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_map_private.h>
13 #include <isl_factorization.h>
16 #include <isl_union_map_private.h>
17 #include <isl_polynomial_private.h>
18 #include <isl_point_private.h>
19 #include <isl_dim_private.h>
20 #include <isl_mat_private.h>
21 #include <isl_range.h>
23 static unsigned pos(__isl_keep isl_dim
*dim
, enum isl_dim_type type
)
26 case isl_dim_param
: return 0;
27 case isl_dim_in
: return dim
->nparam
;
28 case isl_dim_out
: return dim
->nparam
+ dim
->n_in
;
33 int isl_upoly_is_cst(__isl_keep
struct isl_upoly
*up
)
41 __isl_keep
struct isl_upoly_cst
*isl_upoly_as_cst(__isl_keep
struct isl_upoly
*up
)
46 isl_assert(up
->ctx
, up
->var
< 0, return NULL
);
48 return (struct isl_upoly_cst
*)up
;
51 __isl_keep
struct isl_upoly_rec
*isl_upoly_as_rec(__isl_keep
struct isl_upoly
*up
)
56 isl_assert(up
->ctx
, up
->var
>= 0, return NULL
);
58 return (struct isl_upoly_rec
*)up
;
61 int isl_upoly_is_equal(__isl_keep
struct isl_upoly
*up1
,
62 __isl_keep
struct isl_upoly
*up2
)
65 struct isl_upoly_rec
*rec1
, *rec2
;
71 if (up1
->var
!= up2
->var
)
73 if (isl_upoly_is_cst(up1
)) {
74 struct isl_upoly_cst
*cst1
, *cst2
;
75 cst1
= isl_upoly_as_cst(up1
);
76 cst2
= isl_upoly_as_cst(up2
);
79 return isl_int_eq(cst1
->n
, cst2
->n
) &&
80 isl_int_eq(cst1
->d
, cst2
->d
);
83 rec1
= isl_upoly_as_rec(up1
);
84 rec2
= isl_upoly_as_rec(up2
);
88 if (rec1
->n
!= rec2
->n
)
91 for (i
= 0; i
< rec1
->n
; ++i
) {
92 int eq
= isl_upoly_is_equal(rec1
->p
[i
], rec2
->p
[i
]);
100 int isl_upoly_is_zero(__isl_keep
struct isl_upoly
*up
)
102 struct isl_upoly_cst
*cst
;
106 if (!isl_upoly_is_cst(up
))
109 cst
= isl_upoly_as_cst(up
);
113 return isl_int_is_zero(cst
->n
) && isl_int_is_pos(cst
->d
);
116 int isl_upoly_sgn(__isl_keep
struct isl_upoly
*up
)
118 struct isl_upoly_cst
*cst
;
122 if (!isl_upoly_is_cst(up
))
125 cst
= isl_upoly_as_cst(up
);
129 return isl_int_sgn(cst
->n
);
132 int isl_upoly_is_nan(__isl_keep
struct isl_upoly
*up
)
134 struct isl_upoly_cst
*cst
;
138 if (!isl_upoly_is_cst(up
))
141 cst
= isl_upoly_as_cst(up
);
145 return isl_int_is_zero(cst
->n
) && isl_int_is_zero(cst
->d
);
148 int isl_upoly_is_infty(__isl_keep
struct isl_upoly
*up
)
150 struct isl_upoly_cst
*cst
;
154 if (!isl_upoly_is_cst(up
))
157 cst
= isl_upoly_as_cst(up
);
161 return isl_int_is_pos(cst
->n
) && isl_int_is_zero(cst
->d
);
164 int isl_upoly_is_neginfty(__isl_keep
struct isl_upoly
*up
)
166 struct isl_upoly_cst
*cst
;
170 if (!isl_upoly_is_cst(up
))
173 cst
= isl_upoly_as_cst(up
);
177 return isl_int_is_neg(cst
->n
) && isl_int_is_zero(cst
->d
);
180 int isl_upoly_is_one(__isl_keep
struct isl_upoly
*up
)
182 struct isl_upoly_cst
*cst
;
186 if (!isl_upoly_is_cst(up
))
189 cst
= isl_upoly_as_cst(up
);
193 return isl_int_eq(cst
->n
, cst
->d
) && isl_int_is_pos(cst
->d
);
196 int isl_upoly_is_negone(__isl_keep
struct isl_upoly
*up
)
198 struct isl_upoly_cst
*cst
;
202 if (!isl_upoly_is_cst(up
))
205 cst
= isl_upoly_as_cst(up
);
209 return isl_int_is_negone(cst
->n
) && isl_int_is_one(cst
->d
);
212 __isl_give
struct isl_upoly_cst
*isl_upoly_cst_alloc(struct isl_ctx
*ctx
)
214 struct isl_upoly_cst
*cst
;
216 cst
= isl_alloc_type(ctx
, struct isl_upoly_cst
);
225 isl_int_init(cst
->n
);
226 isl_int_init(cst
->d
);
231 __isl_give
struct isl_upoly
*isl_upoly_zero(struct isl_ctx
*ctx
)
233 struct isl_upoly_cst
*cst
;
235 cst
= isl_upoly_cst_alloc(ctx
);
239 isl_int_set_si(cst
->n
, 0);
240 isl_int_set_si(cst
->d
, 1);
245 __isl_give
struct isl_upoly
*isl_upoly_one(struct isl_ctx
*ctx
)
247 struct isl_upoly_cst
*cst
;
249 cst
= isl_upoly_cst_alloc(ctx
);
253 isl_int_set_si(cst
->n
, 1);
254 isl_int_set_si(cst
->d
, 1);
259 __isl_give
struct isl_upoly
*isl_upoly_infty(struct isl_ctx
*ctx
)
261 struct isl_upoly_cst
*cst
;
263 cst
= isl_upoly_cst_alloc(ctx
);
267 isl_int_set_si(cst
->n
, 1);
268 isl_int_set_si(cst
->d
, 0);
273 __isl_give
struct isl_upoly
*isl_upoly_neginfty(struct isl_ctx
*ctx
)
275 struct isl_upoly_cst
*cst
;
277 cst
= isl_upoly_cst_alloc(ctx
);
281 isl_int_set_si(cst
->n
, -1);
282 isl_int_set_si(cst
->d
, 0);
287 __isl_give
struct isl_upoly
*isl_upoly_nan(struct isl_ctx
*ctx
)
289 struct isl_upoly_cst
*cst
;
291 cst
= isl_upoly_cst_alloc(ctx
);
295 isl_int_set_si(cst
->n
, 0);
296 isl_int_set_si(cst
->d
, 0);
301 __isl_give
struct isl_upoly
*isl_upoly_rat_cst(struct isl_ctx
*ctx
,
302 isl_int n
, isl_int d
)
304 struct isl_upoly_cst
*cst
;
306 cst
= isl_upoly_cst_alloc(ctx
);
310 isl_int_set(cst
->n
, n
);
311 isl_int_set(cst
->d
, d
);
316 __isl_give
struct isl_upoly_rec
*isl_upoly_alloc_rec(struct isl_ctx
*ctx
,
319 struct isl_upoly_rec
*rec
;
321 isl_assert(ctx
, var
>= 0, return NULL
);
322 isl_assert(ctx
, size
>= 0, return NULL
);
323 rec
= isl_calloc(ctx
, struct isl_upoly_rec
,
324 sizeof(struct isl_upoly_rec
) +
325 (size
- 1) * sizeof(struct isl_upoly
*));
340 __isl_give isl_qpolynomial
*isl_qpolynomial_reset_dim(
341 __isl_take isl_qpolynomial
*qp
, __isl_take isl_dim
*dim
)
343 qp
= isl_qpolynomial_cow(qp
);
347 isl_dim_free(qp
->dim
);
352 isl_qpolynomial_free(qp
);
357 isl_ctx
*isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial
*qp
)
359 return qp
? qp
->dim
->ctx
: NULL
;
362 __isl_give isl_dim
*isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial
*qp
)
364 return qp
? isl_dim_copy(qp
->dim
) : NULL
;
367 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial
*qp
,
368 enum isl_dim_type type
)
370 return qp
? isl_dim_size(qp
->dim
, type
) : 0;
373 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial
*qp
)
375 return qp
? isl_upoly_is_zero(qp
->upoly
) : -1;
378 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial
*qp
)
380 return qp
? isl_upoly_is_one(qp
->upoly
) : -1;
383 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial
*qp
)
385 return qp
? isl_upoly_is_nan(qp
->upoly
) : -1;
388 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial
*qp
)
390 return qp
? isl_upoly_is_infty(qp
->upoly
) : -1;
393 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial
*qp
)
395 return qp
? isl_upoly_is_neginfty(qp
->upoly
) : -1;
398 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial
*qp
)
400 return qp
? isl_upoly_sgn(qp
->upoly
) : 0;
403 static void upoly_free_cst(__isl_take
struct isl_upoly_cst
*cst
)
405 isl_int_clear(cst
->n
);
406 isl_int_clear(cst
->d
);
409 static void upoly_free_rec(__isl_take
struct isl_upoly_rec
*rec
)
413 for (i
= 0; i
< rec
->n
; ++i
)
414 isl_upoly_free(rec
->p
[i
]);
417 __isl_give
struct isl_upoly
*isl_upoly_copy(__isl_keep
struct isl_upoly
*up
)
426 __isl_give
struct isl_upoly
*isl_upoly_dup_cst(__isl_keep
struct isl_upoly
*up
)
428 struct isl_upoly_cst
*cst
;
429 struct isl_upoly_cst
*dup
;
431 cst
= isl_upoly_as_cst(up
);
435 dup
= isl_upoly_as_cst(isl_upoly_zero(up
->ctx
));
438 isl_int_set(dup
->n
, cst
->n
);
439 isl_int_set(dup
->d
, cst
->d
);
444 __isl_give
struct isl_upoly
*isl_upoly_dup_rec(__isl_keep
struct isl_upoly
*up
)
447 struct isl_upoly_rec
*rec
;
448 struct isl_upoly_rec
*dup
;
450 rec
= isl_upoly_as_rec(up
);
454 dup
= isl_upoly_alloc_rec(up
->ctx
, up
->var
, rec
->n
);
458 for (i
= 0; i
< rec
->n
; ++i
) {
459 dup
->p
[i
] = isl_upoly_copy(rec
->p
[i
]);
467 isl_upoly_free(&dup
->up
);
471 __isl_give
struct isl_upoly
*isl_upoly_dup(__isl_keep
struct isl_upoly
*up
)
473 struct isl_upoly
*dup
;
478 if (isl_upoly_is_cst(up
))
479 return isl_upoly_dup_cst(up
);
481 return isl_upoly_dup_rec(up
);
484 __isl_give
struct isl_upoly
*isl_upoly_cow(__isl_take
struct isl_upoly
*up
)
492 return isl_upoly_dup(up
);
495 void isl_upoly_free(__isl_take
struct isl_upoly
*up
)
504 upoly_free_cst((struct isl_upoly_cst
*)up
);
506 upoly_free_rec((struct isl_upoly_rec
*)up
);
508 isl_ctx_deref(up
->ctx
);
512 static void isl_upoly_cst_reduce(__isl_keep
struct isl_upoly_cst
*cst
)
517 isl_int_gcd(gcd
, cst
->n
, cst
->d
);
518 if (!isl_int_is_zero(gcd
) && !isl_int_is_one(gcd
)) {
519 isl_int_divexact(cst
->n
, cst
->n
, gcd
);
520 isl_int_divexact(cst
->d
, cst
->d
, gcd
);
525 __isl_give
struct isl_upoly
*isl_upoly_sum_cst(__isl_take
struct isl_upoly
*up1
,
526 __isl_take
struct isl_upoly
*up2
)
528 struct isl_upoly_cst
*cst1
;
529 struct isl_upoly_cst
*cst2
;
531 up1
= isl_upoly_cow(up1
);
535 cst1
= isl_upoly_as_cst(up1
);
536 cst2
= isl_upoly_as_cst(up2
);
538 if (isl_int_eq(cst1
->d
, cst2
->d
))
539 isl_int_add(cst1
->n
, cst1
->n
, cst2
->n
);
541 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->d
);
542 isl_int_addmul(cst1
->n
, cst2
->n
, cst1
->d
);
543 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
546 isl_upoly_cst_reduce(cst1
);
556 static __isl_give
struct isl_upoly
*replace_by_zero(
557 __isl_take
struct isl_upoly
*up
)
565 return isl_upoly_zero(ctx
);
568 static __isl_give
struct isl_upoly
*replace_by_constant_term(
569 __isl_take
struct isl_upoly
*up
)
571 struct isl_upoly_rec
*rec
;
572 struct isl_upoly
*cst
;
577 rec
= isl_upoly_as_rec(up
);
580 cst
= isl_upoly_copy(rec
->p
[0]);
588 __isl_give
struct isl_upoly
*isl_upoly_sum(__isl_take
struct isl_upoly
*up1
,
589 __isl_take
struct isl_upoly
*up2
)
592 struct isl_upoly_rec
*rec1
, *rec2
;
597 if (isl_upoly_is_nan(up1
)) {
602 if (isl_upoly_is_nan(up2
)) {
607 if (isl_upoly_is_zero(up1
)) {
612 if (isl_upoly_is_zero(up2
)) {
617 if (up1
->var
< up2
->var
)
618 return isl_upoly_sum(up2
, up1
);
620 if (up2
->var
< up1
->var
) {
621 struct isl_upoly_rec
*rec
;
622 if (isl_upoly_is_infty(up2
) || isl_upoly_is_neginfty(up2
)) {
626 up1
= isl_upoly_cow(up1
);
627 rec
= isl_upoly_as_rec(up1
);
630 rec
->p
[0] = isl_upoly_sum(rec
->p
[0], up2
);
632 up1
= replace_by_constant_term(up1
);
636 if (isl_upoly_is_cst(up1
))
637 return isl_upoly_sum_cst(up1
, up2
);
639 rec1
= isl_upoly_as_rec(up1
);
640 rec2
= isl_upoly_as_rec(up2
);
644 if (rec1
->n
< rec2
->n
)
645 return isl_upoly_sum(up2
, up1
);
647 up1
= isl_upoly_cow(up1
);
648 rec1
= isl_upoly_as_rec(up1
);
652 for (i
= rec2
->n
- 1; i
>= 0; --i
) {
653 rec1
->p
[i
] = isl_upoly_sum(rec1
->p
[i
],
654 isl_upoly_copy(rec2
->p
[i
]));
657 if (i
== rec1
->n
- 1 && isl_upoly_is_zero(rec1
->p
[i
])) {
658 isl_upoly_free(rec1
->p
[i
]);
664 up1
= replace_by_zero(up1
);
665 else if (rec1
->n
== 1)
666 up1
= replace_by_constant_term(up1
);
677 __isl_give
struct isl_upoly
*isl_upoly_cst_add_isl_int(
678 __isl_take
struct isl_upoly
*up
, isl_int v
)
680 struct isl_upoly_cst
*cst
;
682 up
= isl_upoly_cow(up
);
686 cst
= isl_upoly_as_cst(up
);
688 isl_int_addmul(cst
->n
, cst
->d
, v
);
693 __isl_give
struct isl_upoly
*isl_upoly_add_isl_int(
694 __isl_take
struct isl_upoly
*up
, isl_int v
)
696 struct isl_upoly_rec
*rec
;
701 if (isl_upoly_is_cst(up
))
702 return isl_upoly_cst_add_isl_int(up
, v
);
704 up
= isl_upoly_cow(up
);
705 rec
= isl_upoly_as_rec(up
);
709 rec
->p
[0] = isl_upoly_add_isl_int(rec
->p
[0], v
);
719 __isl_give
struct isl_upoly
*isl_upoly_cst_mul_isl_int(
720 __isl_take
struct isl_upoly
*up
, isl_int v
)
722 struct isl_upoly_cst
*cst
;
724 if (isl_upoly_is_zero(up
))
727 up
= isl_upoly_cow(up
);
731 cst
= isl_upoly_as_cst(up
);
733 isl_int_mul(cst
->n
, cst
->n
, v
);
738 __isl_give
struct isl_upoly
*isl_upoly_mul_isl_int(
739 __isl_take
struct isl_upoly
*up
, isl_int v
)
742 struct isl_upoly_rec
*rec
;
747 if (isl_upoly_is_cst(up
))
748 return isl_upoly_cst_mul_isl_int(up
, v
);
750 up
= isl_upoly_cow(up
);
751 rec
= isl_upoly_as_rec(up
);
755 for (i
= 0; i
< rec
->n
; ++i
) {
756 rec
->p
[i
] = isl_upoly_mul_isl_int(rec
->p
[i
], v
);
767 __isl_give
struct isl_upoly
*isl_upoly_mul_cst(__isl_take
struct isl_upoly
*up1
,
768 __isl_take
struct isl_upoly
*up2
)
770 struct isl_upoly_cst
*cst1
;
771 struct isl_upoly_cst
*cst2
;
773 up1
= isl_upoly_cow(up1
);
777 cst1
= isl_upoly_as_cst(up1
);
778 cst2
= isl_upoly_as_cst(up2
);
780 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->n
);
781 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
783 isl_upoly_cst_reduce(cst1
);
793 __isl_give
struct isl_upoly
*isl_upoly_mul_rec(__isl_take
struct isl_upoly
*up1
,
794 __isl_take
struct isl_upoly
*up2
)
796 struct isl_upoly_rec
*rec1
;
797 struct isl_upoly_rec
*rec2
;
798 struct isl_upoly_rec
*res
;
802 rec1
= isl_upoly_as_rec(up1
);
803 rec2
= isl_upoly_as_rec(up2
);
806 size
= rec1
->n
+ rec2
->n
- 1;
807 res
= isl_upoly_alloc_rec(up1
->ctx
, up1
->var
, size
);
811 for (i
= 0; i
< rec1
->n
; ++i
) {
812 res
->p
[i
] = isl_upoly_mul(isl_upoly_copy(rec2
->p
[0]),
813 isl_upoly_copy(rec1
->p
[i
]));
818 for (; i
< size
; ++i
) {
819 res
->p
[i
] = isl_upoly_zero(up1
->ctx
);
824 for (i
= 0; i
< rec1
->n
; ++i
) {
825 for (j
= 1; j
< rec2
->n
; ++j
) {
826 struct isl_upoly
*up
;
827 up
= isl_upoly_mul(isl_upoly_copy(rec2
->p
[j
]),
828 isl_upoly_copy(rec1
->p
[i
]));
829 res
->p
[i
+ j
] = isl_upoly_sum(res
->p
[i
+ j
], up
);
842 isl_upoly_free(&res
->up
);
846 __isl_give
struct isl_upoly
*isl_upoly_mul(__isl_take
struct isl_upoly
*up1
,
847 __isl_take
struct isl_upoly
*up2
)
852 if (isl_upoly_is_nan(up1
)) {
857 if (isl_upoly_is_nan(up2
)) {
862 if (isl_upoly_is_zero(up1
)) {
867 if (isl_upoly_is_zero(up2
)) {
872 if (isl_upoly_is_one(up1
)) {
877 if (isl_upoly_is_one(up2
)) {
882 if (up1
->var
< up2
->var
)
883 return isl_upoly_mul(up2
, up1
);
885 if (up2
->var
< up1
->var
) {
887 struct isl_upoly_rec
*rec
;
888 if (isl_upoly_is_infty(up2
) || isl_upoly_is_neginfty(up2
)) {
889 isl_ctx
*ctx
= up1
->ctx
;
892 return isl_upoly_nan(ctx
);
894 up1
= isl_upoly_cow(up1
);
895 rec
= isl_upoly_as_rec(up1
);
899 for (i
= 0; i
< rec
->n
; ++i
) {
900 rec
->p
[i
] = isl_upoly_mul(rec
->p
[i
],
901 isl_upoly_copy(up2
));
909 if (isl_upoly_is_cst(up1
))
910 return isl_upoly_mul_cst(up1
, up2
);
912 return isl_upoly_mul_rec(up1
, up2
);
919 __isl_give
struct isl_upoly
*isl_upoly_pow(__isl_take
struct isl_upoly
*up
,
922 struct isl_upoly
*res
;
930 res
= isl_upoly_copy(up
);
932 res
= isl_upoly_one(up
->ctx
);
934 while (power
>>= 1) {
935 up
= isl_upoly_mul(up
, isl_upoly_copy(up
));
937 res
= isl_upoly_mul(res
, isl_upoly_copy(up
));
944 __isl_give isl_qpolynomial
*isl_qpolynomial_alloc(__isl_take isl_dim
*dim
,
945 unsigned n_div
, __isl_take
struct isl_upoly
*up
)
947 struct isl_qpolynomial
*qp
= NULL
;
953 total
= isl_dim_total(dim
);
955 qp
= isl_calloc_type(dim
->ctx
, struct isl_qpolynomial
);
960 qp
->div
= isl_mat_alloc(dim
->ctx
, n_div
, 1 + 1 + total
+ n_div
);
971 isl_qpolynomial_free(qp
);
975 __isl_give isl_qpolynomial
*isl_qpolynomial_copy(__isl_keep isl_qpolynomial
*qp
)
984 __isl_give isl_qpolynomial
*isl_qpolynomial_dup(__isl_keep isl_qpolynomial
*qp
)
986 struct isl_qpolynomial
*dup
;
991 dup
= isl_qpolynomial_alloc(isl_dim_copy(qp
->dim
), qp
->div
->n_row
,
992 isl_upoly_copy(qp
->upoly
));
995 isl_mat_free(dup
->div
);
996 dup
->div
= isl_mat_copy(qp
->div
);
1002 isl_qpolynomial_free(dup
);
1006 __isl_give isl_qpolynomial
*isl_qpolynomial_cow(__isl_take isl_qpolynomial
*qp
)
1014 return isl_qpolynomial_dup(qp
);
1017 void isl_qpolynomial_free(__isl_take isl_qpolynomial
*qp
)
1025 isl_dim_free(qp
->dim
);
1026 isl_mat_free(qp
->div
);
1027 isl_upoly_free(qp
->upoly
);
1032 __isl_give
struct isl_upoly
*isl_upoly_var_pow(isl_ctx
*ctx
, int pos
, int power
)
1035 struct isl_upoly
*up
;
1036 struct isl_upoly_rec
*rec
;
1037 struct isl_upoly_cst
*cst
;
1039 rec
= isl_upoly_alloc_rec(ctx
, pos
, 1 + power
);
1042 for (i
= 0; i
< 1 + power
; ++i
) {
1043 rec
->p
[i
] = isl_upoly_zero(ctx
);
1048 cst
= isl_upoly_as_cst(rec
->p
[power
]);
1049 isl_int_set_si(cst
->n
, 1);
1053 isl_upoly_free(&rec
->up
);
1057 /* r array maps original positions to new positions.
1059 static __isl_give
struct isl_upoly
*reorder(__isl_take
struct isl_upoly
*up
,
1063 struct isl_upoly_rec
*rec
;
1064 struct isl_upoly
*base
;
1065 struct isl_upoly
*res
;
1067 if (isl_upoly_is_cst(up
))
1070 rec
= isl_upoly_as_rec(up
);
1074 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
1076 base
= isl_upoly_var_pow(up
->ctx
, r
[up
->var
], 1);
1077 res
= reorder(isl_upoly_copy(rec
->p
[rec
->n
- 1]), r
);
1079 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1080 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
1081 res
= isl_upoly_sum(res
, reorder(isl_upoly_copy(rec
->p
[i
]), r
));
1084 isl_upoly_free(base
);
1093 static int compatible_divs(__isl_keep isl_mat
*div1
, __isl_keep isl_mat
*div2
)
1098 isl_assert(div1
->ctx
, div1
->n_row
>= div2
->n_row
&&
1099 div1
->n_col
>= div2
->n_col
, return -1);
1101 if (div1
->n_row
== div2
->n_row
)
1102 return isl_mat_is_equal(div1
, div2
);
1104 n_row
= div1
->n_row
;
1105 n_col
= div1
->n_col
;
1106 div1
->n_row
= div2
->n_row
;
1107 div1
->n_col
= div2
->n_col
;
1109 equal
= isl_mat_is_equal(div1
, div2
);
1111 div1
->n_row
= n_row
;
1112 div1
->n_col
= n_col
;
1117 static void expand_row(__isl_keep isl_mat
*dst
, int d
,
1118 __isl_keep isl_mat
*src
, int s
, int *exp
)
1121 unsigned c
= src
->n_col
- src
->n_row
;
1123 isl_seq_cpy(dst
->row
[d
], src
->row
[s
], c
);
1124 isl_seq_clr(dst
->row
[d
] + c
, dst
->n_col
- c
);
1126 for (i
= 0; i
< s
; ++i
)
1127 isl_int_set(dst
->row
[d
][c
+ exp
[i
]], src
->row
[s
][c
+ i
]);
1130 static int cmp_row(__isl_keep isl_mat
*div
, int i
, int j
)
1134 li
= isl_seq_last_non_zero(div
->row
[i
], div
->n_col
);
1135 lj
= isl_seq_last_non_zero(div
->row
[j
], div
->n_col
);
1140 return isl_seq_cmp(div
->row
[i
], div
->row
[j
], div
->n_col
);
1143 struct isl_div_sort_info
{
1148 static int div_sort_cmp(const void *p1
, const void *p2
)
1150 const struct isl_div_sort_info
*i1
, *i2
;
1151 i1
= (const struct isl_div_sort_info
*) p1
;
1152 i2
= (const struct isl_div_sort_info
*) p2
;
1154 return cmp_row(i1
->div
, i1
->row
, i2
->row
);
1157 /* Sort divs and remove duplicates.
1159 static __isl_give isl_qpolynomial
*sort_divs(__isl_take isl_qpolynomial
*qp
)
1164 struct isl_div_sort_info
*array
= NULL
;
1165 int *pos
= NULL
, *at
= NULL
;
1166 int *reordering
= NULL
;
1171 if (qp
->div
->n_row
<= 1)
1174 div_pos
= isl_dim_total(qp
->dim
);
1176 array
= isl_alloc_array(qp
->div
->ctx
, struct isl_div_sort_info
,
1178 pos
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1179 at
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1180 len
= qp
->div
->n_col
- 2;
1181 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
1182 if (!array
|| !pos
|| !at
|| !reordering
)
1185 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1186 array
[i
].div
= qp
->div
;
1192 qsort(array
, qp
->div
->n_row
, sizeof(struct isl_div_sort_info
),
1195 for (i
= 0; i
< div_pos
; ++i
)
1198 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1199 if (pos
[array
[i
].row
] == i
)
1201 qp
->div
= isl_mat_swap_rows(qp
->div
, i
, pos
[array
[i
].row
]);
1202 pos
[at
[i
]] = pos
[array
[i
].row
];
1203 at
[pos
[array
[i
].row
]] = at
[i
];
1204 at
[i
] = array
[i
].row
;
1205 pos
[array
[i
].row
] = i
;
1209 for (i
= 0; i
< len
- div_pos
; ++i
) {
1211 isl_seq_eq(qp
->div
->row
[i
- skip
- 1],
1212 qp
->div
->row
[i
- skip
], qp
->div
->n_col
)) {
1213 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
1214 isl_mat_col_add(qp
->div
, 2 + div_pos
+ i
- skip
- 1,
1215 2 + div_pos
+ i
- skip
);
1216 qp
->div
= isl_mat_drop_cols(qp
->div
,
1217 2 + div_pos
+ i
- skip
, 1);
1220 reordering
[div_pos
+ array
[i
].row
] = div_pos
+ i
- skip
;
1223 qp
->upoly
= reorder(qp
->upoly
, reordering
);
1225 if (!qp
->upoly
|| !qp
->div
)
1239 isl_qpolynomial_free(qp
);
1243 static __isl_give isl_mat
*merge_divs(__isl_keep isl_mat
*div1
,
1244 __isl_keep isl_mat
*div2
, int *exp1
, int *exp2
)
1247 isl_mat
*div
= NULL
;
1248 unsigned d
= div1
->n_col
- div1
->n_row
;
1250 div
= isl_mat_alloc(div1
->ctx
, 1 + div1
->n_row
+ div2
->n_row
,
1251 d
+ div1
->n_row
+ div2
->n_row
);
1255 for (i
= 0, j
= 0, k
= 0; i
< div1
->n_row
&& j
< div2
->n_row
; ++k
) {
1258 expand_row(div
, k
, div1
, i
, exp1
);
1259 expand_row(div
, k
+ 1, div2
, j
, exp2
);
1261 cmp
= cmp_row(div
, k
, k
+ 1);
1265 } else if (cmp
< 0) {
1269 isl_seq_cpy(div
->row
[k
], div
->row
[k
+ 1], div
->n_col
);
1272 for (; i
< div1
->n_row
; ++i
, ++k
) {
1273 expand_row(div
, k
, div1
, i
, exp1
);
1276 for (; j
< div2
->n_row
; ++j
, ++k
) {
1277 expand_row(div
, k
, div2
, j
, exp2
);
1287 static __isl_give
struct isl_upoly
*expand(__isl_take
struct isl_upoly
*up
,
1288 int *exp
, int first
)
1291 struct isl_upoly_rec
*rec
;
1293 if (isl_upoly_is_cst(up
))
1296 if (up
->var
< first
)
1299 if (exp
[up
->var
- first
] == up
->var
- first
)
1302 up
= isl_upoly_cow(up
);
1306 up
->var
= exp
[up
->var
- first
] + first
;
1308 rec
= isl_upoly_as_rec(up
);
1312 for (i
= 0; i
< rec
->n
; ++i
) {
1313 rec
->p
[i
] = expand(rec
->p
[i
], exp
, first
);
1324 static __isl_give isl_qpolynomial
*with_merged_divs(
1325 __isl_give isl_qpolynomial
*(*fn
)(__isl_take isl_qpolynomial
*qp1
,
1326 __isl_take isl_qpolynomial
*qp2
),
1327 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
1331 isl_mat
*div
= NULL
;
1333 qp1
= isl_qpolynomial_cow(qp1
);
1334 qp2
= isl_qpolynomial_cow(qp2
);
1339 isl_assert(qp1
->div
->ctx
, qp1
->div
->n_row
>= qp2
->div
->n_row
&&
1340 qp1
->div
->n_col
>= qp2
->div
->n_col
, goto error
);
1342 exp1
= isl_alloc_array(qp1
->div
->ctx
, int, qp1
->div
->n_row
);
1343 exp2
= isl_alloc_array(qp2
->div
->ctx
, int, qp2
->div
->n_row
);
1347 div
= merge_divs(qp1
->div
, qp2
->div
, exp1
, exp2
);
1351 isl_mat_free(qp1
->div
);
1352 qp1
->div
= isl_mat_copy(div
);
1353 isl_mat_free(qp2
->div
);
1354 qp2
->div
= isl_mat_copy(div
);
1356 qp1
->upoly
= expand(qp1
->upoly
, exp1
, div
->n_col
- div
->n_row
- 2);
1357 qp2
->upoly
= expand(qp2
->upoly
, exp2
, div
->n_col
- div
->n_row
- 2);
1359 if (!qp1
->upoly
|| !qp2
->upoly
)
1366 return fn(qp1
, qp2
);
1371 isl_qpolynomial_free(qp1
);
1372 isl_qpolynomial_free(qp2
);
1376 __isl_give isl_qpolynomial
*isl_qpolynomial_add(__isl_take isl_qpolynomial
*qp1
,
1377 __isl_take isl_qpolynomial
*qp2
)
1379 qp1
= isl_qpolynomial_cow(qp1
);
1384 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1385 return isl_qpolynomial_add(qp2
, qp1
);
1387 isl_assert(qp1
->dim
->ctx
, isl_dim_equal(qp1
->dim
, qp2
->dim
), goto error
);
1388 if (!compatible_divs(qp1
->div
, qp2
->div
))
1389 return with_merged_divs(isl_qpolynomial_add
, qp1
, qp2
);
1391 qp1
->upoly
= isl_upoly_sum(qp1
->upoly
, isl_upoly_copy(qp2
->upoly
));
1395 isl_qpolynomial_free(qp2
);
1399 isl_qpolynomial_free(qp1
);
1400 isl_qpolynomial_free(qp2
);
1404 __isl_give isl_qpolynomial
*isl_qpolynomial_add_on_domain(
1405 __isl_keep isl_set
*dom
,
1406 __isl_take isl_qpolynomial
*qp1
,
1407 __isl_take isl_qpolynomial
*qp2
)
1409 qp1
= isl_qpolynomial_add(qp1
, qp2
);
1410 qp1
= isl_qpolynomial_gist(qp1
, isl_set_copy(dom
));
1414 __isl_give isl_qpolynomial
*isl_qpolynomial_sub(__isl_take isl_qpolynomial
*qp1
,
1415 __isl_take isl_qpolynomial
*qp2
)
1417 return isl_qpolynomial_add(qp1
, isl_qpolynomial_neg(qp2
));
1420 __isl_give isl_qpolynomial
*isl_qpolynomial_add_isl_int(
1421 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1423 if (isl_int_is_zero(v
))
1426 qp
= isl_qpolynomial_cow(qp
);
1430 qp
->upoly
= isl_upoly_add_isl_int(qp
->upoly
, v
);
1436 isl_qpolynomial_free(qp
);
1441 __isl_give isl_qpolynomial
*isl_qpolynomial_neg(__isl_take isl_qpolynomial
*qp
)
1446 return isl_qpolynomial_mul_isl_int(qp
, qp
->dim
->ctx
->negone
);
1449 __isl_give isl_qpolynomial
*isl_qpolynomial_mul_isl_int(
1450 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1452 if (isl_int_is_one(v
))
1455 if (qp
&& isl_int_is_zero(v
)) {
1456 isl_qpolynomial
*zero
;
1457 zero
= isl_qpolynomial_zero(isl_dim_copy(qp
->dim
));
1458 isl_qpolynomial_free(qp
);
1462 qp
= isl_qpolynomial_cow(qp
);
1466 qp
->upoly
= isl_upoly_mul_isl_int(qp
->upoly
, v
);
1472 isl_qpolynomial_free(qp
);
1476 __isl_give isl_qpolynomial
*isl_qpolynomial_mul(__isl_take isl_qpolynomial
*qp1
,
1477 __isl_take isl_qpolynomial
*qp2
)
1479 qp1
= isl_qpolynomial_cow(qp1
);
1484 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1485 return isl_qpolynomial_mul(qp2
, qp1
);
1487 isl_assert(qp1
->dim
->ctx
, isl_dim_equal(qp1
->dim
, qp2
->dim
), goto error
);
1488 if (!compatible_divs(qp1
->div
, qp2
->div
))
1489 return with_merged_divs(isl_qpolynomial_mul
, qp1
, qp2
);
1491 qp1
->upoly
= isl_upoly_mul(qp1
->upoly
, isl_upoly_copy(qp2
->upoly
));
1495 isl_qpolynomial_free(qp2
);
1499 isl_qpolynomial_free(qp1
);
1500 isl_qpolynomial_free(qp2
);
1504 __isl_give isl_qpolynomial
*isl_qpolynomial_pow(__isl_take isl_qpolynomial
*qp
,
1507 qp
= isl_qpolynomial_cow(qp
);
1512 qp
->upoly
= isl_upoly_pow(qp
->upoly
, power
);
1518 isl_qpolynomial_free(qp
);
1522 __isl_give isl_qpolynomial
*isl_qpolynomial_zero(__isl_take isl_dim
*dim
)
1524 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
1527 __isl_give isl_qpolynomial
*isl_qpolynomial_one(__isl_take isl_dim
*dim
)
1529 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_one(dim
->ctx
));
1532 __isl_give isl_qpolynomial
*isl_qpolynomial_infty(__isl_take isl_dim
*dim
)
1534 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_infty(dim
->ctx
));
1537 __isl_give isl_qpolynomial
*isl_qpolynomial_neginfty(__isl_take isl_dim
*dim
)
1539 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_neginfty(dim
->ctx
));
1542 __isl_give isl_qpolynomial
*isl_qpolynomial_nan(__isl_take isl_dim
*dim
)
1544 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_nan(dim
->ctx
));
1547 __isl_give isl_qpolynomial
*isl_qpolynomial_cst(__isl_take isl_dim
*dim
,
1550 struct isl_qpolynomial
*qp
;
1551 struct isl_upoly_cst
*cst
;
1553 qp
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
1557 cst
= isl_upoly_as_cst(qp
->upoly
);
1558 isl_int_set(cst
->n
, v
);
1563 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial
*qp
,
1564 isl_int
*n
, isl_int
*d
)
1566 struct isl_upoly_cst
*cst
;
1571 if (!isl_upoly_is_cst(qp
->upoly
))
1574 cst
= isl_upoly_as_cst(qp
->upoly
);
1579 isl_int_set(*n
, cst
->n
);
1581 isl_int_set(*d
, cst
->d
);
1586 int isl_upoly_is_affine(__isl_keep
struct isl_upoly
*up
)
1589 struct isl_upoly_rec
*rec
;
1597 rec
= isl_upoly_as_rec(up
);
1604 isl_assert(up
->ctx
, rec
->n
> 1, return -1);
1606 is_cst
= isl_upoly_is_cst(rec
->p
[1]);
1612 return isl_upoly_is_affine(rec
->p
[0]);
1615 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial
*qp
)
1620 if (qp
->div
->n_row
> 0)
1623 return isl_upoly_is_affine(qp
->upoly
);
1626 static void update_coeff(__isl_keep isl_vec
*aff
,
1627 __isl_keep
struct isl_upoly_cst
*cst
, int pos
)
1632 if (isl_int_is_zero(cst
->n
))
1637 isl_int_gcd(gcd
, cst
->d
, aff
->el
[0]);
1638 isl_int_divexact(f
, cst
->d
, gcd
);
1639 isl_int_divexact(gcd
, aff
->el
[0], gcd
);
1640 isl_seq_scale(aff
->el
, aff
->el
, f
, aff
->size
);
1641 isl_int_mul(aff
->el
[1 + pos
], gcd
, cst
->n
);
1646 int isl_upoly_update_affine(__isl_keep
struct isl_upoly
*up
,
1647 __isl_keep isl_vec
*aff
)
1649 struct isl_upoly_cst
*cst
;
1650 struct isl_upoly_rec
*rec
;
1656 struct isl_upoly_cst
*cst
;
1658 cst
= isl_upoly_as_cst(up
);
1661 update_coeff(aff
, cst
, 0);
1665 rec
= isl_upoly_as_rec(up
);
1668 isl_assert(up
->ctx
, rec
->n
== 2, return -1);
1670 cst
= isl_upoly_as_cst(rec
->p
[1]);
1673 update_coeff(aff
, cst
, 1 + up
->var
);
1675 return isl_upoly_update_affine(rec
->p
[0], aff
);
1678 __isl_give isl_vec
*isl_qpolynomial_extract_affine(
1679 __isl_keep isl_qpolynomial
*qp
)
1687 d
= isl_dim_total(qp
->dim
);
1688 aff
= isl_vec_alloc(qp
->div
->ctx
, 2 + d
+ qp
->div
->n_row
);
1692 isl_seq_clr(aff
->el
+ 1, 1 + d
+ qp
->div
->n_row
);
1693 isl_int_set_si(aff
->el
[0], 1);
1695 if (isl_upoly_update_affine(qp
->upoly
, aff
) < 0)
1704 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial
*qp1
,
1705 __isl_keep isl_qpolynomial
*qp2
)
1710 return isl_upoly_is_equal(qp1
->upoly
, qp2
->upoly
);
1713 static void upoly_update_den(__isl_keep
struct isl_upoly
*up
, isl_int
*d
)
1716 struct isl_upoly_rec
*rec
;
1718 if (isl_upoly_is_cst(up
)) {
1719 struct isl_upoly_cst
*cst
;
1720 cst
= isl_upoly_as_cst(up
);
1723 isl_int_lcm(*d
, *d
, cst
->d
);
1727 rec
= isl_upoly_as_rec(up
);
1731 for (i
= 0; i
< rec
->n
; ++i
)
1732 upoly_update_den(rec
->p
[i
], d
);
1735 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial
*qp
, isl_int
*d
)
1737 isl_int_set_si(*d
, 1);
1740 upoly_update_den(qp
->upoly
, d
);
1743 __isl_give isl_qpolynomial
*isl_qpolynomial_var_pow(__isl_take isl_dim
*dim
,
1746 struct isl_ctx
*ctx
;
1753 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_var_pow(ctx
, pos
, power
));
1756 __isl_give isl_qpolynomial
*isl_qpolynomial_var(__isl_take isl_dim
*dim
,
1757 enum isl_dim_type type
, unsigned pos
)
1762 isl_assert(dim
->ctx
, isl_dim_size(dim
, isl_dim_in
) == 0, goto error
);
1763 isl_assert(dim
->ctx
, pos
< isl_dim_size(dim
, type
), goto error
);
1765 if (type
== isl_dim_set
)
1766 pos
+= isl_dim_size(dim
, isl_dim_param
);
1768 return isl_qpolynomial_var_pow(dim
, pos
, 1);
1774 __isl_give
struct isl_upoly
*isl_upoly_subs(__isl_take
struct isl_upoly
*up
,
1775 unsigned first
, unsigned n
, __isl_keep
struct isl_upoly
**subs
)
1778 struct isl_upoly_rec
*rec
;
1779 struct isl_upoly
*base
, *res
;
1784 if (isl_upoly_is_cst(up
))
1787 if (up
->var
< first
)
1790 rec
= isl_upoly_as_rec(up
);
1794 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
1796 if (up
->var
>= first
+ n
)
1797 base
= isl_upoly_var_pow(up
->ctx
, up
->var
, 1);
1799 base
= isl_upoly_copy(subs
[up
->var
- first
]);
1801 res
= isl_upoly_subs(isl_upoly_copy(rec
->p
[rec
->n
- 1]), first
, n
, subs
);
1802 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1803 struct isl_upoly
*t
;
1804 t
= isl_upoly_subs(isl_upoly_copy(rec
->p
[i
]), first
, n
, subs
);
1805 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
1806 res
= isl_upoly_sum(res
, t
);
1809 isl_upoly_free(base
);
1818 __isl_give
struct isl_upoly
*isl_upoly_from_affine(isl_ctx
*ctx
, isl_int
*f
,
1819 isl_int denom
, unsigned len
)
1822 struct isl_upoly
*up
;
1824 isl_assert(ctx
, len
>= 1, return NULL
);
1826 up
= isl_upoly_rat_cst(ctx
, f
[0], denom
);
1827 for (i
= 0; i
< len
- 1; ++i
) {
1828 struct isl_upoly
*t
;
1829 struct isl_upoly
*c
;
1831 if (isl_int_is_zero(f
[1 + i
]))
1834 c
= isl_upoly_rat_cst(ctx
, f
[1 + i
], denom
);
1835 t
= isl_upoly_var_pow(ctx
, i
, 1);
1836 t
= isl_upoly_mul(c
, t
);
1837 up
= isl_upoly_sum(up
, t
);
1843 /* Remove common factor of non-constant terms and denominator.
1845 static void normalize_div(__isl_keep isl_qpolynomial
*qp
, int div
)
1847 isl_ctx
*ctx
= qp
->div
->ctx
;
1848 unsigned total
= qp
->div
->n_col
- 2;
1850 isl_seq_gcd(qp
->div
->row
[div
] + 2, total
, &ctx
->normalize_gcd
);
1851 isl_int_gcd(ctx
->normalize_gcd
,
1852 ctx
->normalize_gcd
, qp
->div
->row
[div
][0]);
1853 if (isl_int_is_one(ctx
->normalize_gcd
))
1856 isl_seq_scale_down(qp
->div
->row
[div
] + 2, qp
->div
->row
[div
] + 2,
1857 ctx
->normalize_gcd
, total
);
1858 isl_int_divexact(qp
->div
->row
[div
][0], qp
->div
->row
[div
][0],
1859 ctx
->normalize_gcd
);
1860 isl_int_fdiv_q(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1],
1861 ctx
->normalize_gcd
);
1864 /* Replace the integer division identified by "div" by the polynomial "s".
1865 * The integer division is assumed not to appear in the definition
1866 * of any other integer divisions.
1868 static __isl_give isl_qpolynomial
*substitute_div(
1869 __isl_take isl_qpolynomial
*qp
,
1870 int div
, __isl_take
struct isl_upoly
*s
)
1879 qp
= isl_qpolynomial_cow(qp
);
1883 total
= isl_dim_total(qp
->dim
);
1884 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ div
, 1, &s
);
1888 reordering
= isl_alloc_array(qp
->dim
->ctx
, int, total
+ qp
->div
->n_row
);
1891 for (i
= 0; i
< total
+ div
; ++i
)
1893 for (i
= total
+ div
+ 1; i
< total
+ qp
->div
->n_row
; ++i
)
1894 reordering
[i
] = i
- 1;
1895 qp
->div
= isl_mat_drop_rows(qp
->div
, div
, 1);
1896 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + total
+ div
, 1);
1897 qp
->upoly
= reorder(qp
->upoly
, reordering
);
1900 if (!qp
->upoly
|| !qp
->div
)
1906 isl_qpolynomial_free(qp
);
1911 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1912 * divisions because d is equal to 1 by their definition, i.e., e.
1914 static __isl_give isl_qpolynomial
*substitute_non_divs(
1915 __isl_take isl_qpolynomial
*qp
)
1919 struct isl_upoly
*s
;
1924 total
= isl_dim_total(qp
->dim
);
1925 for (i
= 0; qp
&& i
< qp
->div
->n_row
; ++i
) {
1926 if (!isl_int_is_one(qp
->div
->row
[i
][0]))
1928 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
1929 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
1931 isl_seq_combine(qp
->div
->row
[j
] + 1,
1932 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
1933 qp
->div
->row
[j
][2 + total
+ i
],
1934 qp
->div
->row
[i
] + 1, 1 + total
+ i
);
1935 isl_int_set_si(qp
->div
->row
[j
][2 + total
+ i
], 0);
1936 normalize_div(qp
, j
);
1938 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
1939 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
1940 qp
= substitute_div(qp
, i
, s
);
1947 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1948 * with d the denominator. When replacing the coefficient e of x by
1949 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1950 * inside the division, so we need to add floor(e/d) * x outside.
1951 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1952 * to adjust the coefficient of x in each later div that depends on the
1953 * current div "div" and also in the affine expression "aff"
1954 * (if it too depends on "div").
1956 static void reduce_div(__isl_keep isl_qpolynomial
*qp
, int div
,
1957 __isl_keep isl_vec
*aff
)
1961 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
1964 for (i
= 0; i
< 1 + total
+ div
; ++i
) {
1965 if (isl_int_is_nonneg(qp
->div
->row
[div
][1 + i
]) &&
1966 isl_int_lt(qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]))
1968 isl_int_fdiv_q(v
, qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
1969 isl_int_fdiv_r(qp
->div
->row
[div
][1 + i
],
1970 qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
1971 if (!isl_int_is_zero(aff
->el
[1 + total
+ div
]))
1972 isl_int_addmul(aff
->el
[i
], v
, aff
->el
[1 + total
+ div
]);
1973 for (j
= div
+ 1; j
< qp
->div
->n_row
; ++j
) {
1974 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ div
]))
1976 isl_int_addmul(qp
->div
->row
[j
][1 + i
],
1977 v
, qp
->div
->row
[j
][2 + total
+ div
]);
1983 /* Check if the last non-zero coefficient is bigger that half of the
1984 * denominator. If so, we will invert the div to further reduce the number
1985 * of distinct divs that may appear.
1986 * If the last non-zero coefficient is exactly half the denominator,
1987 * then we continue looking for earlier coefficients that are bigger
1988 * than half the denominator.
1990 static int needs_invert(__isl_keep isl_mat
*div
, int row
)
1995 for (i
= div
->n_col
- 1; i
>= 1; --i
) {
1996 if (isl_int_is_zero(div
->row
[row
][i
]))
1998 isl_int_mul_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
1999 cmp
= isl_int_cmp(div
->row
[row
][i
], div
->row
[row
][0]);
2000 isl_int_divexact_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
2010 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
2011 * We only invert the coefficients of e (and the coefficient of q in
2012 * later divs and in "aff"). After calling this function, the
2013 * coefficients of e should be reduced again.
2015 static void invert_div(__isl_keep isl_qpolynomial
*qp
, int div
,
2016 __isl_keep isl_vec
*aff
)
2018 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
2020 isl_seq_neg(qp
->div
->row
[div
] + 1,
2021 qp
->div
->row
[div
] + 1, qp
->div
->n_col
- 1);
2022 isl_int_sub_ui(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1], 1);
2023 isl_int_add(qp
->div
->row
[div
][1],
2024 qp
->div
->row
[div
][1], qp
->div
->row
[div
][0]);
2025 if (!isl_int_is_zero(aff
->el
[1 + total
+ div
]))
2026 isl_int_neg(aff
->el
[1 + total
+ div
], aff
->el
[1 + total
+ div
]);
2027 isl_mat_col_mul(qp
->div
, 2 + total
+ div
,
2028 qp
->div
->ctx
->negone
, 2 + total
+ div
);
2031 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2032 * in the interval [0, d-1], with d the denominator and such that the
2033 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2035 * After the reduction, some divs may have become redundant or identical,
2036 * so we call substitute_non_divs and sort_divs. If these functions
2037 * eliminate divs of merge * two or more divs into one, the coefficients
2038 * of the enclosing divs may have to be reduced again, so we call
2039 * ourselves recursively if the number of divs decreases.
2041 static __isl_give isl_qpolynomial
*reduce_divs(__isl_take isl_qpolynomial
*qp
)
2044 isl_vec
*aff
= NULL
;
2045 struct isl_upoly
*s
;
2051 aff
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
2052 aff
= isl_vec_clr(aff
);
2056 isl_int_set_si(aff
->el
[1 + qp
->upoly
->var
], 1);
2058 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2059 normalize_div(qp
, i
);
2060 reduce_div(qp
, i
, aff
);
2061 if (needs_invert(qp
->div
, i
)) {
2062 invert_div(qp
, i
, aff
);
2063 reduce_div(qp
, i
, aff
);
2067 s
= isl_upoly_from_affine(qp
->div
->ctx
, aff
->el
,
2068 qp
->div
->ctx
->one
, aff
->size
);
2069 qp
->upoly
= isl_upoly_subs(qp
->upoly
, qp
->upoly
->var
, 1, &s
);
2076 n_div
= qp
->div
->n_row
;
2077 qp
= substitute_non_divs(qp
);
2079 if (qp
&& qp
->div
->n_row
< n_div
)
2080 return reduce_divs(qp
);
2084 isl_qpolynomial_free(qp
);
2089 /* Assumes each div only depends on earlier divs.
2091 __isl_give isl_qpolynomial
*isl_qpolynomial_div_pow(__isl_take isl_div
*div
,
2094 struct isl_qpolynomial
*qp
= NULL
;
2095 struct isl_upoly_rec
*rec
;
2096 struct isl_upoly_cst
*cst
;
2103 d
= div
->line
- div
->bmap
->div
;
2105 pos
= isl_dim_total(div
->bmap
->dim
) + d
;
2106 rec
= isl_upoly_alloc_rec(div
->ctx
, pos
, 1 + power
);
2107 qp
= isl_qpolynomial_alloc(isl_basic_map_get_dim(div
->bmap
),
2108 div
->bmap
->n_div
, &rec
->up
);
2112 for (i
= 0; i
< div
->bmap
->n_div
; ++i
)
2113 isl_seq_cpy(qp
->div
->row
[i
], div
->bmap
->div
[i
], qp
->div
->n_col
);
2115 for (i
= 0; i
< 1 + power
; ++i
) {
2116 rec
->p
[i
] = isl_upoly_zero(div
->ctx
);
2121 cst
= isl_upoly_as_cst(rec
->p
[power
]);
2122 isl_int_set_si(cst
->n
, 1);
2126 qp
= reduce_divs(qp
);
2130 isl_qpolynomial_free(qp
);
2135 __isl_give isl_qpolynomial
*isl_qpolynomial_div(__isl_take isl_div
*div
)
2137 return isl_qpolynomial_div_pow(div
, 1);
2140 __isl_give isl_qpolynomial
*isl_qpolynomial_rat_cst(__isl_take isl_dim
*dim
,
2141 const isl_int n
, const isl_int d
)
2143 struct isl_qpolynomial
*qp
;
2144 struct isl_upoly_cst
*cst
;
2146 qp
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
2150 cst
= isl_upoly_as_cst(qp
->upoly
);
2151 isl_int_set(cst
->n
, n
);
2152 isl_int_set(cst
->d
, d
);
2157 static int up_set_active(__isl_keep
struct isl_upoly
*up
, int *active
, int d
)
2159 struct isl_upoly_rec
*rec
;
2165 if (isl_upoly_is_cst(up
))
2169 active
[up
->var
] = 1;
2171 rec
= isl_upoly_as_rec(up
);
2172 for (i
= 0; i
< rec
->n
; ++i
)
2173 if (up_set_active(rec
->p
[i
], active
, d
) < 0)
2179 static int set_active(__isl_keep isl_qpolynomial
*qp
, int *active
)
2182 int d
= isl_dim_total(qp
->dim
);
2187 for (i
= 0; i
< d
; ++i
)
2188 for (j
= 0; j
< qp
->div
->n_row
; ++j
) {
2189 if (isl_int_is_zero(qp
->div
->row
[j
][2 + i
]))
2195 return up_set_active(qp
->upoly
, active
, d
);
2198 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial
*qp
,
2199 enum isl_dim_type type
, unsigned first
, unsigned n
)
2210 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_dim_size(qp
->dim
, type
),
2212 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2213 type
== isl_dim_set
, return -1);
2215 active
= isl_calloc_array(set
->ctx
, int, isl_dim_total(qp
->dim
));
2216 if (set_active(qp
, active
) < 0)
2219 if (type
== isl_dim_set
)
2220 first
+= isl_dim_size(qp
->dim
, isl_dim_param
);
2221 for (i
= 0; i
< n
; ++i
)
2222 if (active
[first
+ i
]) {
2235 __isl_give
struct isl_upoly
*isl_upoly_drop(__isl_take
struct isl_upoly
*up
,
2236 unsigned first
, unsigned n
)
2239 struct isl_upoly_rec
*rec
;
2243 if (n
== 0 || up
->var
< 0 || up
->var
< first
)
2245 if (up
->var
< first
+ n
) {
2246 up
= replace_by_constant_term(up
);
2247 return isl_upoly_drop(up
, first
, n
);
2249 up
= isl_upoly_cow(up
);
2253 rec
= isl_upoly_as_rec(up
);
2257 for (i
= 0; i
< rec
->n
; ++i
) {
2258 rec
->p
[i
] = isl_upoly_drop(rec
->p
[i
], first
, n
);
2269 __isl_give isl_qpolynomial
*isl_qpolynomial_set_dim_name(
2270 __isl_take isl_qpolynomial
*qp
,
2271 enum isl_dim_type type
, unsigned pos
, const char *s
)
2273 qp
= isl_qpolynomial_cow(qp
);
2276 qp
->dim
= isl_dim_set_name(qp
->dim
, type
, pos
, s
);
2281 isl_qpolynomial_free(qp
);
2285 __isl_give isl_qpolynomial
*isl_qpolynomial_drop_dims(
2286 __isl_take isl_qpolynomial
*qp
,
2287 enum isl_dim_type type
, unsigned first
, unsigned n
)
2291 if (n
== 0 && !isl_dim_get_tuple_name(qp
->dim
, type
))
2294 qp
= isl_qpolynomial_cow(qp
);
2298 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_dim_size(qp
->dim
, type
),
2300 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2301 type
== isl_dim_set
, goto error
);
2303 qp
->dim
= isl_dim_drop(qp
->dim
, type
, first
, n
);
2307 if (type
== isl_dim_set
)
2308 first
+= isl_dim_size(qp
->dim
, isl_dim_param
);
2310 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + first
, n
);
2314 qp
->upoly
= isl_upoly_drop(qp
->upoly
, first
, n
);
2320 isl_qpolynomial_free(qp
);
2324 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities(
2325 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2331 struct isl_upoly
*up
;
2335 if (eq
->n_eq
== 0) {
2336 isl_basic_set_free(eq
);
2340 qp
= isl_qpolynomial_cow(qp
);
2343 qp
->div
= isl_mat_cow(qp
->div
);
2347 total
= 1 + isl_dim_total(eq
->dim
);
2349 isl_int_init(denom
);
2350 for (i
= 0; i
< eq
->n_eq
; ++i
) {
2351 j
= isl_seq_last_non_zero(eq
->eq
[i
], total
+ n_div
);
2352 if (j
< 0 || j
== 0 || j
>= total
)
2355 for (k
= 0; k
< qp
->div
->n_row
; ++k
) {
2356 if (isl_int_is_zero(qp
->div
->row
[k
][1 + j
]))
2358 isl_seq_elim(qp
->div
->row
[k
] + 1, eq
->eq
[i
], j
, total
,
2359 &qp
->div
->row
[k
][0]);
2360 normalize_div(qp
, k
);
2363 if (isl_int_is_pos(eq
->eq
[i
][j
]))
2364 isl_seq_neg(eq
->eq
[i
], eq
->eq
[i
], total
);
2365 isl_int_abs(denom
, eq
->eq
[i
][j
]);
2366 isl_int_set_si(eq
->eq
[i
][j
], 0);
2368 up
= isl_upoly_from_affine(qp
->dim
->ctx
,
2369 eq
->eq
[i
], denom
, total
);
2370 qp
->upoly
= isl_upoly_subs(qp
->upoly
, j
- 1, 1, &up
);
2373 isl_int_clear(denom
);
2378 isl_basic_set_free(eq
);
2380 qp
= substitute_non_divs(qp
);
2385 isl_basic_set_free(eq
);
2386 isl_qpolynomial_free(qp
);
2390 static __isl_give isl_basic_set
*add_div_constraints(
2391 __isl_take isl_basic_set
*bset
, __isl_take isl_mat
*div
)
2399 bset
= isl_basic_set_extend_constraints(bset
, 0, 2 * div
->n_row
);
2402 total
= isl_basic_set_total_dim(bset
);
2403 for (i
= 0; i
< div
->n_row
; ++i
)
2404 if (isl_basic_set_add_div_constraints_var(bset
,
2405 total
- div
->n_row
+ i
, div
->row
[i
]) < 0)
2412 isl_basic_set_free(bset
);
2416 /* Look for equalities among the variables shared by context and qp
2417 * and the integer divisions of qp, if any.
2418 * The equalities are then used to eliminate variables and/or integer
2419 * divisions from qp.
2421 __isl_give isl_qpolynomial
*isl_qpolynomial_gist(
2422 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
2428 if (qp
->div
->n_row
> 0) {
2429 isl_basic_set
*bset
;
2430 context
= isl_set_add_dims(context
, isl_dim_set
,
2432 bset
= isl_basic_set_universe(isl_set_get_dim(context
));
2433 bset
= add_div_constraints(bset
, isl_mat_copy(qp
->div
));
2434 context
= isl_set_intersect(context
,
2435 isl_set_from_basic_set(bset
));
2438 aff
= isl_set_affine_hull(context
);
2439 return isl_qpolynomial_substitute_equalities(qp
, aff
);
2441 isl_qpolynomial_free(qp
);
2442 isl_set_free(context
);
2447 #define PW isl_pw_qpolynomial
2449 #define EL isl_qpolynomial
2451 #define IS_ZERO is_zero
2455 #include <isl_pw_templ.c>
2458 #define UNION isl_union_pw_qpolynomial
2460 #define PART isl_pw_qpolynomial
2462 #define PARTS pw_qpolynomial
2464 #include <isl_union_templ.c>
2466 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial
*pwqp
)
2474 if (!isl_set_fast_is_universe(pwqp
->p
[0].set
))
2477 return isl_qpolynomial_is_one(pwqp
->p
[0].qp
);
2480 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_mul(
2481 __isl_take isl_pw_qpolynomial
*pwqp1
,
2482 __isl_take isl_pw_qpolynomial
*pwqp2
)
2485 struct isl_pw_qpolynomial
*res
;
2488 if (!pwqp1
|| !pwqp2
)
2491 isl_assert(pwqp1
->dim
->ctx
, isl_dim_equal(pwqp1
->dim
, pwqp2
->dim
),
2494 if (isl_pw_qpolynomial_is_zero(pwqp1
)) {
2495 isl_pw_qpolynomial_free(pwqp2
);
2499 if (isl_pw_qpolynomial_is_zero(pwqp2
)) {
2500 isl_pw_qpolynomial_free(pwqp1
);
2504 if (isl_pw_qpolynomial_is_one(pwqp1
)) {
2505 isl_pw_qpolynomial_free(pwqp1
);
2509 if (isl_pw_qpolynomial_is_one(pwqp2
)) {
2510 isl_pw_qpolynomial_free(pwqp2
);
2514 n
= pwqp1
->n
* pwqp2
->n
;
2515 res
= isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1
->dim
), n
);
2517 for (i
= 0; i
< pwqp1
->n
; ++i
) {
2518 for (j
= 0; j
< pwqp2
->n
; ++j
) {
2519 struct isl_set
*common
;
2520 struct isl_qpolynomial
*prod
;
2521 common
= isl_set_intersect(isl_set_copy(pwqp1
->p
[i
].set
),
2522 isl_set_copy(pwqp2
->p
[j
].set
));
2523 if (isl_set_fast_is_empty(common
)) {
2524 isl_set_free(common
);
2528 prod
= isl_qpolynomial_mul(
2529 isl_qpolynomial_copy(pwqp1
->p
[i
].qp
),
2530 isl_qpolynomial_copy(pwqp2
->p
[j
].qp
));
2532 res
= isl_pw_qpolynomial_add_piece(res
, common
, prod
);
2536 isl_pw_qpolynomial_free(pwqp1
);
2537 isl_pw_qpolynomial_free(pwqp2
);
2541 isl_pw_qpolynomial_free(pwqp1
);
2542 isl_pw_qpolynomial_free(pwqp2
);
2546 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_neg(
2547 __isl_take isl_pw_qpolynomial
*pwqp
)
2554 if (isl_pw_qpolynomial_is_zero(pwqp
))
2557 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
2561 for (i
= 0; i
< pwqp
->n
; ++i
) {
2562 pwqp
->p
[i
].qp
= isl_qpolynomial_neg(pwqp
->p
[i
].qp
);
2569 isl_pw_qpolynomial_free(pwqp
);
2573 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_sub(
2574 __isl_take isl_pw_qpolynomial
*pwqp1
,
2575 __isl_take isl_pw_qpolynomial
*pwqp2
)
2577 return isl_pw_qpolynomial_add(pwqp1
, isl_pw_qpolynomial_neg(pwqp2
));
2580 __isl_give
struct isl_upoly
*isl_upoly_eval(
2581 __isl_take
struct isl_upoly
*up
, __isl_take isl_vec
*vec
)
2584 struct isl_upoly_rec
*rec
;
2585 struct isl_upoly
*res
;
2586 struct isl_upoly
*base
;
2588 if (isl_upoly_is_cst(up
)) {
2593 rec
= isl_upoly_as_rec(up
);
2597 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
2599 base
= isl_upoly_rat_cst(up
->ctx
, vec
->el
[1 + up
->var
], vec
->el
[0]);
2601 res
= isl_upoly_eval(isl_upoly_copy(rec
->p
[rec
->n
- 1]),
2604 for (i
= rec
->n
- 2; i
>= 0; --i
) {
2605 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
2606 res
= isl_upoly_sum(res
,
2607 isl_upoly_eval(isl_upoly_copy(rec
->p
[i
]),
2608 isl_vec_copy(vec
)));
2611 isl_upoly_free(base
);
2621 __isl_give isl_qpolynomial
*isl_qpolynomial_eval(
2622 __isl_take isl_qpolynomial
*qp
, __isl_take isl_point
*pnt
)
2625 struct isl_upoly
*up
;
2630 isl_assert(pnt
->dim
->ctx
, isl_dim_equal(pnt
->dim
, qp
->dim
), goto error
);
2632 if (qp
->div
->n_row
== 0)
2633 ext
= isl_vec_copy(pnt
->vec
);
2636 unsigned dim
= isl_dim_total(qp
->dim
);
2637 ext
= isl_vec_alloc(qp
->dim
->ctx
, 1 + dim
+ qp
->div
->n_row
);
2641 isl_seq_cpy(ext
->el
, pnt
->vec
->el
, pnt
->vec
->size
);
2642 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2643 isl_seq_inner_product(qp
->div
->row
[i
] + 1, ext
->el
,
2644 1 + dim
+ i
, &ext
->el
[1+dim
+i
]);
2645 isl_int_fdiv_q(ext
->el
[1+dim
+i
], ext
->el
[1+dim
+i
],
2646 qp
->div
->row
[i
][0]);
2650 up
= isl_upoly_eval(isl_upoly_copy(qp
->upoly
), ext
);
2654 dim
= isl_dim_copy(qp
->dim
);
2655 isl_qpolynomial_free(qp
);
2656 isl_point_free(pnt
);
2658 return isl_qpolynomial_alloc(dim
, 0, up
);
2660 isl_qpolynomial_free(qp
);
2661 isl_point_free(pnt
);
2665 int isl_upoly_cmp(__isl_keep
struct isl_upoly_cst
*cst1
,
2666 __isl_keep
struct isl_upoly_cst
*cst2
)
2671 isl_int_mul(t
, cst1
->n
, cst2
->d
);
2672 isl_int_submul(t
, cst2
->n
, cst1
->d
);
2673 cmp
= isl_int_sgn(t
);
2678 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial
*qp1
,
2679 __isl_keep isl_qpolynomial
*qp2
)
2681 struct isl_upoly_cst
*cst1
, *cst2
;
2685 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), return -1);
2686 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), return -1);
2687 if (isl_qpolynomial_is_nan(qp1
))
2689 if (isl_qpolynomial_is_nan(qp2
))
2691 cst1
= isl_upoly_as_cst(qp1
->upoly
);
2692 cst2
= isl_upoly_as_cst(qp2
->upoly
);
2694 return isl_upoly_cmp(cst1
, cst2
) <= 0;
2697 __isl_give isl_qpolynomial
*isl_qpolynomial_min_cst(
2698 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
2700 struct isl_upoly_cst
*cst1
, *cst2
;
2705 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), goto error
);
2706 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), goto error
);
2707 cst1
= isl_upoly_as_cst(qp1
->upoly
);
2708 cst2
= isl_upoly_as_cst(qp2
->upoly
);
2709 cmp
= isl_upoly_cmp(cst1
, cst2
);
2712 isl_qpolynomial_free(qp2
);
2714 isl_qpolynomial_free(qp1
);
2719 isl_qpolynomial_free(qp1
);
2720 isl_qpolynomial_free(qp2
);
2724 __isl_give isl_qpolynomial
*isl_qpolynomial_max_cst(
2725 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
2727 struct isl_upoly_cst
*cst1
, *cst2
;
2732 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), goto error
);
2733 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), goto error
);
2734 cst1
= isl_upoly_as_cst(qp1
->upoly
);
2735 cst2
= isl_upoly_as_cst(qp2
->upoly
);
2736 cmp
= isl_upoly_cmp(cst1
, cst2
);
2739 isl_qpolynomial_free(qp2
);
2741 isl_qpolynomial_free(qp1
);
2746 isl_qpolynomial_free(qp1
);
2747 isl_qpolynomial_free(qp2
);
2751 __isl_give isl_qpolynomial
*isl_qpolynomial_insert_dims(
2752 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
,
2753 unsigned first
, unsigned n
)
2762 qp
= isl_qpolynomial_cow(qp
);
2766 isl_assert(qp
->div
->ctx
, first
<= isl_dim_size(qp
->dim
, type
),
2769 g_pos
= pos(qp
->dim
, type
) + first
;
2771 qp
->div
= isl_mat_insert_cols(qp
->div
, 2 + g_pos
, n
);
2775 total
= qp
->div
->n_col
- 2;
2776 if (total
> g_pos
) {
2778 exp
= isl_alloc_array(qp
->div
->ctx
, int, total
- g_pos
);
2781 for (i
= 0; i
< total
- g_pos
; ++i
)
2783 qp
->upoly
= expand(qp
->upoly
, exp
, g_pos
);
2789 qp
->dim
= isl_dim_insert(qp
->dim
, type
, first
, n
);
2795 isl_qpolynomial_free(qp
);
2799 __isl_give isl_qpolynomial
*isl_qpolynomial_add_dims(
2800 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
, unsigned n
)
2804 pos
= isl_qpolynomial_dim(qp
, type
);
2806 return isl_qpolynomial_insert_dims(qp
, type
, pos
, n
);
2809 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add_dims(
2810 __isl_take isl_pw_qpolynomial
*pwqp
,
2811 enum isl_dim_type type
, unsigned n
)
2815 pos
= isl_pw_qpolynomial_dim(pwqp
, type
);
2817 return isl_pw_qpolynomial_insert_dims(pwqp
, type
, pos
, n
);
2820 static int *reordering_move(isl_ctx
*ctx
,
2821 unsigned len
, unsigned dst
, unsigned src
, unsigned n
)
2826 reordering
= isl_alloc_array(ctx
, int, len
);
2831 for (i
= 0; i
< dst
; ++i
)
2833 for (i
= 0; i
< n
; ++i
)
2834 reordering
[src
+ i
] = dst
+ i
;
2835 for (i
= 0; i
< src
- dst
; ++i
)
2836 reordering
[dst
+ i
] = dst
+ n
+ i
;
2837 for (i
= 0; i
< len
- src
- n
; ++i
)
2838 reordering
[src
+ n
+ i
] = src
+ n
+ i
;
2840 for (i
= 0; i
< src
; ++i
)
2842 for (i
= 0; i
< n
; ++i
)
2843 reordering
[src
+ i
] = dst
+ i
;
2844 for (i
= 0; i
< dst
- src
; ++i
)
2845 reordering
[src
+ n
+ i
] = src
+ i
;
2846 for (i
= 0; i
< len
- dst
- n
; ++i
)
2847 reordering
[dst
+ n
+ i
] = dst
+ n
+ i
;
2853 __isl_give isl_qpolynomial
*isl_qpolynomial_move_dims(
2854 __isl_take isl_qpolynomial
*qp
,
2855 enum isl_dim_type dst_type
, unsigned dst_pos
,
2856 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
2862 qp
= isl_qpolynomial_cow(qp
);
2866 isl_assert(qp
->dim
->ctx
, src_pos
+ n
<= isl_dim_size(qp
->dim
, src_type
),
2869 g_dst_pos
= pos(qp
->dim
, dst_type
) + dst_pos
;
2870 g_src_pos
= pos(qp
->dim
, src_type
) + src_pos
;
2871 if (dst_type
> src_type
)
2874 qp
->div
= isl_mat_move_cols(qp
->div
, 2 + g_dst_pos
, 2 + g_src_pos
, n
);
2881 reordering
= reordering_move(qp
->dim
->ctx
,
2882 qp
->div
->n_col
- 2, g_dst_pos
, g_src_pos
, n
);
2886 qp
->upoly
= reorder(qp
->upoly
, reordering
);
2891 qp
->dim
= isl_dim_move(qp
->dim
, dst_type
, dst_pos
, src_type
, src_pos
, n
);
2897 isl_qpolynomial_free(qp
);
2901 __isl_give isl_qpolynomial
*isl_qpolynomial_from_affine(__isl_take isl_dim
*dim
,
2902 isl_int
*f
, isl_int denom
)
2904 struct isl_upoly
*up
;
2909 up
= isl_upoly_from_affine(dim
->ctx
, f
, denom
, 1 + isl_dim_total(dim
));
2911 return isl_qpolynomial_alloc(dim
, 0, up
);
2914 __isl_give isl_qpolynomial
*isl_qpolynomial_from_constraint(
2915 __isl_take isl_constraint
*c
, enum isl_dim_type type
, unsigned pos
)
2919 struct isl_upoly
*up
;
2920 isl_qpolynomial
*qp
;
2926 isl_int_init(denom
);
2928 isl_constraint_get_coefficient(c
, type
, pos
, &denom
);
2929 isl_constraint_set_coefficient(c
, type
, pos
, c
->ctx
->zero
);
2930 sgn
= isl_int_sgn(denom
);
2931 isl_int_abs(denom
, denom
);
2932 up
= isl_upoly_from_affine(c
->ctx
, c
->line
[0], denom
,
2933 1 + isl_constraint_dim(c
, isl_dim_all
));
2935 isl_int_neg(denom
, denom
);
2936 isl_constraint_set_coefficient(c
, type
, pos
, denom
);
2938 dim
= isl_dim_copy(c
->bmap
->dim
);
2940 isl_int_clear(denom
);
2941 isl_constraint_free(c
);
2943 qp
= isl_qpolynomial_alloc(dim
, 0, up
);
2945 qp
= isl_qpolynomial_neg(qp
);
2949 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
2950 * in "qp" by subs[i].
2952 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute(
2953 __isl_take isl_qpolynomial
*qp
,
2954 enum isl_dim_type type
, unsigned first
, unsigned n
,
2955 __isl_keep isl_qpolynomial
**subs
)
2958 struct isl_upoly
**ups
;
2963 qp
= isl_qpolynomial_cow(qp
);
2966 for (i
= 0; i
< n
; ++i
)
2970 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_dim_size(qp
->dim
, type
),
2973 for (i
= 0; i
< n
; ++i
)
2974 isl_assert(qp
->dim
->ctx
, isl_dim_equal(qp
->dim
, subs
[i
]->dim
),
2977 isl_assert(qp
->dim
->ctx
, qp
->div
->n_row
== 0, goto error
);
2978 for (i
= 0; i
< n
; ++i
)
2979 isl_assert(qp
->dim
->ctx
, subs
[i
]->div
->n_row
== 0, goto error
);
2981 first
+= pos(qp
->dim
, type
);
2983 ups
= isl_alloc_array(qp
->dim
->ctx
, struct isl_upoly
*, n
);
2986 for (i
= 0; i
< n
; ++i
)
2987 ups
[i
] = subs
[i
]->upoly
;
2989 qp
->upoly
= isl_upoly_subs(qp
->upoly
, first
, n
, ups
);
2998 isl_qpolynomial_free(qp
);
3002 /* Extend "bset" with extra set dimensions for each integer division
3003 * in "qp" and then call "fn" with the extended bset and the polynomial
3004 * that results from replacing each of the integer divisions by the
3005 * corresponding extra set dimension.
3007 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial
*qp
,
3008 __isl_keep isl_basic_set
*bset
,
3009 int (*fn
)(__isl_take isl_basic_set
*bset
,
3010 __isl_take isl_qpolynomial
*poly
, void *user
), void *user
)
3014 isl_qpolynomial
*poly
;
3018 if (qp
->div
->n_row
== 0)
3019 return fn(isl_basic_set_copy(bset
), isl_qpolynomial_copy(qp
),
3022 div
= isl_mat_copy(qp
->div
);
3023 dim
= isl_dim_copy(qp
->dim
);
3024 dim
= isl_dim_add(dim
, isl_dim_set
, qp
->div
->n_row
);
3025 poly
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_copy(qp
->upoly
));
3026 bset
= isl_basic_set_copy(bset
);
3027 bset
= isl_basic_set_add(bset
, isl_dim_set
, qp
->div
->n_row
);
3028 bset
= add_div_constraints(bset
, div
);
3030 return fn(bset
, poly
, user
);
3035 /* Return total degree in variables first (inclusive) up to last (exclusive).
3037 int isl_upoly_degree(__isl_keep
struct isl_upoly
*up
, int first
, int last
)
3041 struct isl_upoly_rec
*rec
;
3045 if (isl_upoly_is_zero(up
))
3047 if (isl_upoly_is_cst(up
) || up
->var
< first
)
3050 rec
= isl_upoly_as_rec(up
);
3054 for (i
= 0; i
< rec
->n
; ++i
) {
3057 if (isl_upoly_is_zero(rec
->p
[i
]))
3059 d
= isl_upoly_degree(rec
->p
[i
], first
, last
);
3069 /* Return total degree in set variables.
3071 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial
*poly
)
3079 ovar
= isl_dim_offset(poly
->dim
, isl_dim_set
);
3080 nvar
= isl_dim_size(poly
->dim
, isl_dim_set
);
3081 return isl_upoly_degree(poly
->upoly
, ovar
, ovar
+ nvar
);
3084 __isl_give
struct isl_upoly
*isl_upoly_coeff(__isl_keep
struct isl_upoly
*up
,
3085 unsigned pos
, int deg
)
3088 struct isl_upoly_rec
*rec
;
3093 if (isl_upoly_is_cst(up
) || up
->var
< pos
) {
3095 return isl_upoly_copy(up
);
3097 return isl_upoly_zero(up
->ctx
);
3100 rec
= isl_upoly_as_rec(up
);
3104 if (up
->var
== pos
) {
3106 return isl_upoly_copy(rec
->p
[deg
]);
3108 return isl_upoly_zero(up
->ctx
);
3111 up
= isl_upoly_copy(up
);
3112 up
= isl_upoly_cow(up
);
3113 rec
= isl_upoly_as_rec(up
);
3117 for (i
= 0; i
< rec
->n
; ++i
) {
3118 struct isl_upoly
*t
;
3119 t
= isl_upoly_coeff(rec
->p
[i
], pos
, deg
);
3122 isl_upoly_free(rec
->p
[i
]);
3132 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3134 __isl_give isl_qpolynomial
*isl_qpolynomial_coeff(
3135 __isl_keep isl_qpolynomial
*qp
,
3136 enum isl_dim_type type
, unsigned t_pos
, int deg
)
3139 struct isl_upoly
*up
;
3145 isl_assert(qp
->div
->ctx
, t_pos
< isl_dim_size(qp
->dim
, type
),
3148 g_pos
= pos(qp
->dim
, type
) + t_pos
;
3149 up
= isl_upoly_coeff(qp
->upoly
, g_pos
, deg
);
3151 c
= isl_qpolynomial_alloc(isl_dim_copy(qp
->dim
), qp
->div
->n_row
, up
);
3154 isl_mat_free(c
->div
);
3155 c
->div
= isl_mat_copy(qp
->div
);
3160 isl_qpolynomial_free(c
);
3164 /* Homogenize the polynomial in the variables first (inclusive) up to
3165 * last (exclusive) by inserting powers of variable first.
3166 * Variable first is assumed not to appear in the input.
3168 __isl_give
struct isl_upoly
*isl_upoly_homogenize(
3169 __isl_take
struct isl_upoly
*up
, int deg
, int target
,
3170 int first
, int last
)
3173 struct isl_upoly_rec
*rec
;
3177 if (isl_upoly_is_zero(up
))
3181 if (isl_upoly_is_cst(up
) || up
->var
< first
) {
3182 struct isl_upoly
*hom
;
3184 hom
= isl_upoly_var_pow(up
->ctx
, first
, target
- deg
);
3187 rec
= isl_upoly_as_rec(hom
);
3188 rec
->p
[target
- deg
] = isl_upoly_mul(rec
->p
[target
- deg
], up
);
3193 up
= isl_upoly_cow(up
);
3194 rec
= isl_upoly_as_rec(up
);
3198 for (i
= 0; i
< rec
->n
; ++i
) {
3199 if (isl_upoly_is_zero(rec
->p
[i
]))
3201 rec
->p
[i
] = isl_upoly_homogenize(rec
->p
[i
],
3202 up
->var
< last
? deg
+ i
: i
, target
,
3214 /* Homogenize the polynomial in the set variables by introducing
3215 * powers of an extra set variable at position 0.
3217 __isl_give isl_qpolynomial
*isl_qpolynomial_homogenize(
3218 __isl_take isl_qpolynomial
*poly
)
3222 int deg
= isl_qpolynomial_degree(poly
);
3227 poly
= isl_qpolynomial_insert_dims(poly
, isl_dim_set
, 0, 1);
3228 poly
= isl_qpolynomial_cow(poly
);
3232 ovar
= isl_dim_offset(poly
->dim
, isl_dim_set
);
3233 nvar
= isl_dim_size(poly
->dim
, isl_dim_set
);
3234 poly
->upoly
= isl_upoly_homogenize(poly
->upoly
, 0, deg
,
3241 isl_qpolynomial_free(poly
);
3245 __isl_give isl_term
*isl_term_alloc(__isl_take isl_dim
*dim
,
3246 __isl_take isl_mat
*div
)
3254 n
= isl_dim_total(dim
) + div
->n_row
;
3256 term
= isl_calloc(dim
->ctx
, struct isl_term
,
3257 sizeof(struct isl_term
) + (n
- 1) * sizeof(int));
3264 isl_int_init(term
->n
);
3265 isl_int_init(term
->d
);
3274 __isl_give isl_term
*isl_term_copy(__isl_keep isl_term
*term
)
3283 __isl_give isl_term
*isl_term_dup(__isl_keep isl_term
*term
)
3292 total
= isl_dim_total(term
->dim
) + term
->div
->n_row
;
3294 dup
= isl_term_alloc(isl_dim_copy(term
->dim
), isl_mat_copy(term
->div
));
3298 isl_int_set(dup
->n
, term
->n
);
3299 isl_int_set(dup
->d
, term
->d
);
3301 for (i
= 0; i
< total
; ++i
)
3302 dup
->pow
[i
] = term
->pow
[i
];
3307 __isl_give isl_term
*isl_term_cow(__isl_take isl_term
*term
)
3315 return isl_term_dup(term
);
3318 void isl_term_free(__isl_take isl_term
*term
)
3323 if (--term
->ref
> 0)
3326 isl_dim_free(term
->dim
);
3327 isl_mat_free(term
->div
);
3328 isl_int_clear(term
->n
);
3329 isl_int_clear(term
->d
);
3333 unsigned isl_term_dim(__isl_keep isl_term
*term
, enum isl_dim_type type
)
3341 case isl_dim_out
: return isl_dim_size(term
->dim
, type
);
3342 case isl_dim_div
: return term
->div
->n_row
;
3343 case isl_dim_all
: return isl_dim_total(term
->dim
) + term
->div
->n_row
;
3348 isl_ctx
*isl_term_get_ctx(__isl_keep isl_term
*term
)
3350 return term
? term
->dim
->ctx
: NULL
;
3353 void isl_term_get_num(__isl_keep isl_term
*term
, isl_int
*n
)
3357 isl_int_set(*n
, term
->n
);
3360 void isl_term_get_den(__isl_keep isl_term
*term
, isl_int
*d
)
3364 isl_int_set(*d
, term
->d
);
3367 int isl_term_get_exp(__isl_keep isl_term
*term
,
3368 enum isl_dim_type type
, unsigned pos
)
3373 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, type
), return -1);
3375 if (type
>= isl_dim_set
)
3376 pos
+= isl_dim_size(term
->dim
, isl_dim_param
);
3377 if (type
>= isl_dim_div
)
3378 pos
+= isl_dim_size(term
->dim
, isl_dim_set
);
3380 return term
->pow
[pos
];
3383 __isl_give isl_div
*isl_term_get_div(__isl_keep isl_term
*term
, unsigned pos
)
3385 isl_basic_map
*bmap
;
3392 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, isl_dim_div
),
3395 total
= term
->div
->n_col
- term
->div
->n_row
- 2;
3396 /* No nested divs for now */
3397 isl_assert(term
->dim
->ctx
,
3398 isl_seq_first_non_zero(term
->div
->row
[pos
] + 2 + total
,
3399 term
->div
->n_row
) == -1,
3402 bmap
= isl_basic_map_alloc_dim(isl_dim_copy(term
->dim
), 1, 0, 0);
3403 if ((k
= isl_basic_map_alloc_div(bmap
)) < 0)
3406 isl_seq_cpy(bmap
->div
[k
], term
->div
->row
[pos
], 2 + total
);
3408 return isl_basic_map_div(bmap
, k
);
3410 isl_basic_map_free(bmap
);
3414 __isl_give isl_term
*isl_upoly_foreach_term(__isl_keep
struct isl_upoly
*up
,
3415 int (*fn
)(__isl_take isl_term
*term
, void *user
),
3416 __isl_take isl_term
*term
, void *user
)
3419 struct isl_upoly_rec
*rec
;
3424 if (isl_upoly_is_zero(up
))
3427 isl_assert(up
->ctx
, !isl_upoly_is_nan(up
), goto error
);
3428 isl_assert(up
->ctx
, !isl_upoly_is_infty(up
), goto error
);
3429 isl_assert(up
->ctx
, !isl_upoly_is_neginfty(up
), goto error
);
3431 if (isl_upoly_is_cst(up
)) {
3432 struct isl_upoly_cst
*cst
;
3433 cst
= isl_upoly_as_cst(up
);
3436 term
= isl_term_cow(term
);
3439 isl_int_set(term
->n
, cst
->n
);
3440 isl_int_set(term
->d
, cst
->d
);
3441 if (fn(isl_term_copy(term
), user
) < 0)
3446 rec
= isl_upoly_as_rec(up
);
3450 for (i
= 0; i
< rec
->n
; ++i
) {
3451 term
= isl_term_cow(term
);
3454 term
->pow
[up
->var
] = i
;
3455 term
= isl_upoly_foreach_term(rec
->p
[i
], fn
, term
, user
);
3459 term
->pow
[up
->var
] = 0;
3463 isl_term_free(term
);
3467 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial
*qp
,
3468 int (*fn
)(__isl_take isl_term
*term
, void *user
), void *user
)
3475 term
= isl_term_alloc(isl_dim_copy(qp
->dim
), isl_mat_copy(qp
->div
));
3479 term
= isl_upoly_foreach_term(qp
->upoly
, fn
, term
, user
);
3481 isl_term_free(term
);
3483 return term
? 0 : -1;
3486 __isl_give isl_qpolynomial
*isl_qpolynomial_from_term(__isl_take isl_term
*term
)
3488 struct isl_upoly
*up
;
3489 isl_qpolynomial
*qp
;
3495 n
= isl_dim_total(term
->dim
) + term
->div
->n_row
;
3497 up
= isl_upoly_rat_cst(term
->dim
->ctx
, term
->n
, term
->d
);
3498 for (i
= 0; i
< n
; ++i
) {
3501 up
= isl_upoly_mul(up
,
3502 isl_upoly_var_pow(term
->dim
->ctx
, i
, term
->pow
[i
]));
3505 qp
= isl_qpolynomial_alloc(isl_dim_copy(term
->dim
), term
->div
->n_row
, up
);
3508 isl_mat_free(qp
->div
);
3509 qp
->div
= isl_mat_copy(term
->div
);
3513 isl_term_free(term
);
3516 isl_qpolynomial_free(qp
);
3517 isl_term_free(term
);
3521 __isl_give isl_qpolynomial
*isl_qpolynomial_lift(__isl_take isl_qpolynomial
*qp
,
3522 __isl_take isl_dim
*dim
)
3531 if (isl_dim_equal(qp
->dim
, dim
)) {
3536 qp
= isl_qpolynomial_cow(qp
);
3540 extra
= isl_dim_size(dim
, isl_dim_set
) -
3541 isl_dim_size(qp
->dim
, isl_dim_set
);
3542 total
= isl_dim_total(qp
->dim
);
3543 if (qp
->div
->n_row
) {
3546 exp
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
3549 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3551 qp
->upoly
= expand(qp
->upoly
, exp
, total
);
3556 qp
->div
= isl_mat_insert_cols(qp
->div
, 2 + total
, extra
);
3559 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3560 isl_seq_clr(qp
->div
->row
[i
] + 2 + total
, extra
);
3562 isl_dim_free(qp
->dim
);
3568 isl_qpolynomial_free(qp
);
3572 /* For each parameter or variable that does not appear in qp,
3573 * first eliminate the variable from all constraints and then set it to zero.
3575 static __isl_give isl_set
*fix_inactive(__isl_take isl_set
*set
,
3576 __isl_keep isl_qpolynomial
*qp
)
3587 d
= isl_dim_total(set
->dim
);
3588 active
= isl_calloc_array(set
->ctx
, int, d
);
3589 if (set_active(qp
, active
) < 0)
3592 for (i
= 0; i
< d
; ++i
)
3601 nparam
= isl_dim_size(set
->dim
, isl_dim_param
);
3602 nvar
= isl_dim_size(set
->dim
, isl_dim_set
);
3603 for (i
= 0; i
< nparam
; ++i
) {
3606 set
= isl_set_eliminate(set
, isl_dim_param
, i
, 1);
3607 set
= isl_set_fix_si(set
, isl_dim_param
, i
, 0);
3609 for (i
= 0; i
< nvar
; ++i
) {
3610 if (active
[nparam
+ i
])
3612 set
= isl_set_eliminate(set
, isl_dim_set
, i
, 1);
3613 set
= isl_set_fix_si(set
, isl_dim_set
, i
, 0);
3625 struct isl_opt_data
{
3626 isl_qpolynomial
*qp
;
3628 isl_qpolynomial
*opt
;
3632 static int opt_fn(__isl_take isl_point
*pnt
, void *user
)
3634 struct isl_opt_data
*data
= (struct isl_opt_data
*)user
;
3635 isl_qpolynomial
*val
;
3637 val
= isl_qpolynomial_eval(isl_qpolynomial_copy(data
->qp
), pnt
);
3641 } else if (data
->max
) {
3642 data
->opt
= isl_qpolynomial_max_cst(data
->opt
, val
);
3644 data
->opt
= isl_qpolynomial_min_cst(data
->opt
, val
);
3650 __isl_give isl_qpolynomial
*isl_qpolynomial_opt_on_domain(
3651 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*set
, int max
)
3653 struct isl_opt_data data
= { NULL
, 1, NULL
, max
};
3658 if (isl_upoly_is_cst(qp
->upoly
)) {
3663 set
= fix_inactive(set
, qp
);
3666 if (isl_set_foreach_point(set
, opt_fn
, &data
) < 0)
3670 data
.opt
= isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp
));
3673 isl_qpolynomial_free(qp
);
3677 isl_qpolynomial_free(qp
);
3678 isl_qpolynomial_free(data
.opt
);
3682 __isl_give isl_qpolynomial
*isl_qpolynomial_morph(__isl_take isl_qpolynomial
*qp
,
3683 __isl_take isl_morph
*morph
)
3688 struct isl_upoly
*up
;
3690 struct isl_upoly
**subs
;
3693 qp
= isl_qpolynomial_cow(qp
);
3698 isl_assert(ctx
, isl_dim_equal(qp
->dim
, morph
->dom
->dim
), goto error
);
3700 n_sub
= morph
->inv
->n_row
- 1;
3701 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
3702 n_sub
+= qp
->div
->n_row
;
3703 subs
= isl_calloc_array(ctx
, struct isl_upoly
*, n_sub
);
3707 for (i
= 0; 1 + i
< morph
->inv
->n_row
; ++i
)
3708 subs
[i
] = isl_upoly_from_affine(ctx
, morph
->inv
->row
[1 + i
],
3709 morph
->inv
->row
[0][0], morph
->inv
->n_col
);
3710 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
3711 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3712 subs
[morph
->inv
->n_row
- 1 + i
] =
3713 isl_upoly_var_pow(ctx
, morph
->inv
->n_col
- 1 + i
, 1);
3715 qp
->upoly
= isl_upoly_subs(qp
->upoly
, 0, n_sub
, subs
);
3717 for (i
= 0; i
< n_sub
; ++i
)
3718 isl_upoly_free(subs
[i
]);
3721 mat
= isl_mat_diagonal(isl_mat_identity(ctx
, 1), isl_mat_copy(morph
->inv
));
3722 mat
= isl_mat_diagonal(mat
, isl_mat_identity(ctx
, qp
->div
->n_row
));
3723 qp
->div
= isl_mat_product(qp
->div
, mat
);
3724 isl_dim_free(qp
->dim
);
3725 qp
->dim
= isl_dim_copy(morph
->ran
->dim
);
3727 if (!qp
->upoly
|| !qp
->div
|| !qp
->dim
)
3730 isl_morph_free(morph
);
3734 isl_qpolynomial_free(qp
);
3735 isl_morph_free(morph
);
3739 static int neg_entry(void **entry
, void *user
)
3741 isl_pw_qpolynomial
**pwqp
= (isl_pw_qpolynomial
**)entry
;
3743 *pwqp
= isl_pw_qpolynomial_neg(*pwqp
);
3745 return *pwqp
? 0 : -1;
3748 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_neg(
3749 __isl_take isl_union_pw_qpolynomial
*upwqp
)
3751 upwqp
= isl_union_pw_qpolynomial_cow(upwqp
);
3755 if (isl_hash_table_foreach(upwqp
->dim
->ctx
, &upwqp
->table
,
3756 &neg_entry
, NULL
) < 0)
3761 isl_union_pw_qpolynomial_free(upwqp
);
3765 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_sub(
3766 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
3767 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
3769 return isl_union_pw_qpolynomial_add(upwqp1
,
3770 isl_union_pw_qpolynomial_neg(upwqp2
));
3773 static int mul_entry(void **entry
, void *user
)
3775 struct isl_union_pw_qpolynomial_match_bin_data
*data
= user
;
3777 struct isl_hash_table_entry
*entry2
;
3778 isl_pw_qpolynomial
*pwpq
= *entry
;
3781 hash
= isl_dim_get_hash(pwpq
->dim
);
3782 entry2
= isl_hash_table_find(data
->u2
->dim
->ctx
, &data
->u2
->table
,
3783 hash
, &has_dim
, pwpq
->dim
, 0);
3787 pwpq
= isl_pw_qpolynomial_copy(pwpq
);
3788 pwpq
= isl_pw_qpolynomial_mul(pwpq
,
3789 isl_pw_qpolynomial_copy(entry2
->data
));
3791 empty
= isl_pw_qpolynomial_is_zero(pwpq
);
3793 isl_pw_qpolynomial_free(pwpq
);
3797 isl_pw_qpolynomial_free(pwpq
);
3801 data
->res
= isl_union_pw_qpolynomial_add_pw_qpolynomial(data
->res
, pwpq
);
3806 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_mul(
3807 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
3808 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
3810 return match_bin_op(upwqp1
, upwqp2
, &mul_entry
);
3813 /* Reorder the columns of the given div definitions according to the
3816 static __isl_give isl_mat
*reorder_divs(__isl_take isl_mat
*div
,
3817 __isl_take isl_reordering
*r
)
3826 extra
= isl_dim_total(r
->dim
) + div
->n_row
- r
->len
;
3827 mat
= isl_mat_alloc(div
->ctx
, div
->n_row
, div
->n_col
+ extra
);
3831 for (i
= 0; i
< div
->n_row
; ++i
) {
3832 isl_seq_cpy(mat
->row
[i
], div
->row
[i
], 2);
3833 isl_seq_clr(mat
->row
[i
] + 2, mat
->n_col
- 2);
3834 for (j
= 0; j
< r
->len
; ++j
)
3835 isl_int_set(mat
->row
[i
][2 + r
->pos
[j
]],
3836 div
->row
[i
][2 + j
]);
3839 isl_reordering_free(r
);
3843 isl_reordering_free(r
);
3848 /* Reorder the dimension of "qp" according to the given reordering.
3850 __isl_give isl_qpolynomial
*isl_qpolynomial_realign(
3851 __isl_take isl_qpolynomial
*qp
, __isl_take isl_reordering
*r
)
3853 qp
= isl_qpolynomial_cow(qp
);
3857 r
= isl_reordering_extend(r
, qp
->div
->n_row
);
3861 qp
->div
= reorder_divs(qp
->div
, isl_reordering_copy(r
));
3865 qp
->upoly
= reorder(qp
->upoly
, r
->pos
);
3869 qp
= isl_qpolynomial_reset_dim(qp
, isl_dim_copy(r
->dim
));
3871 isl_reordering_free(r
);
3874 isl_qpolynomial_free(qp
);
3875 isl_reordering_free(r
);
3879 struct isl_split_periods_data
{
3881 isl_pw_qpolynomial
*res
;
3884 /* Create a slice where the integer division "div" has the fixed value "v".
3885 * In particular, if "div" refers to floor(f/m), then create a slice
3887 * m v <= f <= m v + (m - 1)
3892 * -f + m v + (m - 1) >= 0
3894 static __isl_give isl_set
*set_div_slice(__isl_take isl_dim
*dim
,
3895 __isl_keep isl_qpolynomial
*qp
, int div
, isl_int v
)
3898 isl_basic_set
*bset
= NULL
;
3904 total
= isl_dim_total(dim
);
3905 bset
= isl_basic_set_alloc_dim(isl_dim_copy(dim
), 0, 0, 2);
3907 k
= isl_basic_set_alloc_inequality(bset
);
3910 isl_seq_cpy(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
3911 isl_int_submul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
3913 k
= isl_basic_set_alloc_inequality(bset
);
3916 isl_seq_neg(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
3917 isl_int_addmul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
3918 isl_int_add(bset
->ineq
[k
][0], bset
->ineq
[k
][0], qp
->div
->row
[div
][0]);
3919 isl_int_sub_ui(bset
->ineq
[k
][0], bset
->ineq
[k
][0], 1);
3922 return isl_set_from_basic_set(bset
);
3924 isl_basic_set_free(bset
);
3929 static int split_periods(__isl_take isl_set
*set
,
3930 __isl_take isl_qpolynomial
*qp
, void *user
);
3932 /* Create a slice of the domain "set" such that integer division "div"
3933 * has the fixed value "v" and add the results to data->res,
3934 * replacing the integer division by "v" in "qp".
3936 static int set_div(__isl_take isl_set
*set
,
3937 __isl_take isl_qpolynomial
*qp
, int div
, isl_int v
,
3938 struct isl_split_periods_data
*data
)
3943 struct isl_upoly
*cst
;
3945 slice
= set_div_slice(isl_set_get_dim(set
), qp
, div
, v
);
3946 set
= isl_set_intersect(set
, slice
);
3951 total
= isl_dim_total(qp
->dim
);
3953 for (i
= div
+ 1; i
< qp
->div
->n_row
; ++i
) {
3954 if (isl_int_is_zero(qp
->div
->row
[i
][2 + total
+ div
]))
3956 isl_int_addmul(qp
->div
->row
[i
][1],
3957 qp
->div
->row
[i
][2 + total
+ div
], v
);
3958 isl_int_set_si(qp
->div
->row
[i
][2 + total
+ div
], 0);
3961 cst
= isl_upoly_rat_cst(qp
->dim
->ctx
, v
, qp
->dim
->ctx
->one
);
3962 qp
= substitute_div(qp
, div
, cst
);
3964 return split_periods(set
, qp
, data
);
3967 isl_qpolynomial_free(qp
);
3971 /* Split the domain "set" such that integer division "div"
3972 * has a fixed value (ranging from "min" to "max") on each slice
3973 * and add the results to data->res.
3975 static int split_div(__isl_take isl_set
*set
,
3976 __isl_take isl_qpolynomial
*qp
, int div
, isl_int min
, isl_int max
,
3977 struct isl_split_periods_data
*data
)
3979 for (; isl_int_le(min
, max
); isl_int_add_ui(min
, min
, 1)) {
3980 isl_set
*set_i
= isl_set_copy(set
);
3981 isl_qpolynomial
*qp_i
= isl_qpolynomial_copy(qp
);
3983 if (set_div(set_i
, qp_i
, div
, min
, data
) < 0)
3987 isl_qpolynomial_free(qp
);
3991 isl_qpolynomial_free(qp
);
3995 /* If "qp" refers to any integer division
3996 * that can only attain "max_periods" distinct values on "set"
3997 * then split the domain along those distinct values.
3998 * Add the results (or the original if no splitting occurs)
4001 static int split_periods(__isl_take isl_set
*set
,
4002 __isl_take isl_qpolynomial
*qp
, void *user
)
4005 isl_pw_qpolynomial
*pwqp
;
4006 struct isl_split_periods_data
*data
;
4011 data
= (struct isl_split_periods_data
*)user
;
4016 if (qp
->div
->n_row
== 0) {
4017 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4018 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4024 total
= isl_dim_total(qp
->dim
);
4025 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4026 enum isl_lp_result lp_res
;
4028 if (isl_seq_first_non_zero(qp
->div
->row
[i
] + 2 + total
,
4029 qp
->div
->n_row
) != -1)
4032 lp_res
= isl_set_solve_lp(set
, 0, qp
->div
->row
[i
] + 1,
4033 set
->ctx
->one
, &min
, NULL
, NULL
);
4034 if (lp_res
== isl_lp_error
)
4036 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4038 isl_int_fdiv_q(min
, min
, qp
->div
->row
[i
][0]);
4040 lp_res
= isl_set_solve_lp(set
, 1, qp
->div
->row
[i
] + 1,
4041 set
->ctx
->one
, &max
, NULL
, NULL
);
4042 if (lp_res
== isl_lp_error
)
4044 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4046 isl_int_fdiv_q(max
, max
, qp
->div
->row
[i
][0]);
4048 isl_int_sub(max
, max
, min
);
4049 if (isl_int_cmp_si(max
, data
->max_periods
) < 0) {
4050 isl_int_add(max
, max
, min
);
4055 if (i
< qp
->div
->n_row
) {
4056 r
= split_div(set
, qp
, i
, min
, max
, data
);
4058 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4059 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4071 isl_qpolynomial_free(qp
);
4075 /* If any quasi-polynomial in pwqp refers to any integer division
4076 * that can only attain "max_periods" distinct values on its domain
4077 * then split the domain along those distinct values.
4079 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_split_periods(
4080 __isl_take isl_pw_qpolynomial
*pwqp
, int max_periods
)
4082 struct isl_split_periods_data data
;
4084 data
.max_periods
= max_periods
;
4085 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp
));
4087 if (isl_pw_qpolynomial_foreach_piece(pwqp
, &split_periods
, &data
) < 0)
4090 isl_pw_qpolynomial_free(pwqp
);
4094 isl_pw_qpolynomial_free(data
.res
);
4095 isl_pw_qpolynomial_free(pwqp
);
4099 /* Construct a piecewise quasipolynomial that is constant on the given
4100 * domain. In particular, it is
4103 * infinity if cst == -1
4105 static __isl_give isl_pw_qpolynomial
*constant_on_domain(
4106 __isl_take isl_basic_set
*bset
, int cst
)
4109 isl_qpolynomial
*qp
;
4114 bset
= isl_basic_map_domain(isl_basic_map_from_range(bset
));
4115 dim
= isl_basic_set_get_dim(bset
);
4117 qp
= isl_qpolynomial_infty(dim
);
4119 qp
= isl_qpolynomial_zero(dim
);
4121 qp
= isl_qpolynomial_one(dim
);
4122 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset
), qp
);
4125 /* Factor bset, call fn on each of the factors and return the product.
4127 * If no factors can be found, simply call fn on the input.
4128 * Otherwise, construct the factors based on the factorizer,
4129 * call fn on each factor and compute the product.
4131 static __isl_give isl_pw_qpolynomial
*compressed_multiplicative_call(
4132 __isl_take isl_basic_set
*bset
,
4133 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4139 isl_qpolynomial
*qp
;
4140 isl_pw_qpolynomial
*pwqp
;
4144 f
= isl_basic_set_factorizer(bset
);
4147 if (f
->n_group
== 0) {
4148 isl_factorizer_free(f
);
4152 nparam
= isl_basic_set_dim(bset
, isl_dim_param
);
4153 nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
4155 dim
= isl_basic_set_get_dim(bset
);
4156 dim
= isl_dim_domain(dim
);
4157 set
= isl_set_universe(isl_dim_copy(dim
));
4158 qp
= isl_qpolynomial_one(dim
);
4159 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4161 bset
= isl_morph_basic_set(isl_morph_copy(f
->morph
), bset
);
4163 for (i
= 0, n
= 0; i
< f
->n_group
; ++i
) {
4164 isl_basic_set
*bset_i
;
4165 isl_pw_qpolynomial
*pwqp_i
;
4167 bset_i
= isl_basic_set_copy(bset
);
4168 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4169 nparam
+ n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4170 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4172 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
,
4173 n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4174 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
, 0, n
);
4176 pwqp_i
= fn(bset_i
);
4177 pwqp
= isl_pw_qpolynomial_mul(pwqp
, pwqp_i
);
4182 isl_basic_set_free(bset
);
4183 isl_factorizer_free(f
);
4187 isl_basic_set_free(bset
);
4191 /* Factor bset, call fn on each of the factors and return the product.
4192 * The function is assumed to evaluate to zero on empty domains,
4193 * to one on zero-dimensional domains and to infinity on unbounded domains
4194 * and will not be called explicitly on zero-dimensional or unbounded domains.
4196 * We first check for some special cases and remove all equalities.
4197 * Then we hand over control to compressed_multiplicative_call.
4199 __isl_give isl_pw_qpolynomial
*isl_basic_set_multiplicative_call(
4200 __isl_take isl_basic_set
*bset
,
4201 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4205 isl_pw_qpolynomial
*pwqp
;
4206 unsigned orig_nvar
, final_nvar
;
4211 if (isl_basic_set_fast_is_empty(bset
))
4212 return constant_on_domain(bset
, 0);
4214 orig_nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
4217 return constant_on_domain(bset
, 1);
4219 bounded
= isl_basic_set_is_bounded(bset
);
4223 return constant_on_domain(bset
, -1);
4225 if (bset
->n_eq
== 0)
4226 return compressed_multiplicative_call(bset
, fn
);
4228 morph
= isl_basic_set_full_compression(bset
);
4229 bset
= isl_morph_basic_set(isl_morph_copy(morph
), bset
);
4231 final_nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
4233 pwqp
= compressed_multiplicative_call(bset
, fn
);
4235 morph
= isl_morph_remove_dom_dims(morph
, isl_dim_set
, 0, orig_nvar
);
4236 morph
= isl_morph_remove_ran_dims(morph
, isl_dim_set
, 0, final_nvar
);
4237 morph
= isl_morph_inverse(morph
);
4239 pwqp
= isl_pw_qpolynomial_morph(pwqp
, morph
);
4243 isl_basic_set_free(bset
);
4247 /* Drop all floors in "qp", turning each integer division [a/m] into
4248 * a rational division a/m. If "down" is set, then the integer division
4249 * is replaces by (a-(m-1))/m instead.
4251 static __isl_give isl_qpolynomial
*qp_drop_floors(
4252 __isl_take isl_qpolynomial
*qp
, int down
)
4255 struct isl_upoly
*s
;
4259 if (qp
->div
->n_row
== 0)
4262 qp
= isl_qpolynomial_cow(qp
);
4266 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
4268 isl_int_sub(qp
->div
->row
[i
][1],
4269 qp
->div
->row
[i
][1], qp
->div
->row
[i
][0]);
4270 isl_int_add_ui(qp
->div
->row
[i
][1],
4271 qp
->div
->row
[i
][1], 1);
4273 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
4274 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
4275 qp
= substitute_div(qp
, i
, s
);
4283 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4284 * a rational division a/m.
4286 static __isl_give isl_pw_qpolynomial
*pwqp_drop_floors(
4287 __isl_take isl_pw_qpolynomial
*pwqp
)
4294 if (isl_pw_qpolynomial_is_zero(pwqp
))
4297 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
4301 for (i
= 0; i
< pwqp
->n
; ++i
) {
4302 pwqp
->p
[i
].qp
= qp_drop_floors(pwqp
->p
[i
].qp
, 0);
4309 isl_pw_qpolynomial_free(pwqp
);
4313 /* Adjust all the integer divisions in "qp" such that they are at least
4314 * one over the given orthant (identified by "signs"). This ensures
4315 * that they will still be non-negative even after subtracting (m-1)/m.
4317 * In particular, f is replaced by f' + v, changing f = [a/m]
4318 * to f' = [(a - m v)/m].
4319 * If the constant term k in a is smaller than m,
4320 * the constant term of v is set to floor(k/m) - 1.
4321 * For any other term, if the coefficient c and the variable x have
4322 * the same sign, then no changes are needed.
4323 * Otherwise, if the variable is positive (and c is negative),
4324 * then the coefficient of x in v is set to floor(c/m).
4325 * If the variable is negative (and c is positive),
4326 * then the coefficient of x in v is set to ceil(c/m).
4328 static __isl_give isl_qpolynomial
*make_divs_pos(__isl_take isl_qpolynomial
*qp
,
4334 struct isl_upoly
*s
;
4336 qp
= isl_qpolynomial_cow(qp
);
4339 qp
->div
= isl_mat_cow(qp
->div
);
4343 total
= isl_dim_total(qp
->dim
);
4344 v
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
4346 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4347 isl_int
*row
= qp
->div
->row
[i
];
4351 if (isl_int_lt(row
[1], row
[0])) {
4352 isl_int_fdiv_q(v
->el
[0], row
[1], row
[0]);
4353 isl_int_sub_ui(v
->el
[0], v
->el
[0], 1);
4354 isl_int_submul(row
[1], row
[0], v
->el
[0]);
4356 for (j
= 0; j
< total
; ++j
) {
4357 if (isl_int_sgn(row
[2 + j
]) * signs
[j
] >= 0)
4360 isl_int_cdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4362 isl_int_fdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4363 isl_int_submul(row
[2 + j
], row
[0], v
->el
[1 + j
]);
4365 for (j
= 0; j
< i
; ++j
) {
4366 if (isl_int_sgn(row
[2 + total
+ j
]) >= 0)
4368 isl_int_fdiv_q(v
->el
[1 + total
+ j
],
4369 row
[2 + total
+ j
], row
[0]);
4370 isl_int_submul(row
[2 + total
+ j
],
4371 row
[0], v
->el
[1 + total
+ j
]);
4373 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
4374 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
4376 isl_seq_combine(qp
->div
->row
[j
] + 1,
4377 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
4378 qp
->div
->row
[j
][2 + total
+ i
], v
->el
, v
->size
);
4380 isl_int_set_si(v
->el
[1 + total
+ i
], 1);
4381 s
= isl_upoly_from_affine(qp
->dim
->ctx
, v
->el
,
4382 qp
->div
->ctx
->one
, v
->size
);
4383 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ i
, 1, &s
);
4393 isl_qpolynomial_free(qp
);
4397 struct isl_to_poly_data
{
4399 isl_pw_qpolynomial
*res
;
4400 isl_qpolynomial
*qp
;
4403 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4404 * We first make all integer divisions positive and then split the
4405 * quasipolynomials into terms with sign data->sign (the direction
4406 * of the requested approximation) and terms with the opposite sign.
4407 * In the first set of terms, each integer division [a/m] is
4408 * overapproximated by a/m, while in the second it is underapproximated
4411 static int to_polynomial_on_orthant(__isl_take isl_set
*orthant
, int *signs
,
4414 struct isl_to_poly_data
*data
= user
;
4415 isl_pw_qpolynomial
*t
;
4416 isl_qpolynomial
*qp
, *up
, *down
;
4418 qp
= isl_qpolynomial_copy(data
->qp
);
4419 qp
= make_divs_pos(qp
, signs
);
4421 up
= isl_qpolynomial_terms_of_sign(qp
, signs
, data
->sign
);
4422 up
= qp_drop_floors(up
, 0);
4423 down
= isl_qpolynomial_terms_of_sign(qp
, signs
, -data
->sign
);
4424 down
= qp_drop_floors(down
, 1);
4426 isl_qpolynomial_free(qp
);
4427 qp
= isl_qpolynomial_add(up
, down
);
4429 t
= isl_pw_qpolynomial_alloc(orthant
, qp
);
4430 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, t
);
4435 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4436 * the polynomial will be an overapproximation. If "sign" is negative,
4437 * it will be an underapproximation. If "sign" is zero, the approximation
4438 * will lie somewhere in between.
4440 * In particular, is sign == 0, we simply drop the floors, turning
4441 * the integer divisions into rational divisions.
4442 * Otherwise, we split the domains into orthants, make all integer divisions
4443 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4444 * depending on the requested sign and the sign of the term in which
4445 * the integer division appears.
4447 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_to_polynomial(
4448 __isl_take isl_pw_qpolynomial
*pwqp
, int sign
)
4451 struct isl_to_poly_data data
;
4454 return pwqp_drop_floors(pwqp
);
4460 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp
));
4462 for (i
= 0; i
< pwqp
->n
; ++i
) {
4463 if (pwqp
->p
[i
].qp
->div
->n_row
== 0) {
4464 isl_pw_qpolynomial
*t
;
4465 t
= isl_pw_qpolynomial_alloc(
4466 isl_set_copy(pwqp
->p
[i
].set
),
4467 isl_qpolynomial_copy(pwqp
->p
[i
].qp
));
4468 data
.res
= isl_pw_qpolynomial_add_disjoint(data
.res
, t
);
4471 data
.qp
= pwqp
->p
[i
].qp
;
4472 if (isl_set_foreach_orthant(pwqp
->p
[i
].set
,
4473 &to_polynomial_on_orthant
, &data
) < 0)
4477 isl_pw_qpolynomial_free(pwqp
);
4481 isl_pw_qpolynomial_free(pwqp
);
4482 isl_pw_qpolynomial_free(data
.res
);
4486 static int poly_entry(void **entry
, void *user
)
4489 isl_pw_qpolynomial
**pwqp
= (isl_pw_qpolynomial
**)entry
;
4491 *pwqp
= isl_pw_qpolynomial_to_polynomial(*pwqp
, *sign
);
4493 return *pwqp
? 0 : -1;
4496 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_to_polynomial(
4497 __isl_take isl_union_pw_qpolynomial
*upwqp
, int sign
)
4499 upwqp
= isl_union_pw_qpolynomial_cow(upwqp
);
4503 if (isl_hash_table_foreach(upwqp
->dim
->ctx
, &upwqp
->table
,
4504 &poly_entry
, &sign
) < 0)
4509 isl_union_pw_qpolynomial_free(upwqp
);
4513 __isl_give isl_basic_map
*isl_basic_map_from_qpolynomial(
4514 __isl_take isl_qpolynomial
*qp
)
4518 isl_vec
*aff
= NULL
;
4519 isl_basic_map
*bmap
= NULL
;
4525 if (!isl_upoly_is_affine(qp
->upoly
))
4526 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
4527 "input quasi-polynomial not affine", goto error
);
4528 aff
= isl_qpolynomial_extract_affine(qp
);
4531 dim
= isl_qpolynomial_get_dim(qp
);
4532 dim
= isl_dim_from_domain(dim
);
4533 pos
= 1 + isl_dim_offset(dim
, isl_dim_out
);
4534 dim
= isl_dim_add(dim
, isl_dim_out
, 1);
4535 n_div
= qp
->div
->n_row
;
4536 bmap
= isl_basic_map_alloc_dim(dim
, n_div
, 1, 2 * n_div
);
4538 for (i
= 0; i
< n_div
; ++i
) {
4539 k
= isl_basic_map_alloc_div(bmap
);
4542 isl_seq_cpy(bmap
->div
[k
], qp
->div
->row
[i
], qp
->div
->n_col
);
4543 isl_int_set_si(bmap
->div
[k
][qp
->div
->n_col
], 0);
4544 if (isl_basic_map_add_div_constraints(bmap
, k
) < 0)
4547 k
= isl_basic_map_alloc_equality(bmap
);
4550 isl_int_neg(bmap
->eq
[k
][pos
], aff
->el
[0]);
4551 isl_seq_cpy(bmap
->eq
[k
], aff
->el
+ 1, pos
);
4552 isl_seq_cpy(bmap
->eq
[k
] + pos
+ 1, aff
->el
+ 1 + pos
, n_div
);
4555 isl_qpolynomial_free(qp
);
4556 bmap
= isl_basic_map_finalize(bmap
);
4560 isl_qpolynomial_free(qp
);
4561 isl_basic_map_free(bmap
);