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,
14 #include <isl_union_map_private.h>
15 #include <isl_polynomial_private.h>
16 #include <isl_point_private.h>
17 #include <isl_dim_private.h>
18 #include <isl_map_private.h>
19 #include <isl_mat_private.h>
21 static unsigned pos(__isl_keep isl_dim
*dim
, enum isl_dim_type type
)
24 case isl_dim_param
: return 0;
25 case isl_dim_in
: return dim
->nparam
;
26 case isl_dim_out
: return dim
->nparam
+ dim
->n_in
;
31 int isl_upoly_is_cst(__isl_keep
struct isl_upoly
*up
)
39 __isl_keep
struct isl_upoly_cst
*isl_upoly_as_cst(__isl_keep
struct isl_upoly
*up
)
44 isl_assert(up
->ctx
, up
->var
< 0, return NULL
);
46 return (struct isl_upoly_cst
*)up
;
49 __isl_keep
struct isl_upoly_rec
*isl_upoly_as_rec(__isl_keep
struct isl_upoly
*up
)
54 isl_assert(up
->ctx
, up
->var
>= 0, return NULL
);
56 return (struct isl_upoly_rec
*)up
;
59 int isl_upoly_is_equal(__isl_keep
struct isl_upoly
*up1
,
60 __isl_keep
struct isl_upoly
*up2
)
63 struct isl_upoly_rec
*rec1
, *rec2
;
69 if (up1
->var
!= up2
->var
)
71 if (isl_upoly_is_cst(up1
)) {
72 struct isl_upoly_cst
*cst1
, *cst2
;
73 cst1
= isl_upoly_as_cst(up1
);
74 cst2
= isl_upoly_as_cst(up2
);
77 return isl_int_eq(cst1
->n
, cst2
->n
) &&
78 isl_int_eq(cst1
->d
, cst2
->d
);
81 rec1
= isl_upoly_as_rec(up1
);
82 rec2
= isl_upoly_as_rec(up2
);
86 if (rec1
->n
!= rec2
->n
)
89 for (i
= 0; i
< rec1
->n
; ++i
) {
90 int eq
= isl_upoly_is_equal(rec1
->p
[i
], rec2
->p
[i
]);
98 int isl_upoly_is_zero(__isl_keep
struct isl_upoly
*up
)
100 struct isl_upoly_cst
*cst
;
104 if (!isl_upoly_is_cst(up
))
107 cst
= isl_upoly_as_cst(up
);
111 return isl_int_is_zero(cst
->n
) && isl_int_is_pos(cst
->d
);
114 int isl_upoly_sgn(__isl_keep
struct isl_upoly
*up
)
116 struct isl_upoly_cst
*cst
;
120 if (!isl_upoly_is_cst(up
))
123 cst
= isl_upoly_as_cst(up
);
127 return isl_int_sgn(cst
->n
);
130 int isl_upoly_is_nan(__isl_keep
struct isl_upoly
*up
)
132 struct isl_upoly_cst
*cst
;
136 if (!isl_upoly_is_cst(up
))
139 cst
= isl_upoly_as_cst(up
);
143 return isl_int_is_zero(cst
->n
) && isl_int_is_zero(cst
->d
);
146 int isl_upoly_is_infty(__isl_keep
struct isl_upoly
*up
)
148 struct isl_upoly_cst
*cst
;
152 if (!isl_upoly_is_cst(up
))
155 cst
= isl_upoly_as_cst(up
);
159 return isl_int_is_pos(cst
->n
) && isl_int_is_zero(cst
->d
);
162 int isl_upoly_is_neginfty(__isl_keep
struct isl_upoly
*up
)
164 struct isl_upoly_cst
*cst
;
168 if (!isl_upoly_is_cst(up
))
171 cst
= isl_upoly_as_cst(up
);
175 return isl_int_is_neg(cst
->n
) && isl_int_is_zero(cst
->d
);
178 int isl_upoly_is_one(__isl_keep
struct isl_upoly
*up
)
180 struct isl_upoly_cst
*cst
;
184 if (!isl_upoly_is_cst(up
))
187 cst
= isl_upoly_as_cst(up
);
191 return isl_int_eq(cst
->n
, cst
->d
) && isl_int_is_pos(cst
->d
);
194 int isl_upoly_is_negone(__isl_keep
struct isl_upoly
*up
)
196 struct isl_upoly_cst
*cst
;
200 if (!isl_upoly_is_cst(up
))
203 cst
= isl_upoly_as_cst(up
);
207 return isl_int_is_negone(cst
->n
) && isl_int_is_one(cst
->d
);
210 __isl_give
struct isl_upoly_cst
*isl_upoly_cst_alloc(struct isl_ctx
*ctx
)
212 struct isl_upoly_cst
*cst
;
214 cst
= isl_alloc_type(ctx
, struct isl_upoly_cst
);
223 isl_int_init(cst
->n
);
224 isl_int_init(cst
->d
);
229 __isl_give
struct isl_upoly
*isl_upoly_zero(struct isl_ctx
*ctx
)
231 struct isl_upoly_cst
*cst
;
233 cst
= isl_upoly_cst_alloc(ctx
);
237 isl_int_set_si(cst
->n
, 0);
238 isl_int_set_si(cst
->d
, 1);
243 __isl_give
struct isl_upoly
*isl_upoly_infty(struct isl_ctx
*ctx
)
245 struct isl_upoly_cst
*cst
;
247 cst
= isl_upoly_cst_alloc(ctx
);
251 isl_int_set_si(cst
->n
, 1);
252 isl_int_set_si(cst
->d
, 0);
257 __isl_give
struct isl_upoly
*isl_upoly_neginfty(struct isl_ctx
*ctx
)
259 struct isl_upoly_cst
*cst
;
261 cst
= isl_upoly_cst_alloc(ctx
);
265 isl_int_set_si(cst
->n
, -1);
266 isl_int_set_si(cst
->d
, 0);
271 __isl_give
struct isl_upoly
*isl_upoly_nan(struct isl_ctx
*ctx
)
273 struct isl_upoly_cst
*cst
;
275 cst
= isl_upoly_cst_alloc(ctx
);
279 isl_int_set_si(cst
->n
, 0);
280 isl_int_set_si(cst
->d
, 0);
285 __isl_give
struct isl_upoly
*isl_upoly_rat_cst(struct isl_ctx
*ctx
,
286 isl_int n
, isl_int d
)
288 struct isl_upoly_cst
*cst
;
290 cst
= isl_upoly_cst_alloc(ctx
);
294 isl_int_set(cst
->n
, n
);
295 isl_int_set(cst
->d
, d
);
300 __isl_give
struct isl_upoly_rec
*isl_upoly_alloc_rec(struct isl_ctx
*ctx
,
303 struct isl_upoly_rec
*rec
;
305 isl_assert(ctx
, var
>= 0, return NULL
);
306 isl_assert(ctx
, size
>= 0, return NULL
);
307 rec
= isl_calloc(ctx
, struct isl_upoly_rec
,
308 sizeof(struct isl_upoly_rec
) +
309 (size
- 1) * sizeof(struct isl_upoly
*));
324 __isl_give isl_qpolynomial
*isl_qpolynomial_reset_dim(
325 __isl_take isl_qpolynomial
*qp
, __isl_take isl_dim
*dim
)
327 qp
= isl_qpolynomial_cow(qp
);
331 isl_dim_free(qp
->dim
);
336 isl_qpolynomial_free(qp
);
341 isl_ctx
*isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial
*qp
)
343 return qp
? qp
->dim
->ctx
: NULL
;
346 __isl_give isl_dim
*isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial
*qp
)
348 return qp
? isl_dim_copy(qp
->dim
) : NULL
;
351 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial
*qp
,
352 enum isl_dim_type type
)
354 return qp
? isl_dim_size(qp
->dim
, type
) : 0;
357 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial
*qp
)
359 return qp
? isl_upoly_is_zero(qp
->upoly
) : -1;
362 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial
*qp
)
364 return qp
? isl_upoly_is_one(qp
->upoly
) : -1;
367 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial
*qp
)
369 return qp
? isl_upoly_is_nan(qp
->upoly
) : -1;
372 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial
*qp
)
374 return qp
? isl_upoly_is_infty(qp
->upoly
) : -1;
377 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial
*qp
)
379 return qp
? isl_upoly_is_neginfty(qp
->upoly
) : -1;
382 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial
*qp
)
384 return qp
? isl_upoly_sgn(qp
->upoly
) : 0;
387 static void upoly_free_cst(__isl_take
struct isl_upoly_cst
*cst
)
389 isl_int_clear(cst
->n
);
390 isl_int_clear(cst
->d
);
393 static void upoly_free_rec(__isl_take
struct isl_upoly_rec
*rec
)
397 for (i
= 0; i
< rec
->n
; ++i
)
398 isl_upoly_free(rec
->p
[i
]);
401 __isl_give
struct isl_upoly
*isl_upoly_copy(__isl_keep
struct isl_upoly
*up
)
410 __isl_give
struct isl_upoly
*isl_upoly_dup_cst(__isl_keep
struct isl_upoly
*up
)
412 struct isl_upoly_cst
*cst
;
413 struct isl_upoly_cst
*dup
;
415 cst
= isl_upoly_as_cst(up
);
419 dup
= isl_upoly_as_cst(isl_upoly_zero(up
->ctx
));
422 isl_int_set(dup
->n
, cst
->n
);
423 isl_int_set(dup
->d
, cst
->d
);
428 __isl_give
struct isl_upoly
*isl_upoly_dup_rec(__isl_keep
struct isl_upoly
*up
)
431 struct isl_upoly_rec
*rec
;
432 struct isl_upoly_rec
*dup
;
434 rec
= isl_upoly_as_rec(up
);
438 dup
= isl_upoly_alloc_rec(up
->ctx
, up
->var
, rec
->n
);
442 for (i
= 0; i
< rec
->n
; ++i
) {
443 dup
->p
[i
] = isl_upoly_copy(rec
->p
[i
]);
451 isl_upoly_free(&dup
->up
);
455 __isl_give
struct isl_upoly
*isl_upoly_dup(__isl_keep
struct isl_upoly
*up
)
457 struct isl_upoly
*dup
;
462 if (isl_upoly_is_cst(up
))
463 return isl_upoly_dup_cst(up
);
465 return isl_upoly_dup_rec(up
);
468 __isl_give
struct isl_upoly
*isl_upoly_cow(__isl_take
struct isl_upoly
*up
)
476 return isl_upoly_dup(up
);
479 void isl_upoly_free(__isl_take
struct isl_upoly
*up
)
488 upoly_free_cst((struct isl_upoly_cst
*)up
);
490 upoly_free_rec((struct isl_upoly_rec
*)up
);
492 isl_ctx_deref(up
->ctx
);
496 static void isl_upoly_cst_reduce(__isl_keep
struct isl_upoly_cst
*cst
)
501 isl_int_gcd(gcd
, cst
->n
, cst
->d
);
502 if (!isl_int_is_zero(gcd
) && !isl_int_is_one(gcd
)) {
503 isl_int_divexact(cst
->n
, cst
->n
, gcd
);
504 isl_int_divexact(cst
->d
, cst
->d
, gcd
);
509 __isl_give
struct isl_upoly
*isl_upoly_sum_cst(__isl_take
struct isl_upoly
*up1
,
510 __isl_take
struct isl_upoly
*up2
)
512 struct isl_upoly_cst
*cst1
;
513 struct isl_upoly_cst
*cst2
;
515 up1
= isl_upoly_cow(up1
);
519 cst1
= isl_upoly_as_cst(up1
);
520 cst2
= isl_upoly_as_cst(up2
);
522 if (isl_int_eq(cst1
->d
, cst2
->d
))
523 isl_int_add(cst1
->n
, cst1
->n
, cst2
->n
);
525 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->d
);
526 isl_int_addmul(cst1
->n
, cst2
->n
, cst1
->d
);
527 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
530 isl_upoly_cst_reduce(cst1
);
540 static __isl_give
struct isl_upoly
*replace_by_zero(
541 __isl_take
struct isl_upoly
*up
)
549 return isl_upoly_zero(ctx
);
552 static __isl_give
struct isl_upoly
*replace_by_constant_term(
553 __isl_take
struct isl_upoly
*up
)
555 struct isl_upoly_rec
*rec
;
556 struct isl_upoly
*cst
;
561 rec
= isl_upoly_as_rec(up
);
564 cst
= isl_upoly_copy(rec
->p
[0]);
572 __isl_give
struct isl_upoly
*isl_upoly_sum(__isl_take
struct isl_upoly
*up1
,
573 __isl_take
struct isl_upoly
*up2
)
576 struct isl_upoly_rec
*rec1
, *rec2
;
581 if (isl_upoly_is_nan(up1
)) {
586 if (isl_upoly_is_nan(up2
)) {
591 if (isl_upoly_is_zero(up1
)) {
596 if (isl_upoly_is_zero(up2
)) {
601 if (up1
->var
< up2
->var
)
602 return isl_upoly_sum(up2
, up1
);
604 if (up2
->var
< up1
->var
) {
605 struct isl_upoly_rec
*rec
;
606 if (isl_upoly_is_infty(up2
) || isl_upoly_is_neginfty(up2
)) {
610 up1
= isl_upoly_cow(up1
);
611 rec
= isl_upoly_as_rec(up1
);
614 rec
->p
[0] = isl_upoly_sum(rec
->p
[0], up2
);
616 up1
= replace_by_constant_term(up1
);
620 if (isl_upoly_is_cst(up1
))
621 return isl_upoly_sum_cst(up1
, up2
);
623 rec1
= isl_upoly_as_rec(up1
);
624 rec2
= isl_upoly_as_rec(up2
);
628 if (rec1
->n
< rec2
->n
)
629 return isl_upoly_sum(up2
, up1
);
631 up1
= isl_upoly_cow(up1
);
632 rec1
= isl_upoly_as_rec(up1
);
636 for (i
= rec2
->n
- 1; i
>= 0; --i
) {
637 rec1
->p
[i
] = isl_upoly_sum(rec1
->p
[i
],
638 isl_upoly_copy(rec2
->p
[i
]));
641 if (i
== rec1
->n
- 1 && isl_upoly_is_zero(rec1
->p
[i
])) {
642 isl_upoly_free(rec1
->p
[i
]);
648 up1
= replace_by_zero(up1
);
649 else if (rec1
->n
== 1)
650 up1
= replace_by_constant_term(up1
);
661 __isl_give
struct isl_upoly
*isl_upoly_neg_cst(__isl_take
struct isl_upoly
*up
)
663 struct isl_upoly_cst
*cst
;
665 if (isl_upoly_is_zero(up
))
668 up
= isl_upoly_cow(up
);
672 cst
= isl_upoly_as_cst(up
);
674 isl_int_neg(cst
->n
, cst
->n
);
679 __isl_give
struct isl_upoly
*isl_upoly_neg(__isl_take
struct isl_upoly
*up
)
682 struct isl_upoly_rec
*rec
;
687 if (isl_upoly_is_cst(up
))
688 return isl_upoly_neg_cst(up
);
690 up
= isl_upoly_cow(up
);
691 rec
= isl_upoly_as_rec(up
);
695 for (i
= 0; i
< rec
->n
; ++i
) {
696 rec
->p
[i
] = isl_upoly_neg(rec
->p
[i
]);
707 __isl_give
struct isl_upoly
*isl_upoly_mul_cst(__isl_take
struct isl_upoly
*up1
,
708 __isl_take
struct isl_upoly
*up2
)
710 struct isl_upoly_cst
*cst1
;
711 struct isl_upoly_cst
*cst2
;
713 up1
= isl_upoly_cow(up1
);
717 cst1
= isl_upoly_as_cst(up1
);
718 cst2
= isl_upoly_as_cst(up2
);
720 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->n
);
721 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
723 isl_upoly_cst_reduce(cst1
);
733 __isl_give
struct isl_upoly
*isl_upoly_mul_rec(__isl_take
struct isl_upoly
*up1
,
734 __isl_take
struct isl_upoly
*up2
)
736 struct isl_upoly_rec
*rec1
;
737 struct isl_upoly_rec
*rec2
;
738 struct isl_upoly_rec
*res
;
742 rec1
= isl_upoly_as_rec(up1
);
743 rec2
= isl_upoly_as_rec(up2
);
746 size
= rec1
->n
+ rec2
->n
- 1;
747 res
= isl_upoly_alloc_rec(up1
->ctx
, up1
->var
, size
);
751 for (i
= 0; i
< rec1
->n
; ++i
) {
752 res
->p
[i
] = isl_upoly_mul(isl_upoly_copy(rec2
->p
[0]),
753 isl_upoly_copy(rec1
->p
[i
]));
758 for (; i
< size
; ++i
) {
759 res
->p
[i
] = isl_upoly_zero(up1
->ctx
);
764 for (i
= 0; i
< rec1
->n
; ++i
) {
765 for (j
= 1; j
< rec2
->n
; ++j
) {
766 struct isl_upoly
*up
;
767 up
= isl_upoly_mul(isl_upoly_copy(rec2
->p
[j
]),
768 isl_upoly_copy(rec1
->p
[i
]));
769 res
->p
[i
+ j
] = isl_upoly_sum(res
->p
[i
+ j
], up
);
782 isl_upoly_free(&res
->up
);
786 __isl_give
struct isl_upoly
*isl_upoly_mul(__isl_take
struct isl_upoly
*up1
,
787 __isl_take
struct isl_upoly
*up2
)
792 if (isl_upoly_is_nan(up1
)) {
797 if (isl_upoly_is_nan(up2
)) {
802 if (isl_upoly_is_zero(up1
)) {
807 if (isl_upoly_is_zero(up2
)) {
812 if (isl_upoly_is_one(up1
)) {
817 if (isl_upoly_is_one(up2
)) {
822 if (up1
->var
< up2
->var
)
823 return isl_upoly_mul(up2
, up1
);
825 if (up2
->var
< up1
->var
) {
827 struct isl_upoly_rec
*rec
;
828 if (isl_upoly_is_infty(up2
) || isl_upoly_is_neginfty(up2
)) {
829 isl_ctx
*ctx
= up1
->ctx
;
832 return isl_upoly_nan(ctx
);
834 up1
= isl_upoly_cow(up1
);
835 rec
= isl_upoly_as_rec(up1
);
839 for (i
= 0; i
< rec
->n
; ++i
) {
840 rec
->p
[i
] = isl_upoly_mul(rec
->p
[i
],
841 isl_upoly_copy(up2
));
849 if (isl_upoly_is_cst(up1
))
850 return isl_upoly_mul_cst(up1
, up2
);
852 return isl_upoly_mul_rec(up1
, up2
);
859 __isl_give isl_qpolynomial
*isl_qpolynomial_alloc(__isl_take isl_dim
*dim
,
860 unsigned n_div
, __isl_take
struct isl_upoly
*up
)
862 struct isl_qpolynomial
*qp
= NULL
;
868 total
= isl_dim_total(dim
);
870 qp
= isl_calloc_type(dim
->ctx
, struct isl_qpolynomial
);
875 qp
->div
= isl_mat_alloc(dim
->ctx
, n_div
, 1 + 1 + total
+ n_div
);
886 isl_qpolynomial_free(qp
);
890 __isl_give isl_qpolynomial
*isl_qpolynomial_copy(__isl_keep isl_qpolynomial
*qp
)
899 __isl_give isl_qpolynomial
*isl_qpolynomial_dup(__isl_keep isl_qpolynomial
*qp
)
901 struct isl_qpolynomial
*dup
;
906 dup
= isl_qpolynomial_alloc(isl_dim_copy(qp
->dim
), qp
->div
->n_row
,
907 isl_upoly_copy(qp
->upoly
));
910 isl_mat_free(dup
->div
);
911 dup
->div
= isl_mat_copy(qp
->div
);
917 isl_qpolynomial_free(dup
);
921 __isl_give isl_qpolynomial
*isl_qpolynomial_cow(__isl_take isl_qpolynomial
*qp
)
929 return isl_qpolynomial_dup(qp
);
932 void isl_qpolynomial_free(__isl_take isl_qpolynomial
*qp
)
940 isl_dim_free(qp
->dim
);
941 isl_mat_free(qp
->div
);
942 isl_upoly_free(qp
->upoly
);
947 __isl_give
struct isl_upoly
*isl_upoly_pow(isl_ctx
*ctx
, int pos
, int power
)
950 struct isl_upoly
*up
;
951 struct isl_upoly_rec
*rec
;
952 struct isl_upoly_cst
*cst
;
954 rec
= isl_upoly_alloc_rec(ctx
, pos
, 1 + power
);
957 for (i
= 0; i
< 1 + power
; ++i
) {
958 rec
->p
[i
] = isl_upoly_zero(ctx
);
963 cst
= isl_upoly_as_cst(rec
->p
[power
]);
964 isl_int_set_si(cst
->n
, 1);
968 isl_upoly_free(&rec
->up
);
972 /* r array maps original positions to new positions.
974 static __isl_give
struct isl_upoly
*reorder(__isl_take
struct isl_upoly
*up
,
978 struct isl_upoly_rec
*rec
;
979 struct isl_upoly
*base
;
980 struct isl_upoly
*res
;
982 if (isl_upoly_is_cst(up
))
985 rec
= isl_upoly_as_rec(up
);
989 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
991 base
= isl_upoly_pow(up
->ctx
, r
[up
->var
], 1);
992 res
= reorder(isl_upoly_copy(rec
->p
[rec
->n
- 1]), r
);
994 for (i
= rec
->n
- 2; i
>= 0; --i
) {
995 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
996 res
= isl_upoly_sum(res
, reorder(isl_upoly_copy(rec
->p
[i
]), r
));
999 isl_upoly_free(base
);
1008 static int compatible_divs(__isl_keep isl_mat
*div1
, __isl_keep isl_mat
*div2
)
1013 isl_assert(div1
->ctx
, div1
->n_row
>= div2
->n_row
&&
1014 div1
->n_col
>= div2
->n_col
, return -1);
1016 if (div1
->n_row
== div2
->n_row
)
1017 return isl_mat_is_equal(div1
, div2
);
1019 n_row
= div1
->n_row
;
1020 n_col
= div1
->n_col
;
1021 div1
->n_row
= div2
->n_row
;
1022 div1
->n_col
= div2
->n_col
;
1024 equal
= isl_mat_is_equal(div1
, div2
);
1026 div1
->n_row
= n_row
;
1027 div1
->n_col
= n_col
;
1032 static void expand_row(__isl_keep isl_mat
*dst
, int d
,
1033 __isl_keep isl_mat
*src
, int s
, int *exp
)
1036 unsigned c
= src
->n_col
- src
->n_row
;
1038 isl_seq_cpy(dst
->row
[d
], src
->row
[s
], c
);
1039 isl_seq_clr(dst
->row
[d
] + c
, dst
->n_col
- c
);
1041 for (i
= 0; i
< s
; ++i
)
1042 isl_int_set(dst
->row
[d
][c
+ exp
[i
]], src
->row
[s
][c
+ i
]);
1045 static int cmp_row(__isl_keep isl_mat
*div
, int i
, int j
)
1049 li
= isl_seq_last_non_zero(div
->row
[i
], div
->n_col
);
1050 lj
= isl_seq_last_non_zero(div
->row
[j
], div
->n_col
);
1055 return isl_seq_cmp(div
->row
[i
], div
->row
[j
], div
->n_col
);
1058 struct isl_div_sort_info
{
1063 static int div_sort_cmp(const void *p1
, const void *p2
)
1065 const struct isl_div_sort_info
*i1
, *i2
;
1066 i1
= (const struct isl_div_sort_info
*) p1
;
1067 i2
= (const struct isl_div_sort_info
*) p2
;
1069 return cmp_row(i1
->div
, i1
->row
, i2
->row
);
1072 /* Sort divs and remove duplicates.
1074 static __isl_give isl_qpolynomial
*sort_divs(__isl_take isl_qpolynomial
*qp
)
1079 struct isl_div_sort_info
*array
= NULL
;
1080 int *pos
= NULL
, *at
= NULL
;
1081 int *reordering
= NULL
;
1086 if (qp
->div
->n_row
<= 1)
1089 div_pos
= isl_dim_total(qp
->dim
);
1091 array
= isl_alloc_array(qp
->div
->ctx
, struct isl_div_sort_info
,
1093 pos
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1094 at
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1095 len
= qp
->div
->n_col
- 2;
1096 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
1097 if (!array
|| !pos
|| !at
|| !reordering
)
1100 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1101 array
[i
].div
= qp
->div
;
1107 qsort(array
, qp
->div
->n_row
, sizeof(struct isl_div_sort_info
),
1110 for (i
= 0; i
< div_pos
; ++i
)
1113 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1114 if (pos
[array
[i
].row
] == i
)
1116 qp
->div
= isl_mat_swap_rows(qp
->div
, i
, pos
[array
[i
].row
]);
1117 pos
[at
[i
]] = pos
[array
[i
].row
];
1118 at
[pos
[array
[i
].row
]] = at
[i
];
1119 at
[i
] = array
[i
].row
;
1120 pos
[array
[i
].row
] = i
;
1124 for (i
= 0; i
< len
- div_pos
; ++i
) {
1126 isl_seq_eq(qp
->div
->row
[i
- skip
- 1],
1127 qp
->div
->row
[i
- skip
], qp
->div
->n_col
)) {
1128 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
1129 qp
->div
= isl_mat_drop_cols(qp
->div
,
1130 2 + div_pos
+ i
- skip
, 1);
1133 reordering
[div_pos
+ array
[i
].row
] = div_pos
+ i
- skip
;
1136 qp
->upoly
= reorder(qp
->upoly
, reordering
);
1138 if (!qp
->upoly
|| !qp
->div
)
1152 isl_qpolynomial_free(qp
);
1156 static __isl_give isl_mat
*merge_divs(__isl_keep isl_mat
*div1
,
1157 __isl_keep isl_mat
*div2
, int *exp1
, int *exp2
)
1160 isl_mat
*div
= NULL
;
1161 unsigned d
= div1
->n_col
- div1
->n_row
;
1163 div
= isl_mat_alloc(div1
->ctx
, 1 + div1
->n_row
+ div2
->n_row
,
1164 d
+ div1
->n_row
+ div2
->n_row
);
1168 for (i
= 0, j
= 0, k
= 0; i
< div1
->n_row
&& j
< div2
->n_row
; ++k
) {
1171 expand_row(div
, k
, div1
, i
, exp1
);
1172 expand_row(div
, k
+ 1, div2
, j
, exp2
);
1174 cmp
= cmp_row(div
, k
, k
+ 1);
1178 } else if (cmp
< 0) {
1182 isl_seq_cpy(div
->row
[k
], div
->row
[k
+ 1], div
->n_col
);
1185 for (; i
< div1
->n_row
; ++i
, ++k
) {
1186 expand_row(div
, k
, div1
, i
, exp1
);
1189 for (; j
< div2
->n_row
; ++j
, ++k
) {
1190 expand_row(div
, k
, div2
, j
, exp2
);
1200 static __isl_give
struct isl_upoly
*expand(__isl_take
struct isl_upoly
*up
,
1201 int *exp
, int first
)
1204 struct isl_upoly_rec
*rec
;
1206 if (isl_upoly_is_cst(up
))
1209 if (up
->var
< first
)
1212 if (exp
[up
->var
- first
] == up
->var
- first
)
1215 up
= isl_upoly_cow(up
);
1219 up
->var
= exp
[up
->var
- first
] + first
;
1221 rec
= isl_upoly_as_rec(up
);
1225 for (i
= 0; i
< rec
->n
; ++i
) {
1226 rec
->p
[i
] = expand(rec
->p
[i
], exp
, first
);
1237 static __isl_give isl_qpolynomial
*with_merged_divs(
1238 __isl_give isl_qpolynomial
*(*fn
)(__isl_take isl_qpolynomial
*qp1
,
1239 __isl_take isl_qpolynomial
*qp2
),
1240 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
1244 isl_mat
*div
= NULL
;
1246 qp1
= isl_qpolynomial_cow(qp1
);
1247 qp2
= isl_qpolynomial_cow(qp2
);
1252 isl_assert(qp1
->div
->ctx
, qp1
->div
->n_row
>= qp2
->div
->n_row
&&
1253 qp1
->div
->n_col
>= qp2
->div
->n_col
, goto error
);
1255 exp1
= isl_alloc_array(qp1
->div
->ctx
, int, qp1
->div
->n_row
);
1256 exp2
= isl_alloc_array(qp2
->div
->ctx
, int, qp2
->div
->n_row
);
1260 div
= merge_divs(qp1
->div
, qp2
->div
, exp1
, exp2
);
1264 isl_mat_free(qp1
->div
);
1265 qp1
->div
= isl_mat_copy(div
);
1266 isl_mat_free(qp2
->div
);
1267 qp2
->div
= isl_mat_copy(div
);
1269 qp1
->upoly
= expand(qp1
->upoly
, exp1
, div
->n_col
- div
->n_row
- 2);
1270 qp2
->upoly
= expand(qp2
->upoly
, exp2
, div
->n_col
- div
->n_row
- 2);
1272 if (!qp1
->upoly
|| !qp2
->upoly
)
1279 return fn(qp1
, qp2
);
1284 isl_qpolynomial_free(qp1
);
1285 isl_qpolynomial_free(qp2
);
1289 __isl_give isl_qpolynomial
*isl_qpolynomial_add(__isl_take isl_qpolynomial
*qp1
,
1290 __isl_take isl_qpolynomial
*qp2
)
1292 qp1
= isl_qpolynomial_cow(qp1
);
1297 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1298 return isl_qpolynomial_add(qp2
, qp1
);
1300 isl_assert(qp1
->dim
->ctx
, isl_dim_equal(qp1
->dim
, qp2
->dim
), goto error
);
1301 if (!compatible_divs(qp1
->div
, qp2
->div
))
1302 return with_merged_divs(isl_qpolynomial_add
, qp1
, qp2
);
1304 qp1
->upoly
= isl_upoly_sum(qp1
->upoly
, isl_upoly_copy(qp2
->upoly
));
1308 isl_qpolynomial_free(qp2
);
1312 isl_qpolynomial_free(qp1
);
1313 isl_qpolynomial_free(qp2
);
1317 __isl_give isl_qpolynomial
*isl_qpolynomial_add_on_domain(
1318 __isl_keep isl_set
*dom
,
1319 __isl_take isl_qpolynomial
*qp1
,
1320 __isl_take isl_qpolynomial
*qp2
)
1322 return isl_qpolynomial_add(qp1
, qp2
);
1325 __isl_give isl_qpolynomial
*isl_qpolynomial_sub(__isl_take isl_qpolynomial
*qp1
,
1326 __isl_take isl_qpolynomial
*qp2
)
1328 return isl_qpolynomial_add(qp1
, isl_qpolynomial_neg(qp2
));
1331 __isl_give isl_qpolynomial
*isl_qpolynomial_neg(__isl_take isl_qpolynomial
*qp
)
1333 qp
= isl_qpolynomial_cow(qp
);
1338 qp
->upoly
= isl_upoly_neg(qp
->upoly
);
1344 isl_qpolynomial_free(qp
);
1348 __isl_give isl_qpolynomial
*isl_qpolynomial_mul(__isl_take isl_qpolynomial
*qp1
,
1349 __isl_take isl_qpolynomial
*qp2
)
1351 qp1
= isl_qpolynomial_cow(qp1
);
1356 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1357 return isl_qpolynomial_mul(qp2
, qp1
);
1359 isl_assert(qp1
->dim
->ctx
, isl_dim_equal(qp1
->dim
, qp2
->dim
), goto error
);
1360 if (!compatible_divs(qp1
->div
, qp2
->div
))
1361 return with_merged_divs(isl_qpolynomial_mul
, qp1
, qp2
);
1363 qp1
->upoly
= isl_upoly_mul(qp1
->upoly
, isl_upoly_copy(qp2
->upoly
));
1367 isl_qpolynomial_free(qp2
);
1371 isl_qpolynomial_free(qp1
);
1372 isl_qpolynomial_free(qp2
);
1376 __isl_give isl_qpolynomial
*isl_qpolynomial_zero(__isl_take isl_dim
*dim
)
1378 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
1381 __isl_give isl_qpolynomial
*isl_qpolynomial_infty(__isl_take isl_dim
*dim
)
1383 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_infty(dim
->ctx
));
1386 __isl_give isl_qpolynomial
*isl_qpolynomial_neginfty(__isl_take isl_dim
*dim
)
1388 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_neginfty(dim
->ctx
));
1391 __isl_give isl_qpolynomial
*isl_qpolynomial_nan(__isl_take isl_dim
*dim
)
1393 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_nan(dim
->ctx
));
1396 __isl_give isl_qpolynomial
*isl_qpolynomial_cst(__isl_take isl_dim
*dim
,
1399 struct isl_qpolynomial
*qp
;
1400 struct isl_upoly_cst
*cst
;
1402 qp
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
1406 cst
= isl_upoly_as_cst(qp
->upoly
);
1407 isl_int_set(cst
->n
, v
);
1412 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial
*qp
,
1413 isl_int
*n
, isl_int
*d
)
1415 struct isl_upoly_cst
*cst
;
1420 if (!isl_upoly_is_cst(qp
->upoly
))
1423 cst
= isl_upoly_as_cst(qp
->upoly
);
1428 isl_int_set(*n
, cst
->n
);
1430 isl_int_set(*d
, cst
->d
);
1435 int isl_upoly_is_affine(__isl_keep
struct isl_upoly
*up
)
1438 struct isl_upoly_rec
*rec
;
1446 rec
= isl_upoly_as_rec(up
);
1453 isl_assert(up
->ctx
, rec
->n
> 1, return -1);
1455 is_cst
= isl_upoly_is_cst(rec
->p
[1]);
1461 return isl_upoly_is_affine(rec
->p
[0]);
1464 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial
*qp
)
1469 if (qp
->div
->n_row
> 0)
1472 return isl_upoly_is_affine(qp
->upoly
);
1475 static void update_coeff(__isl_keep isl_vec
*aff
,
1476 __isl_keep
struct isl_upoly_cst
*cst
, int pos
)
1481 if (isl_int_is_zero(cst
->n
))
1486 isl_int_gcd(gcd
, cst
->d
, aff
->el
[0]);
1487 isl_int_divexact(f
, cst
->d
, gcd
);
1488 isl_int_divexact(gcd
, aff
->el
[0], gcd
);
1489 isl_seq_scale(aff
->el
, aff
->el
, f
, aff
->size
);
1490 isl_int_mul(aff
->el
[1 + pos
], gcd
, cst
->n
);
1495 int isl_upoly_update_affine(__isl_keep
struct isl_upoly
*up
,
1496 __isl_keep isl_vec
*aff
)
1498 struct isl_upoly_cst
*cst
;
1499 struct isl_upoly_rec
*rec
;
1505 struct isl_upoly_cst
*cst
;
1507 cst
= isl_upoly_as_cst(up
);
1510 update_coeff(aff
, cst
, 0);
1514 rec
= isl_upoly_as_rec(up
);
1517 isl_assert(up
->ctx
, rec
->n
== 2, return -1);
1519 cst
= isl_upoly_as_cst(rec
->p
[1]);
1522 update_coeff(aff
, cst
, 1 + up
->var
);
1524 return isl_upoly_update_affine(rec
->p
[0], aff
);
1527 __isl_give isl_vec
*isl_qpolynomial_extract_affine(
1528 __isl_keep isl_qpolynomial
*qp
)
1536 isl_assert(qp
->div
->ctx
, qp
->div
->n_row
== 0, return NULL
);
1537 d
= isl_dim_total(qp
->dim
);
1538 aff
= isl_vec_alloc(qp
->div
->ctx
, 2 + d
);
1542 isl_seq_clr(aff
->el
+ 1, 1 + d
);
1543 isl_int_set_si(aff
->el
[0], 1);
1545 if (isl_upoly_update_affine(qp
->upoly
, aff
) < 0)
1554 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial
*qp1
,
1555 __isl_keep isl_qpolynomial
*qp2
)
1560 return isl_upoly_is_equal(qp1
->upoly
, qp2
->upoly
);
1563 static void upoly_update_den(__isl_keep
struct isl_upoly
*up
, isl_int
*d
)
1566 struct isl_upoly_rec
*rec
;
1568 if (isl_upoly_is_cst(up
)) {
1569 struct isl_upoly_cst
*cst
;
1570 cst
= isl_upoly_as_cst(up
);
1573 isl_int_lcm(*d
, *d
, cst
->d
);
1577 rec
= isl_upoly_as_rec(up
);
1581 for (i
= 0; i
< rec
->n
; ++i
)
1582 upoly_update_den(rec
->p
[i
], d
);
1585 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial
*qp
, isl_int
*d
)
1587 isl_int_set_si(*d
, 1);
1590 upoly_update_den(qp
->upoly
, d
);
1593 __isl_give isl_qpolynomial
*isl_qpolynomial_pow(__isl_take isl_dim
*dim
,
1596 struct isl_ctx
*ctx
;
1603 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_pow(ctx
, pos
, power
));
1606 __isl_give isl_qpolynomial
*isl_qpolynomial_var(__isl_take isl_dim
*dim
,
1607 enum isl_dim_type type
, unsigned pos
)
1612 isl_assert(dim
->ctx
, isl_dim_size(dim
, isl_dim_in
) == 0, goto error
);
1613 isl_assert(dim
->ctx
, pos
< isl_dim_size(dim
, type
), goto error
);
1615 if (type
== isl_dim_set
)
1616 pos
+= isl_dim_size(dim
, isl_dim_param
);
1618 return isl_qpolynomial_pow(dim
, pos
, 1);
1624 __isl_give isl_qpolynomial
*isl_qpolynomial_div_pow(__isl_take isl_div
*div
,
1627 struct isl_qpolynomial
*qp
= NULL
;
1628 struct isl_upoly_rec
*rec
;
1629 struct isl_upoly_cst
*cst
;
1635 isl_assert(div
->ctx
, div
->bmap
->n_div
== 1, goto error
);
1637 pos
= isl_dim_total(div
->bmap
->dim
);
1638 rec
= isl_upoly_alloc_rec(div
->ctx
, pos
, 1 + power
);
1639 qp
= isl_qpolynomial_alloc(isl_basic_map_get_dim(div
->bmap
), 1,
1644 isl_seq_cpy(qp
->div
->row
[0], div
->line
[0], qp
->div
->n_col
- 1);
1645 isl_int_set_si(qp
->div
->row
[0][qp
->div
->n_col
- 1], 0);
1647 for (i
= 0; i
< 1 + power
; ++i
) {
1648 rec
->p
[i
] = isl_upoly_zero(div
->ctx
);
1653 cst
= isl_upoly_as_cst(rec
->p
[power
]);
1654 isl_int_set_si(cst
->n
, 1);
1660 isl_qpolynomial_free(qp
);
1665 __isl_give isl_qpolynomial
*isl_qpolynomial_div(__isl_take isl_div
*div
)
1667 return isl_qpolynomial_div_pow(div
, 1);
1670 __isl_give isl_qpolynomial
*isl_qpolynomial_rat_cst(__isl_take isl_dim
*dim
,
1671 const isl_int n
, const isl_int d
)
1673 struct isl_qpolynomial
*qp
;
1674 struct isl_upoly_cst
*cst
;
1676 qp
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
1680 cst
= isl_upoly_as_cst(qp
->upoly
);
1681 isl_int_set(cst
->n
, n
);
1682 isl_int_set(cst
->d
, d
);
1687 static int up_set_active(__isl_keep
struct isl_upoly
*up
, int *active
, int d
)
1689 struct isl_upoly_rec
*rec
;
1695 if (isl_upoly_is_cst(up
))
1699 active
[up
->var
] = 1;
1701 rec
= isl_upoly_as_rec(up
);
1702 for (i
= 0; i
< rec
->n
; ++i
)
1703 if (up_set_active(rec
->p
[i
], active
, d
) < 0)
1709 static int set_active(__isl_keep isl_qpolynomial
*qp
, int *active
)
1712 int d
= isl_dim_total(qp
->dim
);
1717 for (i
= 0; i
< d
; ++i
)
1718 for (j
= 0; j
< qp
->div
->n_row
; ++j
) {
1719 if (isl_int_is_zero(qp
->div
->row
[j
][2 + i
]))
1725 return up_set_active(qp
->upoly
, active
, d
);
1728 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial
*qp
,
1729 enum isl_dim_type type
, unsigned first
, unsigned n
)
1740 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_dim_size(qp
->dim
, type
),
1742 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
1743 type
== isl_dim_set
, return -1);
1745 active
= isl_calloc_array(set
->ctx
, int, isl_dim_total(qp
->dim
));
1746 if (set_active(qp
, active
) < 0)
1749 if (type
== isl_dim_set
)
1750 first
+= isl_dim_size(qp
->dim
, isl_dim_param
);
1751 for (i
= 0; i
< n
; ++i
)
1752 if (active
[first
+ i
]) {
1765 __isl_give
struct isl_upoly
*isl_upoly_drop(__isl_take
struct isl_upoly
*up
,
1766 unsigned first
, unsigned n
)
1769 struct isl_upoly_rec
*rec
;
1773 if (n
== 0 || up
->var
< 0 || up
->var
< first
)
1775 if (up
->var
< first
+ n
) {
1776 up
= replace_by_constant_term(up
);
1777 return isl_upoly_drop(up
, first
, n
);
1779 up
= isl_upoly_cow(up
);
1783 rec
= isl_upoly_as_rec(up
);
1787 for (i
= 0; i
< rec
->n
; ++i
) {
1788 rec
->p
[i
] = isl_upoly_drop(rec
->p
[i
], first
, n
);
1799 __isl_give isl_qpolynomial
*isl_qpolynomial_drop_dims(
1800 __isl_take isl_qpolynomial
*qp
,
1801 enum isl_dim_type type
, unsigned first
, unsigned n
)
1805 if (n
== 0 && !isl_dim_get_tuple_name(qp
->dim
, type
))
1808 qp
= isl_qpolynomial_cow(qp
);
1812 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_dim_size(qp
->dim
, type
),
1814 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
1815 type
== isl_dim_set
, goto error
);
1817 qp
->dim
= isl_dim_drop(qp
->dim
, type
, first
, n
);
1821 if (type
== isl_dim_set
)
1822 first
+= isl_dim_size(qp
->dim
, isl_dim_param
);
1824 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + first
, n
);
1828 qp
->upoly
= isl_upoly_drop(qp
->upoly
, first
, n
);
1834 isl_qpolynomial_free(qp
);
1838 __isl_give
struct isl_upoly
*isl_upoly_subs(__isl_take
struct isl_upoly
*up
,
1839 unsigned first
, unsigned n
, __isl_keep
struct isl_upoly
**subs
)
1842 struct isl_upoly_rec
*rec
;
1843 struct isl_upoly
*base
, *res
;
1848 if (isl_upoly_is_cst(up
))
1851 if (up
->var
< first
)
1854 rec
= isl_upoly_as_rec(up
);
1858 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
1860 if (up
->var
>= first
+ n
)
1861 base
= isl_upoly_pow(up
->ctx
, up
->var
, 1);
1863 base
= isl_upoly_copy(subs
[up
->var
- first
]);
1865 res
= isl_upoly_subs(isl_upoly_copy(rec
->p
[rec
->n
- 1]), first
, n
, subs
);
1866 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1867 struct isl_upoly
*t
;
1868 t
= isl_upoly_subs(isl_upoly_copy(rec
->p
[i
]), first
, n
, subs
);
1869 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
1870 res
= isl_upoly_sum(res
, t
);
1873 isl_upoly_free(base
);
1882 __isl_give
struct isl_upoly
*isl_upoly_from_affine(isl_ctx
*ctx
, isl_int
*f
,
1883 isl_int denom
, unsigned len
)
1886 struct isl_upoly
*up
;
1888 isl_assert(ctx
, len
>= 1, return NULL
);
1890 up
= isl_upoly_rat_cst(ctx
, f
[0], denom
);
1891 for (i
= 0; i
< len
- 1; ++i
) {
1892 struct isl_upoly
*t
;
1893 struct isl_upoly
*c
;
1895 if (isl_int_is_zero(f
[1 + i
]))
1898 c
= isl_upoly_rat_cst(ctx
, f
[1 + i
], denom
);
1899 t
= isl_upoly_pow(ctx
, i
, 1);
1900 t
= isl_upoly_mul(c
, t
);
1901 up
= isl_upoly_sum(up
, t
);
1907 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities(
1908 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
1913 struct isl_upoly
*up
;
1917 if (eq
->n_eq
== 0) {
1918 isl_basic_set_free(eq
);
1922 qp
= isl_qpolynomial_cow(qp
);
1925 qp
->div
= isl_mat_cow(qp
->div
);
1929 total
= 1 + isl_dim_total(eq
->dim
);
1930 isl_int_init(denom
);
1931 for (i
= 0; i
< eq
->n_eq
; ++i
) {
1932 j
= isl_seq_last_non_zero(eq
->eq
[i
], total
);
1933 if (j
< 0 || j
== 0)
1936 for (k
= 0; k
< qp
->div
->n_row
; ++k
) {
1937 if (isl_int_is_zero(qp
->div
->row
[k
][1 + j
]))
1939 isl_seq_elim(qp
->div
->row
[k
] + 1, eq
->eq
[i
], j
, total
,
1940 &qp
->div
->row
[k
][0]);
1941 isl_seq_normalize(qp
->div
->ctx
,
1942 qp
->div
->row
[k
], 1 + total
);
1945 if (isl_int_is_pos(eq
->eq
[i
][j
]))
1946 isl_seq_neg(eq
->eq
[i
], eq
->eq
[i
], total
);
1947 isl_int_abs(denom
, eq
->eq
[i
][j
]);
1948 isl_int_set_si(eq
->eq
[i
][j
], 0);
1950 up
= isl_upoly_from_affine(qp
->dim
->ctx
,
1951 eq
->eq
[i
], denom
, total
);
1952 qp
->upoly
= isl_upoly_subs(qp
->upoly
, j
- 1, 1, &up
);
1955 isl_int_clear(denom
);
1960 isl_basic_set_free(eq
);
1966 isl_basic_set_free(eq
);
1967 isl_qpolynomial_free(qp
);
1972 #define PW isl_pw_qpolynomial
1974 #define EL isl_qpolynomial
1976 #define IS_ZERO is_zero
1980 #include <isl_pw_templ.c>
1983 #define UNION isl_union_pw_qpolynomial
1985 #define PART isl_pw_qpolynomial
1987 #define PARTS pw_qpolynomial
1989 #include <isl_union_templ.c>
1991 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial
*pwqp
)
1999 if (!isl_set_fast_is_universe(pwqp
->p
[0].set
))
2002 return isl_qpolynomial_is_one(pwqp
->p
[0].qp
);
2005 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_mul(
2006 __isl_take isl_pw_qpolynomial
*pwqp1
,
2007 __isl_take isl_pw_qpolynomial
*pwqp2
)
2010 struct isl_pw_qpolynomial
*res
;
2013 if (!pwqp1
|| !pwqp2
)
2016 isl_assert(pwqp1
->dim
->ctx
, isl_dim_equal(pwqp1
->dim
, pwqp2
->dim
),
2019 if (isl_pw_qpolynomial_is_zero(pwqp1
)) {
2020 isl_pw_qpolynomial_free(pwqp2
);
2024 if (isl_pw_qpolynomial_is_zero(pwqp2
)) {
2025 isl_pw_qpolynomial_free(pwqp1
);
2029 if (isl_pw_qpolynomial_is_one(pwqp1
)) {
2030 isl_pw_qpolynomial_free(pwqp1
);
2034 if (isl_pw_qpolynomial_is_one(pwqp2
)) {
2035 isl_pw_qpolynomial_free(pwqp2
);
2039 n
= pwqp1
->n
* pwqp2
->n
;
2040 res
= isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1
->dim
), n
);
2042 for (i
= 0; i
< pwqp1
->n
; ++i
) {
2043 for (j
= 0; j
< pwqp2
->n
; ++j
) {
2044 struct isl_set
*common
;
2045 struct isl_qpolynomial
*prod
;
2046 common
= isl_set_intersect(isl_set_copy(pwqp1
->p
[i
].set
),
2047 isl_set_copy(pwqp2
->p
[j
].set
));
2048 if (isl_set_fast_is_empty(common
)) {
2049 isl_set_free(common
);
2053 prod
= isl_qpolynomial_mul(
2054 isl_qpolynomial_copy(pwqp1
->p
[i
].qp
),
2055 isl_qpolynomial_copy(pwqp2
->p
[j
].qp
));
2057 res
= isl_pw_qpolynomial_add_piece(res
, common
, prod
);
2061 isl_pw_qpolynomial_free(pwqp1
);
2062 isl_pw_qpolynomial_free(pwqp2
);
2066 isl_pw_qpolynomial_free(pwqp1
);
2067 isl_pw_qpolynomial_free(pwqp2
);
2071 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_neg(
2072 __isl_take isl_pw_qpolynomial
*pwqp
)
2079 if (isl_pw_qpolynomial_is_zero(pwqp
))
2082 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
2086 for (i
= 0; i
< pwqp
->n
; ++i
) {
2087 pwqp
->p
[i
].qp
= isl_qpolynomial_neg(pwqp
->p
[i
].qp
);
2094 isl_pw_qpolynomial_free(pwqp
);
2098 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_sub(
2099 __isl_take isl_pw_qpolynomial
*pwqp1
,
2100 __isl_take isl_pw_qpolynomial
*pwqp2
)
2102 return isl_pw_qpolynomial_add(pwqp1
, isl_pw_qpolynomial_neg(pwqp2
));
2105 __isl_give
struct isl_upoly
*isl_upoly_eval(
2106 __isl_take
struct isl_upoly
*up
, __isl_take isl_vec
*vec
)
2109 struct isl_upoly_rec
*rec
;
2110 struct isl_upoly
*res
;
2111 struct isl_upoly
*base
;
2113 if (isl_upoly_is_cst(up
)) {
2118 rec
= isl_upoly_as_rec(up
);
2122 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
2124 base
= isl_upoly_rat_cst(up
->ctx
, vec
->el
[1 + up
->var
], vec
->el
[0]);
2126 res
= isl_upoly_eval(isl_upoly_copy(rec
->p
[rec
->n
- 1]),
2129 for (i
= rec
->n
- 2; i
>= 0; --i
) {
2130 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
2131 res
= isl_upoly_sum(res
,
2132 isl_upoly_eval(isl_upoly_copy(rec
->p
[i
]),
2133 isl_vec_copy(vec
)));
2136 isl_upoly_free(base
);
2146 __isl_give isl_qpolynomial
*isl_qpolynomial_eval(
2147 __isl_take isl_qpolynomial
*qp
, __isl_take isl_point
*pnt
)
2150 struct isl_upoly
*up
;
2155 isl_assert(pnt
->dim
->ctx
, isl_dim_equal(pnt
->dim
, qp
->dim
), goto error
);
2157 if (qp
->div
->n_row
== 0)
2158 ext
= isl_vec_copy(pnt
->vec
);
2161 unsigned dim
= isl_dim_total(qp
->dim
);
2162 ext
= isl_vec_alloc(qp
->dim
->ctx
, 1 + dim
+ qp
->div
->n_row
);
2166 isl_seq_cpy(ext
->el
, pnt
->vec
->el
, pnt
->vec
->size
);
2167 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2168 isl_seq_inner_product(qp
->div
->row
[i
] + 1, ext
->el
,
2169 1 + dim
+ i
, &ext
->el
[1+dim
+i
]);
2170 isl_int_fdiv_q(ext
->el
[1+dim
+i
], ext
->el
[1+dim
+i
],
2171 qp
->div
->row
[i
][0]);
2175 up
= isl_upoly_eval(isl_upoly_copy(qp
->upoly
), ext
);
2179 dim
= isl_dim_copy(qp
->dim
);
2180 isl_qpolynomial_free(qp
);
2181 isl_point_free(pnt
);
2183 return isl_qpolynomial_alloc(dim
, 0, up
);
2185 isl_qpolynomial_free(qp
);
2186 isl_point_free(pnt
);
2190 int isl_upoly_cmp(__isl_keep
struct isl_upoly_cst
*cst1
,
2191 __isl_keep
struct isl_upoly_cst
*cst2
)
2196 isl_int_mul(t
, cst1
->n
, cst2
->d
);
2197 isl_int_submul(t
, cst2
->n
, cst1
->d
);
2198 cmp
= isl_int_sgn(t
);
2203 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial
*qp1
,
2204 __isl_keep isl_qpolynomial
*qp2
)
2206 struct isl_upoly_cst
*cst1
, *cst2
;
2210 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), return -1);
2211 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), return -1);
2212 if (isl_qpolynomial_is_nan(qp1
))
2214 if (isl_qpolynomial_is_nan(qp2
))
2216 cst1
= isl_upoly_as_cst(qp1
->upoly
);
2217 cst2
= isl_upoly_as_cst(qp2
->upoly
);
2219 return isl_upoly_cmp(cst1
, cst2
) <= 0;
2222 __isl_give isl_qpolynomial
*isl_qpolynomial_min_cst(
2223 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
2225 struct isl_upoly_cst
*cst1
, *cst2
;
2230 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), goto error
);
2231 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), goto error
);
2232 cst1
= isl_upoly_as_cst(qp1
->upoly
);
2233 cst2
= isl_upoly_as_cst(qp2
->upoly
);
2234 cmp
= isl_upoly_cmp(cst1
, cst2
);
2237 isl_qpolynomial_free(qp2
);
2239 isl_qpolynomial_free(qp1
);
2244 isl_qpolynomial_free(qp1
);
2245 isl_qpolynomial_free(qp2
);
2249 __isl_give isl_qpolynomial
*isl_qpolynomial_max_cst(
2250 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
2252 struct isl_upoly_cst
*cst1
, *cst2
;
2257 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), goto error
);
2258 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), goto error
);
2259 cst1
= isl_upoly_as_cst(qp1
->upoly
);
2260 cst2
= isl_upoly_as_cst(qp2
->upoly
);
2261 cmp
= isl_upoly_cmp(cst1
, cst2
);
2264 isl_qpolynomial_free(qp2
);
2266 isl_qpolynomial_free(qp1
);
2271 isl_qpolynomial_free(qp1
);
2272 isl_qpolynomial_free(qp2
);
2276 __isl_give isl_qpolynomial
*isl_qpolynomial_insert_dims(
2277 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
,
2278 unsigned first
, unsigned n
)
2287 qp
= isl_qpolynomial_cow(qp
);
2291 isl_assert(qp
->div
->ctx
, first
<= isl_dim_size(qp
->dim
, type
),
2294 g_pos
= pos(qp
->dim
, type
) + first
;
2296 qp
->div
= isl_mat_insert_cols(qp
->div
, 2 + g_pos
, n
);
2300 total
= qp
->div
->n_col
- 2;
2301 if (total
> g_pos
) {
2303 exp
= isl_alloc_array(qp
->div
->ctx
, int, total
- g_pos
);
2306 for (i
= 0; i
< total
- g_pos
; ++i
)
2308 qp
->upoly
= expand(qp
->upoly
, exp
, g_pos
);
2314 qp
->dim
= isl_dim_insert(qp
->dim
, type
, first
, n
);
2320 isl_qpolynomial_free(qp
);
2324 __isl_give isl_qpolynomial
*isl_qpolynomial_add_dims(
2325 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
, unsigned n
)
2329 pos
= isl_qpolynomial_dim(qp
, type
);
2331 return isl_qpolynomial_insert_dims(qp
, type
, pos
, n
);
2334 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add_dims(
2335 __isl_take isl_pw_qpolynomial
*pwqp
,
2336 enum isl_dim_type type
, unsigned n
)
2340 pos
= isl_pw_qpolynomial_dim(pwqp
, type
);
2342 return isl_pw_qpolynomial_insert_dims(pwqp
, type
, pos
, n
);
2345 static int *reordering_move(isl_ctx
*ctx
,
2346 unsigned len
, unsigned dst
, unsigned src
, unsigned n
)
2351 reordering
= isl_alloc_array(ctx
, int, len
);
2356 for (i
= 0; i
< dst
; ++i
)
2358 for (i
= 0; i
< n
; ++i
)
2359 reordering
[src
+ i
] = dst
+ i
;
2360 for (i
= 0; i
< src
- dst
; ++i
)
2361 reordering
[dst
+ i
] = dst
+ n
+ i
;
2362 for (i
= 0; i
< len
- src
- n
; ++i
)
2363 reordering
[src
+ n
+ i
] = src
+ n
+ i
;
2365 for (i
= 0; i
< src
; ++i
)
2367 for (i
= 0; i
< n
; ++i
)
2368 reordering
[src
+ i
] = dst
+ i
;
2369 for (i
= 0; i
< dst
- src
; ++i
)
2370 reordering
[src
+ n
+ i
] = src
+ i
;
2371 for (i
= 0; i
< len
- dst
- n
; ++i
)
2372 reordering
[dst
+ n
+ i
] = dst
+ n
+ i
;
2378 __isl_give isl_qpolynomial
*isl_qpolynomial_move_dims(
2379 __isl_take isl_qpolynomial
*qp
,
2380 enum isl_dim_type dst_type
, unsigned dst_pos
,
2381 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
2387 qp
= isl_qpolynomial_cow(qp
);
2391 isl_assert(qp
->dim
->ctx
, src_pos
+ n
<= isl_dim_size(qp
->dim
, src_type
),
2394 g_dst_pos
= pos(qp
->dim
, dst_type
) + dst_pos
;
2395 g_src_pos
= pos(qp
->dim
, src_type
) + src_pos
;
2396 if (dst_type
> src_type
)
2399 qp
->div
= isl_mat_move_cols(qp
->div
, 2 + g_dst_pos
, 2 + g_src_pos
, n
);
2406 reordering
= reordering_move(qp
->dim
->ctx
,
2407 qp
->div
->n_col
- 2, g_dst_pos
, g_src_pos
, n
);
2411 qp
->upoly
= reorder(qp
->upoly
, reordering
);
2416 qp
->dim
= isl_dim_move(qp
->dim
, dst_type
, dst_pos
, src_type
, src_pos
, n
);
2422 isl_qpolynomial_free(qp
);
2426 __isl_give isl_qpolynomial
*isl_qpolynomial_from_affine(__isl_take isl_dim
*dim
,
2427 isl_int
*f
, isl_int denom
)
2429 struct isl_upoly
*up
;
2434 up
= isl_upoly_from_affine(dim
->ctx
, f
, denom
, 1 + isl_dim_total(dim
));
2436 return isl_qpolynomial_alloc(dim
, 0, up
);
2439 __isl_give isl_qpolynomial
*isl_qpolynomial_from_constraint(
2440 __isl_take isl_constraint
*c
, enum isl_dim_type type
, unsigned pos
)
2444 struct isl_upoly
*up
;
2445 isl_qpolynomial
*qp
;
2451 isl_int_init(denom
);
2453 isl_constraint_get_coefficient(c
, type
, pos
, &denom
);
2454 isl_constraint_set_coefficient(c
, type
, pos
, c
->ctx
->zero
);
2455 sgn
= isl_int_sgn(denom
);
2456 isl_int_abs(denom
, denom
);
2457 up
= isl_upoly_from_affine(c
->ctx
, c
->line
[0], denom
,
2458 1 + isl_constraint_dim(c
, isl_dim_all
));
2460 isl_int_neg(denom
, denom
);
2461 isl_constraint_set_coefficient(c
, type
, pos
, denom
);
2463 dim
= isl_dim_copy(c
->bmap
->dim
);
2465 isl_int_clear(denom
);
2466 isl_constraint_free(c
);
2468 qp
= isl_qpolynomial_alloc(dim
, 0, up
);
2470 qp
= isl_qpolynomial_neg(qp
);
2474 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
2475 * in "qp" by subs[i].
2477 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute(
2478 __isl_take isl_qpolynomial
*qp
,
2479 enum isl_dim_type type
, unsigned first
, unsigned n
,
2480 __isl_keep isl_qpolynomial
**subs
)
2483 struct isl_upoly
**ups
;
2488 qp
= isl_qpolynomial_cow(qp
);
2491 for (i
= 0; i
< n
; ++i
)
2495 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_dim_size(qp
->dim
, type
),
2498 for (i
= 0; i
< n
; ++i
)
2499 isl_assert(qp
->dim
->ctx
, isl_dim_equal(qp
->dim
, subs
[i
]->dim
),
2502 isl_assert(qp
->dim
->ctx
, qp
->div
->n_row
== 0, goto error
);
2503 for (i
= 0; i
< n
; ++i
)
2504 isl_assert(qp
->dim
->ctx
, subs
[i
]->div
->n_row
== 0, goto error
);
2506 first
+= pos(qp
->dim
, type
);
2508 ups
= isl_alloc_array(qp
->dim
->ctx
, struct isl_upoly
*, n
);
2511 for (i
= 0; i
< n
; ++i
)
2512 ups
[i
] = subs
[i
]->upoly
;
2514 qp
->upoly
= isl_upoly_subs(qp
->upoly
, first
, n
, ups
);
2523 isl_qpolynomial_free(qp
);
2527 __isl_give isl_basic_set
*add_div_constraints(__isl_take isl_basic_set
*bset
,
2528 __isl_take isl_mat
*div
)
2536 bset
= isl_basic_set_extend_constraints(bset
, 0, 2 * div
->n_row
);
2539 total
= isl_basic_set_total_dim(bset
);
2540 for (i
= 0; i
< div
->n_row
; ++i
)
2541 if (isl_basic_set_add_div_constraints_var(bset
,
2542 total
- div
->n_row
+ i
, div
->row
[i
]) < 0)
2549 isl_basic_set_free(bset
);
2553 /* Extend "bset" with extra set dimensions for each integer division
2554 * in "qp" and then call "fn" with the extended bset and the polynomial
2555 * that results from replacing each of the integer divisions by the
2556 * corresponding extra set dimension.
2558 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial
*qp
,
2559 __isl_keep isl_basic_set
*bset
,
2560 int (*fn
)(__isl_take isl_basic_set
*bset
,
2561 __isl_take isl_qpolynomial
*poly
, void *user
), void *user
)
2565 isl_qpolynomial
*poly
;
2569 if (qp
->div
->n_row
== 0)
2570 return fn(isl_basic_set_copy(bset
), isl_qpolynomial_copy(qp
),
2573 div
= isl_mat_copy(qp
->div
);
2574 dim
= isl_dim_copy(qp
->dim
);
2575 dim
= isl_dim_add(dim
, isl_dim_set
, qp
->div
->n_row
);
2576 poly
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_copy(qp
->upoly
));
2577 bset
= isl_basic_set_copy(bset
);
2578 bset
= isl_basic_set_add(bset
, isl_dim_set
, qp
->div
->n_row
);
2579 bset
= add_div_constraints(bset
, div
);
2581 return fn(bset
, poly
, user
);
2586 /* Return total degree in variables first (inclusive) up to last (exclusive).
2588 int isl_upoly_degree(__isl_keep
struct isl_upoly
*up
, int first
, int last
)
2592 struct isl_upoly_rec
*rec
;
2596 if (isl_upoly_is_zero(up
))
2598 if (isl_upoly_is_cst(up
) || up
->var
< first
)
2601 rec
= isl_upoly_as_rec(up
);
2605 for (i
= 0; i
< rec
->n
; ++i
) {
2608 if (isl_upoly_is_zero(rec
->p
[i
]))
2610 d
= isl_upoly_degree(rec
->p
[i
], first
, last
);
2620 /* Return total degree in set variables.
2622 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial
*poly
)
2630 ovar
= isl_dim_offset(poly
->dim
, isl_dim_set
);
2631 nvar
= isl_dim_size(poly
->dim
, isl_dim_set
);
2632 return isl_upoly_degree(poly
->upoly
, ovar
, ovar
+ nvar
);
2635 __isl_give
struct isl_upoly
*isl_upoly_coeff(__isl_keep
struct isl_upoly
*up
,
2636 unsigned pos
, int deg
)
2639 struct isl_upoly_rec
*rec
;
2644 if (isl_upoly_is_cst(up
) || up
->var
< pos
) {
2646 return isl_upoly_copy(up
);
2648 return isl_upoly_zero(up
->ctx
);
2651 rec
= isl_upoly_as_rec(up
);
2655 if (up
->var
== pos
) {
2657 return isl_upoly_copy(rec
->p
[deg
]);
2659 return isl_upoly_zero(up
->ctx
);
2662 up
= isl_upoly_copy(up
);
2663 up
= isl_upoly_cow(up
);
2664 rec
= isl_upoly_as_rec(up
);
2668 for (i
= 0; i
< rec
->n
; ++i
) {
2669 struct isl_upoly
*t
;
2670 t
= isl_upoly_coeff(rec
->p
[i
], pos
, deg
);
2673 isl_upoly_free(rec
->p
[i
]);
2683 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
2685 __isl_give isl_qpolynomial
*isl_qpolynomial_coeff(
2686 __isl_keep isl_qpolynomial
*qp
,
2687 enum isl_dim_type type
, unsigned t_pos
, int deg
)
2690 struct isl_upoly
*up
;
2696 isl_assert(qp
->div
->ctx
, t_pos
< isl_dim_size(qp
->dim
, type
),
2699 g_pos
= pos(qp
->dim
, type
) + t_pos
;
2700 up
= isl_upoly_coeff(qp
->upoly
, g_pos
, deg
);
2702 c
= isl_qpolynomial_alloc(isl_dim_copy(qp
->dim
), qp
->div
->n_row
, up
);
2705 isl_mat_free(c
->div
);
2706 c
->div
= isl_mat_copy(qp
->div
);
2711 isl_qpolynomial_free(c
);
2715 /* Homogenize the polynomial in the variables first (inclusive) up to
2716 * last (exclusive) by inserting powers of variable first.
2717 * Variable first is assumed not to appear in the input.
2719 __isl_give
struct isl_upoly
*isl_upoly_homogenize(
2720 __isl_take
struct isl_upoly
*up
, int deg
, int target
,
2721 int first
, int last
)
2724 struct isl_upoly_rec
*rec
;
2728 if (isl_upoly_is_zero(up
))
2732 if (isl_upoly_is_cst(up
) || up
->var
< first
) {
2733 struct isl_upoly
*hom
;
2735 hom
= isl_upoly_pow(up
->ctx
, first
, target
- deg
);
2738 rec
= isl_upoly_as_rec(hom
);
2739 rec
->p
[target
- deg
] = isl_upoly_mul(rec
->p
[target
- deg
], up
);
2744 up
= isl_upoly_cow(up
);
2745 rec
= isl_upoly_as_rec(up
);
2749 for (i
= 0; i
< rec
->n
; ++i
) {
2750 if (isl_upoly_is_zero(rec
->p
[i
]))
2752 rec
->p
[i
] = isl_upoly_homogenize(rec
->p
[i
],
2753 up
->var
< last
? deg
+ i
: i
, target
,
2765 /* Homogenize the polynomial in the set variables by introducing
2766 * powers of an extra set variable at position 0.
2768 __isl_give isl_qpolynomial
*isl_qpolynomial_homogenize(
2769 __isl_take isl_qpolynomial
*poly
)
2773 int deg
= isl_qpolynomial_degree(poly
);
2778 poly
= isl_qpolynomial_insert_dims(poly
, isl_dim_set
, 0, 1);
2779 poly
= isl_qpolynomial_cow(poly
);
2783 ovar
= isl_dim_offset(poly
->dim
, isl_dim_set
);
2784 nvar
= isl_dim_size(poly
->dim
, isl_dim_set
);
2785 poly
->upoly
= isl_upoly_homogenize(poly
->upoly
, 0, deg
,
2792 isl_qpolynomial_free(poly
);
2796 __isl_give isl_term
*isl_term_alloc(__isl_take isl_dim
*dim
,
2797 __isl_take isl_mat
*div
)
2805 n
= isl_dim_total(dim
) + div
->n_row
;
2807 term
= isl_calloc(dim
->ctx
, struct isl_term
,
2808 sizeof(struct isl_term
) + (n
- 1) * sizeof(int));
2815 isl_int_init(term
->n
);
2816 isl_int_init(term
->d
);
2825 __isl_give isl_term
*isl_term_copy(__isl_keep isl_term
*term
)
2834 __isl_give isl_term
*isl_term_dup(__isl_keep isl_term
*term
)
2843 total
= isl_dim_total(term
->dim
) + term
->div
->n_row
;
2845 dup
= isl_term_alloc(isl_dim_copy(term
->dim
), isl_mat_copy(term
->div
));
2849 isl_int_set(dup
->n
, term
->n
);
2850 isl_int_set(dup
->d
, term
->d
);
2852 for (i
= 0; i
< total
; ++i
)
2853 dup
->pow
[i
] = term
->pow
[i
];
2858 __isl_give isl_term
*isl_term_cow(__isl_take isl_term
*term
)
2866 return isl_term_dup(term
);
2869 void isl_term_free(__isl_take isl_term
*term
)
2874 if (--term
->ref
> 0)
2877 isl_dim_free(term
->dim
);
2878 isl_mat_free(term
->div
);
2879 isl_int_clear(term
->n
);
2880 isl_int_clear(term
->d
);
2884 unsigned isl_term_dim(__isl_keep isl_term
*term
, enum isl_dim_type type
)
2892 case isl_dim_out
: return isl_dim_size(term
->dim
, type
);
2893 case isl_dim_div
: return term
->div
->n_row
;
2894 case isl_dim_all
: return isl_dim_total(term
->dim
) + term
->div
->n_row
;
2899 isl_ctx
*isl_term_get_ctx(__isl_keep isl_term
*term
)
2901 return term
? term
->dim
->ctx
: NULL
;
2904 void isl_term_get_num(__isl_keep isl_term
*term
, isl_int
*n
)
2908 isl_int_set(*n
, term
->n
);
2911 void isl_term_get_den(__isl_keep isl_term
*term
, isl_int
*d
)
2915 isl_int_set(*d
, term
->d
);
2918 int isl_term_get_exp(__isl_keep isl_term
*term
,
2919 enum isl_dim_type type
, unsigned pos
)
2924 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, type
), return -1);
2926 if (type
>= isl_dim_set
)
2927 pos
+= isl_dim_size(term
->dim
, isl_dim_param
);
2928 if (type
>= isl_dim_div
)
2929 pos
+= isl_dim_size(term
->dim
, isl_dim_set
);
2931 return term
->pow
[pos
];
2934 __isl_give isl_div
*isl_term_get_div(__isl_keep isl_term
*term
, unsigned pos
)
2936 isl_basic_map
*bmap
;
2943 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, isl_dim_div
),
2946 total
= term
->div
->n_col
- term
->div
->n_row
- 2;
2947 /* No nested divs for now */
2948 isl_assert(term
->dim
->ctx
,
2949 isl_seq_first_non_zero(term
->div
->row
[pos
] + 2 + total
,
2950 term
->div
->n_row
) == -1,
2953 bmap
= isl_basic_map_alloc_dim(isl_dim_copy(term
->dim
), 1, 0, 0);
2954 if ((k
= isl_basic_map_alloc_div(bmap
)) < 0)
2957 isl_seq_cpy(bmap
->div
[k
], term
->div
->row
[pos
], 2 + total
);
2959 return isl_basic_map_div(bmap
, k
);
2961 isl_basic_map_free(bmap
);
2965 __isl_give isl_term
*isl_upoly_foreach_term(__isl_keep
struct isl_upoly
*up
,
2966 int (*fn
)(__isl_take isl_term
*term
, void *user
),
2967 __isl_take isl_term
*term
, void *user
)
2970 struct isl_upoly_rec
*rec
;
2975 if (isl_upoly_is_zero(up
))
2978 isl_assert(up
->ctx
, !isl_upoly_is_nan(up
), goto error
);
2979 isl_assert(up
->ctx
, !isl_upoly_is_infty(up
), goto error
);
2980 isl_assert(up
->ctx
, !isl_upoly_is_neginfty(up
), goto error
);
2982 if (isl_upoly_is_cst(up
)) {
2983 struct isl_upoly_cst
*cst
;
2984 cst
= isl_upoly_as_cst(up
);
2987 term
= isl_term_cow(term
);
2990 isl_int_set(term
->n
, cst
->n
);
2991 isl_int_set(term
->d
, cst
->d
);
2992 if (fn(isl_term_copy(term
), user
) < 0)
2997 rec
= isl_upoly_as_rec(up
);
3001 for (i
= 0; i
< rec
->n
; ++i
) {
3002 term
= isl_term_cow(term
);
3005 term
->pow
[up
->var
] = i
;
3006 term
= isl_upoly_foreach_term(rec
->p
[i
], fn
, term
, user
);
3010 term
->pow
[up
->var
] = 0;
3014 isl_term_free(term
);
3018 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial
*qp
,
3019 int (*fn
)(__isl_take isl_term
*term
, void *user
), void *user
)
3026 term
= isl_term_alloc(isl_dim_copy(qp
->dim
), isl_mat_copy(qp
->div
));
3030 term
= isl_upoly_foreach_term(qp
->upoly
, fn
, term
, user
);
3032 isl_term_free(term
);
3034 return term
? 0 : -1;
3037 __isl_give isl_qpolynomial
*isl_qpolynomial_from_term(__isl_take isl_term
*term
)
3039 struct isl_upoly
*up
;
3040 isl_qpolynomial
*qp
;
3046 n
= isl_dim_total(term
->dim
) + term
->div
->n_row
;
3048 up
= isl_upoly_rat_cst(term
->dim
->ctx
, term
->n
, term
->d
);
3049 for (i
= 0; i
< n
; ++i
) {
3052 up
= isl_upoly_mul(up
,
3053 isl_upoly_pow(term
->dim
->ctx
, i
, term
->pow
[i
]));
3056 qp
= isl_qpolynomial_alloc(isl_dim_copy(term
->dim
), term
->div
->n_row
, up
);
3059 isl_mat_free(qp
->div
);
3060 qp
->div
= isl_mat_copy(term
->div
);
3064 isl_term_free(term
);
3067 isl_qpolynomial_free(qp
);
3068 isl_term_free(term
);
3072 __isl_give isl_qpolynomial
*isl_qpolynomial_lift(__isl_take isl_qpolynomial
*qp
,
3073 __isl_take isl_dim
*dim
)
3082 if (isl_dim_equal(qp
->dim
, dim
)) {
3087 qp
= isl_qpolynomial_cow(qp
);
3091 extra
= isl_dim_size(dim
, isl_dim_set
) -
3092 isl_dim_size(qp
->dim
, isl_dim_set
);
3093 total
= isl_dim_total(qp
->dim
);
3094 if (qp
->div
->n_row
) {
3097 exp
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
3100 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3102 qp
->upoly
= expand(qp
->upoly
, exp
, total
);
3107 qp
->div
= isl_mat_insert_cols(qp
->div
, 2 + total
, extra
);
3110 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3111 isl_seq_clr(qp
->div
->row
[i
] + 2 + total
, extra
);
3113 isl_dim_free(qp
->dim
);
3119 isl_qpolynomial_free(qp
);
3123 /* For each parameter or variable that does not appear in qp,
3124 * first eliminate the variable from all constraints and then set it to zero.
3126 static __isl_give isl_set
*fix_inactive(__isl_take isl_set
*set
,
3127 __isl_keep isl_qpolynomial
*qp
)
3138 d
= isl_dim_total(set
->dim
);
3139 active
= isl_calloc_array(set
->ctx
, int, d
);
3140 if (set_active(qp
, active
) < 0)
3143 for (i
= 0; i
< d
; ++i
)
3152 nparam
= isl_dim_size(set
->dim
, isl_dim_param
);
3153 nvar
= isl_dim_size(set
->dim
, isl_dim_set
);
3154 for (i
= 0; i
< nparam
; ++i
) {
3157 set
= isl_set_eliminate(set
, isl_dim_param
, i
, 1);
3158 set
= isl_set_fix_si(set
, isl_dim_param
, i
, 0);
3160 for (i
= 0; i
< nvar
; ++i
) {
3161 if (active
[nparam
+ i
])
3163 set
= isl_set_eliminate(set
, isl_dim_set
, i
, 1);
3164 set
= isl_set_fix_si(set
, isl_dim_set
, i
, 0);
3176 struct isl_opt_data
{
3177 isl_qpolynomial
*qp
;
3179 isl_qpolynomial
*opt
;
3183 static int opt_fn(__isl_take isl_point
*pnt
, void *user
)
3185 struct isl_opt_data
*data
= (struct isl_opt_data
*)user
;
3186 isl_qpolynomial
*val
;
3188 val
= isl_qpolynomial_eval(isl_qpolynomial_copy(data
->qp
), pnt
);
3192 } else if (data
->max
) {
3193 data
->opt
= isl_qpolynomial_max_cst(data
->opt
, val
);
3195 data
->opt
= isl_qpolynomial_min_cst(data
->opt
, val
);
3201 __isl_give isl_qpolynomial
*isl_qpolynomial_opt_on_domain(
3202 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*set
, int max
)
3204 struct isl_opt_data data
= { NULL
, 1, NULL
, max
};
3209 if (isl_upoly_is_cst(qp
->upoly
)) {
3214 set
= fix_inactive(set
, qp
);
3217 if (isl_set_foreach_point(set
, opt_fn
, &data
) < 0)
3221 data
.opt
= isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp
));
3224 isl_qpolynomial_free(qp
);
3228 isl_qpolynomial_free(qp
);
3229 isl_qpolynomial_free(data
.opt
);
3233 __isl_give isl_qpolynomial
*isl_qpolynomial_morph(__isl_take isl_qpolynomial
*qp
,
3234 __isl_take isl_morph
*morph
)
3238 struct isl_upoly
*up
;
3240 struct isl_upoly
**subs
;
3243 qp
= isl_qpolynomial_cow(qp
);
3248 isl_assert(ctx
, isl_dim_equal(qp
->dim
, morph
->dom
->dim
), goto error
);
3250 subs
= isl_calloc_array(ctx
, struct isl_upoly
*, morph
->inv
->n_row
- 1);
3254 for (i
= 0; 1 + i
< morph
->inv
->n_row
; ++i
)
3255 subs
[i
] = isl_upoly_from_affine(ctx
, morph
->inv
->row
[1 + i
],
3256 morph
->inv
->row
[0][0], morph
->inv
->n_col
);
3258 qp
->upoly
= isl_upoly_subs(qp
->upoly
, 0, morph
->inv
->n_row
- 1, subs
);
3260 for (i
= 0; 1 + i
< morph
->inv
->n_row
; ++i
)
3261 isl_upoly_free(subs
[i
]);
3264 mat
= isl_mat_diagonal(isl_mat_identity(ctx
, 1), isl_mat_copy(morph
->inv
));
3265 mat
= isl_mat_diagonal(mat
, isl_mat_identity(ctx
, qp
->div
->n_row
));
3266 qp
->div
= isl_mat_product(qp
->div
, mat
);
3267 isl_dim_free(qp
->dim
);
3268 qp
->dim
= isl_dim_copy(morph
->ran
->dim
);
3270 if (!qp
->upoly
|| !qp
->div
|| !qp
->dim
)
3273 isl_morph_free(morph
);
3277 isl_qpolynomial_free(qp
);
3278 isl_morph_free(morph
);
3282 static int neg_entry(void **entry
, void *user
)
3284 isl_pw_qpolynomial
**pwqp
= (isl_pw_qpolynomial
**)entry
;
3286 *pwqp
= isl_pw_qpolynomial_neg(*pwqp
);
3288 return *pwqp
? 0 : -1;
3291 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_neg(
3292 __isl_take isl_union_pw_qpolynomial
*upwqp
)
3294 upwqp
= isl_union_pw_qpolynomial_cow(upwqp
);
3298 if (isl_hash_table_foreach(upwqp
->dim
->ctx
, &upwqp
->table
,
3299 &neg_entry
, NULL
) < 0)
3304 isl_union_pw_qpolynomial_free(upwqp
);
3308 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_sub(
3309 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
3310 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
3312 return isl_union_pw_qpolynomial_add(upwqp1
,
3313 isl_union_pw_qpolynomial_neg(upwqp2
));
3316 static int mul_entry(void **entry
, void *user
)
3318 struct isl_union_pw_qpolynomial_match_bin_data
*data
= user
;
3320 struct isl_hash_table_entry
*entry2
;
3321 isl_pw_qpolynomial
*pwpq
= *entry
;
3324 hash
= isl_dim_get_hash(pwpq
->dim
);
3325 entry2
= isl_hash_table_find(data
->u2
->dim
->ctx
, &data
->u2
->table
,
3326 hash
, &has_dim
, pwpq
->dim
, 0);
3330 pwpq
= isl_pw_qpolynomial_copy(pwpq
);
3331 pwpq
= isl_pw_qpolynomial_mul(pwpq
,
3332 isl_pw_qpolynomial_copy(entry2
->data
));
3334 empty
= isl_pw_qpolynomial_is_zero(pwpq
);
3336 isl_pw_qpolynomial_free(pwpq
);
3340 isl_pw_qpolynomial_free(pwpq
);
3344 data
->res
= isl_union_pw_qpolynomial_add_pw_qpolynomial(data
->res
, pwpq
);
3349 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_mul(
3350 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
3351 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
3353 return match_bin_op(upwqp1
, upwqp2
, &mul_entry
);
3356 /* Reorder the columns of the given div definitions according to the
3359 static __isl_give isl_mat
*reorder_divs(__isl_take isl_mat
*div
,
3360 __isl_take isl_reordering
*r
)
3369 extra
= isl_dim_total(r
->dim
) + div
->n_row
- r
->len
;
3370 mat
= isl_mat_alloc(div
->ctx
, div
->n_row
, div
->n_col
+ extra
);
3374 for (i
= 0; i
< div
->n_row
; ++i
) {
3375 isl_seq_cpy(mat
->row
[i
], div
->row
[i
], 2);
3376 isl_seq_clr(mat
->row
[i
] + 2, mat
->n_col
- 2);
3377 for (j
= 0; j
< r
->len
; ++j
)
3378 isl_int_set(mat
->row
[i
][2 + r
->pos
[j
]],
3379 div
->row
[i
][2 + j
]);
3382 isl_reordering_free(r
);
3386 isl_reordering_free(r
);
3391 /* Reorder the dimension of "qp" according to the given reordering.
3393 __isl_give isl_qpolynomial
*isl_qpolynomial_realign(
3394 __isl_take isl_qpolynomial
*qp
, __isl_take isl_reordering
*r
)
3396 qp
= isl_qpolynomial_cow(qp
);
3400 r
= isl_reordering_extend(r
, qp
->div
->n_row
);
3404 qp
->div
= reorder_divs(qp
->div
, isl_reordering_copy(r
));
3408 qp
->upoly
= reorder(qp
->upoly
, r
->pos
);
3412 qp
= isl_qpolynomial_reset_dim(qp
, isl_dim_copy(r
->dim
));
3414 isl_reordering_free(r
);
3417 isl_qpolynomial_free(qp
);
3418 isl_reordering_free(r
);
3422 struct isl_split_periods_data
{
3424 isl_pw_qpolynomial
*res
;
3427 /* Create a slice where the integer division "div" has the fixed value "v".
3428 * In particular, if "div" refers to floor(f/m), then create a slice
3430 * m v <= f <= m v + (m - 1)
3435 * -f + m v + (m - 1) >= 0
3437 static __isl_give isl_set
*set_div_slice(__isl_take isl_dim
*dim
,
3438 __isl_keep isl_qpolynomial
*qp
, int div
, isl_int v
)
3441 isl_basic_set
*bset
= NULL
;
3447 total
= isl_dim_total(dim
);
3448 bset
= isl_basic_set_alloc_dim(isl_dim_copy(dim
), 0, 0, 2);
3450 k
= isl_basic_set_alloc_inequality(bset
);
3453 isl_seq_cpy(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
3454 isl_int_submul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
3456 k
= isl_basic_set_alloc_inequality(bset
);
3459 isl_seq_neg(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
3460 isl_int_addmul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
3461 isl_int_add(bset
->ineq
[k
][0], bset
->ineq
[k
][0], qp
->div
->row
[div
][0]);
3462 isl_int_sub_ui(bset
->ineq
[k
][0], bset
->ineq
[k
][0], 1);
3465 return isl_set_from_basic_set(bset
);
3467 isl_basic_set_free(bset
);
3472 static int split_periods(__isl_take isl_set
*set
,
3473 __isl_take isl_qpolynomial
*qp
, void *user
);
3475 /* Create a slice of the domain "set" such that integer division "div"
3476 * has the fixed value "v" and add the results to data->res,
3477 * replacing the integer division by "v" in "qp".
3479 static int set_div(__isl_take isl_set
*set
,
3480 __isl_take isl_qpolynomial
*qp
, int div
, isl_int v
,
3481 struct isl_split_periods_data
*data
)
3486 struct isl_upoly
*cst
;
3489 slice
= set_div_slice(isl_set_get_dim(set
), qp
, div
, v
);
3490 set
= isl_set_intersect(set
, slice
);
3492 qp
= isl_qpolynomial_cow(qp
);
3496 cst
= isl_upoly_rat_cst(qp
->dim
->ctx
, v
, qp
->dim
->ctx
->one
);
3499 total
= isl_dim_total(qp
->dim
);
3500 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ div
, 1, &cst
);
3501 isl_upoly_free(cst
);
3505 reordering
= isl_alloc_array(qp
->dim
->ctx
, int, total
+ qp
->div
->n_row
);
3508 for (i
= 0; i
< total
+ div
; ++i
)
3510 for (i
= total
+ div
+ 1; i
< total
+ qp
->div
->n_row
; ++i
)
3511 reordering
[i
] = i
- 1;
3512 qp
->div
= isl_mat_drop_rows(qp
->div
, div
, 1);
3513 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + total
+ div
, 1);
3514 qp
->upoly
= reorder(qp
->upoly
, reordering
);
3517 if (!qp
->upoly
|| !qp
->div
)
3520 return split_periods(set
, qp
, data
);
3523 isl_qpolynomial_free(qp
);
3527 /* Split the domain "set" such that integer division "div"
3528 * has a fixed value (ranging from "min" to "max") on each slice
3529 * and add the results to data->res.
3531 static int split_div(__isl_take isl_set
*set
,
3532 __isl_take isl_qpolynomial
*qp
, int div
, isl_int min
, isl_int max
,
3533 struct isl_split_periods_data
*data
)
3535 for (; isl_int_le(min
, max
); isl_int_add_ui(min
, min
, 1)) {
3536 isl_set
*set_i
= isl_set_copy(set
);
3537 isl_qpolynomial
*qp_i
= isl_qpolynomial_copy(qp
);
3539 if (set_div(set_i
, qp_i
, div
, min
, data
) < 0)
3543 isl_qpolynomial_free(qp
);
3547 isl_qpolynomial_free(qp
);
3551 /* If "qp" refers to any integer division
3552 * that can only attain "max_periods" distinct values on "set"
3553 * then split the domain along those distinct values.
3554 * Add the results (or the original if no splitting occurs)
3557 static int split_periods(__isl_take isl_set
*set
,
3558 __isl_take isl_qpolynomial
*qp
, void *user
)
3561 isl_pw_qpolynomial
*pwqp
;
3562 struct isl_split_periods_data
*data
;
3567 data
= (struct isl_split_periods_data
*)user
;
3572 if (qp
->div
->n_row
== 0) {
3573 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
3574 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
3580 total
= isl_dim_total(qp
->dim
);
3581 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
3582 enum isl_lp_result lp_res
;
3584 if (isl_seq_first_non_zero(qp
->div
->row
[i
] + 2 + total
,
3585 qp
->div
->n_row
) != -1)
3588 lp_res
= isl_set_solve_lp(set
, 0, qp
->div
->row
[i
] + 1,
3589 set
->ctx
->one
, &min
, NULL
, NULL
);
3590 if (lp_res
== isl_lp_error
)
3592 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
3594 isl_int_fdiv_q(min
, min
, qp
->div
->row
[i
][0]);
3596 lp_res
= isl_set_solve_lp(set
, 1, qp
->div
->row
[i
] + 1,
3597 set
->ctx
->one
, &max
, NULL
, NULL
);
3598 if (lp_res
== isl_lp_error
)
3600 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
3602 isl_int_fdiv_q(max
, max
, qp
->div
->row
[i
][0]);
3604 isl_int_sub(max
, max
, min
);
3605 if (isl_int_cmp_si(max
, data
->max_periods
) < 0) {
3606 isl_int_add(max
, max
, min
);
3611 if (i
< qp
->div
->n_row
) {
3612 r
= split_div(set
, qp
, i
, min
, max
, data
);
3614 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
3615 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
3627 isl_qpolynomial_free(qp
);
3631 /* If any quasi-polynomial in pwqp refers to any integer division
3632 * that can only attain "max_periods" distinct values on its domain
3633 * then split the domain along those distinct values.
3635 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_split_periods(
3636 __isl_take isl_pw_qpolynomial
*pwqp
, int max_periods
)
3638 struct isl_split_periods_data data
;
3640 data
.max_periods
= max_periods
;
3641 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp
));
3643 if (isl_pw_qpolynomial_foreach_piece(pwqp
, &split_periods
, &data
) < 0)
3646 isl_pw_qpolynomial_free(pwqp
);
3650 isl_pw_qpolynomial_free(data
.res
);
3651 isl_pw_qpolynomial_free(pwqp
);