qp
->div
->n_row
, sizeof(struct isl_div_sort_info
),
1280 for (i
= 0; i
< div_pos
; ++i
)
1283 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1284 if (pos
[array
[i
].row
] == i
)
1286 qp
->div
= isl_mat_swap_rows(qp
->div
, i
, pos
[array
[i
].row
]);
1287 pos
[at
[i
]] = pos
[array
[i
].row
];
1288 at
[pos
[array
[i
].row
]] = at
[i
];
1289 at
[i
] = array
[i
].row
;
1290 pos
[array
[i
].row
] = i
;
1294 for (i
= 0; i
< len
- div_pos
; ++i
) {
1296 isl_seq_eq(qp
->div
->row
[i
- skip
- 1],
1297 qp
->div
->row
[i
- skip
], qp
->div
->n_col
)) {
1298 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
1299 isl_mat_col_add(qp
->div
, 2 + div_pos
+ i
- skip
- 1,
1300 2 + div_pos
+ i
- skip
);
1301 qp
->div
= isl_mat_drop_cols(qp
->div
,
1302 2 + div_pos
+ i
- skip
, 1);
1305 reordering
[div_pos
+ array
[i
].row
] = div_pos
+ i
- skip
;
1308 qp
->upoly
= reorder(qp
->upoly
, reordering
);
1310 if (!qp
->upoly
|| !qp
->div
)
1324 isl_qpolynomial_free(qp
);
1328 static __isl_give
struct isl_upoly
*expand(__isl_take
struct isl_upoly
*up
,
1329 int *exp
, int first
)
1332 struct isl_upoly_rec
*rec
;
1334 if (isl_upoly_is_cst(up
))
1337 if (up
->var
< first
)
1340 if (exp
[up
->var
- first
] == up
->var
- first
)
1343 up
= isl_upoly_cow(up
);
1347 up
->var
= exp
[up
->var
- first
] + first
;
1349 rec
= isl_upoly_as_rec(up
);
1353 for (i
= 0; i
< rec
->n
; ++i
) {
1354 rec
->p
[i
] = expand(rec
->p
[i
], exp
, first
);
1365 static __isl_give isl_qpolynomial
*with_merged_divs(
1366 __isl_give isl_qpolynomial
*(*fn
)(__isl_take isl_qpolynomial
*qp1
,
1367 __isl_take isl_qpolynomial
*qp2
),
1368 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
1372 isl_mat
*div
= NULL
;
1375 qp1
= isl_qpolynomial_cow(qp1
);
1376 qp2
= isl_qpolynomial_cow(qp2
);
1381 isl_assert(qp1
->div
->ctx
, qp1
->div
->n_row
>= qp2
->div
->n_row
&&
1382 qp1
->div
->n_col
>= qp2
->div
->n_col
, goto error
);
1384 n_div1
= qp1
->div
->n_row
;
1385 n_div2
= qp2
->div
->n_row
;
1386 exp1
= isl_alloc_array(qp1
->div
->ctx
, int, n_div1
);
1387 exp2
= isl_alloc_array(qp2
->div
->ctx
, int, n_div2
);
1388 if ((n_div1
&& !exp1
) || (n_div2
&& !exp2
))
1391 div
= isl_merge_divs(qp1
->div
, qp2
->div
, exp1
, exp2
);
1395 isl_mat_free(qp1
->div
);
1396 qp1
->div
= isl_mat_copy(div
);
1397 isl_mat_free(qp2
->div
);
1398 qp2
->div
= isl_mat_copy(div
);
1400 qp1
->upoly
= expand(qp1
->upoly
, exp1
, div
->n_col
- div
->n_row
- 2);
1401 qp2
->upoly
= expand(qp2
->upoly
, exp2
, div
->n_col
- div
->n_row
- 2);
1403 if (!qp1
->upoly
|| !qp2
->upoly
)
1410 return fn(qp1
, qp2
);
1415 isl_qpolynomial_free(qp1
);
1416 isl_qpolynomial_free(qp2
);
1420 __isl_give isl_qpolynomial
*isl_qpolynomial_add(__isl_take isl_qpolynomial
*qp1
,
1421 __isl_take isl_qpolynomial
*qp2
)
1423 qp1
= isl_qpolynomial_cow(qp1
);
1428 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1429 return isl_qpolynomial_add(qp2
, qp1
);
1431 isl_assert(qp1
->dim
->ctx
, isl_space_is_equal(qp1
->dim
, qp2
->dim
), goto error
);
1432 if (!compatible_divs(qp1
->div
, qp2
->div
))
1433 return with_merged_divs(isl_qpolynomial_add
, qp1
, qp2
);
1435 qp1
->upoly
= isl_upoly_sum(qp1
->upoly
, isl_upoly_copy(qp2
->upoly
));
1439 isl_qpolynomial_free(qp2
);
1443 isl_qpolynomial_free(qp1
);
1444 isl_qpolynomial_free(qp2
);
1448 __isl_give isl_qpolynomial
*isl_qpolynomial_add_on_domain(
1449 __isl_keep isl_set
*dom
,
1450 __isl_take isl_qpolynomial
*qp1
,
1451 __isl_take isl_qpolynomial
*qp2
)
1453 qp1
= isl_qpolynomial_add(qp1
, qp2
);
1454 qp1
= isl_qpolynomial_gist(qp1
, isl_set_copy(dom
));
1458 __isl_give isl_qpolynomial
*isl_qpolynomial_sub(__isl_take isl_qpolynomial
*qp1
,
1459 __isl_take isl_qpolynomial
*qp2
)
1461 return isl_qpolynomial_add(qp1
, isl_qpolynomial_neg(qp2
));
1464 __isl_give isl_qpolynomial
*isl_qpolynomial_add_isl_int(
1465 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1467 if (isl_int_is_zero(v
))
1470 qp
= isl_qpolynomial_cow(qp
);
1474 qp
->upoly
= isl_upoly_add_isl_int(qp
->upoly
, v
);
1480 isl_qpolynomial_free(qp
);
1485 __isl_give isl_qpolynomial
*isl_qpolynomial_neg(__isl_take isl_qpolynomial
*qp
)
1490 return isl_qpolynomial_mul_isl_int(qp
, qp
->dim
->ctx
->negone
);
1493 __isl_give isl_qpolynomial
*isl_qpolynomial_mul_isl_int(
1494 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1496 if (isl_int_is_one(v
))
1499 if (qp
&& isl_int_is_zero(v
)) {
1500 isl_qpolynomial
*zero
;
1501 zero
= isl_qpolynomial_zero_on_domain(isl_space_copy(qp
->dim
));
1502 isl_qpolynomial_free(qp
);
1506 qp
= isl_qpolynomial_cow(qp
);
1510 qp
->upoly
= isl_upoly_mul_isl_int(qp
->upoly
, v
);
1516 isl_qpolynomial_free(qp
);
1520 __isl_give isl_qpolynomial
*isl_qpolynomial_scale(
1521 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1523 return isl_qpolynomial_mul_isl_int(qp
, v
);
1526 /* Multiply "qp" by "v".
1528 __isl_give isl_qpolynomial
*isl_qpolynomial_scale_val(
1529 __isl_take isl_qpolynomial
*qp
, __isl_take isl_val
*v
)
1534 if (!isl_val_is_rat(v
))
1535 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
1536 "expecting rational factor", goto error
);
1538 if (isl_val_is_one(v
)) {
1543 if (isl_val_is_zero(v
)) {
1546 space
= isl_qpolynomial_get_domain_space(qp
);
1547 isl_qpolynomial_free(qp
);
1549 return isl_qpolynomial_zero_on_domain(space
);
1552 qp
= isl_qpolynomial_cow(qp
);
1556 qp
->upoly
= isl_upoly_scale_val(qp
->upoly
, v
);
1558 qp
= isl_qpolynomial_free(qp
);
1564 isl_qpolynomial_free(qp
);
1568 __isl_give isl_qpolynomial
*isl_qpolynomial_mul(__isl_take isl_qpolynomial
*qp1
,
1569 __isl_take isl_qpolynomial
*qp2
)
1571 qp1
= isl_qpolynomial_cow(qp1
);
1576 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1577 return isl_qpolynomial_mul(qp2
, qp1
);
1579 isl_assert(qp1
->dim
->ctx
, isl_space_is_equal(qp1
->dim
, qp2
->dim
), goto error
);
1580 if (!compatible_divs(qp1
->div
, qp2
->div
))
1581 return with_merged_divs(isl_qpolynomial_mul
, qp1
, qp2
);
1583 qp1
->upoly
= isl_upoly_mul(qp1
->upoly
, isl_upoly_copy(qp2
->upoly
));
1587 isl_qpolynomial_free(qp2
);
1591 isl_qpolynomial_free(qp1
);
1592 isl_qpolynomial_free(qp2
);
1596 __isl_give isl_qpolynomial
*isl_qpolynomial_pow(__isl_take isl_qpolynomial
*qp
,
1599 qp
= isl_qpolynomial_cow(qp
);
1604 qp
->upoly
= isl_upoly_pow(qp
->upoly
, power
);
1610 isl_qpolynomial_free(qp
);
1614 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_pow(
1615 __isl_take isl_pw_qpolynomial
*pwqp
, unsigned power
)
1622 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
1626 for (i
= 0; i
< pwqp
->n
; ++i
) {
1627 pwqp
->p
[i
].qp
= isl_qpolynomial_pow(pwqp
->p
[i
].qp
, power
);
1629 return isl_pw_qpolynomial_free(pwqp
);
1635 __isl_give isl_qpolynomial
*isl_qpolynomial_zero_on_domain(
1636 __isl_take isl_space
*dim
)
1640 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
1643 __isl_give isl_qpolynomial
*isl_qpolynomial_one_on_domain(
1644 __isl_take isl_space
*dim
)
1648 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_one(dim
->ctx
));
1651 __isl_give isl_qpolynomial
*isl_qpolynomial_infty_on_domain(
1652 __isl_take isl_space
*dim
)
1656 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_infty(dim
->ctx
));
1659 __isl_give isl_qpolynomial
*isl_qpolynomial_neginfty_on_domain(
1660 __isl_take isl_space
*dim
)
1664 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_neginfty(dim
->ctx
));
1667 __isl_give isl_qpolynomial
*isl_qpolynomial_nan_on_domain(
1668 __isl_take isl_space
*dim
)
1672 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_nan(dim
->ctx
));
1675 __isl_give isl_qpolynomial
*isl_qpolynomial_cst_on_domain(
1676 __isl_take isl_space
*dim
,
1679 struct isl_qpolynomial
*qp
;
1680 struct isl_upoly_cst
*cst
;
1685 qp
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
1689 cst
= isl_upoly_as_cst(qp
->upoly
);
1690 isl_int_set(cst
->n
, v
);
1695 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial
*qp
,
1696 isl_int
*n
, isl_int
*d
)
1698 struct isl_upoly_cst
*cst
;
1703 if (!isl_upoly_is_cst(qp
->upoly
))
1706 cst
= isl_upoly_as_cst(qp
->upoly
);
1711 isl_int_set(*n
, cst
->n
);
1713 isl_int_set(*d
, cst
->d
);
1718 /* Return the constant term of "up".
1720 static __isl_give isl_val
*isl_upoly_get_constant_val(
1721 __isl_keep
struct isl_upoly
*up
)
1723 struct isl_upoly_cst
*cst
;
1728 while (!isl_upoly_is_cst(up
)) {
1729 struct isl_upoly_rec
*rec
;
1731 rec
= isl_upoly_as_rec(up
);
1737 cst
= isl_upoly_as_cst(up
);
1740 return isl_val_rat_from_isl_int(cst
->up
.ctx
, cst
->n
, cst
->d
);
1743 /* Return the constant term of "qp".
1745 __isl_give isl_val
*isl_qpolynomial_get_constant_val(
1746 __isl_keep isl_qpolynomial
*qp
)
1751 return isl_upoly_get_constant_val(qp
->upoly
);
1754 int isl_upoly_is_affine(__isl_keep
struct isl_upoly
*up
)
1757 struct isl_upoly_rec
*rec
;
1765 rec
= isl_upoly_as_rec(up
);
1772 isl_assert(up
->ctx
, rec
->n
> 1, return -1);
1774 is_cst
= isl_upoly_is_cst(rec
->p
[1]);
1780 return isl_upoly_is_affine(rec
->p
[0]);
1783 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial
*qp
)
1788 if (qp
->div
->n_row
> 0)
1791 return isl_upoly_is_affine(qp
->upoly
);
1794 static void update_coeff(__isl_keep isl_vec
*aff
,
1795 __isl_keep
struct isl_upoly_cst
*cst
, int pos
)
1800 if (isl_int_is_zero(cst
->n
))
1805 isl_int_gcd(gcd
, cst
->d
, aff
->el
[0]);
1806 isl_int_divexact(f
, cst
->d
, gcd
);
1807 isl_int_divexact(gcd
, aff
->el
[0], gcd
);
1808 isl_seq_scale(aff
->el
, aff
->el
, f
, aff
->size
);
1809 isl_int_mul(aff
->el
[1 + pos
], gcd
, cst
->n
);
1814 int isl_upoly_update_affine(__isl_keep
struct isl_upoly
*up
,
1815 __isl_keep isl_vec
*aff
)
1817 struct isl_upoly_cst
*cst
;
1818 struct isl_upoly_rec
*rec
;
1824 struct isl_upoly_cst
*cst
;
1826 cst
= isl_upoly_as_cst(up
);
1829 update_coeff(aff
, cst
, 0);
1833 rec
= isl_upoly_as_rec(up
);
1836 isl_assert(up
->ctx
, rec
->n
== 2, return -1);
1838 cst
= isl_upoly_as_cst(rec
->p
[1]);
1841 update_coeff(aff
, cst
, 1 + up
->var
);
1843 return isl_upoly_update_affine(rec
->p
[0], aff
);
1846 __isl_give isl_vec
*isl_qpolynomial_extract_affine(
1847 __isl_keep isl_qpolynomial
*qp
)
1855 d
= isl_space_dim(qp
->dim
, isl_dim_all
);
1856 aff
= isl_vec_alloc(qp
->div
->ctx
, 2 + d
+ qp
->div
->n_row
);
1860 isl_seq_clr(aff
->el
+ 1, 1 + d
+ qp
->div
->n_row
);
1861 isl_int_set_si(aff
->el
[0], 1);
1863 if (isl_upoly_update_affine(qp
->upoly
, aff
) < 0)
1872 int isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial
*qp1
,
1873 __isl_keep isl_qpolynomial
*qp2
)
1880 equal
= isl_space_is_equal(qp1
->dim
, qp2
->dim
);
1881 if (equal
< 0 || !equal
)
1884 equal
= isl_mat_is_equal(qp1
->div
, qp2
->div
);
1885 if (equal
< 0 || !equal
)
1888 return isl_upoly_is_equal(qp1
->upoly
, qp2
->upoly
);
1891 static void upoly_update_den(__isl_keep
struct isl_upoly
*up
, isl_int
*d
)
1894 struct isl_upoly_rec
*rec
;
1896 if (isl_upoly_is_cst(up
)) {
1897 struct isl_upoly_cst
*cst
;
1898 cst
= isl_upoly_as_cst(up
);
1901 isl_int_lcm(*d
, *d
, cst
->d
);
1905 rec
= isl_upoly_as_rec(up
);
1909 for (i
= 0; i
< rec
->n
; ++i
)
1910 upoly_update_den(rec
->p
[i
], d
);
1913 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial
*qp
, isl_int
*d
)
1915 isl_int_set_si(*d
, 1);
1918 upoly_update_den(qp
->upoly
, d
);
1921 __isl_give isl_qpolynomial
*isl_qpolynomial_var_pow_on_domain(
1922 __isl_take isl_space
*dim
, int pos
, int power
)
1924 struct isl_ctx
*ctx
;
1931 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_var_pow(ctx
, pos
, power
));
1934 __isl_give isl_qpolynomial
*isl_qpolynomial_var_on_domain(__isl_take isl_space
*dim
,
1935 enum isl_dim_type type
, unsigned pos
)
1940 isl_assert(dim
->ctx
, isl_space_dim(dim
, isl_dim_in
) == 0, goto error
);
1941 isl_assert(dim
->ctx
, pos
< isl_space_dim(dim
, type
), goto error
);
1943 if (type
== isl_dim_set
)
1944 pos
+= isl_space_dim(dim
, isl_dim_param
);
1946 return isl_qpolynomial_var_pow_on_domain(dim
, pos
, 1);
1948 isl_space_free(dim
);
1952 __isl_give
struct isl_upoly
*isl_upoly_subs(__isl_take
struct isl_upoly
*up
,
1953 unsigned first
, unsigned n
, __isl_keep
struct isl_upoly
**subs
)
1956 struct isl_upoly_rec
*rec
;
1957 struct isl_upoly
*base
, *res
;
1962 if (isl_upoly_is_cst(up
))
1965 if (up
->var
< first
)
1968 rec
= isl_upoly_as_rec(up
);
1972 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
1974 if (up
->var
>= first
+ n
)
1975 base
= isl_upoly_var_pow(up
->ctx
, up
->var
, 1);
1977 base
= isl_upoly_copy(subs
[up
->var
- first
]);
1979 res
= isl_upoly_subs(isl_upoly_copy(rec
->p
[rec
->n
- 1]), first
, n
, subs
);
1980 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1981 struct isl_upoly
*t
;
1982 t
= isl_upoly_subs(isl_upoly_copy(rec
->p
[i
]), first
, n
, subs
);
1983 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
1984 res
= isl_upoly_sum(res
, t
);
1987 isl_upoly_free(base
);
1996 __isl_give
struct isl_upoly
*isl_upoly_from_affine(isl_ctx
*ctx
, isl_int
*f
,
1997 isl_int denom
, unsigned len
)
2000 struct isl_upoly
*up
;
2002 isl_assert(ctx
, len
>= 1, return NULL
);
2004 up
= isl_upoly_rat_cst(ctx
, f
[0], denom
);
2005 for (i
= 0; i
< len
- 1; ++i
) {
2006 struct isl_upoly
*t
;
2007 struct isl_upoly
*c
;
2009 if (isl_int_is_zero(f
[1 + i
]))
2012 c
= isl_upoly_rat_cst(ctx
, f
[1 + i
], denom
);
2013 t
= isl_upoly_var_pow(ctx
, i
, 1);
2014 t
= isl_upoly_mul(c
, t
);
2015 up
= isl_upoly_sum(up
, t
);
2021 /* Remove common factor of non-constant terms and denominator.
2023 static void normalize_div(__isl_keep isl_qpolynomial
*qp
, int div
)
2025 isl_ctx
*ctx
= qp
->div
->ctx
;
2026 unsigned total
= qp
->div
->n_col
- 2;
2028 isl_seq_gcd(qp
->div
->row
[div
] + 2, total
, &ctx
->normalize_gcd
);
2029 isl_int_gcd(ctx
->normalize_gcd
,
2030 ctx
->normalize_gcd
, qp
->div
->row
[div
][0]);
2031 if (isl_int_is_one(ctx
->normalize_gcd
))
2034 isl_seq_scale_down(qp
->div
->row
[div
] + 2, qp
->div
->row
[div
] + 2,
2035 ctx
->normalize_gcd
, total
);
2036 isl_int_divexact(qp
->div
->row
[div
][0], qp
->div
->row
[div
][0],
2037 ctx
->normalize_gcd
);
2038 isl_int_fdiv_q(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1],
2039 ctx
->normalize_gcd
);
2042 /* Replace the integer division identified by "div" by the polynomial "s".
2043 * The integer division is assumed not to appear in the definition
2044 * of any other integer divisions.
2046 static __isl_give isl_qpolynomial
*substitute_div(
2047 __isl_take isl_qpolynomial
*qp
,
2048 int div
, __isl_take
struct isl_upoly
*s
)
2057 qp
= isl_qpolynomial_cow(qp
);
2061 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
2062 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ div
, 1, &s
);
2066 reordering
= isl_alloc_array(qp
->dim
->ctx
, int, total
+ qp
->div
->n_row
);
2069 for (i
= 0; i
< total
+ div
; ++i
)
2071 for (i
= total
+ div
+ 1; i
< total
+ qp
->div
->n_row
; ++i
)
2072 reordering
[i
] = i
- 1;
2073 qp
->div
= isl_mat_drop_rows(qp
->div
, div
, 1);
2074 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + total
+ div
, 1);
2075 qp
->upoly
= reorder(qp
->upoly
, reordering
);
2078 if (!qp
->upoly
|| !qp
->div
)
2084 isl_qpolynomial_free(qp
);
2089 /* Replace all integer divisions [e/d] that turn out to not actually be integer
2090 * divisions because d is equal to 1 by their definition, i.e., e.
2092 static __isl_give isl_qpolynomial
*substitute_non_divs(
2093 __isl_take isl_qpolynomial
*qp
)
2097 struct isl_upoly
*s
;
2102 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
2103 for (i
= 0; qp
&& i
< qp
->div
->n_row
; ++i
) {
2104 if (!isl_int_is_one(qp
->div
->row
[i
][0]))
2106 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
2107 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
2109 isl_seq_combine(qp
->div
->row
[j
] + 1,
2110 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
2111 qp
->div
->row
[j
][2 + total
+ i
],
2112 qp
->div
->row
[i
] + 1, 1 + total
+ i
);
2113 isl_int_set_si(qp
->div
->row
[j
][2 + total
+ i
], 0);
2114 normalize_div(qp
, j
);
2116 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
2117 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
2118 qp
= substitute_div(qp
, i
, s
);
2125 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
2126 * with d the denominator. When replacing the coefficient e of x by
2127 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
2128 * inside the division, so we need to add floor(e/d) * x outside.
2129 * That is, we replace q by q' + floor(e/d) * x and we therefore need
2130 * to adjust the coefficient of x in each later div that depends on the
2131 * current div "div" and also in the affine expression "aff"
2132 * (if it too depends on "div").
2134 static void reduce_div(__isl_keep isl_qpolynomial
*qp
, int div
,
2135 __isl_keep isl_vec
*aff
)
2139 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
2142 for (i
= 0; i
< 1 + total
+ div
; ++i
) {
2143 if (isl_int_is_nonneg(qp
->div
->row
[div
][1 + i
]) &&
2144 isl_int_lt(qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]))
2146 isl_int_fdiv_q(v
, qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
2147 isl_int_fdiv_r(qp
->div
->row
[div
][1 + i
],
2148 qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
2149 if (!isl_int_is_zero(aff
->el
[1 + total
+ div
]))
2150 isl_int_addmul(aff
->el
[i
], v
, aff
->el
[1 + total
+ div
]);
2151 for (j
= div
+ 1; j
< qp
->div
->n_row
; ++j
) {
2152 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ div
]))
2154 isl_int_addmul(qp
->div
->row
[j
][1 + i
],
2155 v
, qp
->div
->row
[j
][2 + total
+ div
]);
2161 /* Check if the last non-zero coefficient is bigger that half of the
2162 * denominator. If so, we will invert the div to further reduce the number
2163 * of distinct divs that may appear.
2164 * If the last non-zero coefficient is exactly half the denominator,
2165 * then we continue looking for earlier coefficients that are bigger
2166 * than half the denominator.
2168 static int needs_invert(__isl_keep isl_mat
*div
, int row
)
2173 for (i
= div
->n_col
- 1; i
>= 1; --i
) {
2174 if (isl_int_is_zero(div
->row
[row
][i
]))
2176 isl_int_mul_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
2177 cmp
= isl_int_cmp(div
->row
[row
][i
], div
->row
[row
][0]);
2178 isl_int_divexact_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
2188 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
2189 * We only invert the coefficients of e (and the coefficient of q in
2190 * later divs and in "aff"). After calling this function, the
2191 * coefficients of e should be reduced again.
2193 static void invert_div(__isl_keep isl_qpolynomial
*qp
, int div
,
2194 __isl_keep isl_vec
*aff
)
2196 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
2198 isl_seq_neg(qp
->div
->row
[div
] + 1,
2199 qp
->div
->row
[div
] + 1, qp
->div
->n_col
- 1);
2200 isl_int_sub_ui(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1], 1);
2201 isl_int_add(qp
->div
->row
[div
][1],
2202 qp
->div
->row
[div
][1], qp
->div
->row
[div
][0]);
2203 if (!isl_int_is_zero(aff
->el
[1 + total
+ div
]))
2204 isl_int_neg(aff
->el
[1 + total
+ div
], aff
->el
[1 + total
+ div
]);
2205 isl_mat_col_mul(qp
->div
, 2 + total
+ div
,
2206 qp
->div
->ctx
->negone
, 2 + total
+ div
);
2209 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2210 * in the interval [0, d-1], with d the denominator and such that the
2211 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2213 * After the reduction, some divs may have become redundant or identical,
2214 * so we call substitute_non_divs and sort_divs. If these functions
2215 * eliminate divs or merge two or more divs into one, the coefficients
2216 * of the enclosing divs may have to be reduced again, so we call
2217 * ourselves recursively if the number of divs decreases.
2219 static __isl_give isl_qpolynomial
*reduce_divs(__isl_take isl_qpolynomial
*qp
)
2222 isl_vec
*aff
= NULL
;
2223 struct isl_upoly
*s
;
2229 aff
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
2230 aff
= isl_vec_clr(aff
);
2234 isl_int_set_si(aff
->el
[1 + qp
->upoly
->var
], 1);
2236 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2237 normalize_div(qp
, i
);
2238 reduce_div(qp
, i
, aff
);
2239 if (needs_invert(qp
->div
, i
)) {
2240 invert_div(qp
, i
, aff
);
2241 reduce_div(qp
, i
, aff
);
2245 s
= isl_upoly_from_affine(qp
->div
->ctx
, aff
->el
,
2246 qp
->div
->ctx
->one
, aff
->size
);
2247 qp
->upoly
= isl_upoly_subs(qp
->upoly
, qp
->upoly
->var
, 1, &s
);
2254 n_div
= qp
->div
->n_row
;
2255 qp
= substitute_non_divs(qp
);
2257 if (qp
&& qp
->div
->n_row
< n_div
)
2258 return reduce_divs(qp
);
2262 isl_qpolynomial_free(qp
);
2267 __isl_give isl_qpolynomial
*isl_qpolynomial_rat_cst_on_domain(
2268 __isl_take isl_space
*dim
, const isl_int n
, const isl_int d
)
2270 struct isl_qpolynomial
*qp
;
2271 struct isl_upoly_cst
*cst
;
2276 qp
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
2280 cst
= isl_upoly_as_cst(qp
->upoly
);
2281 isl_int_set(cst
->n
, n
);
2282 isl_int_set(cst
->d
, d
);
2287 /* Return an isl_qpolynomial that is equal to "val" on domain space "domain".
2289 __isl_give isl_qpolynomial
*isl_qpolynomial_val_on_domain(
2290 __isl_take isl_space
*domain
, __isl_take isl_val
*val
)
2292 isl_qpolynomial
*qp
;
2293 struct isl_upoly_cst
*cst
;
2295 if (!domain
|| !val
)
2298 qp
= isl_qpolynomial_alloc(isl_space_copy(domain
), 0,
2299 isl_upoly_zero(domain
->ctx
));
2303 cst
= isl_upoly_as_cst(qp
->upoly
);
2304 isl_int_set(cst
->n
, val
->n
);
2305 isl_int_set(cst
->d
, val
->d
);
2307 isl_space_free(domain
);
2311 isl_space_free(domain
);
2316 static int up_set_active(__isl_keep
struct isl_upoly
*up
, int *active
, int d
)
2318 struct isl_upoly_rec
*rec
;
2324 if (isl_upoly_is_cst(up
))
2328 active
[up
->var
] = 1;
2330 rec
= isl_upoly_as_rec(up
);
2331 for (i
= 0; i
< rec
->n
; ++i
)
2332 if (up_set_active(rec
->p
[i
], active
, d
) < 0)
2338 static int set_active(__isl_keep isl_qpolynomial
*qp
, int *active
)
2341 int d
= isl_space_dim(qp
->dim
, isl_dim_all
);
2346 for (i
= 0; i
< d
; ++i
)
2347 for (j
= 0; j
< qp
->div
->n_row
; ++j
) {
2348 if (isl_int_is_zero(qp
->div
->row
[j
][2 + i
]))
2354 return up_set_active(qp
->upoly
, active
, d
);
2357 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial
*qp
,
2358 enum isl_dim_type type
, unsigned first
, unsigned n
)
2369 isl_assert(qp
->dim
->ctx
,
2370 first
+ n
<= isl_qpolynomial_dim(qp
, type
), return -1);
2371 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2372 type
== isl_dim_in
, return -1);
2374 active
= isl_calloc_array(qp
->dim
->ctx
, int,
2375 isl_space_dim(qp
->dim
, isl_dim_all
));
2376 if (set_active(qp
, active
) < 0)
2379 if (type
== isl_dim_in
)
2380 first
+= isl_space_dim(qp
->dim
, isl_dim_param
);
2381 for (i
= 0; i
< n
; ++i
)
2382 if (active
[first
+ i
]) {
2395 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2396 * of the divs that do appear in the quasi-polynomial.
2398 static __isl_give isl_qpolynomial
*remove_redundant_divs(
2399 __isl_take isl_qpolynomial
*qp
)
2406 int *reordering
= NULL
;
2413 if (qp
->div
->n_row
== 0)
2416 d
= isl_space_dim(qp
->dim
, isl_dim_all
);
2417 len
= qp
->div
->n_col
- 2;
2418 ctx
= isl_qpolynomial_get_ctx(qp
);
2419 active
= isl_calloc_array(ctx
, int, len
);
2423 if (up_set_active(qp
->upoly
, active
, len
) < 0)
2426 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
2427 if (!active
[d
+ i
]) {
2431 for (j
= 0; j
< i
; ++j
) {
2432 if (isl_int_is_zero(qp
->div
->row
[i
][2 + d
+ j
]))
2444 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
2448 for (i
= 0; i
< d
; ++i
)
2452 n_div
= qp
->div
->n_row
;
2453 for (i
= 0; i
< n_div
; ++i
) {
2454 if (!active
[d
+ i
]) {
2455 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
2456 qp
->div
= isl_mat_drop_cols(qp
->div
,
2457 2 + d
+ i
- skip
, 1);
2460 reordering
[d
+ i
] = d
+ i
- skip
;
2463 qp
->upoly
= reorder(qp
->upoly
, reordering
);
2465 if (!qp
->upoly
|| !qp
->div
)
2475 isl_qpolynomial_free(qp
);
2479 __isl_give
struct isl_upoly
*isl_upoly_drop(__isl_take
struct isl_upoly
*up
,
2480 unsigned first
, unsigned n
)
2483 struct isl_upoly_rec
*rec
;
2487 if (n
== 0 || up
->var
< 0 || up
->var
< first
)
2489 if (up
->var
< first
+ n
) {
2490 up
= replace_by_constant_term(up
);
2491 return isl_upoly_drop(up
, first
, n
);
2493 up
= isl_upoly_cow(up
);
2497 rec
= isl_upoly_as_rec(up
);
2501 for (i
= 0; i
< rec
->n
; ++i
) {
2502 rec
->p
[i
] = isl_upoly_drop(rec
->p
[i
], first
, n
);
2513 __isl_give isl_qpolynomial
*isl_qpolynomial_set_dim_name(
2514 __isl_take isl_qpolynomial
*qp
,
2515 enum isl_dim_type type
, unsigned pos
, const char *s
)
2517 qp
= isl_qpolynomial_cow(qp
);
2520 qp
->dim
= isl_space_set_dim_name(qp
->dim
, type
, pos
, s
);
2525 isl_qpolynomial_free(qp
);
2529 __isl_give isl_qpolynomial
*isl_qpolynomial_drop_dims(
2530 __isl_take isl_qpolynomial
*qp
,
2531 enum isl_dim_type type
, unsigned first
, unsigned n
)
2535 if (type
== isl_dim_out
)
2536 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
2537 "cannot drop output/set dimension",
2539 if (type
== isl_dim_in
)
2541 if (n
== 0 && !isl_space_is_named_or_nested(qp
->dim
, type
))
2544 qp
= isl_qpolynomial_cow(qp
);
2548 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_space_dim(qp
->dim
, type
),
2550 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2551 type
== isl_dim_set
, goto error
);
2553 qp
->dim
= isl_space_drop_dims(qp
->dim
, type
, first
, n
);
2557 if (type
== isl_dim_set
)
2558 first
+= isl_space_dim(qp
->dim
, isl_dim_param
);
2560 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + first
, n
);
2564 qp
->upoly
= isl_upoly_drop(qp
->upoly
, first
, n
);
2570 isl_qpolynomial_free(qp
);
2574 /* Project the domain of the quasi-polynomial onto its parameter space.
2575 * The quasi-polynomial may not involve any of the domain dimensions.
2577 __isl_give isl_qpolynomial
*isl_qpolynomial_project_domain_on_params(
2578 __isl_take isl_qpolynomial
*qp
)
2584 n
= isl_qpolynomial_dim(qp
, isl_dim_in
);
2585 involves
= isl_qpolynomial_involves_dims(qp
, isl_dim_in
, 0, n
);
2587 return isl_qpolynomial_free(qp
);
2589 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
2590 "polynomial involves some of the domain dimensions",
2591 return isl_qpolynomial_free(qp
));
2592 qp
= isl_qpolynomial_drop_dims(qp
, isl_dim_in
, 0, n
);
2593 space
= isl_qpolynomial_get_domain_space(qp
);
2594 space
= isl_space_params(space
);
2595 qp
= isl_qpolynomial_reset_domain_space(qp
, space
);
2599 static __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities_lifted(
2600 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2606 struct isl_upoly
*up
;
2610 if (eq
->n_eq
== 0) {
2611 isl_basic_set_free(eq
);
2615 qp
= isl_qpolynomial_cow(qp
);
2618 qp
->div
= isl_mat_cow(qp
->div
);
2622 total
= 1 + isl_space_dim(eq
->dim
, isl_dim_all
);
2624 isl_int_init(denom
);
2625 for (i
= 0; i
< eq
->n_eq
; ++i
) {
2626 j
= isl_seq_last_non_zero(eq
->eq
[i
], total
+ n_div
);
2627 if (j
< 0 || j
== 0 || j
>= total
)
2630 for (k
= 0; k
< qp
->div
->n_row
; ++k
) {
2631 if (isl_int_is_zero(qp
->div
->row
[k
][1 + j
]))
2633 isl_seq_elim(qp
->div
->row
[k
] + 1, eq
->eq
[i
], j
, total
,
2634 &qp
->div
->row
[k
][0]);
2635 normalize_div(qp
, k
);
2638 if (isl_int_is_pos(eq
->eq
[i
][j
]))
2639 isl_seq_neg(eq
->eq
[i
], eq
->eq
[i
], total
);
2640 isl_int_abs(denom
, eq
->eq
[i
][j
]);
2641 isl_int_set_si(eq
->eq
[i
][j
], 0);
2643 up
= isl_upoly_from_affine(qp
->dim
->ctx
,
2644 eq
->eq
[i
], denom
, total
);
2645 qp
->upoly
= isl_upoly_subs(qp
->upoly
, j
- 1, 1, &up
);
2648 isl_int_clear(denom
);
2653 isl_basic_set_free(eq
);
2655 qp
= substitute_non_divs(qp
);
2660 isl_basic_set_free(eq
);
2661 isl_qpolynomial_free(qp
);
2665 /* Exploit the equalities in "eq" to simplify the quasi-polynomial.
2667 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities(
2668 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2672 if (qp
->div
->n_row
> 0)
2673 eq
= isl_basic_set_add_dims(eq
, isl_dim_set
, qp
->div
->n_row
);
2674 return isl_qpolynomial_substitute_equalities_lifted(qp
, eq
);
2676 isl_basic_set_free(eq
);
2677 isl_qpolynomial_free(qp
);
2681 static __isl_give isl_basic_set
*add_div_constraints(
2682 __isl_take isl_basic_set
*bset
, __isl_take isl_mat
*div
)
2690 bset
= isl_basic_set_extend_constraints(bset
, 0, 2 * div
->n_row
);
2693 total
= isl_basic_set_total_dim(bset
);
2694 for (i
= 0; i
< div
->n_row
; ++i
)
2695 if (isl_basic_set_add_div_constraints_var(bset
,
2696 total
- div
->n_row
+ i
, div
->row
[i
]) < 0)
2703 isl_basic_set_free(bset
);
2707 /* Look for equalities among the variables shared by context and qp
2708 * and the integer divisions of qp, if any.
2709 * The equalities are then used to eliminate variables and/or integer
2710 * divisions from qp.
2712 __isl_give isl_qpolynomial
*isl_qpolynomial_gist(
2713 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
2719 if (qp
->div
->n_row
> 0) {
2720 isl_basic_set
*bset
;
2721 context
= isl_set_add_dims(context
, isl_dim_set
,
2723 bset
= isl_basic_set_universe(isl_set_get_space(context
));
2724 bset
= add_div_constraints(bset
, isl_mat_copy(qp
->div
));
2725 context
= isl_set_intersect(context
,
2726 isl_set_from_basic_set(bset
));
2729 aff
= isl_set_affine_hull(context
);
2730 return isl_qpolynomial_substitute_equalities_lifted(qp
, aff
);
2732 isl_qpolynomial_free(qp
);
2733 isl_set_free(context
);
2737 __isl_give isl_qpolynomial
*isl_qpolynomial_gist_params(
2738 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
2740 isl_space
*space
= isl_qpolynomial_get_domain_space(qp
);
2741 isl_set
*dom_context
= isl_set_universe(space
);
2742 dom_context
= isl_set_intersect_params(dom_context
, context
);
2743 return isl_qpolynomial_gist(qp
, dom_context
);
2746 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_from_qpolynomial(
2747 __isl_take isl_qpolynomial
*qp
)
2753 if (isl_qpolynomial_is_zero(qp
)) {
2754 isl_space
*dim
= isl_qpolynomial_get_space(qp
);
2755 isl_qpolynomial_free(qp
);
2756 return isl_pw_qpolynomial_zero(dim
);
2759 dom
= isl_set_universe(isl_qpolynomial_get_domain_space(qp
));
2760 return isl_pw_qpolynomial_alloc(dom
, qp
);
2764 #define PW isl_pw_qpolynomial
2766 #define EL isl_qpolynomial
2768 #define EL_IS_ZERO is_zero
2772 #define IS_ZERO is_zero
2775 #undef DEFAULT_IS_ZERO
2776 #define DEFAULT_IS_ZERO 1
2780 #include <isl_pw_templ.c>
2783 #define UNION isl_union_pw_qpolynomial
2785 #define PART isl_pw_qpolynomial
2787 #define PARTS pw_qpolynomial
2788 #define ALIGN_DOMAIN
2790 #include <isl_union_templ.c>
2792 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial
*pwqp
)
2800 if (!isl_set_plain_is_universe(pwqp
->p
[0].set
))
2803 return isl_qpolynomial_is_one(pwqp
->p
[0].qp
);
2806 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add(
2807 __isl_take isl_pw_qpolynomial
*pwqp1
,
2808 __isl_take isl_pw_qpolynomial
*pwqp2
)
2810 return isl_pw_qpolynomial_union_add_(pwqp1
, pwqp2
);
2813 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_mul(
2814 __isl_take isl_pw_qpolynomial
*pwqp1
,
2815 __isl_take isl_pw_qpolynomial
*pwqp2
)
2818 struct isl_pw_qpolynomial
*res
;
2820 if (!pwqp1
|| !pwqp2
)
2823 isl_assert(pwqp1
->dim
->ctx
, isl_space_is_equal(pwqp1
->dim
, pwqp2
->dim
),
2826 if (isl_pw_qpolynomial_is_zero(pwqp1
)) {
2827 isl_pw_qpolynomial_free(pwqp2
);
2831 if (isl_pw_qpolynomial_is_zero(pwqp2
)) {
2832 isl_pw_qpolynomial_free(pwqp1
);
2836 if (isl_pw_qpolynomial_is_one(pwqp1
)) {
2837 isl_pw_qpolynomial_free(pwqp1
);
2841 if (isl_pw_qpolynomial_is_one(pwqp2
)) {
2842 isl_pw_qpolynomial_free(pwqp2
);
2846 n
= pwqp1
->n
* pwqp2
->n
;
2847 res
= isl_pw_qpolynomial_alloc_size(isl_space_copy(pwqp1
->dim
), n
);
2849 for (i
= 0; i
< pwqp1
->n
; ++i
) {
2850 for (j
= 0; j
< pwqp2
->n
; ++j
) {
2851 struct isl_set
*common
;
2852 struct isl_qpolynomial
*prod
;
2853 common
= isl_set_intersect(isl_set_copy(pwqp1
->p
[i
].set
),
2854 isl_set_copy(pwqp2
->p
[j
].set
));
2855 if (isl_set_plain_is_empty(common
)) {
2856 isl_set_free(common
);
2860 prod
= isl_qpolynomial_mul(
2861 isl_qpolynomial_copy(pwqp1
->p
[i
].qp
),
2862 isl_qpolynomial_copy(pwqp2
->p
[j
].qp
));
2864 res
= isl_pw_qpolynomial_add_piece(res
, common
, prod
);
2868 isl_pw_qpolynomial_free(pwqp1
);
2869 isl_pw_qpolynomial_free(pwqp2
);
2873 isl_pw_qpolynomial_free(pwqp1
);
2874 isl_pw_qpolynomial_free(pwqp2
);
2878 __isl_give isl_val
*isl_upoly_eval(__isl_take
struct isl_upoly
*up
,
2879 __isl_take isl_vec
*vec
)
2882 struct isl_upoly_rec
*rec
;
2886 if (isl_upoly_is_cst(up
)) {
2888 res
= isl_upoly_get_constant_val(up
);
2893 rec
= isl_upoly_as_rec(up
);
2897 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
2899 base
= isl_val_rat_from_isl_int(up
->ctx
,
2900 vec
->el
[1 + up
->var
], vec
->el
[0]);
2902 res
= isl_upoly_eval(isl_upoly_copy(rec
->p
[rec
->n
- 1]),
2905 for (i
= rec
->n
- 2; i
>= 0; --i
) {
2906 res
= isl_val_mul(res
, isl_val_copy(base
));
2907 res
= isl_val_add(res
,
2908 isl_upoly_eval(isl_upoly_copy(rec
->p
[i
]),
2909 isl_vec_copy(vec
)));
2922 __isl_give isl_val
*isl_qpolynomial_eval(__isl_take isl_qpolynomial
*qp
,
2923 __isl_take isl_point
*pnt
)
2930 isl_assert(pnt
->dim
->ctx
, isl_space_is_equal(pnt
->dim
, qp
->dim
), goto error
);
2932 if (qp
->div
->n_row
== 0)
2933 ext
= isl_vec_copy(pnt
->vec
);
2936 unsigned dim
= isl_space_dim(qp
->dim
, isl_dim_all
);
2937 ext
= isl_vec_alloc(qp
->dim
->ctx
, 1 + dim
+ qp
->div
->n_row
);
2941 isl_seq_cpy(ext
->el
, pnt
->vec
->el
, pnt
->vec
->size
);
2942 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2943 isl_seq_inner_product(qp
->div
->row
[i
] + 1, ext
->el
,
2944 1 + dim
+ i
, &ext
->el
[1+dim
+i
]);
2945 isl_int_fdiv_q(ext
->el
[1+dim
+i
], ext
->el
[1+dim
+i
],
2946 qp
->div
->row
[i
][0]);
2950 v
= isl_upoly_eval(isl_upoly_copy(qp
->upoly
), ext
);
2952 isl_qpolynomial_free(qp
);
2953 isl_point_free(pnt
);
2957 isl_qpolynomial_free(qp
);
2958 isl_point_free(pnt
);
2962 int isl_upoly_cmp(__isl_keep
struct isl_upoly_cst
*cst1
,
2963 __isl_keep
struct isl_upoly_cst
*cst2
)
2968 isl_int_mul(t
, cst1
->n
, cst2
->d
);
2969 isl_int_submul(t
, cst2
->n
, cst1
->d
);
2970 cmp
= isl_int_sgn(t
);
2975 __isl_give isl_qpolynomial
*isl_qpolynomial_insert_dims(
2976 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
,
2977 unsigned first
, unsigned n
)
2985 if (type
== isl_dim_out
)
2986 isl_die(qp
->div
->ctx
, isl_error_invalid
,
2987 "cannot insert output/set dimensions",
2989 if (type
== isl_dim_in
)
2991 if (n
== 0 && !isl_space_is_named_or_nested(qp
->dim
, type
))
2994 qp
= isl_qpolynomial_cow(qp
);
2998 isl_assert(qp
->div
->ctx
, first
<= isl_space_dim(qp
->dim
, type
),
3001 g_pos
= pos(qp
->dim
, type
) + first
;
3003 qp
->div
= isl_mat_insert_zero_cols(qp
->div
, 2 + g_pos
, n
);
3007 total
= qp
->div
->n_col
- 2;
3008 if (total
> g_pos
) {
3010 exp
= isl_alloc_array(qp
->div
->ctx
, int, total
- g_pos
);
3013 for (i
= 0; i
< total
- g_pos
; ++i
)
3015 qp
->upoly
= expand(qp
->upoly
, exp
, g_pos
);
3021 qp
->dim
= isl_space_insert_dims(qp
->dim
, type
, first
, n
);
3027 isl_qpolynomial_free(qp
);
3031 __isl_give isl_qpolynomial
*isl_qpolynomial_add_dims(
3032 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
, unsigned n
)
3036 pos
= isl_qpolynomial_dim(qp
, type
);
3038 return isl_qpolynomial_insert_dims(qp
, type
, pos
, n
);
3041 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add_dims(
3042 __isl_take isl_pw_qpolynomial
*pwqp
,
3043 enum isl_dim_type type
, unsigned n
)
3047 pos
= isl_pw_qpolynomial_dim(pwqp
, type
);
3049 return isl_pw_qpolynomial_insert_dims(pwqp
, type
, pos
, n
);
3052 static int *reordering_move(isl_ctx
*ctx
,
3053 unsigned len
, unsigned dst
, unsigned src
, unsigned n
)
3058 reordering
= isl_alloc_array(ctx
, int, len
);
3063 for (i
= 0; i
< dst
; ++i
)
3065 for (i
= 0; i
< n
; ++i
)
3066 reordering
[src
+ i
] = dst
+ i
;
3067 for (i
= 0; i
< src
- dst
; ++i
)
3068 reordering
[dst
+ i
] = dst
+ n
+ i
;
3069 for (i
= 0; i
< len
- src
- n
; ++i
)
3070 reordering
[src
+ n
+ i
] = src
+ n
+ i
;
3072 for (i
= 0; i
< src
; ++i
)
3074 for (i
= 0; i
< n
; ++i
)
3075 reordering
[src
+ i
] = dst
+ i
;
3076 for (i
= 0; i
< dst
- src
; ++i
)
3077 reordering
[src
+ n
+ i
] = src
+ i
;
3078 for (i
= 0; i
< len
- dst
- n
; ++i
)
3079 reordering
[dst
+ n
+ i
] = dst
+ n
+ i
;
3085 __isl_give isl_qpolynomial
*isl_qpolynomial_move_dims(
3086 __isl_take isl_qpolynomial
*qp
,
3087 enum isl_dim_type dst_type
, unsigned dst_pos
,
3088 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
3097 qp
= isl_qpolynomial_cow(qp
);
3101 if (dst_type
== isl_dim_out
|| src_type
== isl_dim_out
)
3102 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
3103 "cannot move output/set dimension",
3105 if (dst_type
== isl_dim_in
)
3106 dst_type
= isl_dim_set
;
3107 if (src_type
== isl_dim_in
)
3108 src_type
= isl_dim_set
;
3110 isl_assert(qp
->dim
->ctx
, src_pos
+ n
<= isl_space_dim(qp
->dim
, src_type
),
3113 g_dst_pos
= pos(qp
->dim
, dst_type
) + dst_pos
;
3114 g_src_pos
= pos(qp
->dim
, src_type
) + src_pos
;
3115 if (dst_type
> src_type
)
3118 qp
->div
= isl_mat_move_cols(qp
->div
, 2 + g_dst_pos
, 2 + g_src_pos
, n
);
3125 reordering
= reordering_move(qp
->dim
->ctx
,
3126 qp
->div
->n_col
- 2, g_dst_pos
, g_src_pos
, n
);
3130 qp
->upoly
= reorder(qp
->upoly
, reordering
);
3135 qp
->dim
= isl_space_move_dims(qp
->dim
, dst_type
, dst_pos
, src_type
, src_pos
, n
);
3141 isl_qpolynomial_free(qp
);
3145 __isl_give isl_qpolynomial
*isl_qpolynomial_from_affine(__isl_take isl_space
*dim
,
3146 isl_int
*f
, isl_int denom
)
3148 struct isl_upoly
*up
;
3150 dim
= isl_space_domain(dim
);
3154 up
= isl_upoly_from_affine(dim
->ctx
, f
, denom
,
3155 1 + isl_space_dim(dim
, isl_dim_all
));
3157 return isl_qpolynomial_alloc(dim
, 0, up
);
3160 __isl_give isl_qpolynomial
*isl_qpolynomial_from_aff(__isl_take isl_aff
*aff
)
3163 struct isl_upoly
*up
;
3164 isl_qpolynomial
*qp
;
3169 ctx
= isl_aff_get_ctx(aff
);
3170 up
= isl_upoly_from_affine(ctx
, aff
->v
->el
+ 1, aff
->v
->el
[0],
3173 qp
= isl_qpolynomial_alloc(isl_aff_get_domain_space(aff
),
3174 aff
->ls
->div
->n_row
, up
);
3178 isl_mat_free(qp
->div
);
3179 qp
->div
= isl_mat_copy(aff
->ls
->div
);
3180 qp
->div
= isl_mat_cow(qp
->div
);
3185 qp
= reduce_divs(qp
);
3186 qp
= remove_redundant_divs(qp
);
3193 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_from_pw_aff(
3194 __isl_take isl_pw_aff
*pwaff
)
3197 isl_pw_qpolynomial
*pwqp
;
3202 pwqp
= isl_pw_qpolynomial_alloc_size(isl_pw_aff_get_space(pwaff
),
3205 for (i
= 0; i
< pwaff
->n
; ++i
) {
3207 isl_qpolynomial
*qp
;
3209 dom
= isl_set_copy(pwaff
->p
[i
].set
);
3210 qp
= isl_qpolynomial_from_aff(isl_aff_copy(pwaff
->p
[i
].aff
));
3211 pwqp
= isl_pw_qpolynomial_add_piece(pwqp
, dom
, qp
);
3214 isl_pw_aff_free(pwaff
);
3218 __isl_give isl_qpolynomial
*isl_qpolynomial_from_constraint(
3219 __isl_take isl_constraint
*c
, enum isl_dim_type type
, unsigned pos
)
3223 aff
= isl_constraint_get_bound(c
, type
, pos
);
3224 isl_constraint_free(c
);
3225 return isl_qpolynomial_from_aff(aff
);
3228 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3229 * in "qp" by subs[i].
3231 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute(
3232 __isl_take isl_qpolynomial
*qp
,
3233 enum isl_dim_type type
, unsigned first
, unsigned n
,
3234 __isl_keep isl_qpolynomial
**subs
)
3237 struct isl_upoly
**ups
;
3242 qp
= isl_qpolynomial_cow(qp
);
3246 if (type
== isl_dim_out
)
3247 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
3248 "cannot substitute output/set dimension",
3250 if (type
== isl_dim_in
)
3253 for (i
= 0; i
< n
; ++i
)
3257 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_space_dim(qp
->dim
, type
),
3260 for (i
= 0; i
< n
; ++i
)
3261 isl_assert(qp
->dim
->ctx
, isl_space_is_equal(qp
->dim
, subs
[i
]->dim
),
3264 isl_assert(qp
->dim
->ctx
, qp
->div
->n_row
== 0, goto error
);
3265 for (i
= 0; i
< n
; ++i
)
3266 isl_assert(qp
->dim
->ctx
, subs
[i
]->div
->n_row
== 0, goto error
);
3268 first
+= pos(qp
->dim
, type
);
3270 ups
= isl_alloc_array(qp
->dim
->ctx
, struct isl_upoly
*, n
);
3273 for (i
= 0; i
< n
; ++i
)
3274 ups
[i
] = subs
[i
]->upoly
;
3276 qp
->upoly
= isl_upoly_subs(qp
->upoly
, first
, n
, ups
);
3285 isl_qpolynomial_free(qp
);
3289 /* Extend "bset" with extra set dimensions for each integer division
3290 * in "qp" and then call "fn" with the extended bset and the polynomial
3291 * that results from replacing each of the integer divisions by the
3292 * corresponding extra set dimension.
3294 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial
*qp
,
3295 __isl_keep isl_basic_set
*bset
,
3296 int (*fn
)(__isl_take isl_basic_set
*bset
,
3297 __isl_take isl_qpolynomial
*poly
, void *user
), void *user
)
3301 isl_qpolynomial
*poly
;
3305 if (qp
->div
->n_row
== 0)
3306 return fn(isl_basic_set_copy(bset
), isl_qpolynomial_copy(qp
),
3309 div
= isl_mat_copy(qp
->div
);
3310 dim
= isl_space_copy(qp
->dim
);
3311 dim
= isl_space_add_dims(dim
, isl_dim_set
, qp
->div
->n_row
);
3312 poly
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_copy(qp
->upoly
));
3313 bset
= isl_basic_set_copy(bset
);
3314 bset
= isl_basic_set_add_dims(bset
, isl_dim_set
, qp
->div
->n_row
);
3315 bset
= add_div_constraints(bset
, div
);
3317 return fn(bset
, poly
, user
);
3322 /* Return total degree in variables first (inclusive) up to last (exclusive).
3324 int isl_upoly_degree(__isl_keep
struct isl_upoly
*up
, int first
, int last
)
3328 struct isl_upoly_rec
*rec
;
3332 if (isl_upoly_is_zero(up
))
3334 if (isl_upoly_is_cst(up
) || up
->var
< first
)
3337 rec
= isl_upoly_as_rec(up
);
3341 for (i
= 0; i
< rec
->n
; ++i
) {
3344 if (isl_upoly_is_zero(rec
->p
[i
]))
3346 d
= isl_upoly_degree(rec
->p
[i
], first
, last
);
3356 /* Return total degree in set variables.
3358 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial
*poly
)
3366 ovar
= isl_space_offset(poly
->dim
, isl_dim_set
);
3367 nvar
= isl_space_dim(poly
->dim
, isl_dim_set
);
3368 return isl_upoly_degree(poly
->upoly
, ovar
, ovar
+ nvar
);
3371 __isl_give
struct isl_upoly
*isl_upoly_coeff(__isl_keep
struct isl_upoly
*up
,
3372 unsigned pos
, int deg
)
3375 struct isl_upoly_rec
*rec
;
3380 if (isl_upoly_is_cst(up
) || up
->var
< pos
) {
3382 return isl_upoly_copy(up
);
3384 return isl_upoly_zero(up
->ctx
);
3387 rec
= isl_upoly_as_rec(up
);
3391 if (up
->var
== pos
) {
3393 return isl_upoly_copy(rec
->p
[deg
]);
3395 return isl_upoly_zero(up
->ctx
);
3398 up
= isl_upoly_copy(up
);
3399 up
= isl_upoly_cow(up
);
3400 rec
= isl_upoly_as_rec(up
);
3404 for (i
= 0; i
< rec
->n
; ++i
) {
3405 struct isl_upoly
*t
;
3406 t
= isl_upoly_coeff(rec
->p
[i
], pos
, deg
);
3409 isl_upoly_free(rec
->p
[i
]);
3419 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3421 __isl_give isl_qpolynomial
*isl_qpolynomial_coeff(
3422 __isl_keep isl_qpolynomial
*qp
,
3423 enum isl_dim_type type
, unsigned t_pos
, int deg
)
3426 struct isl_upoly
*up
;
3432 if (type
== isl_dim_out
)
3433 isl_die(qp
->div
->ctx
, isl_error_invalid
,
3434 "output/set dimension does not have a coefficient",
3436 if (type
== isl_dim_in
)
3439 isl_assert(qp
->div
->ctx
, t_pos
< isl_space_dim(qp
->dim
, type
),
3442 g_pos
= pos(qp
->dim
, type
) + t_pos
;
3443 up
= isl_upoly_coeff(qp
->upoly
, g_pos
, deg
);
3445 c
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
), qp
->div
->n_row
, up
);
3448 isl_mat_free(c
->div
);
3449 c
->div
= isl_mat_copy(qp
->div
);
3454 isl_qpolynomial_free(c
);
3458 /* Homogenize the polynomial in the variables first (inclusive) up to
3459 * last (exclusive) by inserting powers of variable first.
3460 * Variable first is assumed not to appear in the input.
3462 __isl_give
struct isl_upoly
*isl_upoly_homogenize(
3463 __isl_take
struct isl_upoly
*up
, int deg
, int target
,
3464 int first
, int last
)
3467 struct isl_upoly_rec
*rec
;
3471 if (isl_upoly_is_zero(up
))
3475 if (isl_upoly_is_cst(up
) || up
->var
< first
) {
3476 struct isl_upoly
*hom
;
3478 hom
= isl_upoly_var_pow(up
->ctx
, first
, target
- deg
);
3481 rec
= isl_upoly_as_rec(hom
);
3482 rec
->p
[target
- deg
] = isl_upoly_mul(rec
->p
[target
- deg
], up
);
3487 up
= isl_upoly_cow(up
);
3488 rec
= isl_upoly_as_rec(up
);
3492 for (i
= 0; i
< rec
->n
; ++i
) {
3493 if (isl_upoly_is_zero(rec
->p
[i
]))
3495 rec
->p
[i
] = isl_upoly_homogenize(rec
->p
[i
],
3496 up
->var
< last
? deg
+ i
: i
, target
,
3508 /* Homogenize the polynomial in the set variables by introducing
3509 * powers of an extra set variable at position 0.
3511 __isl_give isl_qpolynomial
*isl_qpolynomial_homogenize(
3512 __isl_take isl_qpolynomial
*poly
)
3516 int deg
= isl_qpolynomial_degree(poly
);
3521 poly
= isl_qpolynomial_insert_dims(poly
, isl_dim_in
, 0, 1);
3522 poly
= isl_qpolynomial_cow(poly
);
3526 ovar
= isl_space_offset(poly
->dim
, isl_dim_set
);
3527 nvar
= isl_space_dim(poly
->dim
, isl_dim_set
);
3528 poly
->upoly
= isl_upoly_homogenize(poly
->upoly
, 0, deg
,
3535 isl_qpolynomial_free(poly
);
3539 __isl_give isl_term
*isl_term_alloc(__isl_take isl_space
*dim
,
3540 __isl_take isl_mat
*div
)
3548 n
= isl_space_dim(dim
, isl_dim_all
) + div
->n_row
;
3550 term
= isl_calloc(dim
->ctx
, struct isl_term
,
3551 sizeof(struct isl_term
) + (n
- 1) * sizeof(int));
3558 isl_int_init(term
->n
);
3559 isl_int_init(term
->d
);
3563 isl_space_free(dim
);
3568 __isl_give isl_term
*isl_term_copy(__isl_keep isl_term
*term
)
3577 __isl_give isl_term
*isl_term_dup(__isl_keep isl_term
*term
)
3586 total
= isl_space_dim(term
->dim
, isl_dim_all
) + term
->div
->n_row
;
3588 dup
= isl_term_alloc(isl_space_copy(term
->dim
), isl_mat_copy(term
->div
));
3592 isl_int_set(dup
->n
, term
->n
);
3593 isl_int_set(dup
->d
, term
->d
);
3595 for (i
= 0; i
< total
; ++i
)
3596 dup
->pow
[i
] = term
->pow
[i
];
3601 __isl_give isl_term
*isl_term_cow(__isl_take isl_term
*term
)
3609 return isl_term_dup(term
);
3612 void isl_term_free(__isl_take isl_term
*term
)
3617 if (--term
->ref
> 0)
3620 isl_space_free(term
->dim
);
3621 isl_mat_free(term
->div
);
3622 isl_int_clear(term
->n
);
3623 isl_int_clear(term
->d
);
3627 unsigned isl_term_dim(__isl_keep isl_term
*term
, enum isl_dim_type type
)
3635 case isl_dim_out
: return isl_space_dim(term
->dim
, type
);
3636 case isl_dim_div
: return term
->div
->n_row
;
3637 case isl_dim_all
: return isl_space_dim(term
->dim
, isl_dim_all
) +
3643 isl_ctx
*isl_term_get_ctx(__isl_keep isl_term
*term
)
3645 return term
? term
->dim
->ctx
: NULL
;
3648 void isl_term_get_num(__isl_keep isl_term
*term
, isl_int
*n
)
3652 isl_int_set(*n
, term
->n
);
3655 void isl_term_get_den(__isl_keep isl_term
*term
, isl_int
*d
)
3659 isl_int_set(*d
, term
->d
);
3662 /* Return the coefficient of the term "term".
3664 __isl_give isl_val
*isl_term_get_coefficient_val(__isl_keep isl_term
*term
)
3669 return isl_val_rat_from_isl_int(isl_term_get_ctx(term
),
3673 int isl_term_get_exp(__isl_keep isl_term
*term
,
3674 enum isl_dim_type type
, unsigned pos
)
3679 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, type
), return -1);
3681 if (type
>= isl_dim_set
)
3682 pos
+= isl_space_dim(term
->dim
, isl_dim_param
);
3683 if (type
>= isl_dim_div
)
3684 pos
+= isl_space_dim(term
->dim
, isl_dim_set
);
3686 return term
->pow
[pos
];
3689 __isl_give isl_aff
*isl_term_get_div(__isl_keep isl_term
*term
, unsigned pos
)
3691 isl_local_space
*ls
;
3697 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, isl_dim_div
),
3700 ls
= isl_local_space_alloc_div(isl_space_copy(term
->dim
),
3701 isl_mat_copy(term
->div
));
3702 aff
= isl_aff_alloc(ls
);
3706 isl_seq_cpy(aff
->v
->el
, term
->div
->row
[pos
], aff
->v
->size
);
3708 aff
= isl_aff_normalize(aff
);
3713 __isl_give isl_term
*isl_upoly_foreach_term(__isl_keep
struct isl_upoly
*up
,
3714 int (*fn
)(__isl_take isl_term
*term
, void *user
),
3715 __isl_take isl_term
*term
, void *user
)
3718 struct isl_upoly_rec
*rec
;
3723 if (isl_upoly_is_zero(up
))
3726 isl_assert(up
->ctx
, !isl_upoly_is_nan(up
), goto error
);
3727 isl_assert(up
->ctx
, !isl_upoly_is_infty(up
), goto error
);
3728 isl_assert(up
->ctx
, !isl_upoly_is_neginfty(up
), goto error
);
3730 if (isl_upoly_is_cst(up
)) {
3731 struct isl_upoly_cst
*cst
;
3732 cst
= isl_upoly_as_cst(up
);
3735 term
= isl_term_cow(term
);
3738 isl_int_set(term
->n
, cst
->n
);
3739 isl_int_set(term
->d
, cst
->d
);
3740 if (fn(isl_term_copy(term
), user
) < 0)
3745 rec
= isl_upoly_as_rec(up
);
3749 for (i
= 0; i
< rec
->n
; ++i
) {
3750 term
= isl_term_cow(term
);
3753 term
->pow
[up
->var
] = i
;
3754 term
= isl_upoly_foreach_term(rec
->p
[i
], fn
, term
, user
);
3758 term
->pow
[up
->var
] = 0;
3762 isl_term_free(term
);
3766 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial
*qp
,
3767 int (*fn
)(__isl_take isl_term
*term
, void *user
), void *user
)
3774 term
= isl_term_alloc(isl_space_copy(qp
->dim
), isl_mat_copy(qp
->div
));
3778 term
= isl_upoly_foreach_term(qp
->upoly
, fn
, term
, user
);
3780 isl_term_free(term
);
3782 return term
? 0 : -1;
3785 __isl_give isl_qpolynomial
*isl_qpolynomial_from_term(__isl_take isl_term
*term
)
3787 struct isl_upoly
*up
;
3788 isl_qpolynomial
*qp
;
3794 n
= isl_space_dim(term
->dim
, isl_dim_all
) + term
->div
->n_row
;
3796 up
= isl_upoly_rat_cst(term
->dim
->ctx
, term
->n
, term
->d
);
3797 for (i
= 0; i
< n
; ++i
) {
3800 up
= isl_upoly_mul(up
,
3801 isl_upoly_var_pow(term
->dim
->ctx
, i
, term
->pow
[i
]));
3804 qp
= isl_qpolynomial_alloc(isl_space_copy(term
->dim
), term
->div
->n_row
, up
);
3807 isl_mat_free(qp
->div
);
3808 qp
->div
= isl_mat_copy(term
->div
);
3812 isl_term_free(term
);
3815 isl_qpolynomial_free(qp
);
3816 isl_term_free(term
);
3820 __isl_give isl_qpolynomial
*isl_qpolynomial_lift(__isl_take isl_qpolynomial
*qp
,
3821 __isl_take isl_space
*dim
)
3830 if (isl_space_is_equal(qp
->dim
, dim
)) {
3831 isl_space_free(dim
);
3835 qp
= isl_qpolynomial_cow(qp
);
3839 extra
= isl_space_dim(dim
, isl_dim_set
) -
3840 isl_space_dim(qp
->dim
, isl_dim_set
);
3841 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
3842 if (qp
->div
->n_row
) {
3845 exp
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
3848 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3850 qp
->upoly
= expand(qp
->upoly
, exp
, total
);
3855 qp
->div
= isl_mat_insert_cols(qp
->div
, 2 + total
, extra
);
3858 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3859 isl_seq_clr(qp
->div
->row
[i
] + 2 + total
, extra
);
3861 isl_space_free(qp
->dim
);
3866 isl_space_free(dim
);
3867 isl_qpolynomial_free(qp
);
3871 /* For each parameter or variable that does not appear in qp,
3872 * first eliminate the variable from all constraints and then set it to zero.
3874 static __isl_give isl_set
*fix_inactive(__isl_take isl_set
*set
,
3875 __isl_keep isl_qpolynomial
*qp
)
3886 d
= isl_space_dim(set
->dim
, isl_dim_all
);
3887 active
= isl_calloc_array(set
->ctx
, int, d
);
3888 if (set_active(qp
, active
) < 0)
3891 for (i
= 0; i
< d
; ++i
)
3900 nparam
= isl_space_dim(set
->dim
, isl_dim_param
);
3901 nvar
= isl_space_dim(set
->dim
, isl_dim_set
);
3902 for (i
= 0; i
< nparam
; ++i
) {
3905 set
= isl_set_eliminate(set
, isl_dim_param
, i
, 1);
3906 set
= isl_set_fix_si(set
, isl_dim_param
, i
, 0);
3908 for (i
= 0; i
< nvar
; ++i
) {
3909 if (active
[nparam
+ i
])
3911 set
= isl_set_eliminate(set
, isl_dim_set
, i
, 1);
3912 set
= isl_set_fix_si(set
, isl_dim_set
, i
, 0);
3924 struct isl_opt_data
{
3925 isl_qpolynomial
*qp
;
3931 static int opt_fn(__isl_take isl_point
*pnt
, void *user
)
3933 struct isl_opt_data
*data
= (struct isl_opt_data
*)user
;
3936 val
= isl_qpolynomial_eval(isl_qpolynomial_copy(data
->qp
), pnt
);
3940 } else if (data
->max
) {
3941 data
->opt
= isl_val_max(data
->opt
, val
);
3943 data
->opt
= isl_val_min(data
->opt
, val
);
3949 __isl_give isl_val
*isl_qpolynomial_opt_on_domain(
3950 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*set
, int max
)
3952 struct isl_opt_data data
= { NULL
, 1, NULL
, max
};
3957 if (isl_upoly_is_cst(qp
->upoly
)) {
3959 data
.opt
= isl_qpolynomial_get_constant_val(qp
);
3960 isl_qpolynomial_free(qp
);
3964 set
= fix_inactive(set
, qp
);
3967 if (isl_set_foreach_point(set
, opt_fn
, &data
) < 0)
3971 data
.opt
= isl_val_zero(isl_set_get_ctx(set
));
3974 isl_qpolynomial_free(qp
);
3978 isl_qpolynomial_free(qp
);
3979 isl_val_free(data
.opt
);
3983 __isl_give isl_qpolynomial
*isl_qpolynomial_morph_domain(
3984 __isl_take isl_qpolynomial
*qp
, __isl_take isl_morph
*morph
)
3989 struct isl_upoly
**subs
;
3990 isl_mat
*mat
, *diag
;
3992 qp
= isl_qpolynomial_cow(qp
);
3997 isl_assert(ctx
, isl_space_is_equal(qp
->dim
, morph
->dom
->dim
), goto error
);
3999 n_sub
= morph
->inv
->n_row
- 1;
4000 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
4001 n_sub
+= qp
->div
->n_row
;
4002 subs
= isl_calloc_array(ctx
, struct isl_upoly
*, n_sub
);
4006 for (i
= 0; 1 + i
< morph
->inv
->n_row
; ++i
)
4007 subs
[i
] = isl_upoly_from_affine(ctx
, morph
->inv
->row
[1 + i
],
4008 morph
->inv
->row
[0][0], morph
->inv
->n_col
);
4009 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
4010 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4011 subs
[morph
->inv
->n_row
- 1 + i
] =
4012 isl_upoly_var_pow(ctx
, morph
->inv
->n_col
- 1 + i
, 1);
4014 qp
->upoly
= isl_upoly_subs(qp
->upoly
, 0, n_sub
, subs
);
4016 for (i
= 0; i
< n_sub
; ++i
)
4017 isl_upoly_free(subs
[i
]);
4020 diag
= isl_mat_diag(ctx
, 1, morph
->inv
->row
[0][0]);
4021 mat
= isl_mat_diagonal(diag
, isl_mat_copy(morph
->inv
));
4022 diag
= isl_mat_diag(ctx
, qp
->div
->n_row
, morph
->inv
->row
[0][0]);
4023 mat
= isl_mat_diagonal(mat
, diag
);
4024 qp
->div
= isl_mat_product(qp
->div
, mat
);
4025 isl_space_free(qp
->dim
);
4026 qp
->dim
= isl_space_copy(morph
->ran
->dim
);
4028 if (!qp
->upoly
|| !qp
->div
|| !qp
->dim
)
4031 isl_morph_free(morph
);
4035 isl_qpolynomial_free(qp
);
4036 isl_morph_free(morph
);
4040 static int neg_entry(void **entry
, void *user
)
4042 isl_pw_qpolynomial
**pwqp
= (isl_pw_qpolynomial
**)entry
;
4044 *pwqp
= isl_pw_qpolynomial_neg(*pwqp
);
4046 return *pwqp
? 0 : -1;
4049 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_neg(
4050 __isl_take isl_union_pw_qpolynomial
*upwqp
)
4052 upwqp
= isl_union_pw_qpolynomial_cow(upwqp
);
4056 if (isl_hash_table_foreach(upwqp
->dim
->ctx
, &upwqp
->table
,
4057 &neg_entry
, NULL
) < 0)
4062 isl_union_pw_qpolynomial_free(upwqp
);
4066 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_mul(
4067 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
4068 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
4070 return match_bin_op(upwqp1
, upwqp2
, &isl_pw_qpolynomial_mul
);
4073 /* Reorder the columns of the given div definitions according to the
4076 static __isl_give isl_mat
*reorder_divs(__isl_take isl_mat
*div
,
4077 __isl_take isl_reordering
*r
)
4086 extra
= isl_space_dim(r
->dim
, isl_dim_all
) + div
->n_row
- r
->len
;
4087 mat
= isl_mat_alloc(div
->ctx
, div
->n_row
, div
->n_col
+ extra
);
4091 for (i
= 0; i
< div
->n_row
; ++i
) {
4092 isl_seq_cpy(mat
->row
[i
], div
->row
[i
], 2);
4093 isl_seq_clr(mat
->row
[i
] + 2, mat
->n_col
- 2);
4094 for (j
= 0; j
< r
->len
; ++j
)
4095 isl_int_set(mat
->row
[i
][2 + r
->pos
[j
]],
4096 div
->row
[i
][2 + j
]);
4099 isl_reordering_free(r
);
4103 isl_reordering_free(r
);
4108 /* Reorder the dimension of "qp" according to the given reordering.
4110 __isl_give isl_qpolynomial
*isl_qpolynomial_realign_domain(
4111 __isl_take isl_qpolynomial
*qp
, __isl_take isl_reordering
*r
)
4113 qp
= isl_qpolynomial_cow(qp
);
4117 r
= isl_reordering_extend(r
, qp
->div
->n_row
);
4121 qp
->div
= reorder_divs(qp
->div
, isl_reordering_copy(r
));
4125 qp
->upoly
= reorder(qp
->upoly
, r
->pos
);
4129 qp
= isl_qpolynomial_reset_domain_space(qp
, isl_space_copy(r
->dim
));
4131 isl_reordering_free(r
);
4134 isl_qpolynomial_free(qp
);
4135 isl_reordering_free(r
);
4139 __isl_give isl_qpolynomial
*isl_qpolynomial_align_params(
4140 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*model
)
4145 if (!isl_space_match(qp
->dim
, isl_dim_param
, model
, isl_dim_param
)) {
4146 isl_reordering
*exp
;
4148 model
= isl_space_drop_dims(model
, isl_dim_in
,
4149 0, isl_space_dim(model
, isl_dim_in
));
4150 model
= isl_space_drop_dims(model
, isl_dim_out
,
4151 0, isl_space_dim(model
, isl_dim_out
));
4152 exp
= isl_parameter_alignment_reordering(qp
->dim
, model
);
4153 exp
= isl_reordering_extend_space(exp
,
4154 isl_qpolynomial_get_domain_space(qp
));
4155 qp
= isl_qpolynomial_realign_domain(qp
, exp
);
4158 isl_space_free(model
);
4161 isl_space_free(model
);
4162 isl_qpolynomial_free(qp
);
4166 struct isl_split_periods_data
{
4168 isl_pw_qpolynomial
*res
;
4171 /* Create a slice where the integer division "div" has the fixed value "v".
4172 * In particular, if "div" refers to floor(f/m), then create a slice
4174 * m v <= f <= m v + (m - 1)
4179 * -f + m v + (m - 1) >= 0
4181 static __isl_give isl_set
*set_div_slice(__isl_take isl_space
*dim
,
4182 __isl_keep isl_qpolynomial
*qp
, int div
, isl_int v
)
4185 isl_basic_set
*bset
= NULL
;
4191 total
= isl_space_dim(dim
, isl_dim_all
);
4192 bset
= isl_basic_set_alloc_space(isl_space_copy(dim
), 0, 0, 2);
4194 k
= isl_basic_set_alloc_inequality(bset
);
4197 isl_seq_cpy(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4198 isl_int_submul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4200 k
= isl_basic_set_alloc_inequality(bset
);
4203 isl_seq_neg(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4204 isl_int_addmul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4205 isl_int_add(bset
->ineq
[k
][0], bset
->ineq
[k
][0], qp
->div
->row
[div
][0]);
4206 isl_int_sub_ui(bset
->ineq
[k
][0], bset
->ineq
[k
][0], 1);
4208 isl_space_free(dim
);
4209 return isl_set_from_basic_set(bset
);
4211 isl_basic_set_free(bset
);
4212 isl_space_free(dim
);
4216 static int split_periods(__isl_take isl_set
*set
,
4217 __isl_take isl_qpolynomial
*qp
, void *user
);
4219 /* Create a slice of the domain "set" such that integer division "div"
4220 * has the fixed value "v" and add the results to data->res,
4221 * replacing the integer division by "v" in "qp".
4223 static int set_div(__isl_take isl_set
*set
,
4224 __isl_take isl_qpolynomial
*qp
, int div
, isl_int v
,
4225 struct isl_split_periods_data
*data
)
4230 struct isl_upoly
*cst
;
4232 slice
= set_div_slice(isl_set_get_space(set
), qp
, div
, v
);
4233 set
= isl_set_intersect(set
, slice
);
4238 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4240 for (i
= div
+ 1; i
< qp
->div
->n_row
; ++i
) {
4241 if (isl_int_is_zero(qp
->div
->row
[i
][2 + total
+ div
]))
4243 isl_int_addmul(qp
->div
->row
[i
][1],
4244 qp
->div
->row
[i
][2 + total
+ div
], v
);
4245 isl_int_set_si(qp
->div
->row
[i
][2 + total
+ div
], 0);
4248 cst
= isl_upoly_rat_cst(qp
->dim
->ctx
, v
, qp
->dim
->ctx
->one
);
4249 qp
= substitute_div(qp
, div
, cst
);
4251 return split_periods(set
, qp
, data
);
4254 isl_qpolynomial_free(qp
);
4258 /* Split the domain "set" such that integer division "div"
4259 * has a fixed value (ranging from "min" to "max") on each slice
4260 * and add the results to data->res.
4262 static int split_div(__isl_take isl_set
*set
,
4263 __isl_take isl_qpolynomial
*qp
, int div
, isl_int min
, isl_int max
,
4264 struct isl_split_periods_data
*data
)
4266 for (; isl_int_le(min
, max
); isl_int_add_ui(min
, min
, 1)) {
4267 isl_set
*set_i
= isl_set_copy(set
);
4268 isl_qpolynomial
*qp_i
= isl_qpolynomial_copy(qp
);
4270 if (set_div(set_i
, qp_i
, div
, min
, data
) < 0)
4274 isl_qpolynomial_free(qp
);
4278 isl_qpolynomial_free(qp
);
4282 /* If "qp" refers to any integer division
4283 * that can only attain "max_periods" distinct values on "set"
4284 * then split the domain along those distinct values.
4285 * Add the results (or the original if no splitting occurs)
4288 static int split_periods(__isl_take isl_set
*set
,
4289 __isl_take isl_qpolynomial
*qp
, void *user
)
4292 isl_pw_qpolynomial
*pwqp
;
4293 struct isl_split_periods_data
*data
;
4298 data
= (struct isl_split_periods_data
*)user
;
4303 if (qp
->div
->n_row
== 0) {
4304 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4305 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4311 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4312 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4313 enum isl_lp_result lp_res
;
4315 if (isl_seq_first_non_zero(qp
->div
->row
[i
] + 2 + total
,
4316 qp
->div
->n_row
) != -1)
4319 lp_res
= isl_set_solve_lp(set
, 0, qp
->div
->row
[i
] + 1,
4320 set
->ctx
->one
, &min
, NULL
, NULL
);
4321 if (lp_res
== isl_lp_error
)
4323 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4325 isl_int_fdiv_q(min
, min
, qp
->div
->row
[i
][0]);
4327 lp_res
= isl_set_solve_lp(set
, 1, qp
->div
->row
[i
] + 1,
4328 set
->ctx
->one
, &max
, NULL
, NULL
);
4329 if (lp_res
== isl_lp_error
)
4331 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4333 isl_int_fdiv_q(max
, max
, qp
->div
->row
[i
][0]);
4335 isl_int_sub(max
, max
, min
);
4336 if (isl_int_cmp_si(max
, data
->max_periods
) < 0) {
4337 isl_int_add(max
, max
, min
);
4342 if (i
< qp
->div
->n_row
) {
4343 r
= split_div(set
, qp
, i
, min
, max
, data
);
4345 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4346 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4358 isl_qpolynomial_free(qp
);
4362 /* If any quasi-polynomial in pwqp refers to any integer division
4363 * that can only attain "max_periods" distinct values on its domain
4364 * then split the domain along those distinct values.
4366 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_split_periods(
4367 __isl_take isl_pw_qpolynomial
*pwqp
, int max_periods
)
4369 struct isl_split_periods_data data
;
4371 data
.max_periods
= max_periods
;
4372 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp
));
4374 if (isl_pw_qpolynomial_foreach_piece(pwqp
, &split_periods
, &data
) < 0)
4377 isl_pw_qpolynomial_free(pwqp
);
4381 isl_pw_qpolynomial_free(data
.res
);
4382 isl_pw_qpolynomial_free(pwqp
);
4386 /* Construct a piecewise quasipolynomial that is constant on the given
4387 * domain. In particular, it is
4390 * infinity if cst == -1
4392 static __isl_give isl_pw_qpolynomial
*constant_on_domain(
4393 __isl_take isl_basic_set
*bset
, int cst
)
4396 isl_qpolynomial
*qp
;
4401 bset
= isl_basic_set_params(bset
);
4402 dim
= isl_basic_set_get_space(bset
);
4404 qp
= isl_qpolynomial_infty_on_domain(dim
);
4406 qp
= isl_qpolynomial_zero_on_domain(dim
);
4408 qp
= isl_qpolynomial_one_on_domain(dim
);
4409 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset
), qp
);
4412 /* Factor bset, call fn on each of the factors and return the product.
4414 * If no factors can be found, simply call fn on the input.
4415 * Otherwise, construct the factors based on the factorizer,
4416 * call fn on each factor and compute the product.
4418 static __isl_give isl_pw_qpolynomial
*compressed_multiplicative_call(
4419 __isl_take isl_basic_set
*bset
,
4420 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4426 isl_qpolynomial
*qp
;
4427 isl_pw_qpolynomial
*pwqp
;
4431 f
= isl_basic_set_factorizer(bset
);
4434 if (f
->n_group
== 0) {
4435 isl_factorizer_free(f
);
4439 nparam
= isl_basic_set_dim(bset
, isl_dim_param
);
4440 nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
4442 dim
= isl_basic_set_get_space(bset
);
4443 dim
= isl_space_domain(dim
);
4444 set
= isl_set_universe(isl_space_copy(dim
));
4445 qp
= isl_qpolynomial_one_on_domain(dim
);
4446 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4448 bset
= isl_morph_basic_set(isl_morph_copy(f
->morph
), bset
);
4450 for (i
= 0, n
= 0; i
< f
->n_group
; ++i
) {
4451 isl_basic_set
*bset_i
;
4452 isl_pw_qpolynomial
*pwqp_i
;
4454 bset_i
= isl_basic_set_copy(bset
);
4455 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4456 nparam
+ n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4457 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4459 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
,
4460 n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4461 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
, 0, n
);
4463 pwqp_i
= fn(bset_i
);
4464 pwqp
= isl_pw_qpolynomial_mul(pwqp
, pwqp_i
);
4469 isl_basic_set_free(bset
);
4470 isl_factorizer_free(f
);
4474 isl_basic_set_free(bset
);
4478 /* Factor bset, call fn on each of the factors and return the product.
4479 * The function is assumed to evaluate to zero on empty domains,
4480 * to one on zero-dimensional domains and to infinity on unbounded domains
4481 * and will not be called explicitly on zero-dimensional or unbounded domains.
4483 * We first check for some special cases and remove all equalities.
4484 * Then we hand over control to compressed_multiplicative_call.
4486 __isl_give isl_pw_qpolynomial
*isl_basic_set_multiplicative_call(
4487 __isl_take isl_basic_set
*bset
,
4488 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4492 isl_pw_qpolynomial
*pwqp
;
4497 if (isl_basic_set_plain_is_empty(bset
))
4498 return constant_on_domain(bset
, 0);
4500 if (isl_basic_set_dim(bset
, isl_dim_set
) == 0)
4501 return constant_on_domain(bset
, 1);
4503 bounded
= isl_basic_set_is_bounded(bset
);
4507 return constant_on_domain(bset
, -1);
4509 if (bset
->n_eq
== 0)
4510 return compressed_multiplicative_call(bset
, fn
);
4512 morph
= isl_basic_set_full_compression(bset
);
4513 bset
= isl_morph_basic_set(isl_morph_copy(morph
), bset
);
4515 pwqp
= compressed_multiplicative_call(bset
, fn
);
4517 morph
= isl_morph_dom_params(morph
);
4518 morph
= isl_morph_ran_params(morph
);
4519 morph
= isl_morph_inverse(morph
);
4521 pwqp
= isl_pw_qpolynomial_morph_domain(pwqp
, morph
);
4525 isl_basic_set_free(bset
);
4529 /* Drop all floors in "qp", turning each integer division [a/m] into
4530 * a rational division a/m. If "down" is set, then the integer division
4531 * is replaced by (a-(m-1))/m instead.
4533 static __isl_give isl_qpolynomial
*qp_drop_floors(
4534 __isl_take isl_qpolynomial
*qp
, int down
)
4537 struct isl_upoly
*s
;
4541 if (qp
->div
->n_row
== 0)
4544 qp
= isl_qpolynomial_cow(qp
);
4548 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
4550 isl_int_sub(qp
->div
->row
[i
][1],
4551 qp
->div
->row
[i
][1], qp
->div
->row
[i
][0]);
4552 isl_int_add_ui(qp
->div
->row
[i
][1],
4553 qp
->div
->row
[i
][1], 1);
4555 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
4556 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
4557 qp
= substitute_div(qp
, i
, s
);
4565 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4566 * a rational division a/m.
4568 static __isl_give isl_pw_qpolynomial
*pwqp_drop_floors(
4569 __isl_take isl_pw_qpolynomial
*pwqp
)
4576 if (isl_pw_qpolynomial_is_zero(pwqp
))
4579 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
4583 for (i
= 0; i
< pwqp
->n
; ++i
) {
4584 pwqp
->p
[i
].qp
= qp_drop_floors(pwqp
->p
[i
].qp
, 0);
4591 isl_pw_qpolynomial_free(pwqp
);
4595 /* Adjust all the integer divisions in "qp" such that they are at least
4596 * one over the given orthant (identified by "signs"). This ensures
4597 * that they will still be non-negative even after subtracting (m-1)/m.
4599 * In particular, f is replaced by f' + v, changing f = [a/m]
4600 * to f' = [(a - m v)/m].
4601 * If the constant term k in a is smaller than m,
4602 * the constant term of v is set to floor(k/m) - 1.
4603 * For any other term, if the coefficient c and the variable x have
4604 * the same sign, then no changes are needed.
4605 * Otherwise, if the variable is positive (and c is negative),
4606 * then the coefficient of x in v is set to floor(c/m).
4607 * If the variable is negative (and c is positive),
4608 * then the coefficient of x in v is set to ceil(c/m).
4610 static __isl_give isl_qpolynomial
*make_divs_pos(__isl_take isl_qpolynomial
*qp
,
4616 struct isl_upoly
*s
;
4618 qp
= isl_qpolynomial_cow(qp
);
4621 qp
->div
= isl_mat_cow(qp
->div
);
4625 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4626 v
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
4628 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4629 isl_int
*row
= qp
->div
->row
[i
];
4633 if (isl_int_lt(row
[1], row
[0])) {
4634 isl_int_fdiv_q(v
->el
[0], row
[1], row
[0]);
4635 isl_int_sub_ui(v
->el
[0], v
->el
[0], 1);
4636 isl_int_submul(row
[1], row
[0], v
->el
[0]);
4638 for (j
= 0; j
< total
; ++j
) {
4639 if (isl_int_sgn(row
[2 + j
]) * signs
[j
] >= 0)
4642 isl_int_cdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4644 isl_int_fdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4645 isl_int_submul(row
[2 + j
], row
[0], v
->el
[1 + j
]);
4647 for (j
= 0; j
< i
; ++j
) {
4648 if (isl_int_sgn(row
[2 + total
+ j
]) >= 0)
4650 isl_int_fdiv_q(v
->el
[1 + total
+ j
],
4651 row
[2 + total
+ j
], row
[0]);
4652 isl_int_submul(row
[2 + total
+ j
],
4653 row
[0], v
->el
[1 + total
+ j
]);
4655 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
4656 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
4658 isl_seq_combine(qp
->div
->row
[j
] + 1,
4659 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
4660 qp
->div
->row
[j
][2 + total
+ i
], v
->el
, v
->size
);
4662 isl_int_set_si(v
->el
[1 + total
+ i
], 1);
4663 s
= isl_upoly_from_affine(qp
->dim
->ctx
, v
->el
,
4664 qp
->div
->ctx
->one
, v
->size
);
4665 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ i
, 1, &s
);
4675 isl_qpolynomial_free(qp
);
4679 struct isl_to_poly_data
{
4681 isl_pw_qpolynomial
*res
;
4682 isl_qpolynomial
*qp
;
4685 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4686 * We first make all integer divisions positive and then split the
4687 * quasipolynomials into terms with sign data->sign (the direction
4688 * of the requested approximation) and terms with the opposite sign.
4689 * In the first set of terms, each integer division [a/m] is
4690 * overapproximated by a/m, while in the second it is underapproximated
4693 static int to_polynomial_on_orthant(__isl_take isl_set
*orthant
, int *signs
,
4696 struct isl_to_poly_data
*data
= user
;
4697 isl_pw_qpolynomial
*t
;
4698 isl_qpolynomial
*qp
, *up
, *down
;
4700 qp
= isl_qpolynomial_copy(data
->qp
);
4701 qp
= make_divs_pos(qp
, signs
);
4703 up
= isl_qpolynomial_terms_of_sign(qp
, signs
, data
->sign
);
4704 up
= qp_drop_floors(up
, 0);
4705 down
= isl_qpolynomial_terms_of_sign(qp
, signs
, -data
->sign
);
4706 down
= qp_drop_floors(down
, 1);
4708 isl_qpolynomial_free(qp
);
4709 qp
= isl_qpolynomial_add(up
, down
);
4711 t
= isl_pw_qpolynomial_alloc(orthant
, qp
);
4712 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, t
);
4717 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4718 * the polynomial will be an overapproximation. If "sign" is negative,
4719 * it will be an underapproximation. If "sign" is zero, the approximation
4720 * will lie somewhere in between.
4722 * In particular, is sign == 0, we simply drop the floors, turning
4723 * the integer divisions into rational divisions.
4724 * Otherwise, we split the domains into orthants, make all integer divisions
4725 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4726 * depending on the requested sign and the sign of the term in which
4727 * the integer division appears.
4729 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_to_polynomial(
4730 __isl_take isl_pw_qpolynomial
*pwqp
, int sign
)
4733 struct isl_to_poly_data data
;
4736 return pwqp_drop_floors(pwqp
);
4742 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp
));
4744 for (i
= 0; i
< pwqp
->n
; ++i
) {
4745 if (pwqp
->p
[i
].qp
->div
->n_row
== 0) {
4746 isl_pw_qpolynomial
*t
;
4747 t
= isl_pw_qpolynomial_alloc(
4748 isl_set_copy(pwqp
->p
[i
].set
),
4749 isl_qpolynomial_copy(pwqp
->p
[i
].qp
));
4750 data
.res
= isl_pw_qpolynomial_add_disjoint(data
.res
, t
);
4753 data
.qp
= pwqp
->p
[i
].qp
;
4754 if (isl_set_foreach_orthant(pwqp
->p
[i
].set
,
4755 &to_polynomial_on_orthant
, &data
) < 0)
4759 isl_pw_qpolynomial_free(pwqp
);
4763 isl_pw_qpolynomial_free(pwqp
);
4764 isl_pw_qpolynomial_free(data
.res
);
4768 static int poly_entry(void **entry
, void *user
)
4771 isl_pw_qpolynomial
**pwqp
= (isl_pw_qpolynomial
**)entry
;
4773 *pwqp
= isl_pw_qpolynomial_to_polynomial(*pwqp
, *sign
);
4775 return *pwqp
? 0 : -1;
4778 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_to_polynomial(
4779 __isl_take isl_union_pw_qpolynomial
*upwqp
, int sign
)
4781 upwqp
= isl_union_pw_qpolynomial_cow(upwqp
);
4785 if (isl_hash_table_foreach(upwqp
->dim
->ctx
, &upwqp
->table
,
4786 &poly_entry
, &sign
) < 0)
4791 isl_union_pw_qpolynomial_free(upwqp
);
4795 __isl_give isl_basic_map
*isl_basic_map_from_qpolynomial(
4796 __isl_take isl_qpolynomial
*qp
)
4800 isl_vec
*aff
= NULL
;
4801 isl_basic_map
*bmap
= NULL
;
4807 if (!isl_upoly_is_affine(qp
->upoly
))
4808 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
4809 "input quasi-polynomial not affine", goto error
);
4810 aff
= isl_qpolynomial_extract_affine(qp
);
4813 dim
= isl_qpolynomial_get_space(qp
);
4814 pos
= 1 + isl_space_offset(dim
, isl_dim_out
);
4815 n_div
= qp
->div
->n_row
;
4816 bmap
= isl_basic_map_alloc_space(dim
, n_div
, 1, 2 * n_div
);
4818 for (i
= 0; i
< n_div
; ++i
) {
4819 k
= isl_basic_map_alloc_div(bmap
);
4822 isl_seq_cpy(bmap
->div
[k
], qp
->div
->row
[i
], qp
->div
->n_col
);
4823 isl_int_set_si(bmap
->div
[k
][qp
->div
->n_col
], 0);
4824 if (isl_basic_map_add_div_constraints(bmap
, k
) < 0)
4827 k
= isl_basic_map_alloc_equality(bmap
);
4830 isl_int_neg(bmap
->eq
[k
][pos
], aff
->el
[0]);
4831 isl_seq_cpy(bmap
->eq
[k
], aff
->el
+ 1, pos
);
4832 isl_seq_cpy(bmap
->eq
[k
] + pos
+ 1, aff
->el
+ 1 + pos
, n_div
);
4835 isl_qpolynomial_free(qp
);
4836 bmap
= isl_basic_map_finalize(bmap
);
4840 isl_qpolynomial_free(qp
);
4841 isl_basic_map_free(bmap
);