2 * Copyright 2010 INRIA Saclay
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
7 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
12 #include <isl_ctx_private.h>
13 #include <isl_map_private.h>
14 #include <isl_factorization.h>
17 #include <isl_union_map_private.h>
18 #include <isl_polynomial_private.h>
19 #include <isl_point_private.h>
20 #include <isl_dim_private.h>
21 #include <isl_div_private.h>
22 #include <isl_mat_private.h>
23 #include <isl_range.h>
24 #include <isl_local_space_private.h>
25 #include <isl_aff_private.h>
27 static unsigned pos(__isl_keep isl_dim
*dim
, enum isl_dim_type type
)
30 case isl_dim_param
: return 0;
31 case isl_dim_in
: return dim
->nparam
;
32 case isl_dim_out
: return dim
->nparam
+ dim
->n_in
;
37 int isl_upoly_is_cst(__isl_keep
struct isl_upoly
*up
)
45 __isl_keep
struct isl_upoly_cst
*isl_upoly_as_cst(__isl_keep
struct isl_upoly
*up
)
50 isl_assert(up
->ctx
, up
->var
< 0, return NULL
);
52 return (struct isl_upoly_cst
*)up
;
55 __isl_keep
struct isl_upoly_rec
*isl_upoly_as_rec(__isl_keep
struct isl_upoly
*up
)
60 isl_assert(up
->ctx
, up
->var
>= 0, return NULL
);
62 return (struct isl_upoly_rec
*)up
;
65 int isl_upoly_is_equal(__isl_keep
struct isl_upoly
*up1
,
66 __isl_keep
struct isl_upoly
*up2
)
69 struct isl_upoly_rec
*rec1
, *rec2
;
75 if (up1
->var
!= up2
->var
)
77 if (isl_upoly_is_cst(up1
)) {
78 struct isl_upoly_cst
*cst1
, *cst2
;
79 cst1
= isl_upoly_as_cst(up1
);
80 cst2
= isl_upoly_as_cst(up2
);
83 return isl_int_eq(cst1
->n
, cst2
->n
) &&
84 isl_int_eq(cst1
->d
, cst2
->d
);
87 rec1
= isl_upoly_as_rec(up1
);
88 rec2
= isl_upoly_as_rec(up2
);
92 if (rec1
->n
!= rec2
->n
)
95 for (i
= 0; i
< rec1
->n
; ++i
) {
96 int eq
= isl_upoly_is_equal(rec1
->p
[i
], rec2
->p
[i
]);
104 int isl_upoly_is_zero(__isl_keep
struct isl_upoly
*up
)
106 struct isl_upoly_cst
*cst
;
110 if (!isl_upoly_is_cst(up
))
113 cst
= isl_upoly_as_cst(up
);
117 return isl_int_is_zero(cst
->n
) && isl_int_is_pos(cst
->d
);
120 int isl_upoly_sgn(__isl_keep
struct isl_upoly
*up
)
122 struct isl_upoly_cst
*cst
;
126 if (!isl_upoly_is_cst(up
))
129 cst
= isl_upoly_as_cst(up
);
133 return isl_int_sgn(cst
->n
);
136 int isl_upoly_is_nan(__isl_keep
struct isl_upoly
*up
)
138 struct isl_upoly_cst
*cst
;
142 if (!isl_upoly_is_cst(up
))
145 cst
= isl_upoly_as_cst(up
);
149 return isl_int_is_zero(cst
->n
) && isl_int_is_zero(cst
->d
);
152 int isl_upoly_is_infty(__isl_keep
struct isl_upoly
*up
)
154 struct isl_upoly_cst
*cst
;
158 if (!isl_upoly_is_cst(up
))
161 cst
= isl_upoly_as_cst(up
);
165 return isl_int_is_pos(cst
->n
) && isl_int_is_zero(cst
->d
);
168 int isl_upoly_is_neginfty(__isl_keep
struct isl_upoly
*up
)
170 struct isl_upoly_cst
*cst
;
174 if (!isl_upoly_is_cst(up
))
177 cst
= isl_upoly_as_cst(up
);
181 return isl_int_is_neg(cst
->n
) && isl_int_is_zero(cst
->d
);
184 int isl_upoly_is_one(__isl_keep
struct isl_upoly
*up
)
186 struct isl_upoly_cst
*cst
;
190 if (!isl_upoly_is_cst(up
))
193 cst
= isl_upoly_as_cst(up
);
197 return isl_int_eq(cst
->n
, cst
->d
) && isl_int_is_pos(cst
->d
);
200 int isl_upoly_is_negone(__isl_keep
struct isl_upoly
*up
)
202 struct isl_upoly_cst
*cst
;
206 if (!isl_upoly_is_cst(up
))
209 cst
= isl_upoly_as_cst(up
);
213 return isl_int_is_negone(cst
->n
) && isl_int_is_one(cst
->d
);
216 __isl_give
struct isl_upoly_cst
*isl_upoly_cst_alloc(struct isl_ctx
*ctx
)
218 struct isl_upoly_cst
*cst
;
220 cst
= isl_alloc_type(ctx
, struct isl_upoly_cst
);
229 isl_int_init(cst
->n
);
230 isl_int_init(cst
->d
);
235 __isl_give
struct isl_upoly
*isl_upoly_zero(struct isl_ctx
*ctx
)
237 struct isl_upoly_cst
*cst
;
239 cst
= isl_upoly_cst_alloc(ctx
);
243 isl_int_set_si(cst
->n
, 0);
244 isl_int_set_si(cst
->d
, 1);
249 __isl_give
struct isl_upoly
*isl_upoly_one(struct isl_ctx
*ctx
)
251 struct isl_upoly_cst
*cst
;
253 cst
= isl_upoly_cst_alloc(ctx
);
257 isl_int_set_si(cst
->n
, 1);
258 isl_int_set_si(cst
->d
, 1);
263 __isl_give
struct isl_upoly
*isl_upoly_infty(struct isl_ctx
*ctx
)
265 struct isl_upoly_cst
*cst
;
267 cst
= isl_upoly_cst_alloc(ctx
);
271 isl_int_set_si(cst
->n
, 1);
272 isl_int_set_si(cst
->d
, 0);
277 __isl_give
struct isl_upoly
*isl_upoly_neginfty(struct isl_ctx
*ctx
)
279 struct isl_upoly_cst
*cst
;
281 cst
= isl_upoly_cst_alloc(ctx
);
285 isl_int_set_si(cst
->n
, -1);
286 isl_int_set_si(cst
->d
, 0);
291 __isl_give
struct isl_upoly
*isl_upoly_nan(struct isl_ctx
*ctx
)
293 struct isl_upoly_cst
*cst
;
295 cst
= isl_upoly_cst_alloc(ctx
);
299 isl_int_set_si(cst
->n
, 0);
300 isl_int_set_si(cst
->d
, 0);
305 __isl_give
struct isl_upoly
*isl_upoly_rat_cst(struct isl_ctx
*ctx
,
306 isl_int n
, isl_int d
)
308 struct isl_upoly_cst
*cst
;
310 cst
= isl_upoly_cst_alloc(ctx
);
314 isl_int_set(cst
->n
, n
);
315 isl_int_set(cst
->d
, d
);
320 __isl_give
struct isl_upoly_rec
*isl_upoly_alloc_rec(struct isl_ctx
*ctx
,
323 struct isl_upoly_rec
*rec
;
325 isl_assert(ctx
, var
>= 0, return NULL
);
326 isl_assert(ctx
, size
>= 0, return NULL
);
327 rec
= isl_calloc(ctx
, struct isl_upoly_rec
,
328 sizeof(struct isl_upoly_rec
) +
329 (size
- 1) * sizeof(struct isl_upoly
*));
344 __isl_give isl_qpolynomial
*isl_qpolynomial_reset_dim(
345 __isl_take isl_qpolynomial
*qp
, __isl_take isl_dim
*dim
)
347 qp
= isl_qpolynomial_cow(qp
);
351 isl_dim_free(qp
->dim
);
356 isl_qpolynomial_free(qp
);
361 isl_ctx
*isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial
*qp
)
363 return qp
? qp
->dim
->ctx
: NULL
;
366 __isl_give isl_dim
*isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial
*qp
)
368 return qp
? isl_dim_copy(qp
->dim
) : NULL
;
371 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial
*qp
,
372 enum isl_dim_type type
)
374 return qp
? isl_dim_size(qp
->dim
, type
) : 0;
377 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial
*qp
)
379 return qp
? isl_upoly_is_zero(qp
->upoly
) : -1;
382 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial
*qp
)
384 return qp
? isl_upoly_is_one(qp
->upoly
) : -1;
387 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial
*qp
)
389 return qp
? isl_upoly_is_nan(qp
->upoly
) : -1;
392 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial
*qp
)
394 return qp
? isl_upoly_is_infty(qp
->upoly
) : -1;
397 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial
*qp
)
399 return qp
? isl_upoly_is_neginfty(qp
->upoly
) : -1;
402 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial
*qp
)
404 return qp
? isl_upoly_sgn(qp
->upoly
) : 0;
407 static void upoly_free_cst(__isl_take
struct isl_upoly_cst
*cst
)
409 isl_int_clear(cst
->n
);
410 isl_int_clear(cst
->d
);
413 static void upoly_free_rec(__isl_take
struct isl_upoly_rec
*rec
)
417 for (i
= 0; i
< rec
->n
; ++i
)
418 isl_upoly_free(rec
->p
[i
]);
421 __isl_give
struct isl_upoly
*isl_upoly_copy(__isl_keep
struct isl_upoly
*up
)
430 __isl_give
struct isl_upoly
*isl_upoly_dup_cst(__isl_keep
struct isl_upoly
*up
)
432 struct isl_upoly_cst
*cst
;
433 struct isl_upoly_cst
*dup
;
435 cst
= isl_upoly_as_cst(up
);
439 dup
= isl_upoly_as_cst(isl_upoly_zero(up
->ctx
));
442 isl_int_set(dup
->n
, cst
->n
);
443 isl_int_set(dup
->d
, cst
->d
);
448 __isl_give
struct isl_upoly
*isl_upoly_dup_rec(__isl_keep
struct isl_upoly
*up
)
451 struct isl_upoly_rec
*rec
;
452 struct isl_upoly_rec
*dup
;
454 rec
= isl_upoly_as_rec(up
);
458 dup
= isl_upoly_alloc_rec(up
->ctx
, up
->var
, rec
->n
);
462 for (i
= 0; i
< rec
->n
; ++i
) {
463 dup
->p
[i
] = isl_upoly_copy(rec
->p
[i
]);
471 isl_upoly_free(&dup
->up
);
475 __isl_give
struct isl_upoly
*isl_upoly_dup(__isl_keep
struct isl_upoly
*up
)
480 if (isl_upoly_is_cst(up
))
481 return isl_upoly_dup_cst(up
);
483 return isl_upoly_dup_rec(up
);
486 __isl_give
struct isl_upoly
*isl_upoly_cow(__isl_take
struct isl_upoly
*up
)
494 return isl_upoly_dup(up
);
497 void isl_upoly_free(__isl_take
struct isl_upoly
*up
)
506 upoly_free_cst((struct isl_upoly_cst
*)up
);
508 upoly_free_rec((struct isl_upoly_rec
*)up
);
510 isl_ctx_deref(up
->ctx
);
514 static void isl_upoly_cst_reduce(__isl_keep
struct isl_upoly_cst
*cst
)
519 isl_int_gcd(gcd
, cst
->n
, cst
->d
);
520 if (!isl_int_is_zero(gcd
) && !isl_int_is_one(gcd
)) {
521 isl_int_divexact(cst
->n
, cst
->n
, gcd
);
522 isl_int_divexact(cst
->d
, cst
->d
, gcd
);
527 __isl_give
struct isl_upoly
*isl_upoly_sum_cst(__isl_take
struct isl_upoly
*up1
,
528 __isl_take
struct isl_upoly
*up2
)
530 struct isl_upoly_cst
*cst1
;
531 struct isl_upoly_cst
*cst2
;
533 up1
= isl_upoly_cow(up1
);
537 cst1
= isl_upoly_as_cst(up1
);
538 cst2
= isl_upoly_as_cst(up2
);
540 if (isl_int_eq(cst1
->d
, cst2
->d
))
541 isl_int_add(cst1
->n
, cst1
->n
, cst2
->n
);
543 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->d
);
544 isl_int_addmul(cst1
->n
, cst2
->n
, cst1
->d
);
545 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
548 isl_upoly_cst_reduce(cst1
);
558 static __isl_give
struct isl_upoly
*replace_by_zero(
559 __isl_take
struct isl_upoly
*up
)
567 return isl_upoly_zero(ctx
);
570 static __isl_give
struct isl_upoly
*replace_by_constant_term(
571 __isl_take
struct isl_upoly
*up
)
573 struct isl_upoly_rec
*rec
;
574 struct isl_upoly
*cst
;
579 rec
= isl_upoly_as_rec(up
);
582 cst
= isl_upoly_copy(rec
->p
[0]);
590 __isl_give
struct isl_upoly
*isl_upoly_sum(__isl_take
struct isl_upoly
*up1
,
591 __isl_take
struct isl_upoly
*up2
)
594 struct isl_upoly_rec
*rec1
, *rec2
;
599 if (isl_upoly_is_nan(up1
)) {
604 if (isl_upoly_is_nan(up2
)) {
609 if (isl_upoly_is_zero(up1
)) {
614 if (isl_upoly_is_zero(up2
)) {
619 if (up1
->var
< up2
->var
)
620 return isl_upoly_sum(up2
, up1
);
622 if (up2
->var
< up1
->var
) {
623 struct isl_upoly_rec
*rec
;
624 if (isl_upoly_is_infty(up2
) || isl_upoly_is_neginfty(up2
)) {
628 up1
= isl_upoly_cow(up1
);
629 rec
= isl_upoly_as_rec(up1
);
632 rec
->p
[0] = isl_upoly_sum(rec
->p
[0], up2
);
634 up1
= replace_by_constant_term(up1
);
638 if (isl_upoly_is_cst(up1
))
639 return isl_upoly_sum_cst(up1
, up2
);
641 rec1
= isl_upoly_as_rec(up1
);
642 rec2
= isl_upoly_as_rec(up2
);
646 if (rec1
->n
< rec2
->n
)
647 return isl_upoly_sum(up2
, up1
);
649 up1
= isl_upoly_cow(up1
);
650 rec1
= isl_upoly_as_rec(up1
);
654 for (i
= rec2
->n
- 1; i
>= 0; --i
) {
655 rec1
->p
[i
] = isl_upoly_sum(rec1
->p
[i
],
656 isl_upoly_copy(rec2
->p
[i
]));
659 if (i
== rec1
->n
- 1 && isl_upoly_is_zero(rec1
->p
[i
])) {
660 isl_upoly_free(rec1
->p
[i
]);
666 up1
= replace_by_zero(up1
);
667 else if (rec1
->n
== 1)
668 up1
= replace_by_constant_term(up1
);
679 __isl_give
struct isl_upoly
*isl_upoly_cst_add_isl_int(
680 __isl_take
struct isl_upoly
*up
, isl_int v
)
682 struct isl_upoly_cst
*cst
;
684 up
= isl_upoly_cow(up
);
688 cst
= isl_upoly_as_cst(up
);
690 isl_int_addmul(cst
->n
, cst
->d
, v
);
695 __isl_give
struct isl_upoly
*isl_upoly_add_isl_int(
696 __isl_take
struct isl_upoly
*up
, isl_int v
)
698 struct isl_upoly_rec
*rec
;
703 if (isl_upoly_is_cst(up
))
704 return isl_upoly_cst_add_isl_int(up
, v
);
706 up
= isl_upoly_cow(up
);
707 rec
= isl_upoly_as_rec(up
);
711 rec
->p
[0] = isl_upoly_add_isl_int(rec
->p
[0], v
);
721 __isl_give
struct isl_upoly
*isl_upoly_cst_mul_isl_int(
722 __isl_take
struct isl_upoly
*up
, isl_int v
)
724 struct isl_upoly_cst
*cst
;
726 if (isl_upoly_is_zero(up
))
729 up
= isl_upoly_cow(up
);
733 cst
= isl_upoly_as_cst(up
);
735 isl_int_mul(cst
->n
, cst
->n
, v
);
740 __isl_give
struct isl_upoly
*isl_upoly_mul_isl_int(
741 __isl_take
struct isl_upoly
*up
, isl_int v
)
744 struct isl_upoly_rec
*rec
;
749 if (isl_upoly_is_cst(up
))
750 return isl_upoly_cst_mul_isl_int(up
, v
);
752 up
= isl_upoly_cow(up
);
753 rec
= isl_upoly_as_rec(up
);
757 for (i
= 0; i
< rec
->n
; ++i
) {
758 rec
->p
[i
] = isl_upoly_mul_isl_int(rec
->p
[i
], v
);
769 __isl_give
struct isl_upoly
*isl_upoly_mul_cst(__isl_take
struct isl_upoly
*up1
,
770 __isl_take
struct isl_upoly
*up2
)
772 struct isl_upoly_cst
*cst1
;
773 struct isl_upoly_cst
*cst2
;
775 up1
= isl_upoly_cow(up1
);
779 cst1
= isl_upoly_as_cst(up1
);
780 cst2
= isl_upoly_as_cst(up2
);
782 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->n
);
783 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
785 isl_upoly_cst_reduce(cst1
);
795 __isl_give
struct isl_upoly
*isl_upoly_mul_rec(__isl_take
struct isl_upoly
*up1
,
796 __isl_take
struct isl_upoly
*up2
)
798 struct isl_upoly_rec
*rec1
;
799 struct isl_upoly_rec
*rec2
;
800 struct isl_upoly_rec
*res
;
804 rec1
= isl_upoly_as_rec(up1
);
805 rec2
= isl_upoly_as_rec(up2
);
808 size
= rec1
->n
+ rec2
->n
- 1;
809 res
= isl_upoly_alloc_rec(up1
->ctx
, up1
->var
, size
);
813 for (i
= 0; i
< rec1
->n
; ++i
) {
814 res
->p
[i
] = isl_upoly_mul(isl_upoly_copy(rec2
->p
[0]),
815 isl_upoly_copy(rec1
->p
[i
]));
820 for (; i
< size
; ++i
) {
821 res
->p
[i
] = isl_upoly_zero(up1
->ctx
);
826 for (i
= 0; i
< rec1
->n
; ++i
) {
827 for (j
= 1; j
< rec2
->n
; ++j
) {
828 struct isl_upoly
*up
;
829 up
= isl_upoly_mul(isl_upoly_copy(rec2
->p
[j
]),
830 isl_upoly_copy(rec1
->p
[i
]));
831 res
->p
[i
+ j
] = isl_upoly_sum(res
->p
[i
+ j
], up
);
844 isl_upoly_free(&res
->up
);
848 __isl_give
struct isl_upoly
*isl_upoly_mul(__isl_take
struct isl_upoly
*up1
,
849 __isl_take
struct isl_upoly
*up2
)
854 if (isl_upoly_is_nan(up1
)) {
859 if (isl_upoly_is_nan(up2
)) {
864 if (isl_upoly_is_zero(up1
)) {
869 if (isl_upoly_is_zero(up2
)) {
874 if (isl_upoly_is_one(up1
)) {
879 if (isl_upoly_is_one(up2
)) {
884 if (up1
->var
< up2
->var
)
885 return isl_upoly_mul(up2
, up1
);
887 if (up2
->var
< up1
->var
) {
889 struct isl_upoly_rec
*rec
;
890 if (isl_upoly_is_infty(up2
) || isl_upoly_is_neginfty(up2
)) {
891 isl_ctx
*ctx
= up1
->ctx
;
894 return isl_upoly_nan(ctx
);
896 up1
= isl_upoly_cow(up1
);
897 rec
= isl_upoly_as_rec(up1
);
901 for (i
= 0; i
< rec
->n
; ++i
) {
902 rec
->p
[i
] = isl_upoly_mul(rec
->p
[i
],
903 isl_upoly_copy(up2
));
911 if (isl_upoly_is_cst(up1
))
912 return isl_upoly_mul_cst(up1
, up2
);
914 return isl_upoly_mul_rec(up1
, up2
);
921 __isl_give
struct isl_upoly
*isl_upoly_pow(__isl_take
struct isl_upoly
*up
,
924 struct isl_upoly
*res
;
932 res
= isl_upoly_copy(up
);
934 res
= isl_upoly_one(up
->ctx
);
936 while (power
>>= 1) {
937 up
= isl_upoly_mul(up
, isl_upoly_copy(up
));
939 res
= isl_upoly_mul(res
, isl_upoly_copy(up
));
946 __isl_give isl_qpolynomial
*isl_qpolynomial_alloc(__isl_take isl_dim
*dim
,
947 unsigned n_div
, __isl_take
struct isl_upoly
*up
)
949 struct isl_qpolynomial
*qp
= NULL
;
955 total
= isl_dim_total(dim
);
957 qp
= isl_calloc_type(dim
->ctx
, struct isl_qpolynomial
);
962 qp
->div
= isl_mat_alloc(dim
->ctx
, n_div
, 1 + 1 + total
+ n_div
);
973 isl_qpolynomial_free(qp
);
977 __isl_give isl_qpolynomial
*isl_qpolynomial_copy(__isl_keep isl_qpolynomial
*qp
)
986 __isl_give isl_qpolynomial
*isl_qpolynomial_dup(__isl_keep isl_qpolynomial
*qp
)
988 struct isl_qpolynomial
*dup
;
993 dup
= isl_qpolynomial_alloc(isl_dim_copy(qp
->dim
), qp
->div
->n_row
,
994 isl_upoly_copy(qp
->upoly
));
997 isl_mat_free(dup
->div
);
998 dup
->div
= isl_mat_copy(qp
->div
);
1004 isl_qpolynomial_free(dup
);
1008 __isl_give isl_qpolynomial
*isl_qpolynomial_cow(__isl_take isl_qpolynomial
*qp
)
1016 return isl_qpolynomial_dup(qp
);
1019 void isl_qpolynomial_free(__isl_take isl_qpolynomial
*qp
)
1027 isl_dim_free(qp
->dim
);
1028 isl_mat_free(qp
->div
);
1029 isl_upoly_free(qp
->upoly
);
1034 __isl_give
struct isl_upoly
*isl_upoly_var_pow(isl_ctx
*ctx
, int pos
, int power
)
1037 struct isl_upoly_rec
*rec
;
1038 struct isl_upoly_cst
*cst
;
1040 rec
= isl_upoly_alloc_rec(ctx
, pos
, 1 + power
);
1043 for (i
= 0; i
< 1 + power
; ++i
) {
1044 rec
->p
[i
] = isl_upoly_zero(ctx
);
1049 cst
= isl_upoly_as_cst(rec
->p
[power
]);
1050 isl_int_set_si(cst
->n
, 1);
1054 isl_upoly_free(&rec
->up
);
1058 /* r array maps original positions to new positions.
1060 static __isl_give
struct isl_upoly
*reorder(__isl_take
struct isl_upoly
*up
,
1064 struct isl_upoly_rec
*rec
;
1065 struct isl_upoly
*base
;
1066 struct isl_upoly
*res
;
1068 if (isl_upoly_is_cst(up
))
1071 rec
= isl_upoly_as_rec(up
);
1075 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
1077 base
= isl_upoly_var_pow(up
->ctx
, r
[up
->var
], 1);
1078 res
= reorder(isl_upoly_copy(rec
->p
[rec
->n
- 1]), r
);
1080 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1081 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
1082 res
= isl_upoly_sum(res
, reorder(isl_upoly_copy(rec
->p
[i
]), r
));
1085 isl_upoly_free(base
);
1094 static int compatible_divs(__isl_keep isl_mat
*div1
, __isl_keep isl_mat
*div2
)
1099 isl_assert(div1
->ctx
, div1
->n_row
>= div2
->n_row
&&
1100 div1
->n_col
>= div2
->n_col
, return -1);
1102 if (div1
->n_row
== div2
->n_row
)
1103 return isl_mat_is_equal(div1
, div2
);
1105 n_row
= div1
->n_row
;
1106 n_col
= div1
->n_col
;
1107 div1
->n_row
= div2
->n_row
;
1108 div1
->n_col
= div2
->n_col
;
1110 equal
= isl_mat_is_equal(div1
, div2
);
1112 div1
->n_row
= n_row
;
1113 div1
->n_col
= n_col
;
1118 static int cmp_row(__isl_keep isl_mat
*div
, int i
, int j
)
1122 li
= isl_seq_last_non_zero(div
->row
[i
], div
->n_col
);
1123 lj
= isl_seq_last_non_zero(div
->row
[j
], div
->n_col
);
1128 return isl_seq_cmp(div
->row
[i
], div
->row
[j
], div
->n_col
);
1131 struct isl_div_sort_info
{
1136 static int div_sort_cmp(const void *p1
, const void *p2
)
1138 const struct isl_div_sort_info
*i1
, *i2
;
1139 i1
= (const struct isl_div_sort_info
*) p1
;
1140 i2
= (const struct isl_div_sort_info
*) p2
;
1142 return cmp_row(i1
->div
, i1
->row
, i2
->row
);
1145 /* Sort divs and remove duplicates.
1147 static __isl_give isl_qpolynomial
*sort_divs(__isl_take isl_qpolynomial
*qp
)
1152 struct isl_div_sort_info
*array
= NULL
;
1153 int *pos
= NULL
, *at
= NULL
;
1154 int *reordering
= NULL
;
1159 if (qp
->div
->n_row
<= 1)
1162 div_pos
= isl_dim_total(qp
->dim
);
1164 array
= isl_alloc_array(qp
->div
->ctx
, struct isl_div_sort_info
,
1166 pos
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1167 at
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1168 len
= qp
->div
->n_col
- 2;
1169 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
1170 if (!array
|| !pos
|| !at
|| !reordering
)
1173 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1174 array
[i
].div
= qp
->div
;
1180 qsort(array
, qp
->div
->n_row
, sizeof(struct isl_div_sort_info
),
1183 for (i
= 0; i
< div_pos
; ++i
)
1186 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1187 if (pos
[array
[i
].row
] == i
)
1189 qp
->div
= isl_mat_swap_rows(qp
->div
, i
, pos
[array
[i
].row
]);
1190 pos
[at
[i
]] = pos
[array
[i
].row
];
1191 at
[pos
[array
[i
].row
]] = at
[i
];
1192 at
[i
] = array
[i
].row
;
1193 pos
[array
[i
].row
] = i
;
1197 for (i
= 0; i
< len
- div_pos
; ++i
) {
1199 isl_seq_eq(qp
->div
->row
[i
- skip
- 1],
1200 qp
->div
->row
[i
- skip
], qp
->div
->n_col
)) {
1201 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
1202 isl_mat_col_add(qp
->div
, 2 + div_pos
+ i
- skip
- 1,
1203 2 + div_pos
+ i
- skip
);
1204 qp
->div
= isl_mat_drop_cols(qp
->div
,
1205 2 + div_pos
+ i
- skip
, 1);
1208 reordering
[div_pos
+ array
[i
].row
] = div_pos
+ i
- skip
;
1211 qp
->upoly
= reorder(qp
->upoly
, reordering
);
1213 if (!qp
->upoly
|| !qp
->div
)
1227 isl_qpolynomial_free(qp
);
1231 static __isl_give
struct isl_upoly
*expand(__isl_take
struct isl_upoly
*up
,
1232 int *exp
, int first
)
1235 struct isl_upoly_rec
*rec
;
1237 if (isl_upoly_is_cst(up
))
1240 if (up
->var
< first
)
1243 if (exp
[up
->var
- first
] == up
->var
- first
)
1246 up
= isl_upoly_cow(up
);
1250 up
->var
= exp
[up
->var
- first
] + first
;
1252 rec
= isl_upoly_as_rec(up
);
1256 for (i
= 0; i
< rec
->n
; ++i
) {
1257 rec
->p
[i
] = expand(rec
->p
[i
], exp
, first
);
1268 static __isl_give isl_qpolynomial
*with_merged_divs(
1269 __isl_give isl_qpolynomial
*(*fn
)(__isl_take isl_qpolynomial
*qp1
,
1270 __isl_take isl_qpolynomial
*qp2
),
1271 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
1275 isl_mat
*div
= NULL
;
1277 qp1
= isl_qpolynomial_cow(qp1
);
1278 qp2
= isl_qpolynomial_cow(qp2
);
1283 isl_assert(qp1
->div
->ctx
, qp1
->div
->n_row
>= qp2
->div
->n_row
&&
1284 qp1
->div
->n_col
>= qp2
->div
->n_col
, goto error
);
1286 exp1
= isl_alloc_array(qp1
->div
->ctx
, int, qp1
->div
->n_row
);
1287 exp2
= isl_alloc_array(qp2
->div
->ctx
, int, qp2
->div
->n_row
);
1291 div
= isl_merge_divs(qp1
->div
, qp2
->div
, exp1
, exp2
);
1295 isl_mat_free(qp1
->div
);
1296 qp1
->div
= isl_mat_copy(div
);
1297 isl_mat_free(qp2
->div
);
1298 qp2
->div
= isl_mat_copy(div
);
1300 qp1
->upoly
= expand(qp1
->upoly
, exp1
, div
->n_col
- div
->n_row
- 2);
1301 qp2
->upoly
= expand(qp2
->upoly
, exp2
, div
->n_col
- div
->n_row
- 2);
1303 if (!qp1
->upoly
|| !qp2
->upoly
)
1310 return fn(qp1
, qp2
);
1315 isl_qpolynomial_free(qp1
);
1316 isl_qpolynomial_free(qp2
);
1320 __isl_give isl_qpolynomial
*isl_qpolynomial_add(__isl_take isl_qpolynomial
*qp1
,
1321 __isl_take isl_qpolynomial
*qp2
)
1323 qp1
= isl_qpolynomial_cow(qp1
);
1328 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1329 return isl_qpolynomial_add(qp2
, qp1
);
1331 isl_assert(qp1
->dim
->ctx
, isl_dim_equal(qp1
->dim
, qp2
->dim
), goto error
);
1332 if (!compatible_divs(qp1
->div
, qp2
->div
))
1333 return with_merged_divs(isl_qpolynomial_add
, qp1
, qp2
);
1335 qp1
->upoly
= isl_upoly_sum(qp1
->upoly
, isl_upoly_copy(qp2
->upoly
));
1339 isl_qpolynomial_free(qp2
);
1343 isl_qpolynomial_free(qp1
);
1344 isl_qpolynomial_free(qp2
);
1348 __isl_give isl_qpolynomial
*isl_qpolynomial_add_on_domain(
1349 __isl_keep isl_set
*dom
,
1350 __isl_take isl_qpolynomial
*qp1
,
1351 __isl_take isl_qpolynomial
*qp2
)
1353 qp1
= isl_qpolynomial_add(qp1
, qp2
);
1354 qp1
= isl_qpolynomial_gist(qp1
, isl_set_copy(dom
));
1358 __isl_give isl_qpolynomial
*isl_qpolynomial_sub(__isl_take isl_qpolynomial
*qp1
,
1359 __isl_take isl_qpolynomial
*qp2
)
1361 return isl_qpolynomial_add(qp1
, isl_qpolynomial_neg(qp2
));
1364 __isl_give isl_qpolynomial
*isl_qpolynomial_add_isl_int(
1365 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1367 if (isl_int_is_zero(v
))
1370 qp
= isl_qpolynomial_cow(qp
);
1374 qp
->upoly
= isl_upoly_add_isl_int(qp
->upoly
, v
);
1380 isl_qpolynomial_free(qp
);
1385 __isl_give isl_qpolynomial
*isl_qpolynomial_neg(__isl_take isl_qpolynomial
*qp
)
1390 return isl_qpolynomial_mul_isl_int(qp
, qp
->dim
->ctx
->negone
);
1393 __isl_give isl_qpolynomial
*isl_qpolynomial_mul_isl_int(
1394 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1396 if (isl_int_is_one(v
))
1399 if (qp
&& isl_int_is_zero(v
)) {
1400 isl_qpolynomial
*zero
;
1401 zero
= isl_qpolynomial_zero(isl_dim_copy(qp
->dim
));
1402 isl_qpolynomial_free(qp
);
1406 qp
= isl_qpolynomial_cow(qp
);
1410 qp
->upoly
= isl_upoly_mul_isl_int(qp
->upoly
, v
);
1416 isl_qpolynomial_free(qp
);
1420 __isl_give isl_qpolynomial
*isl_qpolynomial_mul(__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_mul(qp2
, qp1
);
1431 isl_assert(qp1
->dim
->ctx
, isl_dim_equal(qp1
->dim
, qp2
->dim
), goto error
);
1432 if (!compatible_divs(qp1
->div
, qp2
->div
))
1433 return with_merged_divs(isl_qpolynomial_mul
, qp1
, qp2
);
1435 qp1
->upoly
= isl_upoly_mul(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_pow(__isl_take isl_qpolynomial
*qp
,
1451 qp
= isl_qpolynomial_cow(qp
);
1456 qp
->upoly
= isl_upoly_pow(qp
->upoly
, power
);
1462 isl_qpolynomial_free(qp
);
1466 __isl_give isl_qpolynomial
*isl_qpolynomial_zero(__isl_take isl_dim
*dim
)
1470 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
1473 __isl_give isl_qpolynomial
*isl_qpolynomial_one(__isl_take isl_dim
*dim
)
1477 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_one(dim
->ctx
));
1480 __isl_give isl_qpolynomial
*isl_qpolynomial_infty(__isl_take isl_dim
*dim
)
1484 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_infty(dim
->ctx
));
1487 __isl_give isl_qpolynomial
*isl_qpolynomial_neginfty(__isl_take isl_dim
*dim
)
1491 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_neginfty(dim
->ctx
));
1494 __isl_give isl_qpolynomial
*isl_qpolynomial_nan(__isl_take isl_dim
*dim
)
1498 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_nan(dim
->ctx
));
1501 __isl_give isl_qpolynomial
*isl_qpolynomial_cst(__isl_take isl_dim
*dim
,
1504 struct isl_qpolynomial
*qp
;
1505 struct isl_upoly_cst
*cst
;
1510 qp
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
1514 cst
= isl_upoly_as_cst(qp
->upoly
);
1515 isl_int_set(cst
->n
, v
);
1520 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial
*qp
,
1521 isl_int
*n
, isl_int
*d
)
1523 struct isl_upoly_cst
*cst
;
1528 if (!isl_upoly_is_cst(qp
->upoly
))
1531 cst
= isl_upoly_as_cst(qp
->upoly
);
1536 isl_int_set(*n
, cst
->n
);
1538 isl_int_set(*d
, cst
->d
);
1543 int isl_upoly_is_affine(__isl_keep
struct isl_upoly
*up
)
1546 struct isl_upoly_rec
*rec
;
1554 rec
= isl_upoly_as_rec(up
);
1561 isl_assert(up
->ctx
, rec
->n
> 1, return -1);
1563 is_cst
= isl_upoly_is_cst(rec
->p
[1]);
1569 return isl_upoly_is_affine(rec
->p
[0]);
1572 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial
*qp
)
1577 if (qp
->div
->n_row
> 0)
1580 return isl_upoly_is_affine(qp
->upoly
);
1583 static void update_coeff(__isl_keep isl_vec
*aff
,
1584 __isl_keep
struct isl_upoly_cst
*cst
, int pos
)
1589 if (isl_int_is_zero(cst
->n
))
1594 isl_int_gcd(gcd
, cst
->d
, aff
->el
[0]);
1595 isl_int_divexact(f
, cst
->d
, gcd
);
1596 isl_int_divexact(gcd
, aff
->el
[0], gcd
);
1597 isl_seq_scale(aff
->el
, aff
->el
, f
, aff
->size
);
1598 isl_int_mul(aff
->el
[1 + pos
], gcd
, cst
->n
);
1603 int isl_upoly_update_affine(__isl_keep
struct isl_upoly
*up
,
1604 __isl_keep isl_vec
*aff
)
1606 struct isl_upoly_cst
*cst
;
1607 struct isl_upoly_rec
*rec
;
1613 struct isl_upoly_cst
*cst
;
1615 cst
= isl_upoly_as_cst(up
);
1618 update_coeff(aff
, cst
, 0);
1622 rec
= isl_upoly_as_rec(up
);
1625 isl_assert(up
->ctx
, rec
->n
== 2, return -1);
1627 cst
= isl_upoly_as_cst(rec
->p
[1]);
1630 update_coeff(aff
, cst
, 1 + up
->var
);
1632 return isl_upoly_update_affine(rec
->p
[0], aff
);
1635 __isl_give isl_vec
*isl_qpolynomial_extract_affine(
1636 __isl_keep isl_qpolynomial
*qp
)
1644 d
= isl_dim_total(qp
->dim
);
1645 aff
= isl_vec_alloc(qp
->div
->ctx
, 2 + d
+ qp
->div
->n_row
);
1649 isl_seq_clr(aff
->el
+ 1, 1 + d
+ qp
->div
->n_row
);
1650 isl_int_set_si(aff
->el
[0], 1);
1652 if (isl_upoly_update_affine(qp
->upoly
, aff
) < 0)
1661 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial
*qp1
,
1662 __isl_keep isl_qpolynomial
*qp2
)
1667 return isl_upoly_is_equal(qp1
->upoly
, qp2
->upoly
);
1670 static void upoly_update_den(__isl_keep
struct isl_upoly
*up
, isl_int
*d
)
1673 struct isl_upoly_rec
*rec
;
1675 if (isl_upoly_is_cst(up
)) {
1676 struct isl_upoly_cst
*cst
;
1677 cst
= isl_upoly_as_cst(up
);
1680 isl_int_lcm(*d
, *d
, cst
->d
);
1684 rec
= isl_upoly_as_rec(up
);
1688 for (i
= 0; i
< rec
->n
; ++i
)
1689 upoly_update_den(rec
->p
[i
], d
);
1692 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial
*qp
, isl_int
*d
)
1694 isl_int_set_si(*d
, 1);
1697 upoly_update_den(qp
->upoly
, d
);
1700 __isl_give isl_qpolynomial
*isl_qpolynomial_var_pow(__isl_take isl_dim
*dim
,
1703 struct isl_ctx
*ctx
;
1710 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_var_pow(ctx
, pos
, power
));
1713 __isl_give isl_qpolynomial
*isl_qpolynomial_var(__isl_take isl_dim
*dim
,
1714 enum isl_dim_type type
, unsigned pos
)
1719 isl_assert(dim
->ctx
, isl_dim_size(dim
, isl_dim_in
) == 0, goto error
);
1720 isl_assert(dim
->ctx
, pos
< isl_dim_size(dim
, type
), goto error
);
1722 if (type
== isl_dim_set
)
1723 pos
+= isl_dim_size(dim
, isl_dim_param
);
1725 return isl_qpolynomial_var_pow(dim
, pos
, 1);
1731 __isl_give
struct isl_upoly
*isl_upoly_subs(__isl_take
struct isl_upoly
*up
,
1732 unsigned first
, unsigned n
, __isl_keep
struct isl_upoly
**subs
)
1735 struct isl_upoly_rec
*rec
;
1736 struct isl_upoly
*base
, *res
;
1741 if (isl_upoly_is_cst(up
))
1744 if (up
->var
< first
)
1747 rec
= isl_upoly_as_rec(up
);
1751 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
1753 if (up
->var
>= first
+ n
)
1754 base
= isl_upoly_var_pow(up
->ctx
, up
->var
, 1);
1756 base
= isl_upoly_copy(subs
[up
->var
- first
]);
1758 res
= isl_upoly_subs(isl_upoly_copy(rec
->p
[rec
->n
- 1]), first
, n
, subs
);
1759 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1760 struct isl_upoly
*t
;
1761 t
= isl_upoly_subs(isl_upoly_copy(rec
->p
[i
]), first
, n
, subs
);
1762 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
1763 res
= isl_upoly_sum(res
, t
);
1766 isl_upoly_free(base
);
1775 __isl_give
struct isl_upoly
*isl_upoly_from_affine(isl_ctx
*ctx
, isl_int
*f
,
1776 isl_int denom
, unsigned len
)
1779 struct isl_upoly
*up
;
1781 isl_assert(ctx
, len
>= 1, return NULL
);
1783 up
= isl_upoly_rat_cst(ctx
, f
[0], denom
);
1784 for (i
= 0; i
< len
- 1; ++i
) {
1785 struct isl_upoly
*t
;
1786 struct isl_upoly
*c
;
1788 if (isl_int_is_zero(f
[1 + i
]))
1791 c
= isl_upoly_rat_cst(ctx
, f
[1 + i
], denom
);
1792 t
= isl_upoly_var_pow(ctx
, i
, 1);
1793 t
= isl_upoly_mul(c
, t
);
1794 up
= isl_upoly_sum(up
, t
);
1800 /* Remove common factor of non-constant terms and denominator.
1802 static void normalize_div(__isl_keep isl_qpolynomial
*qp
, int div
)
1804 isl_ctx
*ctx
= qp
->div
->ctx
;
1805 unsigned total
= qp
->div
->n_col
- 2;
1807 isl_seq_gcd(qp
->div
->row
[div
] + 2, total
, &ctx
->normalize_gcd
);
1808 isl_int_gcd(ctx
->normalize_gcd
,
1809 ctx
->normalize_gcd
, qp
->div
->row
[div
][0]);
1810 if (isl_int_is_one(ctx
->normalize_gcd
))
1813 isl_seq_scale_down(qp
->div
->row
[div
] + 2, qp
->div
->row
[div
] + 2,
1814 ctx
->normalize_gcd
, total
);
1815 isl_int_divexact(qp
->div
->row
[div
][0], qp
->div
->row
[div
][0],
1816 ctx
->normalize_gcd
);
1817 isl_int_fdiv_q(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1],
1818 ctx
->normalize_gcd
);
1821 /* Replace the integer division identified by "div" by the polynomial "s".
1822 * The integer division is assumed not to appear in the definition
1823 * of any other integer divisions.
1825 static __isl_give isl_qpolynomial
*substitute_div(
1826 __isl_take isl_qpolynomial
*qp
,
1827 int div
, __isl_take
struct isl_upoly
*s
)
1836 qp
= isl_qpolynomial_cow(qp
);
1840 total
= isl_dim_total(qp
->dim
);
1841 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ div
, 1, &s
);
1845 reordering
= isl_alloc_array(qp
->dim
->ctx
, int, total
+ qp
->div
->n_row
);
1848 for (i
= 0; i
< total
+ div
; ++i
)
1850 for (i
= total
+ div
+ 1; i
< total
+ qp
->div
->n_row
; ++i
)
1851 reordering
[i
] = i
- 1;
1852 qp
->div
= isl_mat_drop_rows(qp
->div
, div
, 1);
1853 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + total
+ div
, 1);
1854 qp
->upoly
= reorder(qp
->upoly
, reordering
);
1857 if (!qp
->upoly
|| !qp
->div
)
1863 isl_qpolynomial_free(qp
);
1868 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1869 * divisions because d is equal to 1 by their definition, i.e., e.
1871 static __isl_give isl_qpolynomial
*substitute_non_divs(
1872 __isl_take isl_qpolynomial
*qp
)
1876 struct isl_upoly
*s
;
1881 total
= isl_dim_total(qp
->dim
);
1882 for (i
= 0; qp
&& i
< qp
->div
->n_row
; ++i
) {
1883 if (!isl_int_is_one(qp
->div
->row
[i
][0]))
1885 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
1886 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
1888 isl_seq_combine(qp
->div
->row
[j
] + 1,
1889 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
1890 qp
->div
->row
[j
][2 + total
+ i
],
1891 qp
->div
->row
[i
] + 1, 1 + total
+ i
);
1892 isl_int_set_si(qp
->div
->row
[j
][2 + total
+ i
], 0);
1893 normalize_div(qp
, j
);
1895 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
1896 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
1897 qp
= substitute_div(qp
, i
, s
);
1904 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1905 * with d the denominator. When replacing the coefficient e of x by
1906 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1907 * inside the division, so we need to add floor(e/d) * x outside.
1908 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1909 * to adjust the coefficient of x in each later div that depends on the
1910 * current div "div" and also in the affine expression "aff"
1911 * (if it too depends on "div").
1913 static void reduce_div(__isl_keep isl_qpolynomial
*qp
, int div
,
1914 __isl_keep isl_vec
*aff
)
1918 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
1921 for (i
= 0; i
< 1 + total
+ div
; ++i
) {
1922 if (isl_int_is_nonneg(qp
->div
->row
[div
][1 + i
]) &&
1923 isl_int_lt(qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]))
1925 isl_int_fdiv_q(v
, qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
1926 isl_int_fdiv_r(qp
->div
->row
[div
][1 + i
],
1927 qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
1928 if (!isl_int_is_zero(aff
->el
[1 + total
+ div
]))
1929 isl_int_addmul(aff
->el
[i
], v
, aff
->el
[1 + total
+ div
]);
1930 for (j
= div
+ 1; j
< qp
->div
->n_row
; ++j
) {
1931 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ div
]))
1933 isl_int_addmul(qp
->div
->row
[j
][1 + i
],
1934 v
, qp
->div
->row
[j
][2 + total
+ div
]);
1940 /* Check if the last non-zero coefficient is bigger that half of the
1941 * denominator. If so, we will invert the div to further reduce the number
1942 * of distinct divs that may appear.
1943 * If the last non-zero coefficient is exactly half the denominator,
1944 * then we continue looking for earlier coefficients that are bigger
1945 * than half the denominator.
1947 static int needs_invert(__isl_keep isl_mat
*div
, int row
)
1952 for (i
= div
->n_col
- 1; i
>= 1; --i
) {
1953 if (isl_int_is_zero(div
->row
[row
][i
]))
1955 isl_int_mul_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
1956 cmp
= isl_int_cmp(div
->row
[row
][i
], div
->row
[row
][0]);
1957 isl_int_divexact_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
1967 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
1968 * We only invert the coefficients of e (and the coefficient of q in
1969 * later divs and in "aff"). After calling this function, the
1970 * coefficients of e should be reduced again.
1972 static void invert_div(__isl_keep isl_qpolynomial
*qp
, int div
,
1973 __isl_keep isl_vec
*aff
)
1975 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
1977 isl_seq_neg(qp
->div
->row
[div
] + 1,
1978 qp
->div
->row
[div
] + 1, qp
->div
->n_col
- 1);
1979 isl_int_sub_ui(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1], 1);
1980 isl_int_add(qp
->div
->row
[div
][1],
1981 qp
->div
->row
[div
][1], qp
->div
->row
[div
][0]);
1982 if (!isl_int_is_zero(aff
->el
[1 + total
+ div
]))
1983 isl_int_neg(aff
->el
[1 + total
+ div
], aff
->el
[1 + total
+ div
]);
1984 isl_mat_col_mul(qp
->div
, 2 + total
+ div
,
1985 qp
->div
->ctx
->negone
, 2 + total
+ div
);
1988 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
1989 * in the interval [0, d-1], with d the denominator and such that the
1990 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
1992 * After the reduction, some divs may have become redundant or identical,
1993 * so we call substitute_non_divs and sort_divs. If these functions
1994 * eliminate divs or merge two or more divs into one, the coefficients
1995 * of the enclosing divs may have to be reduced again, so we call
1996 * ourselves recursively if the number of divs decreases.
1998 static __isl_give isl_qpolynomial
*reduce_divs(__isl_take isl_qpolynomial
*qp
)
2001 isl_vec
*aff
= NULL
;
2002 struct isl_upoly
*s
;
2008 aff
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
2009 aff
= isl_vec_clr(aff
);
2013 isl_int_set_si(aff
->el
[1 + qp
->upoly
->var
], 1);
2015 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2016 normalize_div(qp
, i
);
2017 reduce_div(qp
, i
, aff
);
2018 if (needs_invert(qp
->div
, i
)) {
2019 invert_div(qp
, i
, aff
);
2020 reduce_div(qp
, i
, aff
);
2024 s
= isl_upoly_from_affine(qp
->div
->ctx
, aff
->el
,
2025 qp
->div
->ctx
->one
, aff
->size
);
2026 qp
->upoly
= isl_upoly_subs(qp
->upoly
, qp
->upoly
->var
, 1, &s
);
2033 n_div
= qp
->div
->n_row
;
2034 qp
= substitute_non_divs(qp
);
2036 if (qp
&& qp
->div
->n_row
< n_div
)
2037 return reduce_divs(qp
);
2041 isl_qpolynomial_free(qp
);
2046 /* Assumes each div only depends on earlier divs.
2048 __isl_give isl_qpolynomial
*isl_qpolynomial_div_pow(__isl_take isl_div
*div
,
2051 struct isl_qpolynomial
*qp
= NULL
;
2052 struct isl_upoly_rec
*rec
;
2053 struct isl_upoly_cst
*cst
;
2060 d
= div
->line
- div
->bmap
->div
;
2062 pos
= isl_dim_total(div
->bmap
->dim
) + d
;
2063 rec
= isl_upoly_alloc_rec(div
->ctx
, pos
, 1 + power
);
2064 qp
= isl_qpolynomial_alloc(isl_basic_map_get_dim(div
->bmap
),
2065 div
->bmap
->n_div
, &rec
->up
);
2069 for (i
= 0; i
< div
->bmap
->n_div
; ++i
)
2070 isl_seq_cpy(qp
->div
->row
[i
], div
->bmap
->div
[i
], qp
->div
->n_col
);
2072 for (i
= 0; i
< 1 + power
; ++i
) {
2073 rec
->p
[i
] = isl_upoly_zero(div
->ctx
);
2078 cst
= isl_upoly_as_cst(rec
->p
[power
]);
2079 isl_int_set_si(cst
->n
, 1);
2083 qp
= reduce_divs(qp
);
2087 isl_qpolynomial_free(qp
);
2092 __isl_give isl_qpolynomial
*isl_qpolynomial_div(__isl_take isl_div
*div
)
2094 return isl_qpolynomial_div_pow(div
, 1);
2097 __isl_give isl_qpolynomial
*isl_qpolynomial_rat_cst(__isl_take isl_dim
*dim
,
2098 const isl_int n
, const isl_int d
)
2100 struct isl_qpolynomial
*qp
;
2101 struct isl_upoly_cst
*cst
;
2103 qp
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
2107 cst
= isl_upoly_as_cst(qp
->upoly
);
2108 isl_int_set(cst
->n
, n
);
2109 isl_int_set(cst
->d
, d
);
2114 static int up_set_active(__isl_keep
struct isl_upoly
*up
, int *active
, int d
)
2116 struct isl_upoly_rec
*rec
;
2122 if (isl_upoly_is_cst(up
))
2126 active
[up
->var
] = 1;
2128 rec
= isl_upoly_as_rec(up
);
2129 for (i
= 0; i
< rec
->n
; ++i
)
2130 if (up_set_active(rec
->p
[i
], active
, d
) < 0)
2136 static int set_active(__isl_keep isl_qpolynomial
*qp
, int *active
)
2139 int d
= isl_dim_total(qp
->dim
);
2144 for (i
= 0; i
< d
; ++i
)
2145 for (j
= 0; j
< qp
->div
->n_row
; ++j
) {
2146 if (isl_int_is_zero(qp
->div
->row
[j
][2 + i
]))
2152 return up_set_active(qp
->upoly
, active
, d
);
2155 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial
*qp
,
2156 enum isl_dim_type type
, unsigned first
, unsigned n
)
2167 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_dim_size(qp
->dim
, type
),
2169 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2170 type
== isl_dim_set
, return -1);
2172 active
= isl_calloc_array(qp
->dim
->ctx
, int, isl_dim_total(qp
->dim
));
2173 if (set_active(qp
, active
) < 0)
2176 if (type
== isl_dim_set
)
2177 first
+= isl_dim_size(qp
->dim
, isl_dim_param
);
2178 for (i
= 0; i
< n
; ++i
)
2179 if (active
[first
+ i
]) {
2192 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2193 * of the divs that do appear in the quasi-polynomial.
2195 static __isl_give isl_qpolynomial
*remove_redundant_divs(
2196 __isl_take isl_qpolynomial
*qp
)
2203 int *reordering
= NULL
;
2209 if (qp
->div
->n_row
== 0)
2212 d
= isl_dim_total(qp
->dim
);
2213 len
= qp
->div
->n_col
- 2;
2214 active
= isl_calloc_array(qp
->ctx
, int, len
);
2218 if (up_set_active(qp
->upoly
, active
, len
) < 0)
2221 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
2222 if (!active
[d
+ i
]) {
2226 for (j
= 0; j
< i
; ++j
) {
2227 if (isl_int_is_zero(qp
->div
->row
[i
][2 + d
+ j
]))
2239 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
2243 for (i
= 0; i
< d
; ++i
)
2247 n_div
= qp
->div
->n_row
;
2248 for (i
= 0; i
< n_div
; ++i
) {
2249 if (!active
[d
+ i
]) {
2250 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
2251 qp
->div
= isl_mat_drop_cols(qp
->div
,
2252 2 + d
+ i
- skip
, 1);
2255 reordering
[d
+ i
] = d
+ i
- skip
;
2258 qp
->upoly
= reorder(qp
->upoly
, reordering
);
2260 if (!qp
->upoly
|| !qp
->div
)
2270 isl_qpolynomial_free(qp
);
2274 __isl_give
struct isl_upoly
*isl_upoly_drop(__isl_take
struct isl_upoly
*up
,
2275 unsigned first
, unsigned n
)
2278 struct isl_upoly_rec
*rec
;
2282 if (n
== 0 || up
->var
< 0 || up
->var
< first
)
2284 if (up
->var
< first
+ n
) {
2285 up
= replace_by_constant_term(up
);
2286 return isl_upoly_drop(up
, first
, n
);
2288 up
= isl_upoly_cow(up
);
2292 rec
= isl_upoly_as_rec(up
);
2296 for (i
= 0; i
< rec
->n
; ++i
) {
2297 rec
->p
[i
] = isl_upoly_drop(rec
->p
[i
], first
, n
);
2308 __isl_give isl_qpolynomial
*isl_qpolynomial_set_dim_name(
2309 __isl_take isl_qpolynomial
*qp
,
2310 enum isl_dim_type type
, unsigned pos
, const char *s
)
2312 qp
= isl_qpolynomial_cow(qp
);
2315 qp
->dim
= isl_dim_set_name(qp
->dim
, type
, pos
, s
);
2320 isl_qpolynomial_free(qp
);
2324 __isl_give isl_qpolynomial
*isl_qpolynomial_drop_dims(
2325 __isl_take isl_qpolynomial
*qp
,
2326 enum isl_dim_type type
, unsigned first
, unsigned n
)
2330 if (n
== 0 && !isl_dim_get_tuple_name(qp
->dim
, type
))
2333 qp
= isl_qpolynomial_cow(qp
);
2337 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_dim_size(qp
->dim
, type
),
2339 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2340 type
== isl_dim_set
, goto error
);
2342 qp
->dim
= isl_dim_drop(qp
->dim
, type
, first
, n
);
2346 if (type
== isl_dim_set
)
2347 first
+= isl_dim_size(qp
->dim
, isl_dim_param
);
2349 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + first
, n
);
2353 qp
->upoly
= isl_upoly_drop(qp
->upoly
, first
, n
);
2359 isl_qpolynomial_free(qp
);
2363 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities(
2364 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2370 struct isl_upoly
*up
;
2374 if (eq
->n_eq
== 0) {
2375 isl_basic_set_free(eq
);
2379 qp
= isl_qpolynomial_cow(qp
);
2382 qp
->div
= isl_mat_cow(qp
->div
);
2386 total
= 1 + isl_dim_total(eq
->dim
);
2388 isl_int_init(denom
);
2389 for (i
= 0; i
< eq
->n_eq
; ++i
) {
2390 j
= isl_seq_last_non_zero(eq
->eq
[i
], total
+ n_div
);
2391 if (j
< 0 || j
== 0 || j
>= total
)
2394 for (k
= 0; k
< qp
->div
->n_row
; ++k
) {
2395 if (isl_int_is_zero(qp
->div
->row
[k
][1 + j
]))
2397 isl_seq_elim(qp
->div
->row
[k
] + 1, eq
->eq
[i
], j
, total
,
2398 &qp
->div
->row
[k
][0]);
2399 normalize_div(qp
, k
);
2402 if (isl_int_is_pos(eq
->eq
[i
][j
]))
2403 isl_seq_neg(eq
->eq
[i
], eq
->eq
[i
], total
);
2404 isl_int_abs(denom
, eq
->eq
[i
][j
]);
2405 isl_int_set_si(eq
->eq
[i
][j
], 0);
2407 up
= isl_upoly_from_affine(qp
->dim
->ctx
,
2408 eq
->eq
[i
], denom
, total
);
2409 qp
->upoly
= isl_upoly_subs(qp
->upoly
, j
- 1, 1, &up
);
2412 isl_int_clear(denom
);
2417 isl_basic_set_free(eq
);
2419 qp
= substitute_non_divs(qp
);
2424 isl_basic_set_free(eq
);
2425 isl_qpolynomial_free(qp
);
2429 static __isl_give isl_basic_set
*add_div_constraints(
2430 __isl_take isl_basic_set
*bset
, __isl_take isl_mat
*div
)
2438 bset
= isl_basic_set_extend_constraints(bset
, 0, 2 * div
->n_row
);
2441 total
= isl_basic_set_total_dim(bset
);
2442 for (i
= 0; i
< div
->n_row
; ++i
)
2443 if (isl_basic_set_add_div_constraints_var(bset
,
2444 total
- div
->n_row
+ i
, div
->row
[i
]) < 0)
2451 isl_basic_set_free(bset
);
2455 /* Look for equalities among the variables shared by context and qp
2456 * and the integer divisions of qp, if any.
2457 * The equalities are then used to eliminate variables and/or integer
2458 * divisions from qp.
2460 __isl_give isl_qpolynomial
*isl_qpolynomial_gist(
2461 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
2467 if (qp
->div
->n_row
> 0) {
2468 isl_basic_set
*bset
;
2469 context
= isl_set_add_dims(context
, isl_dim_set
,
2471 bset
= isl_basic_set_universe(isl_set_get_dim(context
));
2472 bset
= add_div_constraints(bset
, isl_mat_copy(qp
->div
));
2473 context
= isl_set_intersect(context
,
2474 isl_set_from_basic_set(bset
));
2477 aff
= isl_set_affine_hull(context
);
2478 return isl_qpolynomial_substitute_equalities(qp
, aff
);
2480 isl_qpolynomial_free(qp
);
2481 isl_set_free(context
);
2486 #define PW isl_pw_qpolynomial
2488 #define EL isl_qpolynomial
2490 #define IS_ZERO is_zero
2494 #include <isl_pw_templ.c>
2497 #define UNION isl_union_pw_qpolynomial
2499 #define PART isl_pw_qpolynomial
2501 #define PARTS pw_qpolynomial
2503 #include <isl_union_templ.c>
2505 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial
*pwqp
)
2513 if (!isl_set_plain_is_universe(pwqp
->p
[0].set
))
2516 return isl_qpolynomial_is_one(pwqp
->p
[0].qp
);
2519 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_mul(
2520 __isl_take isl_pw_qpolynomial
*pwqp1
,
2521 __isl_take isl_pw_qpolynomial
*pwqp2
)
2524 struct isl_pw_qpolynomial
*res
;
2526 if (!pwqp1
|| !pwqp2
)
2529 isl_assert(pwqp1
->dim
->ctx
, isl_dim_equal(pwqp1
->dim
, pwqp2
->dim
),
2532 if (isl_pw_qpolynomial_is_zero(pwqp1
)) {
2533 isl_pw_qpolynomial_free(pwqp2
);
2537 if (isl_pw_qpolynomial_is_zero(pwqp2
)) {
2538 isl_pw_qpolynomial_free(pwqp1
);
2542 if (isl_pw_qpolynomial_is_one(pwqp1
)) {
2543 isl_pw_qpolynomial_free(pwqp1
);
2547 if (isl_pw_qpolynomial_is_one(pwqp2
)) {
2548 isl_pw_qpolynomial_free(pwqp2
);
2552 n
= pwqp1
->n
* pwqp2
->n
;
2553 res
= isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1
->dim
), n
);
2555 for (i
= 0; i
< pwqp1
->n
; ++i
) {
2556 for (j
= 0; j
< pwqp2
->n
; ++j
) {
2557 struct isl_set
*common
;
2558 struct isl_qpolynomial
*prod
;
2559 common
= isl_set_intersect(isl_set_copy(pwqp1
->p
[i
].set
),
2560 isl_set_copy(pwqp2
->p
[j
].set
));
2561 if (isl_set_plain_is_empty(common
)) {
2562 isl_set_free(common
);
2566 prod
= isl_qpolynomial_mul(
2567 isl_qpolynomial_copy(pwqp1
->p
[i
].qp
),
2568 isl_qpolynomial_copy(pwqp2
->p
[j
].qp
));
2570 res
= isl_pw_qpolynomial_add_piece(res
, common
, prod
);
2574 isl_pw_qpolynomial_free(pwqp1
);
2575 isl_pw_qpolynomial_free(pwqp2
);
2579 isl_pw_qpolynomial_free(pwqp1
);
2580 isl_pw_qpolynomial_free(pwqp2
);
2584 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_neg(
2585 __isl_take isl_pw_qpolynomial
*pwqp
)
2592 if (isl_pw_qpolynomial_is_zero(pwqp
))
2595 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
2599 for (i
= 0; i
< pwqp
->n
; ++i
) {
2600 pwqp
->p
[i
].qp
= isl_qpolynomial_neg(pwqp
->p
[i
].qp
);
2607 isl_pw_qpolynomial_free(pwqp
);
2611 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_sub(
2612 __isl_take isl_pw_qpolynomial
*pwqp1
,
2613 __isl_take isl_pw_qpolynomial
*pwqp2
)
2615 return isl_pw_qpolynomial_add(pwqp1
, isl_pw_qpolynomial_neg(pwqp2
));
2618 __isl_give
struct isl_upoly
*isl_upoly_eval(
2619 __isl_take
struct isl_upoly
*up
, __isl_take isl_vec
*vec
)
2622 struct isl_upoly_rec
*rec
;
2623 struct isl_upoly
*res
;
2624 struct isl_upoly
*base
;
2626 if (isl_upoly_is_cst(up
)) {
2631 rec
= isl_upoly_as_rec(up
);
2635 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
2637 base
= isl_upoly_rat_cst(up
->ctx
, vec
->el
[1 + up
->var
], vec
->el
[0]);
2639 res
= isl_upoly_eval(isl_upoly_copy(rec
->p
[rec
->n
- 1]),
2642 for (i
= rec
->n
- 2; i
>= 0; --i
) {
2643 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
2644 res
= isl_upoly_sum(res
,
2645 isl_upoly_eval(isl_upoly_copy(rec
->p
[i
]),
2646 isl_vec_copy(vec
)));
2649 isl_upoly_free(base
);
2659 __isl_give isl_qpolynomial
*isl_qpolynomial_eval(
2660 __isl_take isl_qpolynomial
*qp
, __isl_take isl_point
*pnt
)
2663 struct isl_upoly
*up
;
2668 isl_assert(pnt
->dim
->ctx
, isl_dim_equal(pnt
->dim
, qp
->dim
), goto error
);
2670 if (qp
->div
->n_row
== 0)
2671 ext
= isl_vec_copy(pnt
->vec
);
2674 unsigned dim
= isl_dim_total(qp
->dim
);
2675 ext
= isl_vec_alloc(qp
->dim
->ctx
, 1 + dim
+ qp
->div
->n_row
);
2679 isl_seq_cpy(ext
->el
, pnt
->vec
->el
, pnt
->vec
->size
);
2680 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2681 isl_seq_inner_product(qp
->div
->row
[i
] + 1, ext
->el
,
2682 1 + dim
+ i
, &ext
->el
[1+dim
+i
]);
2683 isl_int_fdiv_q(ext
->el
[1+dim
+i
], ext
->el
[1+dim
+i
],
2684 qp
->div
->row
[i
][0]);
2688 up
= isl_upoly_eval(isl_upoly_copy(qp
->upoly
), ext
);
2692 dim
= isl_dim_copy(qp
->dim
);
2693 isl_qpolynomial_free(qp
);
2694 isl_point_free(pnt
);
2696 return isl_qpolynomial_alloc(dim
, 0, up
);
2698 isl_qpolynomial_free(qp
);
2699 isl_point_free(pnt
);
2703 int isl_upoly_cmp(__isl_keep
struct isl_upoly_cst
*cst1
,
2704 __isl_keep
struct isl_upoly_cst
*cst2
)
2709 isl_int_mul(t
, cst1
->n
, cst2
->d
);
2710 isl_int_submul(t
, cst2
->n
, cst1
->d
);
2711 cmp
= isl_int_sgn(t
);
2716 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial
*qp1
,
2717 __isl_keep isl_qpolynomial
*qp2
)
2719 struct isl_upoly_cst
*cst1
, *cst2
;
2723 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), return -1);
2724 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), return -1);
2725 if (isl_qpolynomial_is_nan(qp1
))
2727 if (isl_qpolynomial_is_nan(qp2
))
2729 cst1
= isl_upoly_as_cst(qp1
->upoly
);
2730 cst2
= isl_upoly_as_cst(qp2
->upoly
);
2732 return isl_upoly_cmp(cst1
, cst2
) <= 0;
2735 __isl_give isl_qpolynomial
*isl_qpolynomial_min_cst(
2736 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
2738 struct isl_upoly_cst
*cst1
, *cst2
;
2743 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), goto error
);
2744 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), goto error
);
2745 cst1
= isl_upoly_as_cst(qp1
->upoly
);
2746 cst2
= isl_upoly_as_cst(qp2
->upoly
);
2747 cmp
= isl_upoly_cmp(cst1
, cst2
);
2750 isl_qpolynomial_free(qp2
);
2752 isl_qpolynomial_free(qp1
);
2757 isl_qpolynomial_free(qp1
);
2758 isl_qpolynomial_free(qp2
);
2762 __isl_give isl_qpolynomial
*isl_qpolynomial_max_cst(
2763 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
2765 struct isl_upoly_cst
*cst1
, *cst2
;
2770 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), goto error
);
2771 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), goto error
);
2772 cst1
= isl_upoly_as_cst(qp1
->upoly
);
2773 cst2
= isl_upoly_as_cst(qp2
->upoly
);
2774 cmp
= isl_upoly_cmp(cst1
, cst2
);
2777 isl_qpolynomial_free(qp2
);
2779 isl_qpolynomial_free(qp1
);
2784 isl_qpolynomial_free(qp1
);
2785 isl_qpolynomial_free(qp2
);
2789 __isl_give isl_qpolynomial
*isl_qpolynomial_insert_dims(
2790 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
,
2791 unsigned first
, unsigned n
)
2800 qp
= isl_qpolynomial_cow(qp
);
2804 isl_assert(qp
->div
->ctx
, first
<= isl_dim_size(qp
->dim
, type
),
2807 g_pos
= pos(qp
->dim
, type
) + first
;
2809 qp
->div
= isl_mat_insert_cols(qp
->div
, 2 + g_pos
, n
);
2813 total
= qp
->div
->n_col
- 2;
2814 if (total
> g_pos
) {
2816 exp
= isl_alloc_array(qp
->div
->ctx
, int, total
- g_pos
);
2819 for (i
= 0; i
< total
- g_pos
; ++i
)
2821 qp
->upoly
= expand(qp
->upoly
, exp
, g_pos
);
2827 qp
->dim
= isl_dim_insert(qp
->dim
, type
, first
, n
);
2833 isl_qpolynomial_free(qp
);
2837 __isl_give isl_qpolynomial
*isl_qpolynomial_add_dims(
2838 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
, unsigned n
)
2842 pos
= isl_qpolynomial_dim(qp
, type
);
2844 return isl_qpolynomial_insert_dims(qp
, type
, pos
, n
);
2847 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add_dims(
2848 __isl_take isl_pw_qpolynomial
*pwqp
,
2849 enum isl_dim_type type
, unsigned n
)
2853 pos
= isl_pw_qpolynomial_dim(pwqp
, type
);
2855 return isl_pw_qpolynomial_insert_dims(pwqp
, type
, pos
, n
);
2858 static int *reordering_move(isl_ctx
*ctx
,
2859 unsigned len
, unsigned dst
, unsigned src
, unsigned n
)
2864 reordering
= isl_alloc_array(ctx
, int, len
);
2869 for (i
= 0; i
< dst
; ++i
)
2871 for (i
= 0; i
< n
; ++i
)
2872 reordering
[src
+ i
] = dst
+ i
;
2873 for (i
= 0; i
< src
- dst
; ++i
)
2874 reordering
[dst
+ i
] = dst
+ n
+ i
;
2875 for (i
= 0; i
< len
- src
- n
; ++i
)
2876 reordering
[src
+ n
+ i
] = src
+ n
+ i
;
2878 for (i
= 0; i
< src
; ++i
)
2880 for (i
= 0; i
< n
; ++i
)
2881 reordering
[src
+ i
] = dst
+ i
;
2882 for (i
= 0; i
< dst
- src
; ++i
)
2883 reordering
[src
+ n
+ i
] = src
+ i
;
2884 for (i
= 0; i
< len
- dst
- n
; ++i
)
2885 reordering
[dst
+ n
+ i
] = dst
+ n
+ i
;
2891 __isl_give isl_qpolynomial
*isl_qpolynomial_move_dims(
2892 __isl_take isl_qpolynomial
*qp
,
2893 enum isl_dim_type dst_type
, unsigned dst_pos
,
2894 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
2900 qp
= isl_qpolynomial_cow(qp
);
2904 isl_assert(qp
->dim
->ctx
, src_pos
+ n
<= isl_dim_size(qp
->dim
, src_type
),
2907 g_dst_pos
= pos(qp
->dim
, dst_type
) + dst_pos
;
2908 g_src_pos
= pos(qp
->dim
, src_type
) + src_pos
;
2909 if (dst_type
> src_type
)
2912 qp
->div
= isl_mat_move_cols(qp
->div
, 2 + g_dst_pos
, 2 + g_src_pos
, n
);
2919 reordering
= reordering_move(qp
->dim
->ctx
,
2920 qp
->div
->n_col
- 2, g_dst_pos
, g_src_pos
, n
);
2924 qp
->upoly
= reorder(qp
->upoly
, reordering
);
2929 qp
->dim
= isl_dim_move(qp
->dim
, dst_type
, dst_pos
, src_type
, src_pos
, n
);
2935 isl_qpolynomial_free(qp
);
2939 __isl_give isl_qpolynomial
*isl_qpolynomial_from_affine(__isl_take isl_dim
*dim
,
2940 isl_int
*f
, isl_int denom
)
2942 struct isl_upoly
*up
;
2947 up
= isl_upoly_from_affine(dim
->ctx
, f
, denom
, 1 + isl_dim_total(dim
));
2949 return isl_qpolynomial_alloc(dim
, 0, up
);
2952 __isl_give isl_qpolynomial
*isl_qpolynomial_from_aff(__isl_take isl_aff
*aff
)
2955 struct isl_upoly
*up
;
2956 isl_qpolynomial
*qp
;
2961 ctx
= isl_aff_get_ctx(aff
);
2962 up
= isl_upoly_from_affine(ctx
, aff
->v
->el
+ 1, aff
->v
->el
[0],
2965 qp
= isl_qpolynomial_alloc(isl_aff_get_dim(aff
),
2966 aff
->ls
->div
->n_row
, up
);
2970 isl_mat_free(qp
->div
);
2971 qp
->div
= isl_mat_copy(aff
->ls
->div
);
2972 qp
->div
= isl_mat_cow(qp
->div
);
2977 qp
= reduce_divs(qp
);
2978 qp
= remove_redundant_divs(qp
);
2985 __isl_give isl_qpolynomial
*isl_qpolynomial_from_constraint(
2986 __isl_take isl_constraint
*c
, enum isl_dim_type type
, unsigned pos
)
2990 struct isl_upoly
*up
;
2991 isl_qpolynomial
*qp
;
2997 isl_int_init(denom
);
2999 isl_constraint_get_coefficient(c
, type
, pos
, &denom
);
3000 isl_constraint_set_coefficient(c
, type
, pos
, c
->ctx
->zero
);
3001 sgn
= isl_int_sgn(denom
);
3002 isl_int_abs(denom
, denom
);
3003 up
= isl_upoly_from_affine(c
->ctx
, c
->line
[0], denom
,
3004 1 + isl_constraint_dim(c
, isl_dim_all
));
3006 isl_int_neg(denom
, denom
);
3007 isl_constraint_set_coefficient(c
, type
, pos
, denom
);
3009 dim
= isl_dim_copy(c
->bmap
->dim
);
3011 isl_int_clear(denom
);
3012 isl_constraint_free(c
);
3014 qp
= isl_qpolynomial_alloc(dim
, 0, up
);
3016 qp
= isl_qpolynomial_neg(qp
);
3020 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3021 * in "qp" by subs[i].
3023 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute(
3024 __isl_take isl_qpolynomial
*qp
,
3025 enum isl_dim_type type
, unsigned first
, unsigned n
,
3026 __isl_keep isl_qpolynomial
**subs
)
3029 struct isl_upoly
**ups
;
3034 qp
= isl_qpolynomial_cow(qp
);
3037 for (i
= 0; i
< n
; ++i
)
3041 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_dim_size(qp
->dim
, type
),
3044 for (i
= 0; i
< n
; ++i
)
3045 isl_assert(qp
->dim
->ctx
, isl_dim_equal(qp
->dim
, subs
[i
]->dim
),
3048 isl_assert(qp
->dim
->ctx
, qp
->div
->n_row
== 0, goto error
);
3049 for (i
= 0; i
< n
; ++i
)
3050 isl_assert(qp
->dim
->ctx
, subs
[i
]->div
->n_row
== 0, goto error
);
3052 first
+= pos(qp
->dim
, type
);
3054 ups
= isl_alloc_array(qp
->dim
->ctx
, struct isl_upoly
*, n
);
3057 for (i
= 0; i
< n
; ++i
)
3058 ups
[i
] = subs
[i
]->upoly
;
3060 qp
->upoly
= isl_upoly_subs(qp
->upoly
, first
, n
, ups
);
3069 isl_qpolynomial_free(qp
);
3073 /* Extend "bset" with extra set dimensions for each integer division
3074 * in "qp" and then call "fn" with the extended bset and the polynomial
3075 * that results from replacing each of the integer divisions by the
3076 * corresponding extra set dimension.
3078 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial
*qp
,
3079 __isl_keep isl_basic_set
*bset
,
3080 int (*fn
)(__isl_take isl_basic_set
*bset
,
3081 __isl_take isl_qpolynomial
*poly
, void *user
), void *user
)
3085 isl_qpolynomial
*poly
;
3089 if (qp
->div
->n_row
== 0)
3090 return fn(isl_basic_set_copy(bset
), isl_qpolynomial_copy(qp
),
3093 div
= isl_mat_copy(qp
->div
);
3094 dim
= isl_dim_copy(qp
->dim
);
3095 dim
= isl_dim_add(dim
, isl_dim_set
, qp
->div
->n_row
);
3096 poly
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_copy(qp
->upoly
));
3097 bset
= isl_basic_set_copy(bset
);
3098 bset
= isl_basic_set_add(bset
, isl_dim_set
, qp
->div
->n_row
);
3099 bset
= add_div_constraints(bset
, div
);
3101 return fn(bset
, poly
, user
);
3106 /* Return total degree in variables first (inclusive) up to last (exclusive).
3108 int isl_upoly_degree(__isl_keep
struct isl_upoly
*up
, int first
, int last
)
3112 struct isl_upoly_rec
*rec
;
3116 if (isl_upoly_is_zero(up
))
3118 if (isl_upoly_is_cst(up
) || up
->var
< first
)
3121 rec
= isl_upoly_as_rec(up
);
3125 for (i
= 0; i
< rec
->n
; ++i
) {
3128 if (isl_upoly_is_zero(rec
->p
[i
]))
3130 d
= isl_upoly_degree(rec
->p
[i
], first
, last
);
3140 /* Return total degree in set variables.
3142 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial
*poly
)
3150 ovar
= isl_dim_offset(poly
->dim
, isl_dim_set
);
3151 nvar
= isl_dim_size(poly
->dim
, isl_dim_set
);
3152 return isl_upoly_degree(poly
->upoly
, ovar
, ovar
+ nvar
);
3155 __isl_give
struct isl_upoly
*isl_upoly_coeff(__isl_keep
struct isl_upoly
*up
,
3156 unsigned pos
, int deg
)
3159 struct isl_upoly_rec
*rec
;
3164 if (isl_upoly_is_cst(up
) || up
->var
< pos
) {
3166 return isl_upoly_copy(up
);
3168 return isl_upoly_zero(up
->ctx
);
3171 rec
= isl_upoly_as_rec(up
);
3175 if (up
->var
== pos
) {
3177 return isl_upoly_copy(rec
->p
[deg
]);
3179 return isl_upoly_zero(up
->ctx
);
3182 up
= isl_upoly_copy(up
);
3183 up
= isl_upoly_cow(up
);
3184 rec
= isl_upoly_as_rec(up
);
3188 for (i
= 0; i
< rec
->n
; ++i
) {
3189 struct isl_upoly
*t
;
3190 t
= isl_upoly_coeff(rec
->p
[i
], pos
, deg
);
3193 isl_upoly_free(rec
->p
[i
]);
3203 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3205 __isl_give isl_qpolynomial
*isl_qpolynomial_coeff(
3206 __isl_keep isl_qpolynomial
*qp
,
3207 enum isl_dim_type type
, unsigned t_pos
, int deg
)
3210 struct isl_upoly
*up
;
3216 isl_assert(qp
->div
->ctx
, t_pos
< isl_dim_size(qp
->dim
, type
),
3219 g_pos
= pos(qp
->dim
, type
) + t_pos
;
3220 up
= isl_upoly_coeff(qp
->upoly
, g_pos
, deg
);
3222 c
= isl_qpolynomial_alloc(isl_dim_copy(qp
->dim
), qp
->div
->n_row
, up
);
3225 isl_mat_free(c
->div
);
3226 c
->div
= isl_mat_copy(qp
->div
);
3231 isl_qpolynomial_free(c
);
3235 /* Homogenize the polynomial in the variables first (inclusive) up to
3236 * last (exclusive) by inserting powers of variable first.
3237 * Variable first is assumed not to appear in the input.
3239 __isl_give
struct isl_upoly
*isl_upoly_homogenize(
3240 __isl_take
struct isl_upoly
*up
, int deg
, int target
,
3241 int first
, int last
)
3244 struct isl_upoly_rec
*rec
;
3248 if (isl_upoly_is_zero(up
))
3252 if (isl_upoly_is_cst(up
) || up
->var
< first
) {
3253 struct isl_upoly
*hom
;
3255 hom
= isl_upoly_var_pow(up
->ctx
, first
, target
- deg
);
3258 rec
= isl_upoly_as_rec(hom
);
3259 rec
->p
[target
- deg
] = isl_upoly_mul(rec
->p
[target
- deg
], up
);
3264 up
= isl_upoly_cow(up
);
3265 rec
= isl_upoly_as_rec(up
);
3269 for (i
= 0; i
< rec
->n
; ++i
) {
3270 if (isl_upoly_is_zero(rec
->p
[i
]))
3272 rec
->p
[i
] = isl_upoly_homogenize(rec
->p
[i
],
3273 up
->var
< last
? deg
+ i
: i
, target
,
3285 /* Homogenize the polynomial in the set variables by introducing
3286 * powers of an extra set variable at position 0.
3288 __isl_give isl_qpolynomial
*isl_qpolynomial_homogenize(
3289 __isl_take isl_qpolynomial
*poly
)
3293 int deg
= isl_qpolynomial_degree(poly
);
3298 poly
= isl_qpolynomial_insert_dims(poly
, isl_dim_set
, 0, 1);
3299 poly
= isl_qpolynomial_cow(poly
);
3303 ovar
= isl_dim_offset(poly
->dim
, isl_dim_set
);
3304 nvar
= isl_dim_size(poly
->dim
, isl_dim_set
);
3305 poly
->upoly
= isl_upoly_homogenize(poly
->upoly
, 0, deg
,
3312 isl_qpolynomial_free(poly
);
3316 __isl_give isl_term
*isl_term_alloc(__isl_take isl_dim
*dim
,
3317 __isl_take isl_mat
*div
)
3325 n
= isl_dim_total(dim
) + div
->n_row
;
3327 term
= isl_calloc(dim
->ctx
, struct isl_term
,
3328 sizeof(struct isl_term
) + (n
- 1) * sizeof(int));
3335 isl_int_init(term
->n
);
3336 isl_int_init(term
->d
);
3345 __isl_give isl_term
*isl_term_copy(__isl_keep isl_term
*term
)
3354 __isl_give isl_term
*isl_term_dup(__isl_keep isl_term
*term
)
3363 total
= isl_dim_total(term
->dim
) + term
->div
->n_row
;
3365 dup
= isl_term_alloc(isl_dim_copy(term
->dim
), isl_mat_copy(term
->div
));
3369 isl_int_set(dup
->n
, term
->n
);
3370 isl_int_set(dup
->d
, term
->d
);
3372 for (i
= 0; i
< total
; ++i
)
3373 dup
->pow
[i
] = term
->pow
[i
];
3378 __isl_give isl_term
*isl_term_cow(__isl_take isl_term
*term
)
3386 return isl_term_dup(term
);
3389 void isl_term_free(__isl_take isl_term
*term
)
3394 if (--term
->ref
> 0)
3397 isl_dim_free(term
->dim
);
3398 isl_mat_free(term
->div
);
3399 isl_int_clear(term
->n
);
3400 isl_int_clear(term
->d
);
3404 unsigned isl_term_dim(__isl_keep isl_term
*term
, enum isl_dim_type type
)
3412 case isl_dim_out
: return isl_dim_size(term
->dim
, type
);
3413 case isl_dim_div
: return term
->div
->n_row
;
3414 case isl_dim_all
: return isl_dim_total(term
->dim
) + term
->div
->n_row
;
3419 isl_ctx
*isl_term_get_ctx(__isl_keep isl_term
*term
)
3421 return term
? term
->dim
->ctx
: NULL
;
3424 void isl_term_get_num(__isl_keep isl_term
*term
, isl_int
*n
)
3428 isl_int_set(*n
, term
->n
);
3431 void isl_term_get_den(__isl_keep isl_term
*term
, isl_int
*d
)
3435 isl_int_set(*d
, term
->d
);
3438 int isl_term_get_exp(__isl_keep isl_term
*term
,
3439 enum isl_dim_type type
, unsigned pos
)
3444 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, type
), return -1);
3446 if (type
>= isl_dim_set
)
3447 pos
+= isl_dim_size(term
->dim
, isl_dim_param
);
3448 if (type
>= isl_dim_div
)
3449 pos
+= isl_dim_size(term
->dim
, isl_dim_set
);
3451 return term
->pow
[pos
];
3454 __isl_give isl_div
*isl_term_get_div(__isl_keep isl_term
*term
, unsigned pos
)
3456 isl_basic_map
*bmap
;
3463 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, isl_dim_div
),
3466 total
= term
->div
->n_col
- term
->div
->n_row
- 2;
3467 /* No nested divs for now */
3468 isl_assert(term
->dim
->ctx
,
3469 isl_seq_first_non_zero(term
->div
->row
[pos
] + 2 + total
,
3470 term
->div
->n_row
) == -1,
3473 bmap
= isl_basic_map_alloc_dim(isl_dim_copy(term
->dim
), 1, 0, 0);
3474 if ((k
= isl_basic_map_alloc_div(bmap
)) < 0)
3477 isl_seq_cpy(bmap
->div
[k
], term
->div
->row
[pos
], 2 + total
);
3479 return isl_basic_map_div(bmap
, k
);
3481 isl_basic_map_free(bmap
);
3485 __isl_give isl_term
*isl_upoly_foreach_term(__isl_keep
struct isl_upoly
*up
,
3486 int (*fn
)(__isl_take isl_term
*term
, void *user
),
3487 __isl_take isl_term
*term
, void *user
)
3490 struct isl_upoly_rec
*rec
;
3495 if (isl_upoly_is_zero(up
))
3498 isl_assert(up
->ctx
, !isl_upoly_is_nan(up
), goto error
);
3499 isl_assert(up
->ctx
, !isl_upoly_is_infty(up
), goto error
);
3500 isl_assert(up
->ctx
, !isl_upoly_is_neginfty(up
), goto error
);
3502 if (isl_upoly_is_cst(up
)) {
3503 struct isl_upoly_cst
*cst
;
3504 cst
= isl_upoly_as_cst(up
);
3507 term
= isl_term_cow(term
);
3510 isl_int_set(term
->n
, cst
->n
);
3511 isl_int_set(term
->d
, cst
->d
);
3512 if (fn(isl_term_copy(term
), user
) < 0)
3517 rec
= isl_upoly_as_rec(up
);
3521 for (i
= 0; i
< rec
->n
; ++i
) {
3522 term
= isl_term_cow(term
);
3525 term
->pow
[up
->var
] = i
;
3526 term
= isl_upoly_foreach_term(rec
->p
[i
], fn
, term
, user
);
3530 term
->pow
[up
->var
] = 0;
3534 isl_term_free(term
);
3538 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial
*qp
,
3539 int (*fn
)(__isl_take isl_term
*term
, void *user
), void *user
)
3546 term
= isl_term_alloc(isl_dim_copy(qp
->dim
), isl_mat_copy(qp
->div
));
3550 term
= isl_upoly_foreach_term(qp
->upoly
, fn
, term
, user
);
3552 isl_term_free(term
);
3554 return term
? 0 : -1;
3557 __isl_give isl_qpolynomial
*isl_qpolynomial_from_term(__isl_take isl_term
*term
)
3559 struct isl_upoly
*up
;
3560 isl_qpolynomial
*qp
;
3566 n
= isl_dim_total(term
->dim
) + term
->div
->n_row
;
3568 up
= isl_upoly_rat_cst(term
->dim
->ctx
, term
->n
, term
->d
);
3569 for (i
= 0; i
< n
; ++i
) {
3572 up
= isl_upoly_mul(up
,
3573 isl_upoly_var_pow(term
->dim
->ctx
, i
, term
->pow
[i
]));
3576 qp
= isl_qpolynomial_alloc(isl_dim_copy(term
->dim
), term
->div
->n_row
, up
);
3579 isl_mat_free(qp
->div
);
3580 qp
->div
= isl_mat_copy(term
->div
);
3584 isl_term_free(term
);
3587 isl_qpolynomial_free(qp
);
3588 isl_term_free(term
);
3592 __isl_give isl_qpolynomial
*isl_qpolynomial_lift(__isl_take isl_qpolynomial
*qp
,
3593 __isl_take isl_dim
*dim
)
3602 if (isl_dim_equal(qp
->dim
, dim
)) {
3607 qp
= isl_qpolynomial_cow(qp
);
3611 extra
= isl_dim_size(dim
, isl_dim_set
) -
3612 isl_dim_size(qp
->dim
, isl_dim_set
);
3613 total
= isl_dim_total(qp
->dim
);
3614 if (qp
->div
->n_row
) {
3617 exp
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
3620 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3622 qp
->upoly
= expand(qp
->upoly
, exp
, total
);
3627 qp
->div
= isl_mat_insert_cols(qp
->div
, 2 + total
, extra
);
3630 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3631 isl_seq_clr(qp
->div
->row
[i
] + 2 + total
, extra
);
3633 isl_dim_free(qp
->dim
);
3639 isl_qpolynomial_free(qp
);
3643 /* For each parameter or variable that does not appear in qp,
3644 * first eliminate the variable from all constraints and then set it to zero.
3646 static __isl_give isl_set
*fix_inactive(__isl_take isl_set
*set
,
3647 __isl_keep isl_qpolynomial
*qp
)
3658 d
= isl_dim_total(set
->dim
);
3659 active
= isl_calloc_array(set
->ctx
, int, d
);
3660 if (set_active(qp
, active
) < 0)
3663 for (i
= 0; i
< d
; ++i
)
3672 nparam
= isl_dim_size(set
->dim
, isl_dim_param
);
3673 nvar
= isl_dim_size(set
->dim
, isl_dim_set
);
3674 for (i
= 0; i
< nparam
; ++i
) {
3677 set
= isl_set_eliminate(set
, isl_dim_param
, i
, 1);
3678 set
= isl_set_fix_si(set
, isl_dim_param
, i
, 0);
3680 for (i
= 0; i
< nvar
; ++i
) {
3681 if (active
[nparam
+ i
])
3683 set
= isl_set_eliminate(set
, isl_dim_set
, i
, 1);
3684 set
= isl_set_fix_si(set
, isl_dim_set
, i
, 0);
3696 struct isl_opt_data
{
3697 isl_qpolynomial
*qp
;
3699 isl_qpolynomial
*opt
;
3703 static int opt_fn(__isl_take isl_point
*pnt
, void *user
)
3705 struct isl_opt_data
*data
= (struct isl_opt_data
*)user
;
3706 isl_qpolynomial
*val
;
3708 val
= isl_qpolynomial_eval(isl_qpolynomial_copy(data
->qp
), pnt
);
3712 } else if (data
->max
) {
3713 data
->opt
= isl_qpolynomial_max_cst(data
->opt
, val
);
3715 data
->opt
= isl_qpolynomial_min_cst(data
->opt
, val
);
3721 __isl_give isl_qpolynomial
*isl_qpolynomial_opt_on_domain(
3722 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*set
, int max
)
3724 struct isl_opt_data data
= { NULL
, 1, NULL
, max
};
3729 if (isl_upoly_is_cst(qp
->upoly
)) {
3734 set
= fix_inactive(set
, qp
);
3737 if (isl_set_foreach_point(set
, opt_fn
, &data
) < 0)
3741 data
.opt
= isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp
));
3744 isl_qpolynomial_free(qp
);
3748 isl_qpolynomial_free(qp
);
3749 isl_qpolynomial_free(data
.opt
);
3753 __isl_give isl_qpolynomial
*isl_qpolynomial_morph(__isl_take isl_qpolynomial
*qp
,
3754 __isl_take isl_morph
*morph
)
3759 struct isl_upoly
**subs
;
3762 qp
= isl_qpolynomial_cow(qp
);
3767 isl_assert(ctx
, isl_dim_equal(qp
->dim
, morph
->dom
->dim
), goto error
);
3769 n_sub
= morph
->inv
->n_row
- 1;
3770 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
3771 n_sub
+= qp
->div
->n_row
;
3772 subs
= isl_calloc_array(ctx
, struct isl_upoly
*, n_sub
);
3776 for (i
= 0; 1 + i
< morph
->inv
->n_row
; ++i
)
3777 subs
[i
] = isl_upoly_from_affine(ctx
, morph
->inv
->row
[1 + i
],
3778 morph
->inv
->row
[0][0], morph
->inv
->n_col
);
3779 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
3780 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3781 subs
[morph
->inv
->n_row
- 1 + i
] =
3782 isl_upoly_var_pow(ctx
, morph
->inv
->n_col
- 1 + i
, 1);
3784 qp
->upoly
= isl_upoly_subs(qp
->upoly
, 0, n_sub
, subs
);
3786 for (i
= 0; i
< n_sub
; ++i
)
3787 isl_upoly_free(subs
[i
]);
3790 mat
= isl_mat_diagonal(isl_mat_identity(ctx
, 1), isl_mat_copy(morph
->inv
));
3791 mat
= isl_mat_diagonal(mat
, isl_mat_identity(ctx
, qp
->div
->n_row
));
3792 qp
->div
= isl_mat_product(qp
->div
, mat
);
3793 isl_dim_free(qp
->dim
);
3794 qp
->dim
= isl_dim_copy(morph
->ran
->dim
);
3796 if (!qp
->upoly
|| !qp
->div
|| !qp
->dim
)
3799 isl_morph_free(morph
);
3803 isl_qpolynomial_free(qp
);
3804 isl_morph_free(morph
);
3808 static int neg_entry(void **entry
, void *user
)
3810 isl_pw_qpolynomial
**pwqp
= (isl_pw_qpolynomial
**)entry
;
3812 *pwqp
= isl_pw_qpolynomial_neg(*pwqp
);
3814 return *pwqp
? 0 : -1;
3817 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_neg(
3818 __isl_take isl_union_pw_qpolynomial
*upwqp
)
3820 upwqp
= isl_union_pw_qpolynomial_cow(upwqp
);
3824 if (isl_hash_table_foreach(upwqp
->dim
->ctx
, &upwqp
->table
,
3825 &neg_entry
, NULL
) < 0)
3830 isl_union_pw_qpolynomial_free(upwqp
);
3834 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_sub(
3835 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
3836 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
3838 return isl_union_pw_qpolynomial_add(upwqp1
,
3839 isl_union_pw_qpolynomial_neg(upwqp2
));
3842 static int mul_entry(void **entry
, void *user
)
3844 struct isl_union_pw_qpolynomial_match_bin_data
*data
= user
;
3846 struct isl_hash_table_entry
*entry2
;
3847 isl_pw_qpolynomial
*pwpq
= *entry
;
3850 hash
= isl_dim_get_hash(pwpq
->dim
);
3851 entry2
= isl_hash_table_find(data
->u2
->dim
->ctx
, &data
->u2
->table
,
3852 hash
, &has_dim
, pwpq
->dim
, 0);
3856 pwpq
= isl_pw_qpolynomial_copy(pwpq
);
3857 pwpq
= isl_pw_qpolynomial_mul(pwpq
,
3858 isl_pw_qpolynomial_copy(entry2
->data
));
3860 empty
= isl_pw_qpolynomial_is_zero(pwpq
);
3862 isl_pw_qpolynomial_free(pwpq
);
3866 isl_pw_qpolynomial_free(pwpq
);
3870 data
->res
= isl_union_pw_qpolynomial_add_pw_qpolynomial(data
->res
, pwpq
);
3875 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_mul(
3876 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
3877 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
3879 return match_bin_op(upwqp1
, upwqp2
, &mul_entry
);
3882 /* Reorder the columns of the given div definitions according to the
3885 static __isl_give isl_mat
*reorder_divs(__isl_take isl_mat
*div
,
3886 __isl_take isl_reordering
*r
)
3895 extra
= isl_dim_total(r
->dim
) + div
->n_row
- r
->len
;
3896 mat
= isl_mat_alloc(div
->ctx
, div
->n_row
, div
->n_col
+ extra
);
3900 for (i
= 0; i
< div
->n_row
; ++i
) {
3901 isl_seq_cpy(mat
->row
[i
], div
->row
[i
], 2);
3902 isl_seq_clr(mat
->row
[i
] + 2, mat
->n_col
- 2);
3903 for (j
= 0; j
< r
->len
; ++j
)
3904 isl_int_set(mat
->row
[i
][2 + r
->pos
[j
]],
3905 div
->row
[i
][2 + j
]);
3908 isl_reordering_free(r
);
3912 isl_reordering_free(r
);
3917 /* Reorder the dimension of "qp" according to the given reordering.
3919 __isl_give isl_qpolynomial
*isl_qpolynomial_realign(
3920 __isl_take isl_qpolynomial
*qp
, __isl_take isl_reordering
*r
)
3922 qp
= isl_qpolynomial_cow(qp
);
3926 r
= isl_reordering_extend(r
, qp
->div
->n_row
);
3930 qp
->div
= reorder_divs(qp
->div
, isl_reordering_copy(r
));
3934 qp
->upoly
= reorder(qp
->upoly
, r
->pos
);
3938 qp
= isl_qpolynomial_reset_dim(qp
, isl_dim_copy(r
->dim
));
3940 isl_reordering_free(r
);
3943 isl_qpolynomial_free(qp
);
3944 isl_reordering_free(r
);
3948 __isl_give isl_qpolynomial
*isl_qpolynomial_align_params(
3949 __isl_take isl_qpolynomial
*qp
, __isl_take isl_dim
*model
)
3954 if (!isl_dim_match(qp
->dim
, isl_dim_param
, model
, isl_dim_param
)) {
3955 isl_reordering
*exp
;
3957 model
= isl_dim_drop(model
, isl_dim_in
,
3958 0, isl_dim_size(model
, isl_dim_in
));
3959 model
= isl_dim_drop(model
, isl_dim_out
,
3960 0, isl_dim_size(model
, isl_dim_out
));
3961 exp
= isl_parameter_alignment_reordering(qp
->dim
, model
);
3962 exp
= isl_reordering_extend_dim(exp
,
3963 isl_qpolynomial_get_dim(qp
));
3964 qp
= isl_qpolynomial_realign(qp
, exp
);
3967 isl_dim_free(model
);
3970 isl_dim_free(model
);
3971 isl_qpolynomial_free(qp
);
3975 struct isl_split_periods_data
{
3977 isl_pw_qpolynomial
*res
;
3980 /* Create a slice where the integer division "div" has the fixed value "v".
3981 * In particular, if "div" refers to floor(f/m), then create a slice
3983 * m v <= f <= m v + (m - 1)
3988 * -f + m v + (m - 1) >= 0
3990 static __isl_give isl_set
*set_div_slice(__isl_take isl_dim
*dim
,
3991 __isl_keep isl_qpolynomial
*qp
, int div
, isl_int v
)
3994 isl_basic_set
*bset
= NULL
;
4000 total
= isl_dim_total(dim
);
4001 bset
= isl_basic_set_alloc_dim(isl_dim_copy(dim
), 0, 0, 2);
4003 k
= isl_basic_set_alloc_inequality(bset
);
4006 isl_seq_cpy(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4007 isl_int_submul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4009 k
= isl_basic_set_alloc_inequality(bset
);
4012 isl_seq_neg(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4013 isl_int_addmul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4014 isl_int_add(bset
->ineq
[k
][0], bset
->ineq
[k
][0], qp
->div
->row
[div
][0]);
4015 isl_int_sub_ui(bset
->ineq
[k
][0], bset
->ineq
[k
][0], 1);
4018 return isl_set_from_basic_set(bset
);
4020 isl_basic_set_free(bset
);
4025 static int split_periods(__isl_take isl_set
*set
,
4026 __isl_take isl_qpolynomial
*qp
, void *user
);
4028 /* Create a slice of the domain "set" such that integer division "div"
4029 * has the fixed value "v" and add the results to data->res,
4030 * replacing the integer division by "v" in "qp".
4032 static int set_div(__isl_take isl_set
*set
,
4033 __isl_take isl_qpolynomial
*qp
, int div
, isl_int v
,
4034 struct isl_split_periods_data
*data
)
4039 struct isl_upoly
*cst
;
4041 slice
= set_div_slice(isl_set_get_dim(set
), qp
, div
, v
);
4042 set
= isl_set_intersect(set
, slice
);
4047 total
= isl_dim_total(qp
->dim
);
4049 for (i
= div
+ 1; i
< qp
->div
->n_row
; ++i
) {
4050 if (isl_int_is_zero(qp
->div
->row
[i
][2 + total
+ div
]))
4052 isl_int_addmul(qp
->div
->row
[i
][1],
4053 qp
->div
->row
[i
][2 + total
+ div
], v
);
4054 isl_int_set_si(qp
->div
->row
[i
][2 + total
+ div
], 0);
4057 cst
= isl_upoly_rat_cst(qp
->dim
->ctx
, v
, qp
->dim
->ctx
->one
);
4058 qp
= substitute_div(qp
, div
, cst
);
4060 return split_periods(set
, qp
, data
);
4063 isl_qpolynomial_free(qp
);
4067 /* Split the domain "set" such that integer division "div"
4068 * has a fixed value (ranging from "min" to "max") on each slice
4069 * and add the results to data->res.
4071 static int split_div(__isl_take isl_set
*set
,
4072 __isl_take isl_qpolynomial
*qp
, int div
, isl_int min
, isl_int max
,
4073 struct isl_split_periods_data
*data
)
4075 for (; isl_int_le(min
, max
); isl_int_add_ui(min
, min
, 1)) {
4076 isl_set
*set_i
= isl_set_copy(set
);
4077 isl_qpolynomial
*qp_i
= isl_qpolynomial_copy(qp
);
4079 if (set_div(set_i
, qp_i
, div
, min
, data
) < 0)
4083 isl_qpolynomial_free(qp
);
4087 isl_qpolynomial_free(qp
);
4091 /* If "qp" refers to any integer division
4092 * that can only attain "max_periods" distinct values on "set"
4093 * then split the domain along those distinct values.
4094 * Add the results (or the original if no splitting occurs)
4097 static int split_periods(__isl_take isl_set
*set
,
4098 __isl_take isl_qpolynomial
*qp
, void *user
)
4101 isl_pw_qpolynomial
*pwqp
;
4102 struct isl_split_periods_data
*data
;
4107 data
= (struct isl_split_periods_data
*)user
;
4112 if (qp
->div
->n_row
== 0) {
4113 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4114 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4120 total
= isl_dim_total(qp
->dim
);
4121 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4122 enum isl_lp_result lp_res
;
4124 if (isl_seq_first_non_zero(qp
->div
->row
[i
] + 2 + total
,
4125 qp
->div
->n_row
) != -1)
4128 lp_res
= isl_set_solve_lp(set
, 0, qp
->div
->row
[i
] + 1,
4129 set
->ctx
->one
, &min
, NULL
, NULL
);
4130 if (lp_res
== isl_lp_error
)
4132 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4134 isl_int_fdiv_q(min
, min
, qp
->div
->row
[i
][0]);
4136 lp_res
= isl_set_solve_lp(set
, 1, qp
->div
->row
[i
] + 1,
4137 set
->ctx
->one
, &max
, NULL
, NULL
);
4138 if (lp_res
== isl_lp_error
)
4140 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4142 isl_int_fdiv_q(max
, max
, qp
->div
->row
[i
][0]);
4144 isl_int_sub(max
, max
, min
);
4145 if (isl_int_cmp_si(max
, data
->max_periods
) < 0) {
4146 isl_int_add(max
, max
, min
);
4151 if (i
< qp
->div
->n_row
) {
4152 r
= split_div(set
, qp
, i
, min
, max
, data
);
4154 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4155 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4167 isl_qpolynomial_free(qp
);
4171 /* If any quasi-polynomial in pwqp refers to any integer division
4172 * that can only attain "max_periods" distinct values on its domain
4173 * then split the domain along those distinct values.
4175 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_split_periods(
4176 __isl_take isl_pw_qpolynomial
*pwqp
, int max_periods
)
4178 struct isl_split_periods_data data
;
4180 data
.max_periods
= max_periods
;
4181 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp
));
4183 if (isl_pw_qpolynomial_foreach_piece(pwqp
, &split_periods
, &data
) < 0)
4186 isl_pw_qpolynomial_free(pwqp
);
4190 isl_pw_qpolynomial_free(data
.res
);
4191 isl_pw_qpolynomial_free(pwqp
);
4195 /* Construct a piecewise quasipolynomial that is constant on the given
4196 * domain. In particular, it is
4199 * infinity if cst == -1
4201 static __isl_give isl_pw_qpolynomial
*constant_on_domain(
4202 __isl_take isl_basic_set
*bset
, int cst
)
4205 isl_qpolynomial
*qp
;
4210 bset
= isl_basic_map_domain(isl_basic_map_from_range(bset
));
4211 dim
= isl_basic_set_get_dim(bset
);
4213 qp
= isl_qpolynomial_infty(dim
);
4215 qp
= isl_qpolynomial_zero(dim
);
4217 qp
= isl_qpolynomial_one(dim
);
4218 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset
), qp
);
4221 /* Factor bset, call fn on each of the factors and return the product.
4223 * If no factors can be found, simply call fn on the input.
4224 * Otherwise, construct the factors based on the factorizer,
4225 * call fn on each factor and compute the product.
4227 static __isl_give isl_pw_qpolynomial
*compressed_multiplicative_call(
4228 __isl_take isl_basic_set
*bset
,
4229 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4235 isl_qpolynomial
*qp
;
4236 isl_pw_qpolynomial
*pwqp
;
4240 f
= isl_basic_set_factorizer(bset
);
4243 if (f
->n_group
== 0) {
4244 isl_factorizer_free(f
);
4248 nparam
= isl_basic_set_dim(bset
, isl_dim_param
);
4249 nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
4251 dim
= isl_basic_set_get_dim(bset
);
4252 dim
= isl_dim_domain(dim
);
4253 set
= isl_set_universe(isl_dim_copy(dim
));
4254 qp
= isl_qpolynomial_one(dim
);
4255 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4257 bset
= isl_morph_basic_set(isl_morph_copy(f
->morph
), bset
);
4259 for (i
= 0, n
= 0; i
< f
->n_group
; ++i
) {
4260 isl_basic_set
*bset_i
;
4261 isl_pw_qpolynomial
*pwqp_i
;
4263 bset_i
= isl_basic_set_copy(bset
);
4264 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4265 nparam
+ n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4266 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4268 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
,
4269 n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4270 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
, 0, n
);
4272 pwqp_i
= fn(bset_i
);
4273 pwqp
= isl_pw_qpolynomial_mul(pwqp
, pwqp_i
);
4278 isl_basic_set_free(bset
);
4279 isl_factorizer_free(f
);
4283 isl_basic_set_free(bset
);
4287 /* Factor bset, call fn on each of the factors and return the product.
4288 * The function is assumed to evaluate to zero on empty domains,
4289 * to one on zero-dimensional domains and to infinity on unbounded domains
4290 * and will not be called explicitly on zero-dimensional or unbounded domains.
4292 * We first check for some special cases and remove all equalities.
4293 * Then we hand over control to compressed_multiplicative_call.
4295 __isl_give isl_pw_qpolynomial
*isl_basic_set_multiplicative_call(
4296 __isl_take isl_basic_set
*bset
,
4297 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4301 isl_pw_qpolynomial
*pwqp
;
4302 unsigned orig_nvar
, final_nvar
;
4307 if (isl_basic_set_plain_is_empty(bset
))
4308 return constant_on_domain(bset
, 0);
4310 orig_nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
4313 return constant_on_domain(bset
, 1);
4315 bounded
= isl_basic_set_is_bounded(bset
);
4319 return constant_on_domain(bset
, -1);
4321 if (bset
->n_eq
== 0)
4322 return compressed_multiplicative_call(bset
, fn
);
4324 morph
= isl_basic_set_full_compression(bset
);
4325 bset
= isl_morph_basic_set(isl_morph_copy(morph
), bset
);
4327 final_nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
4329 pwqp
= compressed_multiplicative_call(bset
, fn
);
4331 morph
= isl_morph_remove_dom_dims(morph
, isl_dim_set
, 0, orig_nvar
);
4332 morph
= isl_morph_remove_ran_dims(morph
, isl_dim_set
, 0, final_nvar
);
4333 morph
= isl_morph_inverse(morph
);
4335 pwqp
= isl_pw_qpolynomial_morph(pwqp
, morph
);
4339 isl_basic_set_free(bset
);
4343 /* Drop all floors in "qp", turning each integer division [a/m] into
4344 * a rational division a/m. If "down" is set, then the integer division
4345 * is replaces by (a-(m-1))/m instead.
4347 static __isl_give isl_qpolynomial
*qp_drop_floors(
4348 __isl_take isl_qpolynomial
*qp
, int down
)
4351 struct isl_upoly
*s
;
4355 if (qp
->div
->n_row
== 0)
4358 qp
= isl_qpolynomial_cow(qp
);
4362 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
4364 isl_int_sub(qp
->div
->row
[i
][1],
4365 qp
->div
->row
[i
][1], qp
->div
->row
[i
][0]);
4366 isl_int_add_ui(qp
->div
->row
[i
][1],
4367 qp
->div
->row
[i
][1], 1);
4369 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
4370 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
4371 qp
= substitute_div(qp
, i
, s
);
4379 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4380 * a rational division a/m.
4382 static __isl_give isl_pw_qpolynomial
*pwqp_drop_floors(
4383 __isl_take isl_pw_qpolynomial
*pwqp
)
4390 if (isl_pw_qpolynomial_is_zero(pwqp
))
4393 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
4397 for (i
= 0; i
< pwqp
->n
; ++i
) {
4398 pwqp
->p
[i
].qp
= qp_drop_floors(pwqp
->p
[i
].qp
, 0);
4405 isl_pw_qpolynomial_free(pwqp
);
4409 /* Adjust all the integer divisions in "qp" such that they are at least
4410 * one over the given orthant (identified by "signs"). This ensures
4411 * that they will still be non-negative even after subtracting (m-1)/m.
4413 * In particular, f is replaced by f' + v, changing f = [a/m]
4414 * to f' = [(a - m v)/m].
4415 * If the constant term k in a is smaller than m,
4416 * the constant term of v is set to floor(k/m) - 1.
4417 * For any other term, if the coefficient c and the variable x have
4418 * the same sign, then no changes are needed.
4419 * Otherwise, if the variable is positive (and c is negative),
4420 * then the coefficient of x in v is set to floor(c/m).
4421 * If the variable is negative (and c is positive),
4422 * then the coefficient of x in v is set to ceil(c/m).
4424 static __isl_give isl_qpolynomial
*make_divs_pos(__isl_take isl_qpolynomial
*qp
,
4430 struct isl_upoly
*s
;
4432 qp
= isl_qpolynomial_cow(qp
);
4435 qp
->div
= isl_mat_cow(qp
->div
);
4439 total
= isl_dim_total(qp
->dim
);
4440 v
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
4442 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4443 isl_int
*row
= qp
->div
->row
[i
];
4447 if (isl_int_lt(row
[1], row
[0])) {
4448 isl_int_fdiv_q(v
->el
[0], row
[1], row
[0]);
4449 isl_int_sub_ui(v
->el
[0], v
->el
[0], 1);
4450 isl_int_submul(row
[1], row
[0], v
->el
[0]);
4452 for (j
= 0; j
< total
; ++j
) {
4453 if (isl_int_sgn(row
[2 + j
]) * signs
[j
] >= 0)
4456 isl_int_cdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4458 isl_int_fdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4459 isl_int_submul(row
[2 + j
], row
[0], v
->el
[1 + j
]);
4461 for (j
= 0; j
< i
; ++j
) {
4462 if (isl_int_sgn(row
[2 + total
+ j
]) >= 0)
4464 isl_int_fdiv_q(v
->el
[1 + total
+ j
],
4465 row
[2 + total
+ j
], row
[0]);
4466 isl_int_submul(row
[2 + total
+ j
],
4467 row
[0], v
->el
[1 + total
+ j
]);
4469 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
4470 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
4472 isl_seq_combine(qp
->div
->row
[j
] + 1,
4473 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
4474 qp
->div
->row
[j
][2 + total
+ i
], v
->el
, v
->size
);
4476 isl_int_set_si(v
->el
[1 + total
+ i
], 1);
4477 s
= isl_upoly_from_affine(qp
->dim
->ctx
, v
->el
,
4478 qp
->div
->ctx
->one
, v
->size
);
4479 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ i
, 1, &s
);
4489 isl_qpolynomial_free(qp
);
4493 struct isl_to_poly_data
{
4495 isl_pw_qpolynomial
*res
;
4496 isl_qpolynomial
*qp
;
4499 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4500 * We first make all integer divisions positive and then split the
4501 * quasipolynomials into terms with sign data->sign (the direction
4502 * of the requested approximation) and terms with the opposite sign.
4503 * In the first set of terms, each integer division [a/m] is
4504 * overapproximated by a/m, while in the second it is underapproximated
4507 static int to_polynomial_on_orthant(__isl_take isl_set
*orthant
, int *signs
,
4510 struct isl_to_poly_data
*data
= user
;
4511 isl_pw_qpolynomial
*t
;
4512 isl_qpolynomial
*qp
, *up
, *down
;
4514 qp
= isl_qpolynomial_copy(data
->qp
);
4515 qp
= make_divs_pos(qp
, signs
);
4517 up
= isl_qpolynomial_terms_of_sign(qp
, signs
, data
->sign
);
4518 up
= qp_drop_floors(up
, 0);
4519 down
= isl_qpolynomial_terms_of_sign(qp
, signs
, -data
->sign
);
4520 down
= qp_drop_floors(down
, 1);
4522 isl_qpolynomial_free(qp
);
4523 qp
= isl_qpolynomial_add(up
, down
);
4525 t
= isl_pw_qpolynomial_alloc(orthant
, qp
);
4526 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, t
);
4531 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4532 * the polynomial will be an overapproximation. If "sign" is negative,
4533 * it will be an underapproximation. If "sign" is zero, the approximation
4534 * will lie somewhere in between.
4536 * In particular, is sign == 0, we simply drop the floors, turning
4537 * the integer divisions into rational divisions.
4538 * Otherwise, we split the domains into orthants, make all integer divisions
4539 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4540 * depending on the requested sign and the sign of the term in which
4541 * the integer division appears.
4543 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_to_polynomial(
4544 __isl_take isl_pw_qpolynomial
*pwqp
, int sign
)
4547 struct isl_to_poly_data data
;
4550 return pwqp_drop_floors(pwqp
);
4556 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp
));
4558 for (i
= 0; i
< pwqp
->n
; ++i
) {
4559 if (pwqp
->p
[i
].qp
->div
->n_row
== 0) {
4560 isl_pw_qpolynomial
*t
;
4561 t
= isl_pw_qpolynomial_alloc(
4562 isl_set_copy(pwqp
->p
[i
].set
),
4563 isl_qpolynomial_copy(pwqp
->p
[i
].qp
));
4564 data
.res
= isl_pw_qpolynomial_add_disjoint(data
.res
, t
);
4567 data
.qp
= pwqp
->p
[i
].qp
;
4568 if (isl_set_foreach_orthant(pwqp
->p
[i
].set
,
4569 &to_polynomial_on_orthant
, &data
) < 0)
4573 isl_pw_qpolynomial_free(pwqp
);
4577 isl_pw_qpolynomial_free(pwqp
);
4578 isl_pw_qpolynomial_free(data
.res
);
4582 static int poly_entry(void **entry
, void *user
)
4585 isl_pw_qpolynomial
**pwqp
= (isl_pw_qpolynomial
**)entry
;
4587 *pwqp
= isl_pw_qpolynomial_to_polynomial(*pwqp
, *sign
);
4589 return *pwqp
? 0 : -1;
4592 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_to_polynomial(
4593 __isl_take isl_union_pw_qpolynomial
*upwqp
, int sign
)
4595 upwqp
= isl_union_pw_qpolynomial_cow(upwqp
);
4599 if (isl_hash_table_foreach(upwqp
->dim
->ctx
, &upwqp
->table
,
4600 &poly_entry
, &sign
) < 0)
4605 isl_union_pw_qpolynomial_free(upwqp
);
4609 __isl_give isl_basic_map
*isl_basic_map_from_qpolynomial(
4610 __isl_take isl_qpolynomial
*qp
)
4614 isl_vec
*aff
= NULL
;
4615 isl_basic_map
*bmap
= NULL
;
4621 if (!isl_upoly_is_affine(qp
->upoly
))
4622 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
4623 "input quasi-polynomial not affine", goto error
);
4624 aff
= isl_qpolynomial_extract_affine(qp
);
4627 dim
= isl_qpolynomial_get_dim(qp
);
4628 dim
= isl_dim_from_domain(dim
);
4629 pos
= 1 + isl_dim_offset(dim
, isl_dim_out
);
4630 dim
= isl_dim_add(dim
, isl_dim_out
, 1);
4631 n_div
= qp
->div
->n_row
;
4632 bmap
= isl_basic_map_alloc_dim(dim
, n_div
, 1, 2 * n_div
);
4634 for (i
= 0; i
< n_div
; ++i
) {
4635 k
= isl_basic_map_alloc_div(bmap
);
4638 isl_seq_cpy(bmap
->div
[k
], qp
->div
->row
[i
], qp
->div
->n_col
);
4639 isl_int_set_si(bmap
->div
[k
][qp
->div
->n_col
], 0);
4640 if (isl_basic_map_add_div_constraints(bmap
, k
) < 0)
4643 k
= isl_basic_map_alloc_equality(bmap
);
4646 isl_int_neg(bmap
->eq
[k
][pos
], aff
->el
[0]);
4647 isl_seq_cpy(bmap
->eq
[k
], aff
->el
+ 1, pos
);
4648 isl_seq_cpy(bmap
->eq
[k
] + pos
+ 1, aff
->el
+ 1 + pos
, n_div
);
4651 isl_qpolynomial_free(qp
);
4652 bmap
= isl_basic_map_finalize(bmap
);
4656 isl_qpolynomial_free(qp
);
4657 isl_basic_map_free(bmap
);