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_factorization.h>
15 #include <isl_union_map_private.h>
16 #include <isl_polynomial_private.h>
17 #include <isl_point_private.h>
18 #include <isl_dim_private.h>
19 #include <isl_map_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_neg_cst(__isl_take
struct isl_upoly
*up
)
679 struct isl_upoly_cst
*cst
;
681 if (isl_upoly_is_zero(up
))
684 up
= isl_upoly_cow(up
);
688 cst
= isl_upoly_as_cst(up
);
690 isl_int_neg(cst
->n
, cst
->n
);
695 __isl_give
struct isl_upoly
*isl_upoly_neg(__isl_take
struct isl_upoly
*up
)
698 struct isl_upoly_rec
*rec
;
703 if (isl_upoly_is_cst(up
))
704 return isl_upoly_neg_cst(up
);
706 up
= isl_upoly_cow(up
);
707 rec
= isl_upoly_as_rec(up
);
711 for (i
= 0; i
< rec
->n
; ++i
) {
712 rec
->p
[i
] = isl_upoly_neg(rec
->p
[i
]);
723 __isl_give
struct isl_upoly
*isl_upoly_mul_cst(__isl_take
struct isl_upoly
*up1
,
724 __isl_take
struct isl_upoly
*up2
)
726 struct isl_upoly_cst
*cst1
;
727 struct isl_upoly_cst
*cst2
;
729 up1
= isl_upoly_cow(up1
);
733 cst1
= isl_upoly_as_cst(up1
);
734 cst2
= isl_upoly_as_cst(up2
);
736 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->n
);
737 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
739 isl_upoly_cst_reduce(cst1
);
749 __isl_give
struct isl_upoly
*isl_upoly_mul_rec(__isl_take
struct isl_upoly
*up1
,
750 __isl_take
struct isl_upoly
*up2
)
752 struct isl_upoly_rec
*rec1
;
753 struct isl_upoly_rec
*rec2
;
754 struct isl_upoly_rec
*res
;
758 rec1
= isl_upoly_as_rec(up1
);
759 rec2
= isl_upoly_as_rec(up2
);
762 size
= rec1
->n
+ rec2
->n
- 1;
763 res
= isl_upoly_alloc_rec(up1
->ctx
, up1
->var
, size
);
767 for (i
= 0; i
< rec1
->n
; ++i
) {
768 res
->p
[i
] = isl_upoly_mul(isl_upoly_copy(rec2
->p
[0]),
769 isl_upoly_copy(rec1
->p
[i
]));
774 for (; i
< size
; ++i
) {
775 res
->p
[i
] = isl_upoly_zero(up1
->ctx
);
780 for (i
= 0; i
< rec1
->n
; ++i
) {
781 for (j
= 1; j
< rec2
->n
; ++j
) {
782 struct isl_upoly
*up
;
783 up
= isl_upoly_mul(isl_upoly_copy(rec2
->p
[j
]),
784 isl_upoly_copy(rec1
->p
[i
]));
785 res
->p
[i
+ j
] = isl_upoly_sum(res
->p
[i
+ j
], up
);
798 isl_upoly_free(&res
->up
);
802 __isl_give
struct isl_upoly
*isl_upoly_mul(__isl_take
struct isl_upoly
*up1
,
803 __isl_take
struct isl_upoly
*up2
)
808 if (isl_upoly_is_nan(up1
)) {
813 if (isl_upoly_is_nan(up2
)) {
818 if (isl_upoly_is_zero(up1
)) {
823 if (isl_upoly_is_zero(up2
)) {
828 if (isl_upoly_is_one(up1
)) {
833 if (isl_upoly_is_one(up2
)) {
838 if (up1
->var
< up2
->var
)
839 return isl_upoly_mul(up2
, up1
);
841 if (up2
->var
< up1
->var
) {
843 struct isl_upoly_rec
*rec
;
844 if (isl_upoly_is_infty(up2
) || isl_upoly_is_neginfty(up2
)) {
845 isl_ctx
*ctx
= up1
->ctx
;
848 return isl_upoly_nan(ctx
);
850 up1
= isl_upoly_cow(up1
);
851 rec
= isl_upoly_as_rec(up1
);
855 for (i
= 0; i
< rec
->n
; ++i
) {
856 rec
->p
[i
] = isl_upoly_mul(rec
->p
[i
],
857 isl_upoly_copy(up2
));
865 if (isl_upoly_is_cst(up1
))
866 return isl_upoly_mul_cst(up1
, up2
);
868 return isl_upoly_mul_rec(up1
, up2
);
875 __isl_give isl_qpolynomial
*isl_qpolynomial_alloc(__isl_take isl_dim
*dim
,
876 unsigned n_div
, __isl_take
struct isl_upoly
*up
)
878 struct isl_qpolynomial
*qp
= NULL
;
884 total
= isl_dim_total(dim
);
886 qp
= isl_calloc_type(dim
->ctx
, struct isl_qpolynomial
);
891 qp
->div
= isl_mat_alloc(dim
->ctx
, n_div
, 1 + 1 + total
+ n_div
);
902 isl_qpolynomial_free(qp
);
906 __isl_give isl_qpolynomial
*isl_qpolynomial_copy(__isl_keep isl_qpolynomial
*qp
)
915 __isl_give isl_qpolynomial
*isl_qpolynomial_dup(__isl_keep isl_qpolynomial
*qp
)
917 struct isl_qpolynomial
*dup
;
922 dup
= isl_qpolynomial_alloc(isl_dim_copy(qp
->dim
), qp
->div
->n_row
,
923 isl_upoly_copy(qp
->upoly
));
926 isl_mat_free(dup
->div
);
927 dup
->div
= isl_mat_copy(qp
->div
);
933 isl_qpolynomial_free(dup
);
937 __isl_give isl_qpolynomial
*isl_qpolynomial_cow(__isl_take isl_qpolynomial
*qp
)
945 return isl_qpolynomial_dup(qp
);
948 void isl_qpolynomial_free(__isl_take isl_qpolynomial
*qp
)
956 isl_dim_free(qp
->dim
);
957 isl_mat_free(qp
->div
);
958 isl_upoly_free(qp
->upoly
);
963 __isl_give
struct isl_upoly
*isl_upoly_pow(isl_ctx
*ctx
, int pos
, int power
)
966 struct isl_upoly
*up
;
967 struct isl_upoly_rec
*rec
;
968 struct isl_upoly_cst
*cst
;
970 rec
= isl_upoly_alloc_rec(ctx
, pos
, 1 + power
);
973 for (i
= 0; i
< 1 + power
; ++i
) {
974 rec
->p
[i
] = isl_upoly_zero(ctx
);
979 cst
= isl_upoly_as_cst(rec
->p
[power
]);
980 isl_int_set_si(cst
->n
, 1);
984 isl_upoly_free(&rec
->up
);
988 /* r array maps original positions to new positions.
990 static __isl_give
struct isl_upoly
*reorder(__isl_take
struct isl_upoly
*up
,
994 struct isl_upoly_rec
*rec
;
995 struct isl_upoly
*base
;
996 struct isl_upoly
*res
;
998 if (isl_upoly_is_cst(up
))
1001 rec
= isl_upoly_as_rec(up
);
1005 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
1007 base
= isl_upoly_pow(up
->ctx
, r
[up
->var
], 1);
1008 res
= reorder(isl_upoly_copy(rec
->p
[rec
->n
- 1]), r
);
1010 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1011 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
1012 res
= isl_upoly_sum(res
, reorder(isl_upoly_copy(rec
->p
[i
]), r
));
1015 isl_upoly_free(base
);
1024 static int compatible_divs(__isl_keep isl_mat
*div1
, __isl_keep isl_mat
*div2
)
1029 isl_assert(div1
->ctx
, div1
->n_row
>= div2
->n_row
&&
1030 div1
->n_col
>= div2
->n_col
, return -1);
1032 if (div1
->n_row
== div2
->n_row
)
1033 return isl_mat_is_equal(div1
, div2
);
1035 n_row
= div1
->n_row
;
1036 n_col
= div1
->n_col
;
1037 div1
->n_row
= div2
->n_row
;
1038 div1
->n_col
= div2
->n_col
;
1040 equal
= isl_mat_is_equal(div1
, div2
);
1042 div1
->n_row
= n_row
;
1043 div1
->n_col
= n_col
;
1048 static void expand_row(__isl_keep isl_mat
*dst
, int d
,
1049 __isl_keep isl_mat
*src
, int s
, int *exp
)
1052 unsigned c
= src
->n_col
- src
->n_row
;
1054 isl_seq_cpy(dst
->row
[d
], src
->row
[s
], c
);
1055 isl_seq_clr(dst
->row
[d
] + c
, dst
->n_col
- c
);
1057 for (i
= 0; i
< s
; ++i
)
1058 isl_int_set(dst
->row
[d
][c
+ exp
[i
]], src
->row
[s
][c
+ i
]);
1061 static int cmp_row(__isl_keep isl_mat
*div
, int i
, int j
)
1065 li
= isl_seq_last_non_zero(div
->row
[i
], div
->n_col
);
1066 lj
= isl_seq_last_non_zero(div
->row
[j
], div
->n_col
);
1071 return isl_seq_cmp(div
->row
[i
], div
->row
[j
], div
->n_col
);
1074 struct isl_div_sort_info
{
1079 static int div_sort_cmp(const void *p1
, const void *p2
)
1081 const struct isl_div_sort_info
*i1
, *i2
;
1082 i1
= (const struct isl_div_sort_info
*) p1
;
1083 i2
= (const struct isl_div_sort_info
*) p2
;
1085 return cmp_row(i1
->div
, i1
->row
, i2
->row
);
1088 /* Sort divs and remove duplicates.
1090 static __isl_give isl_qpolynomial
*sort_divs(__isl_take isl_qpolynomial
*qp
)
1095 struct isl_div_sort_info
*array
= NULL
;
1096 int *pos
= NULL
, *at
= NULL
;
1097 int *reordering
= NULL
;
1102 if (qp
->div
->n_row
<= 1)
1105 div_pos
= isl_dim_total(qp
->dim
);
1107 array
= isl_alloc_array(qp
->div
->ctx
, struct isl_div_sort_info
,
1109 pos
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1110 at
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1111 len
= qp
->div
->n_col
- 2;
1112 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
1113 if (!array
|| !pos
|| !at
|| !reordering
)
1116 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1117 array
[i
].div
= qp
->div
;
1123 qsort(array
, qp
->div
->n_row
, sizeof(struct isl_div_sort_info
),
1126 for (i
= 0; i
< div_pos
; ++i
)
1129 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1130 if (pos
[array
[i
].row
] == i
)
1132 qp
->div
= isl_mat_swap_rows(qp
->div
, i
, pos
[array
[i
].row
]);
1133 pos
[at
[i
]] = pos
[array
[i
].row
];
1134 at
[pos
[array
[i
].row
]] = at
[i
];
1135 at
[i
] = array
[i
].row
;
1136 pos
[array
[i
].row
] = i
;
1140 for (i
= 0; i
< len
- div_pos
; ++i
) {
1142 isl_seq_eq(qp
->div
->row
[i
- skip
- 1],
1143 qp
->div
->row
[i
- skip
], qp
->div
->n_col
)) {
1144 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
1145 qp
->div
= isl_mat_drop_cols(qp
->div
,
1146 2 + div_pos
+ i
- skip
, 1);
1149 reordering
[div_pos
+ array
[i
].row
] = div_pos
+ i
- skip
;
1152 qp
->upoly
= reorder(qp
->upoly
, reordering
);
1154 if (!qp
->upoly
|| !qp
->div
)
1168 isl_qpolynomial_free(qp
);
1172 static __isl_give isl_mat
*merge_divs(__isl_keep isl_mat
*div1
,
1173 __isl_keep isl_mat
*div2
, int *exp1
, int *exp2
)
1176 isl_mat
*div
= NULL
;
1177 unsigned d
= div1
->n_col
- div1
->n_row
;
1179 div
= isl_mat_alloc(div1
->ctx
, 1 + div1
->n_row
+ div2
->n_row
,
1180 d
+ div1
->n_row
+ div2
->n_row
);
1184 for (i
= 0, j
= 0, k
= 0; i
< div1
->n_row
&& j
< div2
->n_row
; ++k
) {
1187 expand_row(div
, k
, div1
, i
, exp1
);
1188 expand_row(div
, k
+ 1, div2
, j
, exp2
);
1190 cmp
= cmp_row(div
, k
, k
+ 1);
1194 } else if (cmp
< 0) {
1198 isl_seq_cpy(div
->row
[k
], div
->row
[k
+ 1], div
->n_col
);
1201 for (; i
< div1
->n_row
; ++i
, ++k
) {
1202 expand_row(div
, k
, div1
, i
, exp1
);
1205 for (; j
< div2
->n_row
; ++j
, ++k
) {
1206 expand_row(div
, k
, div2
, j
, exp2
);
1216 static __isl_give
struct isl_upoly
*expand(__isl_take
struct isl_upoly
*up
,
1217 int *exp
, int first
)
1220 struct isl_upoly_rec
*rec
;
1222 if (isl_upoly_is_cst(up
))
1225 if (up
->var
< first
)
1228 if (exp
[up
->var
- first
] == up
->var
- first
)
1231 up
= isl_upoly_cow(up
);
1235 up
->var
= exp
[up
->var
- first
] + first
;
1237 rec
= isl_upoly_as_rec(up
);
1241 for (i
= 0; i
< rec
->n
; ++i
) {
1242 rec
->p
[i
] = expand(rec
->p
[i
], exp
, first
);
1253 static __isl_give isl_qpolynomial
*with_merged_divs(
1254 __isl_give isl_qpolynomial
*(*fn
)(__isl_take isl_qpolynomial
*qp1
,
1255 __isl_take isl_qpolynomial
*qp2
),
1256 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
1260 isl_mat
*div
= NULL
;
1262 qp1
= isl_qpolynomial_cow(qp1
);
1263 qp2
= isl_qpolynomial_cow(qp2
);
1268 isl_assert(qp1
->div
->ctx
, qp1
->div
->n_row
>= qp2
->div
->n_row
&&
1269 qp1
->div
->n_col
>= qp2
->div
->n_col
, goto error
);
1271 exp1
= isl_alloc_array(qp1
->div
->ctx
, int, qp1
->div
->n_row
);
1272 exp2
= isl_alloc_array(qp2
->div
->ctx
, int, qp2
->div
->n_row
);
1276 div
= merge_divs(qp1
->div
, qp2
->div
, exp1
, exp2
);
1280 isl_mat_free(qp1
->div
);
1281 qp1
->div
= isl_mat_copy(div
);
1282 isl_mat_free(qp2
->div
);
1283 qp2
->div
= isl_mat_copy(div
);
1285 qp1
->upoly
= expand(qp1
->upoly
, exp1
, div
->n_col
- div
->n_row
- 2);
1286 qp2
->upoly
= expand(qp2
->upoly
, exp2
, div
->n_col
- div
->n_row
- 2);
1288 if (!qp1
->upoly
|| !qp2
->upoly
)
1295 return fn(qp1
, qp2
);
1300 isl_qpolynomial_free(qp1
);
1301 isl_qpolynomial_free(qp2
);
1305 __isl_give isl_qpolynomial
*isl_qpolynomial_add(__isl_take isl_qpolynomial
*qp1
,
1306 __isl_take isl_qpolynomial
*qp2
)
1308 qp1
= isl_qpolynomial_cow(qp1
);
1313 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1314 return isl_qpolynomial_add(qp2
, qp1
);
1316 isl_assert(qp1
->dim
->ctx
, isl_dim_equal(qp1
->dim
, qp2
->dim
), goto error
);
1317 if (!compatible_divs(qp1
->div
, qp2
->div
))
1318 return with_merged_divs(isl_qpolynomial_add
, qp1
, qp2
);
1320 qp1
->upoly
= isl_upoly_sum(qp1
->upoly
, isl_upoly_copy(qp2
->upoly
));
1324 isl_qpolynomial_free(qp2
);
1328 isl_qpolynomial_free(qp1
);
1329 isl_qpolynomial_free(qp2
);
1333 __isl_give isl_qpolynomial
*isl_qpolynomial_add_on_domain(
1334 __isl_keep isl_set
*dom
,
1335 __isl_take isl_qpolynomial
*qp1
,
1336 __isl_take isl_qpolynomial
*qp2
)
1338 return isl_qpolynomial_add(qp1
, qp2
);
1341 __isl_give isl_qpolynomial
*isl_qpolynomial_sub(__isl_take isl_qpolynomial
*qp1
,
1342 __isl_take isl_qpolynomial
*qp2
)
1344 return isl_qpolynomial_add(qp1
, isl_qpolynomial_neg(qp2
));
1347 __isl_give isl_qpolynomial
*isl_qpolynomial_neg(__isl_take isl_qpolynomial
*qp
)
1349 qp
= isl_qpolynomial_cow(qp
);
1354 qp
->upoly
= isl_upoly_neg(qp
->upoly
);
1360 isl_qpolynomial_free(qp
);
1364 __isl_give isl_qpolynomial
*isl_qpolynomial_mul(__isl_take isl_qpolynomial
*qp1
,
1365 __isl_take isl_qpolynomial
*qp2
)
1367 qp1
= isl_qpolynomial_cow(qp1
);
1372 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1373 return isl_qpolynomial_mul(qp2
, qp1
);
1375 isl_assert(qp1
->dim
->ctx
, isl_dim_equal(qp1
->dim
, qp2
->dim
), goto error
);
1376 if (!compatible_divs(qp1
->div
, qp2
->div
))
1377 return with_merged_divs(isl_qpolynomial_mul
, qp1
, qp2
);
1379 qp1
->upoly
= isl_upoly_mul(qp1
->upoly
, isl_upoly_copy(qp2
->upoly
));
1383 isl_qpolynomial_free(qp2
);
1387 isl_qpolynomial_free(qp1
);
1388 isl_qpolynomial_free(qp2
);
1392 __isl_give isl_qpolynomial
*isl_qpolynomial_zero(__isl_take isl_dim
*dim
)
1394 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
1397 __isl_give isl_qpolynomial
*isl_qpolynomial_one(__isl_take isl_dim
*dim
)
1399 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_one(dim
->ctx
));
1402 __isl_give isl_qpolynomial
*isl_qpolynomial_infty(__isl_take isl_dim
*dim
)
1404 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_infty(dim
->ctx
));
1407 __isl_give isl_qpolynomial
*isl_qpolynomial_neginfty(__isl_take isl_dim
*dim
)
1409 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_neginfty(dim
->ctx
));
1412 __isl_give isl_qpolynomial
*isl_qpolynomial_nan(__isl_take isl_dim
*dim
)
1414 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_nan(dim
->ctx
));
1417 __isl_give isl_qpolynomial
*isl_qpolynomial_cst(__isl_take isl_dim
*dim
,
1420 struct isl_qpolynomial
*qp
;
1421 struct isl_upoly_cst
*cst
;
1423 qp
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
1427 cst
= isl_upoly_as_cst(qp
->upoly
);
1428 isl_int_set(cst
->n
, v
);
1433 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial
*qp
,
1434 isl_int
*n
, isl_int
*d
)
1436 struct isl_upoly_cst
*cst
;
1441 if (!isl_upoly_is_cst(qp
->upoly
))
1444 cst
= isl_upoly_as_cst(qp
->upoly
);
1449 isl_int_set(*n
, cst
->n
);
1451 isl_int_set(*d
, cst
->d
);
1456 int isl_upoly_is_affine(__isl_keep
struct isl_upoly
*up
)
1459 struct isl_upoly_rec
*rec
;
1467 rec
= isl_upoly_as_rec(up
);
1474 isl_assert(up
->ctx
, rec
->n
> 1, return -1);
1476 is_cst
= isl_upoly_is_cst(rec
->p
[1]);
1482 return isl_upoly_is_affine(rec
->p
[0]);
1485 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial
*qp
)
1490 if (qp
->div
->n_row
> 0)
1493 return isl_upoly_is_affine(qp
->upoly
);
1496 static void update_coeff(__isl_keep isl_vec
*aff
,
1497 __isl_keep
struct isl_upoly_cst
*cst
, int pos
)
1502 if (isl_int_is_zero(cst
->n
))
1507 isl_int_gcd(gcd
, cst
->d
, aff
->el
[0]);
1508 isl_int_divexact(f
, cst
->d
, gcd
);
1509 isl_int_divexact(gcd
, aff
->el
[0], gcd
);
1510 isl_seq_scale(aff
->el
, aff
->el
, f
, aff
->size
);
1511 isl_int_mul(aff
->el
[1 + pos
], gcd
, cst
->n
);
1516 int isl_upoly_update_affine(__isl_keep
struct isl_upoly
*up
,
1517 __isl_keep isl_vec
*aff
)
1519 struct isl_upoly_cst
*cst
;
1520 struct isl_upoly_rec
*rec
;
1526 struct isl_upoly_cst
*cst
;
1528 cst
= isl_upoly_as_cst(up
);
1531 update_coeff(aff
, cst
, 0);
1535 rec
= isl_upoly_as_rec(up
);
1538 isl_assert(up
->ctx
, rec
->n
== 2, return -1);
1540 cst
= isl_upoly_as_cst(rec
->p
[1]);
1543 update_coeff(aff
, cst
, 1 + up
->var
);
1545 return isl_upoly_update_affine(rec
->p
[0], aff
);
1548 __isl_give isl_vec
*isl_qpolynomial_extract_affine(
1549 __isl_keep isl_qpolynomial
*qp
)
1557 isl_assert(qp
->div
->ctx
, qp
->div
->n_row
== 0, return NULL
);
1558 d
= isl_dim_total(qp
->dim
);
1559 aff
= isl_vec_alloc(qp
->div
->ctx
, 2 + d
);
1563 isl_seq_clr(aff
->el
+ 1, 1 + d
);
1564 isl_int_set_si(aff
->el
[0], 1);
1566 if (isl_upoly_update_affine(qp
->upoly
, aff
) < 0)
1575 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial
*qp1
,
1576 __isl_keep isl_qpolynomial
*qp2
)
1581 return isl_upoly_is_equal(qp1
->upoly
, qp2
->upoly
);
1584 static void upoly_update_den(__isl_keep
struct isl_upoly
*up
, isl_int
*d
)
1587 struct isl_upoly_rec
*rec
;
1589 if (isl_upoly_is_cst(up
)) {
1590 struct isl_upoly_cst
*cst
;
1591 cst
= isl_upoly_as_cst(up
);
1594 isl_int_lcm(*d
, *d
, cst
->d
);
1598 rec
= isl_upoly_as_rec(up
);
1602 for (i
= 0; i
< rec
->n
; ++i
)
1603 upoly_update_den(rec
->p
[i
], d
);
1606 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial
*qp
, isl_int
*d
)
1608 isl_int_set_si(*d
, 1);
1611 upoly_update_den(qp
->upoly
, d
);
1614 __isl_give isl_qpolynomial
*isl_qpolynomial_pow(__isl_take isl_dim
*dim
,
1617 struct isl_ctx
*ctx
;
1624 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_pow(ctx
, pos
, power
));
1627 __isl_give isl_qpolynomial
*isl_qpolynomial_var(__isl_take isl_dim
*dim
,
1628 enum isl_dim_type type
, unsigned pos
)
1633 isl_assert(dim
->ctx
, isl_dim_size(dim
, isl_dim_in
) == 0, goto error
);
1634 isl_assert(dim
->ctx
, pos
< isl_dim_size(dim
, type
), goto error
);
1636 if (type
== isl_dim_set
)
1637 pos
+= isl_dim_size(dim
, isl_dim_param
);
1639 return isl_qpolynomial_pow(dim
, pos
, 1);
1645 /* Remove common factor of non-constant terms and denominator.
1647 static void normalize_div(__isl_keep isl_qpolynomial
*qp
, int div
)
1649 isl_ctx
*ctx
= qp
->div
->ctx
;
1650 unsigned total
= qp
->div
->n_col
- 2;
1652 isl_seq_gcd(qp
->div
->row
[div
] + 2, total
, &ctx
->normalize_gcd
);
1653 isl_int_gcd(ctx
->normalize_gcd
,
1654 ctx
->normalize_gcd
, qp
->div
->row
[div
][0]);
1655 if (isl_int_is_one(ctx
->normalize_gcd
))
1658 isl_seq_scale_down(qp
->div
->row
[div
] + 2, qp
->div
->row
[div
] + 2,
1659 ctx
->normalize_gcd
, total
);
1660 isl_int_divexact(qp
->div
->row
[div
][0], qp
->div
->row
[div
][0],
1661 ctx
->normalize_gcd
);
1662 isl_int_fdiv_q(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1],
1663 ctx
->normalize_gcd
);
1666 __isl_give isl_qpolynomial
*isl_qpolynomial_div_pow(__isl_take isl_div
*div
,
1669 struct isl_qpolynomial
*qp
= NULL
;
1670 struct isl_upoly_rec
*rec
;
1671 struct isl_upoly_cst
*cst
;
1678 d
= div
->line
- div
->bmap
->div
;
1680 pos
= isl_dim_total(div
->bmap
->dim
) + d
;
1681 rec
= isl_upoly_alloc_rec(div
->ctx
, pos
, 1 + power
);
1682 qp
= isl_qpolynomial_alloc(isl_basic_map_get_dim(div
->bmap
),
1683 div
->bmap
->n_div
, &rec
->up
);
1687 for (i
= 0; i
< div
->bmap
->n_div
; ++i
) {
1688 isl_seq_cpy(qp
->div
->row
[i
], div
->bmap
->div
[i
], qp
->div
->n_col
);
1689 normalize_div(qp
, i
);
1692 for (i
= 0; i
< 1 + power
; ++i
) {
1693 rec
->p
[i
] = isl_upoly_zero(div
->ctx
);
1698 cst
= isl_upoly_as_cst(rec
->p
[power
]);
1699 isl_int_set_si(cst
->n
, 1);
1705 isl_qpolynomial_free(qp
);
1710 __isl_give isl_qpolynomial
*isl_qpolynomial_div(__isl_take isl_div
*div
)
1712 return isl_qpolynomial_div_pow(div
, 1);
1715 __isl_give isl_qpolynomial
*isl_qpolynomial_rat_cst(__isl_take isl_dim
*dim
,
1716 const isl_int n
, const isl_int d
)
1718 struct isl_qpolynomial
*qp
;
1719 struct isl_upoly_cst
*cst
;
1721 qp
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
1725 cst
= isl_upoly_as_cst(qp
->upoly
);
1726 isl_int_set(cst
->n
, n
);
1727 isl_int_set(cst
->d
, d
);
1732 static int up_set_active(__isl_keep
struct isl_upoly
*up
, int *active
, int d
)
1734 struct isl_upoly_rec
*rec
;
1740 if (isl_upoly_is_cst(up
))
1744 active
[up
->var
] = 1;
1746 rec
= isl_upoly_as_rec(up
);
1747 for (i
= 0; i
< rec
->n
; ++i
)
1748 if (up_set_active(rec
->p
[i
], active
, d
) < 0)
1754 static int set_active(__isl_keep isl_qpolynomial
*qp
, int *active
)
1757 int d
= isl_dim_total(qp
->dim
);
1762 for (i
= 0; i
< d
; ++i
)
1763 for (j
= 0; j
< qp
->div
->n_row
; ++j
) {
1764 if (isl_int_is_zero(qp
->div
->row
[j
][2 + i
]))
1770 return up_set_active(qp
->upoly
, active
, d
);
1773 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial
*qp
,
1774 enum isl_dim_type type
, unsigned first
, unsigned n
)
1785 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_dim_size(qp
->dim
, type
),
1787 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
1788 type
== isl_dim_set
, return -1);
1790 active
= isl_calloc_array(set
->ctx
, int, isl_dim_total(qp
->dim
));
1791 if (set_active(qp
, active
) < 0)
1794 if (type
== isl_dim_set
)
1795 first
+= isl_dim_size(qp
->dim
, isl_dim_param
);
1796 for (i
= 0; i
< n
; ++i
)
1797 if (active
[first
+ i
]) {
1810 __isl_give
struct isl_upoly
*isl_upoly_drop(__isl_take
struct isl_upoly
*up
,
1811 unsigned first
, unsigned n
)
1814 struct isl_upoly_rec
*rec
;
1818 if (n
== 0 || up
->var
< 0 || up
->var
< first
)
1820 if (up
->var
< first
+ n
) {
1821 up
= replace_by_constant_term(up
);
1822 return isl_upoly_drop(up
, first
, n
);
1824 up
= isl_upoly_cow(up
);
1828 rec
= isl_upoly_as_rec(up
);
1832 for (i
= 0; i
< rec
->n
; ++i
) {
1833 rec
->p
[i
] = isl_upoly_drop(rec
->p
[i
], first
, n
);
1844 __isl_give isl_qpolynomial
*isl_qpolynomial_set_dim_name(
1845 __isl_take isl_qpolynomial
*qp
,
1846 enum isl_dim_type type
, unsigned pos
, const char *s
)
1848 qp
= isl_qpolynomial_cow(qp
);
1851 qp
->dim
= isl_dim_set_name(qp
->dim
, type
, pos
, s
);
1856 isl_qpolynomial_free(qp
);
1860 __isl_give isl_qpolynomial
*isl_qpolynomial_drop_dims(
1861 __isl_take isl_qpolynomial
*qp
,
1862 enum isl_dim_type type
, unsigned first
, unsigned n
)
1866 if (n
== 0 && !isl_dim_get_tuple_name(qp
->dim
, type
))
1869 qp
= isl_qpolynomial_cow(qp
);
1873 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_dim_size(qp
->dim
, type
),
1875 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
1876 type
== isl_dim_set
, goto error
);
1878 qp
->dim
= isl_dim_drop(qp
->dim
, type
, first
, n
);
1882 if (type
== isl_dim_set
)
1883 first
+= isl_dim_size(qp
->dim
, isl_dim_param
);
1885 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + first
, n
);
1889 qp
->upoly
= isl_upoly_drop(qp
->upoly
, first
, n
);
1895 isl_qpolynomial_free(qp
);
1899 __isl_give
struct isl_upoly
*isl_upoly_subs(__isl_take
struct isl_upoly
*up
,
1900 unsigned first
, unsigned n
, __isl_keep
struct isl_upoly
**subs
)
1903 struct isl_upoly_rec
*rec
;
1904 struct isl_upoly
*base
, *res
;
1909 if (isl_upoly_is_cst(up
))
1912 if (up
->var
< first
)
1915 rec
= isl_upoly_as_rec(up
);
1919 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
1921 if (up
->var
>= first
+ n
)
1922 base
= isl_upoly_pow(up
->ctx
, up
->var
, 1);
1924 base
= isl_upoly_copy(subs
[up
->var
- first
]);
1926 res
= isl_upoly_subs(isl_upoly_copy(rec
->p
[rec
->n
- 1]), first
, n
, subs
);
1927 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1928 struct isl_upoly
*t
;
1929 t
= isl_upoly_subs(isl_upoly_copy(rec
->p
[i
]), first
, n
, subs
);
1930 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
1931 res
= isl_upoly_sum(res
, t
);
1934 isl_upoly_free(base
);
1943 __isl_give
struct isl_upoly
*isl_upoly_from_affine(isl_ctx
*ctx
, isl_int
*f
,
1944 isl_int denom
, unsigned len
)
1947 struct isl_upoly
*up
;
1949 isl_assert(ctx
, len
>= 1, return NULL
);
1951 up
= isl_upoly_rat_cst(ctx
, f
[0], denom
);
1952 for (i
= 0; i
< len
- 1; ++i
) {
1953 struct isl_upoly
*t
;
1954 struct isl_upoly
*c
;
1956 if (isl_int_is_zero(f
[1 + i
]))
1959 c
= isl_upoly_rat_cst(ctx
, f
[1 + i
], denom
);
1960 t
= isl_upoly_pow(ctx
, i
, 1);
1961 t
= isl_upoly_mul(c
, t
);
1962 up
= isl_upoly_sum(up
, t
);
1968 /* Replace the integer division identified by "div" by the polynomial "s".
1969 * The integer division is assumed not to appear in the definition
1970 * of any other integer divisions.
1972 static __isl_give isl_qpolynomial
*substitute_div(
1973 __isl_take isl_qpolynomial
*qp
,
1974 int div
, __isl_take
struct isl_upoly
*s
)
1983 qp
= isl_qpolynomial_cow(qp
);
1987 total
= isl_dim_total(qp
->dim
);
1988 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ div
, 1, &s
);
1992 reordering
= isl_alloc_array(qp
->dim
->ctx
, int, total
+ qp
->div
->n_row
);
1995 for (i
= 0; i
< total
+ div
; ++i
)
1997 for (i
= total
+ div
+ 1; i
< total
+ qp
->div
->n_row
; ++i
)
1998 reordering
[i
] = i
- 1;
1999 qp
->div
= isl_mat_drop_rows(qp
->div
, div
, 1);
2000 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + total
+ div
, 1);
2001 qp
->upoly
= reorder(qp
->upoly
, reordering
);
2004 if (!qp
->upoly
|| !qp
->div
)
2010 isl_qpolynomial_free(qp
);
2015 /* Replace all integer divisions [e/d] that turn out to not actually be integer
2016 * divisions because d is equal to 1 by their definition, i.e., e.
2018 static __isl_give isl_qpolynomial
*substitute_non_divs(
2019 __isl_take isl_qpolynomial
*qp
)
2023 struct isl_upoly
*s
;
2028 total
= isl_dim_total(qp
->dim
);
2029 for (i
= 0; qp
&& i
< qp
->div
->n_row
; ++i
) {
2030 if (!isl_int_is_one(qp
->div
->row
[i
][0]))
2032 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
2033 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
2035 isl_seq_combine(qp
->div
->row
[j
] + 1,
2036 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
2037 qp
->div
->row
[j
][2 + total
+ i
],
2038 qp
->div
->row
[i
] + 1, 1 + total
+ i
);
2039 isl_int_set_si(qp
->div
->row
[j
][2 + total
+ i
], 0);
2040 normalize_div(qp
, j
);
2042 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
2043 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
2044 qp
= substitute_div(qp
, i
, s
);
2051 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities(
2052 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2058 struct isl_upoly
*up
;
2062 if (eq
->n_eq
== 0) {
2063 isl_basic_set_free(eq
);
2067 qp
= isl_qpolynomial_cow(qp
);
2070 qp
->div
= isl_mat_cow(qp
->div
);
2074 total
= 1 + isl_dim_total(eq
->dim
);
2076 isl_int_init(denom
);
2077 for (i
= 0; i
< eq
->n_eq
; ++i
) {
2078 j
= isl_seq_last_non_zero(eq
->eq
[i
], total
+ n_div
);
2079 if (j
< 0 || j
== 0 || j
>= total
)
2082 for (k
= 0; k
< qp
->div
->n_row
; ++k
) {
2083 if (isl_int_is_zero(qp
->div
->row
[k
][1 + j
]))
2085 isl_seq_elim(qp
->div
->row
[k
] + 1, eq
->eq
[i
], j
, total
,
2086 &qp
->div
->row
[k
][0]);
2087 normalize_div(qp
, k
);
2090 if (isl_int_is_pos(eq
->eq
[i
][j
]))
2091 isl_seq_neg(eq
->eq
[i
], eq
->eq
[i
], total
);
2092 isl_int_abs(denom
, eq
->eq
[i
][j
]);
2093 isl_int_set_si(eq
->eq
[i
][j
], 0);
2095 up
= isl_upoly_from_affine(qp
->dim
->ctx
,
2096 eq
->eq
[i
], denom
, total
);
2097 qp
->upoly
= isl_upoly_subs(qp
->upoly
, j
- 1, 1, &up
);
2100 isl_int_clear(denom
);
2105 isl_basic_set_free(eq
);
2107 qp
= substitute_non_divs(qp
);
2112 isl_basic_set_free(eq
);
2113 isl_qpolynomial_free(qp
);
2117 static __isl_give isl_basic_set
*add_div_constraints(
2118 __isl_take isl_basic_set
*bset
, __isl_take isl_mat
*div
)
2126 bset
= isl_basic_set_extend_constraints(bset
, 0, 2 * div
->n_row
);
2129 total
= isl_basic_set_total_dim(bset
);
2130 for (i
= 0; i
< div
->n_row
; ++i
)
2131 if (isl_basic_set_add_div_constraints_var(bset
,
2132 total
- div
->n_row
+ i
, div
->row
[i
]) < 0)
2139 isl_basic_set_free(bset
);
2143 /* Look for equalities among the variables shared by context and qp
2144 * and the integer divisions of qp, if any.
2145 * The equalities are then used to eliminate variables and/or integer
2146 * divisions from qp.
2148 __isl_give isl_qpolynomial
*isl_qpolynomial_gist(
2149 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
2155 if (qp
->div
->n_row
> 0) {
2156 isl_basic_set
*bset
;
2157 context
= isl_set_add_dims(context
, isl_dim_set
,
2159 bset
= isl_basic_set_universe(isl_set_get_dim(context
));
2160 bset
= add_div_constraints(bset
, isl_mat_copy(qp
->div
));
2161 context
= isl_set_intersect(context
,
2162 isl_set_from_basic_set(bset
));
2165 aff
= isl_set_affine_hull(context
);
2166 return isl_qpolynomial_substitute_equalities(qp
, aff
);
2168 isl_qpolynomial_free(qp
);
2169 isl_set_free(context
);
2174 #define PW isl_pw_qpolynomial
2176 #define EL isl_qpolynomial
2178 #define IS_ZERO is_zero
2182 #include <isl_pw_templ.c>
2185 #define UNION isl_union_pw_qpolynomial
2187 #define PART isl_pw_qpolynomial
2189 #define PARTS pw_qpolynomial
2191 #include <isl_union_templ.c>
2193 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial
*pwqp
)
2201 if (!isl_set_fast_is_universe(pwqp
->p
[0].set
))
2204 return isl_qpolynomial_is_one(pwqp
->p
[0].qp
);
2207 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_mul(
2208 __isl_take isl_pw_qpolynomial
*pwqp1
,
2209 __isl_take isl_pw_qpolynomial
*pwqp2
)
2212 struct isl_pw_qpolynomial
*res
;
2215 if (!pwqp1
|| !pwqp2
)
2218 isl_assert(pwqp1
->dim
->ctx
, isl_dim_equal(pwqp1
->dim
, pwqp2
->dim
),
2221 if (isl_pw_qpolynomial_is_zero(pwqp1
)) {
2222 isl_pw_qpolynomial_free(pwqp2
);
2226 if (isl_pw_qpolynomial_is_zero(pwqp2
)) {
2227 isl_pw_qpolynomial_free(pwqp1
);
2231 if (isl_pw_qpolynomial_is_one(pwqp1
)) {
2232 isl_pw_qpolynomial_free(pwqp1
);
2236 if (isl_pw_qpolynomial_is_one(pwqp2
)) {
2237 isl_pw_qpolynomial_free(pwqp2
);
2241 n
= pwqp1
->n
* pwqp2
->n
;
2242 res
= isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1
->dim
), n
);
2244 for (i
= 0; i
< pwqp1
->n
; ++i
) {
2245 for (j
= 0; j
< pwqp2
->n
; ++j
) {
2246 struct isl_set
*common
;
2247 struct isl_qpolynomial
*prod
;
2248 common
= isl_set_intersect(isl_set_copy(pwqp1
->p
[i
].set
),
2249 isl_set_copy(pwqp2
->p
[j
].set
));
2250 if (isl_set_fast_is_empty(common
)) {
2251 isl_set_free(common
);
2255 prod
= isl_qpolynomial_mul(
2256 isl_qpolynomial_copy(pwqp1
->p
[i
].qp
),
2257 isl_qpolynomial_copy(pwqp2
->p
[j
].qp
));
2259 res
= isl_pw_qpolynomial_add_piece(res
, common
, prod
);
2263 isl_pw_qpolynomial_free(pwqp1
);
2264 isl_pw_qpolynomial_free(pwqp2
);
2268 isl_pw_qpolynomial_free(pwqp1
);
2269 isl_pw_qpolynomial_free(pwqp2
);
2273 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_neg(
2274 __isl_take isl_pw_qpolynomial
*pwqp
)
2281 if (isl_pw_qpolynomial_is_zero(pwqp
))
2284 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
2288 for (i
= 0; i
< pwqp
->n
; ++i
) {
2289 pwqp
->p
[i
].qp
= isl_qpolynomial_neg(pwqp
->p
[i
].qp
);
2296 isl_pw_qpolynomial_free(pwqp
);
2300 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_sub(
2301 __isl_take isl_pw_qpolynomial
*pwqp1
,
2302 __isl_take isl_pw_qpolynomial
*pwqp2
)
2304 return isl_pw_qpolynomial_add(pwqp1
, isl_pw_qpolynomial_neg(pwqp2
));
2307 __isl_give
struct isl_upoly
*isl_upoly_eval(
2308 __isl_take
struct isl_upoly
*up
, __isl_take isl_vec
*vec
)
2311 struct isl_upoly_rec
*rec
;
2312 struct isl_upoly
*res
;
2313 struct isl_upoly
*base
;
2315 if (isl_upoly_is_cst(up
)) {
2320 rec
= isl_upoly_as_rec(up
);
2324 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
2326 base
= isl_upoly_rat_cst(up
->ctx
, vec
->el
[1 + up
->var
], vec
->el
[0]);
2328 res
= isl_upoly_eval(isl_upoly_copy(rec
->p
[rec
->n
- 1]),
2331 for (i
= rec
->n
- 2; i
>= 0; --i
) {
2332 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
2333 res
= isl_upoly_sum(res
,
2334 isl_upoly_eval(isl_upoly_copy(rec
->p
[i
]),
2335 isl_vec_copy(vec
)));
2338 isl_upoly_free(base
);
2348 __isl_give isl_qpolynomial
*isl_qpolynomial_eval(
2349 __isl_take isl_qpolynomial
*qp
, __isl_take isl_point
*pnt
)
2352 struct isl_upoly
*up
;
2357 isl_assert(pnt
->dim
->ctx
, isl_dim_equal(pnt
->dim
, qp
->dim
), goto error
);
2359 if (qp
->div
->n_row
== 0)
2360 ext
= isl_vec_copy(pnt
->vec
);
2363 unsigned dim
= isl_dim_total(qp
->dim
);
2364 ext
= isl_vec_alloc(qp
->dim
->ctx
, 1 + dim
+ qp
->div
->n_row
);
2368 isl_seq_cpy(ext
->el
, pnt
->vec
->el
, pnt
->vec
->size
);
2369 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2370 isl_seq_inner_product(qp
->div
->row
[i
] + 1, ext
->el
,
2371 1 + dim
+ i
, &ext
->el
[1+dim
+i
]);
2372 isl_int_fdiv_q(ext
->el
[1+dim
+i
], ext
->el
[1+dim
+i
],
2373 qp
->div
->row
[i
][0]);
2377 up
= isl_upoly_eval(isl_upoly_copy(qp
->upoly
), ext
);
2381 dim
= isl_dim_copy(qp
->dim
);
2382 isl_qpolynomial_free(qp
);
2383 isl_point_free(pnt
);
2385 return isl_qpolynomial_alloc(dim
, 0, up
);
2387 isl_qpolynomial_free(qp
);
2388 isl_point_free(pnt
);
2392 int isl_upoly_cmp(__isl_keep
struct isl_upoly_cst
*cst1
,
2393 __isl_keep
struct isl_upoly_cst
*cst2
)
2398 isl_int_mul(t
, cst1
->n
, cst2
->d
);
2399 isl_int_submul(t
, cst2
->n
, cst1
->d
);
2400 cmp
= isl_int_sgn(t
);
2405 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial
*qp1
,
2406 __isl_keep isl_qpolynomial
*qp2
)
2408 struct isl_upoly_cst
*cst1
, *cst2
;
2412 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), return -1);
2413 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), return -1);
2414 if (isl_qpolynomial_is_nan(qp1
))
2416 if (isl_qpolynomial_is_nan(qp2
))
2418 cst1
= isl_upoly_as_cst(qp1
->upoly
);
2419 cst2
= isl_upoly_as_cst(qp2
->upoly
);
2421 return isl_upoly_cmp(cst1
, cst2
) <= 0;
2424 __isl_give isl_qpolynomial
*isl_qpolynomial_min_cst(
2425 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
2427 struct isl_upoly_cst
*cst1
, *cst2
;
2432 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), goto error
);
2433 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), goto error
);
2434 cst1
= isl_upoly_as_cst(qp1
->upoly
);
2435 cst2
= isl_upoly_as_cst(qp2
->upoly
);
2436 cmp
= isl_upoly_cmp(cst1
, cst2
);
2439 isl_qpolynomial_free(qp2
);
2441 isl_qpolynomial_free(qp1
);
2446 isl_qpolynomial_free(qp1
);
2447 isl_qpolynomial_free(qp2
);
2451 __isl_give isl_qpolynomial
*isl_qpolynomial_max_cst(
2452 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
2454 struct isl_upoly_cst
*cst1
, *cst2
;
2459 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), goto error
);
2460 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), goto error
);
2461 cst1
= isl_upoly_as_cst(qp1
->upoly
);
2462 cst2
= isl_upoly_as_cst(qp2
->upoly
);
2463 cmp
= isl_upoly_cmp(cst1
, cst2
);
2466 isl_qpolynomial_free(qp2
);
2468 isl_qpolynomial_free(qp1
);
2473 isl_qpolynomial_free(qp1
);
2474 isl_qpolynomial_free(qp2
);
2478 __isl_give isl_qpolynomial
*isl_qpolynomial_insert_dims(
2479 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
,
2480 unsigned first
, unsigned n
)
2489 qp
= isl_qpolynomial_cow(qp
);
2493 isl_assert(qp
->div
->ctx
, first
<= isl_dim_size(qp
->dim
, type
),
2496 g_pos
= pos(qp
->dim
, type
) + first
;
2498 qp
->div
= isl_mat_insert_cols(qp
->div
, 2 + g_pos
, n
);
2502 total
= qp
->div
->n_col
- 2;
2503 if (total
> g_pos
) {
2505 exp
= isl_alloc_array(qp
->div
->ctx
, int, total
- g_pos
);
2508 for (i
= 0; i
< total
- g_pos
; ++i
)
2510 qp
->upoly
= expand(qp
->upoly
, exp
, g_pos
);
2516 qp
->dim
= isl_dim_insert(qp
->dim
, type
, first
, n
);
2522 isl_qpolynomial_free(qp
);
2526 __isl_give isl_qpolynomial
*isl_qpolynomial_add_dims(
2527 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
, unsigned n
)
2531 pos
= isl_qpolynomial_dim(qp
, type
);
2533 return isl_qpolynomial_insert_dims(qp
, type
, pos
, n
);
2536 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add_dims(
2537 __isl_take isl_pw_qpolynomial
*pwqp
,
2538 enum isl_dim_type type
, unsigned n
)
2542 pos
= isl_pw_qpolynomial_dim(pwqp
, type
);
2544 return isl_pw_qpolynomial_insert_dims(pwqp
, type
, pos
, n
);
2547 static int *reordering_move(isl_ctx
*ctx
,
2548 unsigned len
, unsigned dst
, unsigned src
, unsigned n
)
2553 reordering
= isl_alloc_array(ctx
, int, len
);
2558 for (i
= 0; i
< dst
; ++i
)
2560 for (i
= 0; i
< n
; ++i
)
2561 reordering
[src
+ i
] = dst
+ i
;
2562 for (i
= 0; i
< src
- dst
; ++i
)
2563 reordering
[dst
+ i
] = dst
+ n
+ i
;
2564 for (i
= 0; i
< len
- src
- n
; ++i
)
2565 reordering
[src
+ n
+ i
] = src
+ n
+ i
;
2567 for (i
= 0; i
< src
; ++i
)
2569 for (i
= 0; i
< n
; ++i
)
2570 reordering
[src
+ i
] = dst
+ i
;
2571 for (i
= 0; i
< dst
- src
; ++i
)
2572 reordering
[src
+ n
+ i
] = src
+ i
;
2573 for (i
= 0; i
< len
- dst
- n
; ++i
)
2574 reordering
[dst
+ n
+ i
] = dst
+ n
+ i
;
2580 __isl_give isl_qpolynomial
*isl_qpolynomial_move_dims(
2581 __isl_take isl_qpolynomial
*qp
,
2582 enum isl_dim_type dst_type
, unsigned dst_pos
,
2583 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
2589 qp
= isl_qpolynomial_cow(qp
);
2593 isl_assert(qp
->dim
->ctx
, src_pos
+ n
<= isl_dim_size(qp
->dim
, src_type
),
2596 g_dst_pos
= pos(qp
->dim
, dst_type
) + dst_pos
;
2597 g_src_pos
= pos(qp
->dim
, src_type
) + src_pos
;
2598 if (dst_type
> src_type
)
2601 qp
->div
= isl_mat_move_cols(qp
->div
, 2 + g_dst_pos
, 2 + g_src_pos
, n
);
2608 reordering
= reordering_move(qp
->dim
->ctx
,
2609 qp
->div
->n_col
- 2, g_dst_pos
, g_src_pos
, n
);
2613 qp
->upoly
= reorder(qp
->upoly
, reordering
);
2618 qp
->dim
= isl_dim_move(qp
->dim
, dst_type
, dst_pos
, src_type
, src_pos
, n
);
2624 isl_qpolynomial_free(qp
);
2628 __isl_give isl_qpolynomial
*isl_qpolynomial_from_affine(__isl_take isl_dim
*dim
,
2629 isl_int
*f
, isl_int denom
)
2631 struct isl_upoly
*up
;
2636 up
= isl_upoly_from_affine(dim
->ctx
, f
, denom
, 1 + isl_dim_total(dim
));
2638 return isl_qpolynomial_alloc(dim
, 0, up
);
2641 __isl_give isl_qpolynomial
*isl_qpolynomial_from_constraint(
2642 __isl_take isl_constraint
*c
, enum isl_dim_type type
, unsigned pos
)
2646 struct isl_upoly
*up
;
2647 isl_qpolynomial
*qp
;
2653 isl_int_init(denom
);
2655 isl_constraint_get_coefficient(c
, type
, pos
, &denom
);
2656 isl_constraint_set_coefficient(c
, type
, pos
, c
->ctx
->zero
);
2657 sgn
= isl_int_sgn(denom
);
2658 isl_int_abs(denom
, denom
);
2659 up
= isl_upoly_from_affine(c
->ctx
, c
->line
[0], denom
,
2660 1 + isl_constraint_dim(c
, isl_dim_all
));
2662 isl_int_neg(denom
, denom
);
2663 isl_constraint_set_coefficient(c
, type
, pos
, denom
);
2665 dim
= isl_dim_copy(c
->bmap
->dim
);
2667 isl_int_clear(denom
);
2668 isl_constraint_free(c
);
2670 qp
= isl_qpolynomial_alloc(dim
, 0, up
);
2672 qp
= isl_qpolynomial_neg(qp
);
2676 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
2677 * in "qp" by subs[i].
2679 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute(
2680 __isl_take isl_qpolynomial
*qp
,
2681 enum isl_dim_type type
, unsigned first
, unsigned n
,
2682 __isl_keep isl_qpolynomial
**subs
)
2685 struct isl_upoly
**ups
;
2690 qp
= isl_qpolynomial_cow(qp
);
2693 for (i
= 0; i
< n
; ++i
)
2697 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_dim_size(qp
->dim
, type
),
2700 for (i
= 0; i
< n
; ++i
)
2701 isl_assert(qp
->dim
->ctx
, isl_dim_equal(qp
->dim
, subs
[i
]->dim
),
2704 isl_assert(qp
->dim
->ctx
, qp
->div
->n_row
== 0, goto error
);
2705 for (i
= 0; i
< n
; ++i
)
2706 isl_assert(qp
->dim
->ctx
, subs
[i
]->div
->n_row
== 0, goto error
);
2708 first
+= pos(qp
->dim
, type
);
2710 ups
= isl_alloc_array(qp
->dim
->ctx
, struct isl_upoly
*, n
);
2713 for (i
= 0; i
< n
; ++i
)
2714 ups
[i
] = subs
[i
]->upoly
;
2716 qp
->upoly
= isl_upoly_subs(qp
->upoly
, first
, n
, ups
);
2725 isl_qpolynomial_free(qp
);
2729 /* Extend "bset" with extra set dimensions for each integer division
2730 * in "qp" and then call "fn" with the extended bset and the polynomial
2731 * that results from replacing each of the integer divisions by the
2732 * corresponding extra set dimension.
2734 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial
*qp
,
2735 __isl_keep isl_basic_set
*bset
,
2736 int (*fn
)(__isl_take isl_basic_set
*bset
,
2737 __isl_take isl_qpolynomial
*poly
, void *user
), void *user
)
2741 isl_qpolynomial
*poly
;
2745 if (qp
->div
->n_row
== 0)
2746 return fn(isl_basic_set_copy(bset
), isl_qpolynomial_copy(qp
),
2749 div
= isl_mat_copy(qp
->div
);
2750 dim
= isl_dim_copy(qp
->dim
);
2751 dim
= isl_dim_add(dim
, isl_dim_set
, qp
->div
->n_row
);
2752 poly
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_copy(qp
->upoly
));
2753 bset
= isl_basic_set_copy(bset
);
2754 bset
= isl_basic_set_add(bset
, isl_dim_set
, qp
->div
->n_row
);
2755 bset
= add_div_constraints(bset
, div
);
2757 return fn(bset
, poly
, user
);
2762 /* Return total degree in variables first (inclusive) up to last (exclusive).
2764 int isl_upoly_degree(__isl_keep
struct isl_upoly
*up
, int first
, int last
)
2768 struct isl_upoly_rec
*rec
;
2772 if (isl_upoly_is_zero(up
))
2774 if (isl_upoly_is_cst(up
) || up
->var
< first
)
2777 rec
= isl_upoly_as_rec(up
);
2781 for (i
= 0; i
< rec
->n
; ++i
) {
2784 if (isl_upoly_is_zero(rec
->p
[i
]))
2786 d
= isl_upoly_degree(rec
->p
[i
], first
, last
);
2796 /* Return total degree in set variables.
2798 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial
*poly
)
2806 ovar
= isl_dim_offset(poly
->dim
, isl_dim_set
);
2807 nvar
= isl_dim_size(poly
->dim
, isl_dim_set
);
2808 return isl_upoly_degree(poly
->upoly
, ovar
, ovar
+ nvar
);
2811 __isl_give
struct isl_upoly
*isl_upoly_coeff(__isl_keep
struct isl_upoly
*up
,
2812 unsigned pos
, int deg
)
2815 struct isl_upoly_rec
*rec
;
2820 if (isl_upoly_is_cst(up
) || up
->var
< pos
) {
2822 return isl_upoly_copy(up
);
2824 return isl_upoly_zero(up
->ctx
);
2827 rec
= isl_upoly_as_rec(up
);
2831 if (up
->var
== pos
) {
2833 return isl_upoly_copy(rec
->p
[deg
]);
2835 return isl_upoly_zero(up
->ctx
);
2838 up
= isl_upoly_copy(up
);
2839 up
= isl_upoly_cow(up
);
2840 rec
= isl_upoly_as_rec(up
);
2844 for (i
= 0; i
< rec
->n
; ++i
) {
2845 struct isl_upoly
*t
;
2846 t
= isl_upoly_coeff(rec
->p
[i
], pos
, deg
);
2849 isl_upoly_free(rec
->p
[i
]);
2859 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
2861 __isl_give isl_qpolynomial
*isl_qpolynomial_coeff(
2862 __isl_keep isl_qpolynomial
*qp
,
2863 enum isl_dim_type type
, unsigned t_pos
, int deg
)
2866 struct isl_upoly
*up
;
2872 isl_assert(qp
->div
->ctx
, t_pos
< isl_dim_size(qp
->dim
, type
),
2875 g_pos
= pos(qp
->dim
, type
) + t_pos
;
2876 up
= isl_upoly_coeff(qp
->upoly
, g_pos
, deg
);
2878 c
= isl_qpolynomial_alloc(isl_dim_copy(qp
->dim
), qp
->div
->n_row
, up
);
2881 isl_mat_free(c
->div
);
2882 c
->div
= isl_mat_copy(qp
->div
);
2887 isl_qpolynomial_free(c
);
2891 /* Homogenize the polynomial in the variables first (inclusive) up to
2892 * last (exclusive) by inserting powers of variable first.
2893 * Variable first is assumed not to appear in the input.
2895 __isl_give
struct isl_upoly
*isl_upoly_homogenize(
2896 __isl_take
struct isl_upoly
*up
, int deg
, int target
,
2897 int first
, int last
)
2900 struct isl_upoly_rec
*rec
;
2904 if (isl_upoly_is_zero(up
))
2908 if (isl_upoly_is_cst(up
) || up
->var
< first
) {
2909 struct isl_upoly
*hom
;
2911 hom
= isl_upoly_pow(up
->ctx
, first
, target
- deg
);
2914 rec
= isl_upoly_as_rec(hom
);
2915 rec
->p
[target
- deg
] = isl_upoly_mul(rec
->p
[target
- deg
], up
);
2920 up
= isl_upoly_cow(up
);
2921 rec
= isl_upoly_as_rec(up
);
2925 for (i
= 0; i
< rec
->n
; ++i
) {
2926 if (isl_upoly_is_zero(rec
->p
[i
]))
2928 rec
->p
[i
] = isl_upoly_homogenize(rec
->p
[i
],
2929 up
->var
< last
? deg
+ i
: i
, target
,
2941 /* Homogenize the polynomial in the set variables by introducing
2942 * powers of an extra set variable at position 0.
2944 __isl_give isl_qpolynomial
*isl_qpolynomial_homogenize(
2945 __isl_take isl_qpolynomial
*poly
)
2949 int deg
= isl_qpolynomial_degree(poly
);
2954 poly
= isl_qpolynomial_insert_dims(poly
, isl_dim_set
, 0, 1);
2955 poly
= isl_qpolynomial_cow(poly
);
2959 ovar
= isl_dim_offset(poly
->dim
, isl_dim_set
);
2960 nvar
= isl_dim_size(poly
->dim
, isl_dim_set
);
2961 poly
->upoly
= isl_upoly_homogenize(poly
->upoly
, 0, deg
,
2968 isl_qpolynomial_free(poly
);
2972 __isl_give isl_term
*isl_term_alloc(__isl_take isl_dim
*dim
,
2973 __isl_take isl_mat
*div
)
2981 n
= isl_dim_total(dim
) + div
->n_row
;
2983 term
= isl_calloc(dim
->ctx
, struct isl_term
,
2984 sizeof(struct isl_term
) + (n
- 1) * sizeof(int));
2991 isl_int_init(term
->n
);
2992 isl_int_init(term
->d
);
3001 __isl_give isl_term
*isl_term_copy(__isl_keep isl_term
*term
)
3010 __isl_give isl_term
*isl_term_dup(__isl_keep isl_term
*term
)
3019 total
= isl_dim_total(term
->dim
) + term
->div
->n_row
;
3021 dup
= isl_term_alloc(isl_dim_copy(term
->dim
), isl_mat_copy(term
->div
));
3025 isl_int_set(dup
->n
, term
->n
);
3026 isl_int_set(dup
->d
, term
->d
);
3028 for (i
= 0; i
< total
; ++i
)
3029 dup
->pow
[i
] = term
->pow
[i
];
3034 __isl_give isl_term
*isl_term_cow(__isl_take isl_term
*term
)
3042 return isl_term_dup(term
);
3045 void isl_term_free(__isl_take isl_term
*term
)
3050 if (--term
->ref
> 0)
3053 isl_dim_free(term
->dim
);
3054 isl_mat_free(term
->div
);
3055 isl_int_clear(term
->n
);
3056 isl_int_clear(term
->d
);
3060 unsigned isl_term_dim(__isl_keep isl_term
*term
, enum isl_dim_type type
)
3068 case isl_dim_out
: return isl_dim_size(term
->dim
, type
);
3069 case isl_dim_div
: return term
->div
->n_row
;
3070 case isl_dim_all
: return isl_dim_total(term
->dim
) + term
->div
->n_row
;
3075 isl_ctx
*isl_term_get_ctx(__isl_keep isl_term
*term
)
3077 return term
? term
->dim
->ctx
: NULL
;
3080 void isl_term_get_num(__isl_keep isl_term
*term
, isl_int
*n
)
3084 isl_int_set(*n
, term
->n
);
3087 void isl_term_get_den(__isl_keep isl_term
*term
, isl_int
*d
)
3091 isl_int_set(*d
, term
->d
);
3094 int isl_term_get_exp(__isl_keep isl_term
*term
,
3095 enum isl_dim_type type
, unsigned pos
)
3100 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, type
), return -1);
3102 if (type
>= isl_dim_set
)
3103 pos
+= isl_dim_size(term
->dim
, isl_dim_param
);
3104 if (type
>= isl_dim_div
)
3105 pos
+= isl_dim_size(term
->dim
, isl_dim_set
);
3107 return term
->pow
[pos
];
3110 __isl_give isl_div
*isl_term_get_div(__isl_keep isl_term
*term
, unsigned pos
)
3112 isl_basic_map
*bmap
;
3119 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, isl_dim_div
),
3122 total
= term
->div
->n_col
- term
->div
->n_row
- 2;
3123 /* No nested divs for now */
3124 isl_assert(term
->dim
->ctx
,
3125 isl_seq_first_non_zero(term
->div
->row
[pos
] + 2 + total
,
3126 term
->div
->n_row
) == -1,
3129 bmap
= isl_basic_map_alloc_dim(isl_dim_copy(term
->dim
), 1, 0, 0);
3130 if ((k
= isl_basic_map_alloc_div(bmap
)) < 0)
3133 isl_seq_cpy(bmap
->div
[k
], term
->div
->row
[pos
], 2 + total
);
3135 return isl_basic_map_div(bmap
, k
);
3137 isl_basic_map_free(bmap
);
3141 __isl_give isl_term
*isl_upoly_foreach_term(__isl_keep
struct isl_upoly
*up
,
3142 int (*fn
)(__isl_take isl_term
*term
, void *user
),
3143 __isl_take isl_term
*term
, void *user
)
3146 struct isl_upoly_rec
*rec
;
3151 if (isl_upoly_is_zero(up
))
3154 isl_assert(up
->ctx
, !isl_upoly_is_nan(up
), goto error
);
3155 isl_assert(up
->ctx
, !isl_upoly_is_infty(up
), goto error
);
3156 isl_assert(up
->ctx
, !isl_upoly_is_neginfty(up
), goto error
);
3158 if (isl_upoly_is_cst(up
)) {
3159 struct isl_upoly_cst
*cst
;
3160 cst
= isl_upoly_as_cst(up
);
3163 term
= isl_term_cow(term
);
3166 isl_int_set(term
->n
, cst
->n
);
3167 isl_int_set(term
->d
, cst
->d
);
3168 if (fn(isl_term_copy(term
), user
) < 0)
3173 rec
= isl_upoly_as_rec(up
);
3177 for (i
= 0; i
< rec
->n
; ++i
) {
3178 term
= isl_term_cow(term
);
3181 term
->pow
[up
->var
] = i
;
3182 term
= isl_upoly_foreach_term(rec
->p
[i
], fn
, term
, user
);
3186 term
->pow
[up
->var
] = 0;
3190 isl_term_free(term
);
3194 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial
*qp
,
3195 int (*fn
)(__isl_take isl_term
*term
, void *user
), void *user
)
3202 term
= isl_term_alloc(isl_dim_copy(qp
->dim
), isl_mat_copy(qp
->div
));
3206 term
= isl_upoly_foreach_term(qp
->upoly
, fn
, term
, user
);
3208 isl_term_free(term
);
3210 return term
? 0 : -1;
3213 __isl_give isl_qpolynomial
*isl_qpolynomial_from_term(__isl_take isl_term
*term
)
3215 struct isl_upoly
*up
;
3216 isl_qpolynomial
*qp
;
3222 n
= isl_dim_total(term
->dim
) + term
->div
->n_row
;
3224 up
= isl_upoly_rat_cst(term
->dim
->ctx
, term
->n
, term
->d
);
3225 for (i
= 0; i
< n
; ++i
) {
3228 up
= isl_upoly_mul(up
,
3229 isl_upoly_pow(term
->dim
->ctx
, i
, term
->pow
[i
]));
3232 qp
= isl_qpolynomial_alloc(isl_dim_copy(term
->dim
), term
->div
->n_row
, up
);
3235 isl_mat_free(qp
->div
);
3236 qp
->div
= isl_mat_copy(term
->div
);
3240 isl_term_free(term
);
3243 isl_qpolynomial_free(qp
);
3244 isl_term_free(term
);
3248 __isl_give isl_qpolynomial
*isl_qpolynomial_lift(__isl_take isl_qpolynomial
*qp
,
3249 __isl_take isl_dim
*dim
)
3258 if (isl_dim_equal(qp
->dim
, dim
)) {
3263 qp
= isl_qpolynomial_cow(qp
);
3267 extra
= isl_dim_size(dim
, isl_dim_set
) -
3268 isl_dim_size(qp
->dim
, isl_dim_set
);
3269 total
= isl_dim_total(qp
->dim
);
3270 if (qp
->div
->n_row
) {
3273 exp
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
3276 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3278 qp
->upoly
= expand(qp
->upoly
, exp
, total
);
3283 qp
->div
= isl_mat_insert_cols(qp
->div
, 2 + total
, extra
);
3286 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3287 isl_seq_clr(qp
->div
->row
[i
] + 2 + total
, extra
);
3289 isl_dim_free(qp
->dim
);
3295 isl_qpolynomial_free(qp
);
3299 /* For each parameter or variable that does not appear in qp,
3300 * first eliminate the variable from all constraints and then set it to zero.
3302 static __isl_give isl_set
*fix_inactive(__isl_take isl_set
*set
,
3303 __isl_keep isl_qpolynomial
*qp
)
3314 d
= isl_dim_total(set
->dim
);
3315 active
= isl_calloc_array(set
->ctx
, int, d
);
3316 if (set_active(qp
, active
) < 0)
3319 for (i
= 0; i
< d
; ++i
)
3328 nparam
= isl_dim_size(set
->dim
, isl_dim_param
);
3329 nvar
= isl_dim_size(set
->dim
, isl_dim_set
);
3330 for (i
= 0; i
< nparam
; ++i
) {
3333 set
= isl_set_eliminate(set
, isl_dim_param
, i
, 1);
3334 set
= isl_set_fix_si(set
, isl_dim_param
, i
, 0);
3336 for (i
= 0; i
< nvar
; ++i
) {
3337 if (active
[nparam
+ i
])
3339 set
= isl_set_eliminate(set
, isl_dim_set
, i
, 1);
3340 set
= isl_set_fix_si(set
, isl_dim_set
, i
, 0);
3352 struct isl_opt_data
{
3353 isl_qpolynomial
*qp
;
3355 isl_qpolynomial
*opt
;
3359 static int opt_fn(__isl_take isl_point
*pnt
, void *user
)
3361 struct isl_opt_data
*data
= (struct isl_opt_data
*)user
;
3362 isl_qpolynomial
*val
;
3364 val
= isl_qpolynomial_eval(isl_qpolynomial_copy(data
->qp
), pnt
);
3368 } else if (data
->max
) {
3369 data
->opt
= isl_qpolynomial_max_cst(data
->opt
, val
);
3371 data
->opt
= isl_qpolynomial_min_cst(data
->opt
, val
);
3377 __isl_give isl_qpolynomial
*isl_qpolynomial_opt_on_domain(
3378 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*set
, int max
)
3380 struct isl_opt_data data
= { NULL
, 1, NULL
, max
};
3385 if (isl_upoly_is_cst(qp
->upoly
)) {
3390 set
= fix_inactive(set
, qp
);
3393 if (isl_set_foreach_point(set
, opt_fn
, &data
) < 0)
3397 data
.opt
= isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp
));
3400 isl_qpolynomial_free(qp
);
3404 isl_qpolynomial_free(qp
);
3405 isl_qpolynomial_free(data
.opt
);
3409 __isl_give isl_qpolynomial
*isl_qpolynomial_morph(__isl_take isl_qpolynomial
*qp
,
3410 __isl_take isl_morph
*morph
)
3415 struct isl_upoly
*up
;
3417 struct isl_upoly
**subs
;
3420 qp
= isl_qpolynomial_cow(qp
);
3425 isl_assert(ctx
, isl_dim_equal(qp
->dim
, morph
->dom
->dim
), goto error
);
3427 n_sub
= morph
->inv
->n_row
- 1;
3428 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
3429 n_sub
+= qp
->div
->n_row
;
3430 subs
= isl_calloc_array(ctx
, struct isl_upoly
*, n_sub
);
3434 for (i
= 0; 1 + i
< morph
->inv
->n_row
; ++i
)
3435 subs
[i
] = isl_upoly_from_affine(ctx
, morph
->inv
->row
[1 + i
],
3436 morph
->inv
->row
[0][0], morph
->inv
->n_col
);
3437 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
3438 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3439 subs
[morph
->inv
->n_row
- 1 + i
] =
3440 isl_upoly_pow(ctx
, morph
->inv
->n_col
- 1 + i
, 1);
3442 qp
->upoly
= isl_upoly_subs(qp
->upoly
, 0, n_sub
, subs
);
3444 for (i
= 0; i
< n_sub
; ++i
)
3445 isl_upoly_free(subs
[i
]);
3448 mat
= isl_mat_diagonal(isl_mat_identity(ctx
, 1), isl_mat_copy(morph
->inv
));
3449 mat
= isl_mat_diagonal(mat
, isl_mat_identity(ctx
, qp
->div
->n_row
));
3450 qp
->div
= isl_mat_product(qp
->div
, mat
);
3451 isl_dim_free(qp
->dim
);
3452 qp
->dim
= isl_dim_copy(morph
->ran
->dim
);
3454 if (!qp
->upoly
|| !qp
->div
|| !qp
->dim
)
3457 isl_morph_free(morph
);
3461 isl_qpolynomial_free(qp
);
3462 isl_morph_free(morph
);
3466 static int neg_entry(void **entry
, void *user
)
3468 isl_pw_qpolynomial
**pwqp
= (isl_pw_qpolynomial
**)entry
;
3470 *pwqp
= isl_pw_qpolynomial_neg(*pwqp
);
3472 return *pwqp
? 0 : -1;
3475 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_neg(
3476 __isl_take isl_union_pw_qpolynomial
*upwqp
)
3478 upwqp
= isl_union_pw_qpolynomial_cow(upwqp
);
3482 if (isl_hash_table_foreach(upwqp
->dim
->ctx
, &upwqp
->table
,
3483 &neg_entry
, NULL
) < 0)
3488 isl_union_pw_qpolynomial_free(upwqp
);
3492 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_sub(
3493 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
3494 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
3496 return isl_union_pw_qpolynomial_add(upwqp1
,
3497 isl_union_pw_qpolynomial_neg(upwqp2
));
3500 static int mul_entry(void **entry
, void *user
)
3502 struct isl_union_pw_qpolynomial_match_bin_data
*data
= user
;
3504 struct isl_hash_table_entry
*entry2
;
3505 isl_pw_qpolynomial
*pwpq
= *entry
;
3508 hash
= isl_dim_get_hash(pwpq
->dim
);
3509 entry2
= isl_hash_table_find(data
->u2
->dim
->ctx
, &data
->u2
->table
,
3510 hash
, &has_dim
, pwpq
->dim
, 0);
3514 pwpq
= isl_pw_qpolynomial_copy(pwpq
);
3515 pwpq
= isl_pw_qpolynomial_mul(pwpq
,
3516 isl_pw_qpolynomial_copy(entry2
->data
));
3518 empty
= isl_pw_qpolynomial_is_zero(pwpq
);
3520 isl_pw_qpolynomial_free(pwpq
);
3524 isl_pw_qpolynomial_free(pwpq
);
3528 data
->res
= isl_union_pw_qpolynomial_add_pw_qpolynomial(data
->res
, pwpq
);
3533 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_mul(
3534 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
3535 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
3537 return match_bin_op(upwqp1
, upwqp2
, &mul_entry
);
3540 /* Reorder the columns of the given div definitions according to the
3543 static __isl_give isl_mat
*reorder_divs(__isl_take isl_mat
*div
,
3544 __isl_take isl_reordering
*r
)
3553 extra
= isl_dim_total(r
->dim
) + div
->n_row
- r
->len
;
3554 mat
= isl_mat_alloc(div
->ctx
, div
->n_row
, div
->n_col
+ extra
);
3558 for (i
= 0; i
< div
->n_row
; ++i
) {
3559 isl_seq_cpy(mat
->row
[i
], div
->row
[i
], 2);
3560 isl_seq_clr(mat
->row
[i
] + 2, mat
->n_col
- 2);
3561 for (j
= 0; j
< r
->len
; ++j
)
3562 isl_int_set(mat
->row
[i
][2 + r
->pos
[j
]],
3563 div
->row
[i
][2 + j
]);
3566 isl_reordering_free(r
);
3570 isl_reordering_free(r
);
3575 /* Reorder the dimension of "qp" according to the given reordering.
3577 __isl_give isl_qpolynomial
*isl_qpolynomial_realign(
3578 __isl_take isl_qpolynomial
*qp
, __isl_take isl_reordering
*r
)
3580 qp
= isl_qpolynomial_cow(qp
);
3584 r
= isl_reordering_extend(r
, qp
->div
->n_row
);
3588 qp
->div
= reorder_divs(qp
->div
, isl_reordering_copy(r
));
3592 qp
->upoly
= reorder(qp
->upoly
, r
->pos
);
3596 qp
= isl_qpolynomial_reset_dim(qp
, isl_dim_copy(r
->dim
));
3598 isl_reordering_free(r
);
3601 isl_qpolynomial_free(qp
);
3602 isl_reordering_free(r
);
3606 struct isl_split_periods_data
{
3608 isl_pw_qpolynomial
*res
;
3611 /* Create a slice where the integer division "div" has the fixed value "v".
3612 * In particular, if "div" refers to floor(f/m), then create a slice
3614 * m v <= f <= m v + (m - 1)
3619 * -f + m v + (m - 1) >= 0
3621 static __isl_give isl_set
*set_div_slice(__isl_take isl_dim
*dim
,
3622 __isl_keep isl_qpolynomial
*qp
, int div
, isl_int v
)
3625 isl_basic_set
*bset
= NULL
;
3631 total
= isl_dim_total(dim
);
3632 bset
= isl_basic_set_alloc_dim(isl_dim_copy(dim
), 0, 0, 2);
3634 k
= isl_basic_set_alloc_inequality(bset
);
3637 isl_seq_cpy(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
3638 isl_int_submul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
3640 k
= isl_basic_set_alloc_inequality(bset
);
3643 isl_seq_neg(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
3644 isl_int_addmul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
3645 isl_int_add(bset
->ineq
[k
][0], bset
->ineq
[k
][0], qp
->div
->row
[div
][0]);
3646 isl_int_sub_ui(bset
->ineq
[k
][0], bset
->ineq
[k
][0], 1);
3649 return isl_set_from_basic_set(bset
);
3651 isl_basic_set_free(bset
);
3656 static int split_periods(__isl_take isl_set
*set
,
3657 __isl_take isl_qpolynomial
*qp
, void *user
);
3659 /* Create a slice of the domain "set" such that integer division "div"
3660 * has the fixed value "v" and add the results to data->res,
3661 * replacing the integer division by "v" in "qp".
3663 static int set_div(__isl_take isl_set
*set
,
3664 __isl_take isl_qpolynomial
*qp
, int div
, isl_int v
,
3665 struct isl_split_periods_data
*data
)
3670 struct isl_upoly
*cst
;
3672 slice
= set_div_slice(isl_set_get_dim(set
), qp
, div
, v
);
3673 set
= isl_set_intersect(set
, slice
);
3678 total
= isl_dim_total(qp
->dim
);
3680 for (i
= div
+ 1; i
< qp
->div
->n_row
; ++i
) {
3681 if (isl_int_is_zero(qp
->div
->row
[i
][2 + total
+ div
]))
3683 isl_int_addmul(qp
->div
->row
[i
][1],
3684 qp
->div
->row
[i
][2 + total
+ div
], v
);
3685 isl_int_set_si(qp
->div
->row
[i
][2 + total
+ div
], 0);
3688 cst
= isl_upoly_rat_cst(qp
->dim
->ctx
, v
, qp
->dim
->ctx
->one
);
3689 qp
= substitute_div(qp
, div
, cst
);
3691 return split_periods(set
, qp
, data
);
3694 isl_qpolynomial_free(qp
);
3698 /* Split the domain "set" such that integer division "div"
3699 * has a fixed value (ranging from "min" to "max") on each slice
3700 * and add the results to data->res.
3702 static int split_div(__isl_take isl_set
*set
,
3703 __isl_take isl_qpolynomial
*qp
, int div
, isl_int min
, isl_int max
,
3704 struct isl_split_periods_data
*data
)
3706 for (; isl_int_le(min
, max
); isl_int_add_ui(min
, min
, 1)) {
3707 isl_set
*set_i
= isl_set_copy(set
);
3708 isl_qpolynomial
*qp_i
= isl_qpolynomial_copy(qp
);
3710 if (set_div(set_i
, qp_i
, div
, min
, data
) < 0)
3714 isl_qpolynomial_free(qp
);
3718 isl_qpolynomial_free(qp
);
3722 /* If "qp" refers to any integer division
3723 * that can only attain "max_periods" distinct values on "set"
3724 * then split the domain along those distinct values.
3725 * Add the results (or the original if no splitting occurs)
3728 static int split_periods(__isl_take isl_set
*set
,
3729 __isl_take isl_qpolynomial
*qp
, void *user
)
3732 isl_pw_qpolynomial
*pwqp
;
3733 struct isl_split_periods_data
*data
;
3738 data
= (struct isl_split_periods_data
*)user
;
3743 if (qp
->div
->n_row
== 0) {
3744 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
3745 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
3751 total
= isl_dim_total(qp
->dim
);
3752 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
3753 enum isl_lp_result lp_res
;
3755 if (isl_seq_first_non_zero(qp
->div
->row
[i
] + 2 + total
,
3756 qp
->div
->n_row
) != -1)
3759 lp_res
= isl_set_solve_lp(set
, 0, qp
->div
->row
[i
] + 1,
3760 set
->ctx
->one
, &min
, NULL
, NULL
);
3761 if (lp_res
== isl_lp_error
)
3763 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
3765 isl_int_fdiv_q(min
, min
, qp
->div
->row
[i
][0]);
3767 lp_res
= isl_set_solve_lp(set
, 1, qp
->div
->row
[i
] + 1,
3768 set
->ctx
->one
, &max
, NULL
, NULL
);
3769 if (lp_res
== isl_lp_error
)
3771 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
3773 isl_int_fdiv_q(max
, max
, qp
->div
->row
[i
][0]);
3775 isl_int_sub(max
, max
, min
);
3776 if (isl_int_cmp_si(max
, data
->max_periods
) < 0) {
3777 isl_int_add(max
, max
, min
);
3782 if (i
< qp
->div
->n_row
) {
3783 r
= split_div(set
, qp
, i
, min
, max
, data
);
3785 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
3786 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
3798 isl_qpolynomial_free(qp
);
3802 /* If any quasi-polynomial in pwqp refers to any integer division
3803 * that can only attain "max_periods" distinct values on its domain
3804 * then split the domain along those distinct values.
3806 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_split_periods(
3807 __isl_take isl_pw_qpolynomial
*pwqp
, int max_periods
)
3809 struct isl_split_periods_data data
;
3811 data
.max_periods
= max_periods
;
3812 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp
));
3814 if (isl_pw_qpolynomial_foreach_piece(pwqp
, &split_periods
, &data
) < 0)
3817 isl_pw_qpolynomial_free(pwqp
);
3821 isl_pw_qpolynomial_free(data
.res
);
3822 isl_pw_qpolynomial_free(pwqp
);
3826 /* Construct a piecewise quasipolynomial that is constant on the given
3827 * domain. In particular, it is
3830 * infinity if cst == -1
3832 static __isl_give isl_pw_qpolynomial
*constant_on_domain(
3833 __isl_take isl_basic_set
*bset
, int cst
)
3836 isl_qpolynomial
*qp
;
3841 bset
= isl_basic_map_domain(isl_basic_map_from_range(bset
));
3842 dim
= isl_basic_set_get_dim(bset
);
3844 qp
= isl_qpolynomial_infty(dim
);
3846 qp
= isl_qpolynomial_zero(dim
);
3848 qp
= isl_qpolynomial_one(dim
);
3849 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset
), qp
);
3852 /* Factor bset, call fn on each of the factors and return the product.
3854 * If no factors can be found, simply call fn on the input.
3855 * Otherwise, construct the factors based on the factorizer,
3856 * call fn on each factor and compute the product.
3858 static __isl_give isl_pw_qpolynomial
*compressed_multiplicative_call(
3859 __isl_take isl_basic_set
*bset
,
3860 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
3866 isl_qpolynomial
*qp
;
3867 isl_pw_qpolynomial
*pwqp
;
3871 f
= isl_basic_set_factorizer(bset
);
3874 if (f
->n_group
== 0) {
3875 isl_factorizer_free(f
);
3879 nparam
= isl_basic_set_dim(bset
, isl_dim_param
);
3880 nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
3882 dim
= isl_basic_set_get_dim(bset
);
3883 dim
= isl_dim_domain(dim
);
3884 set
= isl_set_universe(isl_dim_copy(dim
));
3885 qp
= isl_qpolynomial_one(dim
);
3886 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
3888 bset
= isl_morph_basic_set(isl_morph_copy(f
->morph
), bset
);
3890 for (i
= 0, n
= 0; i
< f
->n_group
; ++i
) {
3891 isl_basic_set
*bset_i
;
3892 isl_pw_qpolynomial
*pwqp_i
;
3894 bset_i
= isl_basic_set_copy(bset
);
3895 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
3896 nparam
+ n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
3897 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
3899 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
,
3900 n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
3901 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
, 0, n
);
3903 pwqp_i
= fn(bset_i
);
3904 pwqp
= isl_pw_qpolynomial_mul(pwqp
, pwqp_i
);
3909 isl_basic_set_free(bset
);
3910 isl_factorizer_free(f
);
3914 isl_basic_set_free(bset
);
3918 /* Factor bset, call fn on each of the factors and return the product.
3919 * The function is assumed to evaluate to zero on empty domains,
3920 * to one on zero-dimensional domains and to infinity on unbounded domains
3921 * and will not be called explicitly on zero-dimensional or unbounded domains.
3923 * We first check for some special cases and remove all equalities.
3924 * Then we hand over control to compressed_multiplicative_call.
3926 __isl_give isl_pw_qpolynomial
*isl_basic_set_multiplicative_call(
3927 __isl_take isl_basic_set
*bset
,
3928 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
3932 isl_pw_qpolynomial
*pwqp
;
3933 unsigned orig_nvar
, final_nvar
;
3938 if (isl_basic_set_fast_is_empty(bset
))
3939 return constant_on_domain(bset
, 0);
3941 orig_nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
3944 return constant_on_domain(bset
, 1);
3946 bounded
= isl_basic_set_is_bounded(bset
);
3950 return constant_on_domain(bset
, -1);
3952 if (bset
->n_eq
== 0)
3953 return compressed_multiplicative_call(bset
, fn
);
3955 morph
= isl_basic_set_full_compression(bset
);
3956 bset
= isl_morph_basic_set(isl_morph_copy(morph
), bset
);
3958 final_nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
3960 pwqp
= compressed_multiplicative_call(bset
, fn
);
3962 morph
= isl_morph_remove_dom_dims(morph
, isl_dim_set
, 0, orig_nvar
);
3963 morph
= isl_morph_remove_ran_dims(morph
, isl_dim_set
, 0, final_nvar
);
3964 morph
= isl_morph_inverse(morph
);
3966 pwqp
= isl_pw_qpolynomial_morph(pwqp
, morph
);
3970 isl_basic_set_free(bset
);
3974 /* Drop all floors in "qp", turning each integer division [a/m] into
3975 * a rational division a/m. If "down" is set, then the integer division
3976 * is replaces by (a-(m-1))/m instead.
3978 static __isl_give isl_qpolynomial
*qp_drop_floors(
3979 __isl_take isl_qpolynomial
*qp
, int down
)
3982 struct isl_upoly
*s
;
3986 if (qp
->div
->n_row
== 0)
3989 qp
= isl_qpolynomial_cow(qp
);
3993 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
3995 isl_int_sub(qp
->div
->row
[i
][1],
3996 qp
->div
->row
[i
][1], qp
->div
->row
[i
][0]);
3997 isl_int_add_ui(qp
->div
->row
[i
][1],
3998 qp
->div
->row
[i
][1], 1);
4000 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
4001 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
4002 qp
= substitute_div(qp
, i
, s
);
4010 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4011 * a rational division a/m.
4013 static __isl_give isl_pw_qpolynomial
*pwqp_drop_floors(
4014 __isl_take isl_pw_qpolynomial
*pwqp
)
4021 if (isl_pw_qpolynomial_is_zero(pwqp
))
4024 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
4028 for (i
= 0; i
< pwqp
->n
; ++i
) {
4029 pwqp
->p
[i
].qp
= qp_drop_floors(pwqp
->p
[i
].qp
, 0);
4036 isl_pw_qpolynomial_free(pwqp
);
4040 /* Adjust all the integer divisions in "qp" such that they are at least
4041 * one over the given orthant (identified by "signs"). This ensures
4042 * that they will still be non-negative even after subtracting (m-1)/m.
4044 * In particular, f is replaced by f' + v, changing f = [a/m]
4045 * to f' = [(a - m v)/m].
4046 * If the constant term k in a is smaller than m,
4047 * the constant term of v is set to floor(k/m) - 1.
4048 * For any other term, if the coefficient c and the variable x have
4049 * the same sign, then no changes are needed.
4050 * Otherwise, if the variable is positive (and c is negative),
4051 * then the coefficient of x in v is set to floor(c/m).
4052 * If the variable is negative (and c is positive),
4053 * then the coefficient of x in v is set to ceil(c/m).
4055 static __isl_give isl_qpolynomial
*make_divs_pos(__isl_take isl_qpolynomial
*qp
,
4061 struct isl_upoly
*s
;
4063 qp
= isl_qpolynomial_cow(qp
);
4066 qp
->div
= isl_mat_cow(qp
->div
);
4070 total
= isl_dim_total(qp
->dim
);
4071 v
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
4073 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4074 isl_int
*row
= qp
->div
->row
[i
];
4078 if (isl_int_lt(row
[1], row
[0])) {
4079 isl_int_fdiv_q(v
->el
[0], row
[1], row
[0]);
4080 isl_int_sub_ui(v
->el
[0], v
->el
[0], 1);
4081 isl_int_submul(row
[1], row
[0], v
->el
[0]);
4083 for (j
= 0; j
< total
; ++j
) {
4084 if (isl_int_sgn(row
[2 + j
]) * signs
[j
] >= 0)
4087 isl_int_cdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4089 isl_int_fdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4090 isl_int_submul(row
[2 + j
], row
[0], v
->el
[1 + j
]);
4092 for (j
= 0; j
< i
; ++j
) {
4093 if (isl_int_sgn(row
[2 + total
+ j
]) >= 0)
4095 isl_int_fdiv_q(v
->el
[1 + total
+ j
],
4096 row
[2 + total
+ j
], row
[0]);
4097 isl_int_submul(row
[2 + total
+ j
],
4098 row
[0], v
->el
[1 + total
+ j
]);
4100 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
4101 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
4103 isl_seq_combine(qp
->div
->row
[j
] + 1,
4104 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
4105 qp
->div
->row
[j
][2 + total
+ i
], v
->el
, v
->size
);
4107 isl_int_set_si(v
->el
[1 + total
+ i
], 1);
4108 s
= isl_upoly_from_affine(qp
->dim
->ctx
, v
->el
,
4109 qp
->div
->ctx
->one
, v
->size
);
4110 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ i
, 1, &s
);
4120 isl_qpolynomial_free(qp
);
4124 struct isl_to_poly_data
{
4126 isl_pw_qpolynomial
*res
;
4127 isl_qpolynomial
*qp
;
4130 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4131 * We first make all integer divisions positive and then split the
4132 * quasipolynomials into terms with sign data->sign (the direction
4133 * of the requested approximation) and terms with the opposite sign.
4134 * In the first set of terms, each integer division [a/m] is
4135 * overapproximated by a/m, while in the second it is underapproximated
4138 static int to_polynomial_on_orthant(__isl_take isl_set
*orthant
, int *signs
,
4141 struct isl_to_poly_data
*data
= user
;
4142 isl_pw_qpolynomial
*t
;
4143 isl_qpolynomial
*qp
, *up
, *down
;
4145 qp
= isl_qpolynomial_copy(data
->qp
);
4146 qp
= make_divs_pos(qp
, signs
);
4148 up
= isl_qpolynomial_terms_of_sign(qp
, signs
, data
->sign
);
4149 up
= qp_drop_floors(up
, 0);
4150 down
= isl_qpolynomial_terms_of_sign(qp
, signs
, -data
->sign
);
4151 down
= qp_drop_floors(down
, 1);
4153 isl_qpolynomial_free(qp
);
4154 qp
= isl_qpolynomial_add(up
, down
);
4156 t
= isl_pw_qpolynomial_alloc(orthant
, qp
);
4157 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, t
);
4162 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4163 * the polynomial will be an overapproximation. If "sign" is negative,
4164 * it will be an underapproximation. If "sign" is zero, the approximation
4165 * will lie somewhere in between.
4167 * In particular, is sign == 0, we simply drop the floors, turning
4168 * the integer divisions into rational divisions.
4169 * Otherwise, we split the domains into orthants, make all integer divisions
4170 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4171 * depending on the requested sign and the sign of the term in which
4172 * the integer division appears.
4174 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_to_polynomial(
4175 __isl_take isl_pw_qpolynomial
*pwqp
, int sign
)
4178 struct isl_to_poly_data data
;
4181 return pwqp_drop_floors(pwqp
);
4187 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp
));
4189 for (i
= 0; i
< pwqp
->n
; ++i
) {
4190 if (pwqp
->p
[i
].qp
->div
->n_row
== 0) {
4191 isl_pw_qpolynomial
*t
;
4192 t
= isl_pw_qpolynomial_alloc(
4193 isl_set_copy(pwqp
->p
[i
].set
),
4194 isl_qpolynomial_copy(pwqp
->p
[i
].qp
));
4195 data
.res
= isl_pw_qpolynomial_add_disjoint(data
.res
, t
);
4198 data
.qp
= pwqp
->p
[i
].qp
;
4199 if (isl_set_foreach_orthant(pwqp
->p
[i
].set
,
4200 &to_polynomial_on_orthant
, &data
) < 0)
4204 isl_pw_qpolynomial_free(pwqp
);
4208 isl_pw_qpolynomial_free(pwqp
);
4209 isl_pw_qpolynomial_free(data
.res
);
4213 static int poly_entry(void **entry
, void *user
)
4216 isl_pw_qpolynomial
**pwqp
= (isl_pw_qpolynomial
**)entry
;
4218 *pwqp
= isl_pw_qpolynomial_to_polynomial(*pwqp
, *sign
);
4220 return *pwqp
? 0 : -1;
4223 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_to_polynomial(
4224 __isl_take isl_union_pw_qpolynomial
*upwqp
, int sign
)
4226 upwqp
= isl_union_pw_qpolynomial_cow(upwqp
);
4230 if (isl_hash_table_foreach(upwqp
->dim
->ctx
, &upwqp
->table
,
4231 &poly_entry
, &sign
) < 0)
4236 isl_union_pw_qpolynomial_free(upwqp
);