2 * Copyright 2010 INRIA Saclay
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
7 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
12 #include <isl_ctx_private.h>
13 #include <isl_map_private.h>
14 #include <isl_factorization.h>
17 #include <isl_union_map_private.h>
18 #include <isl_polynomial_private.h>
19 #include <isl_point_private.h>
20 #include <isl_dim_private.h>
21 #include <isl_div_private.h>
22 #include <isl_mat_private.h>
23 #include <isl_range.h>
24 #include <isl_local_space_private.h>
25 #include <isl_aff_private.h>
26 #include <isl_config.h>
28 static unsigned pos(__isl_keep isl_dim
*dim
, enum isl_dim_type type
)
31 case isl_dim_param
: return 0;
32 case isl_dim_in
: return dim
->nparam
;
33 case isl_dim_out
: return dim
->nparam
+ dim
->n_in
;
38 int isl_upoly_is_cst(__isl_keep
struct isl_upoly
*up
)
46 __isl_keep
struct isl_upoly_cst
*isl_upoly_as_cst(__isl_keep
struct isl_upoly
*up
)
51 isl_assert(up
->ctx
, up
->var
< 0, return NULL
);
53 return (struct isl_upoly_cst
*)up
;
56 __isl_keep
struct isl_upoly_rec
*isl_upoly_as_rec(__isl_keep
struct isl_upoly
*up
)
61 isl_assert(up
->ctx
, up
->var
>= 0, return NULL
);
63 return (struct isl_upoly_rec
*)up
;
66 int isl_upoly_is_equal(__isl_keep
struct isl_upoly
*up1
,
67 __isl_keep
struct isl_upoly
*up2
)
70 struct isl_upoly_rec
*rec1
, *rec2
;
76 if (up1
->var
!= up2
->var
)
78 if (isl_upoly_is_cst(up1
)) {
79 struct isl_upoly_cst
*cst1
, *cst2
;
80 cst1
= isl_upoly_as_cst(up1
);
81 cst2
= isl_upoly_as_cst(up2
);
84 return isl_int_eq(cst1
->n
, cst2
->n
) &&
85 isl_int_eq(cst1
->d
, cst2
->d
);
88 rec1
= isl_upoly_as_rec(up1
);
89 rec2
= isl_upoly_as_rec(up2
);
93 if (rec1
->n
!= rec2
->n
)
96 for (i
= 0; i
< rec1
->n
; ++i
) {
97 int eq
= isl_upoly_is_equal(rec1
->p
[i
], rec2
->p
[i
]);
105 int isl_upoly_is_zero(__isl_keep
struct isl_upoly
*up
)
107 struct isl_upoly_cst
*cst
;
111 if (!isl_upoly_is_cst(up
))
114 cst
= isl_upoly_as_cst(up
);
118 return isl_int_is_zero(cst
->n
) && isl_int_is_pos(cst
->d
);
121 int isl_upoly_sgn(__isl_keep
struct isl_upoly
*up
)
123 struct isl_upoly_cst
*cst
;
127 if (!isl_upoly_is_cst(up
))
130 cst
= isl_upoly_as_cst(up
);
134 return isl_int_sgn(cst
->n
);
137 int isl_upoly_is_nan(__isl_keep
struct isl_upoly
*up
)
139 struct isl_upoly_cst
*cst
;
143 if (!isl_upoly_is_cst(up
))
146 cst
= isl_upoly_as_cst(up
);
150 return isl_int_is_zero(cst
->n
) && isl_int_is_zero(cst
->d
);
153 int isl_upoly_is_infty(__isl_keep
struct isl_upoly
*up
)
155 struct isl_upoly_cst
*cst
;
159 if (!isl_upoly_is_cst(up
))
162 cst
= isl_upoly_as_cst(up
);
166 return isl_int_is_pos(cst
->n
) && isl_int_is_zero(cst
->d
);
169 int isl_upoly_is_neginfty(__isl_keep
struct isl_upoly
*up
)
171 struct isl_upoly_cst
*cst
;
175 if (!isl_upoly_is_cst(up
))
178 cst
= isl_upoly_as_cst(up
);
182 return isl_int_is_neg(cst
->n
) && isl_int_is_zero(cst
->d
);
185 int isl_upoly_is_one(__isl_keep
struct isl_upoly
*up
)
187 struct isl_upoly_cst
*cst
;
191 if (!isl_upoly_is_cst(up
))
194 cst
= isl_upoly_as_cst(up
);
198 return isl_int_eq(cst
->n
, cst
->d
) && isl_int_is_pos(cst
->d
);
201 int isl_upoly_is_negone(__isl_keep
struct isl_upoly
*up
)
203 struct isl_upoly_cst
*cst
;
207 if (!isl_upoly_is_cst(up
))
210 cst
= isl_upoly_as_cst(up
);
214 return isl_int_is_negone(cst
->n
) && isl_int_is_one(cst
->d
);
217 __isl_give
struct isl_upoly_cst
*isl_upoly_cst_alloc(struct isl_ctx
*ctx
)
219 struct isl_upoly_cst
*cst
;
221 cst
= isl_alloc_type(ctx
, struct isl_upoly_cst
);
230 isl_int_init(cst
->n
);
231 isl_int_init(cst
->d
);
236 __isl_give
struct isl_upoly
*isl_upoly_zero(struct isl_ctx
*ctx
)
238 struct isl_upoly_cst
*cst
;
240 cst
= isl_upoly_cst_alloc(ctx
);
244 isl_int_set_si(cst
->n
, 0);
245 isl_int_set_si(cst
->d
, 1);
250 __isl_give
struct isl_upoly
*isl_upoly_one(struct isl_ctx
*ctx
)
252 struct isl_upoly_cst
*cst
;
254 cst
= isl_upoly_cst_alloc(ctx
);
258 isl_int_set_si(cst
->n
, 1);
259 isl_int_set_si(cst
->d
, 1);
264 __isl_give
struct isl_upoly
*isl_upoly_infty(struct isl_ctx
*ctx
)
266 struct isl_upoly_cst
*cst
;
268 cst
= isl_upoly_cst_alloc(ctx
);
272 isl_int_set_si(cst
->n
, 1);
273 isl_int_set_si(cst
->d
, 0);
278 __isl_give
struct isl_upoly
*isl_upoly_neginfty(struct isl_ctx
*ctx
)
280 struct isl_upoly_cst
*cst
;
282 cst
= isl_upoly_cst_alloc(ctx
);
286 isl_int_set_si(cst
->n
, -1);
287 isl_int_set_si(cst
->d
, 0);
292 __isl_give
struct isl_upoly
*isl_upoly_nan(struct isl_ctx
*ctx
)
294 struct isl_upoly_cst
*cst
;
296 cst
= isl_upoly_cst_alloc(ctx
);
300 isl_int_set_si(cst
->n
, 0);
301 isl_int_set_si(cst
->d
, 0);
306 __isl_give
struct isl_upoly
*isl_upoly_rat_cst(struct isl_ctx
*ctx
,
307 isl_int n
, isl_int d
)
309 struct isl_upoly_cst
*cst
;
311 cst
= isl_upoly_cst_alloc(ctx
);
315 isl_int_set(cst
->n
, n
);
316 isl_int_set(cst
->d
, d
);
321 __isl_give
struct isl_upoly_rec
*isl_upoly_alloc_rec(struct isl_ctx
*ctx
,
324 struct isl_upoly_rec
*rec
;
326 isl_assert(ctx
, var
>= 0, return NULL
);
327 isl_assert(ctx
, size
>= 0, return NULL
);
328 rec
= isl_calloc(ctx
, struct isl_upoly_rec
,
329 sizeof(struct isl_upoly_rec
) +
330 size
* sizeof(struct isl_upoly
*));
345 __isl_give isl_qpolynomial
*isl_qpolynomial_reset_dim(
346 __isl_take isl_qpolynomial
*qp
, __isl_take isl_dim
*dim
)
348 qp
= isl_qpolynomial_cow(qp
);
352 isl_dim_free(qp
->dim
);
357 isl_qpolynomial_free(qp
);
362 isl_ctx
*isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial
*qp
)
364 return qp
? qp
->dim
->ctx
: NULL
;
367 __isl_give isl_dim
*isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial
*qp
)
369 return qp
? isl_dim_copy(qp
->dim
) : NULL
;
372 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial
*qp
,
373 enum isl_dim_type type
)
375 return qp
? isl_dim_size(qp
->dim
, type
) : 0;
378 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial
*qp
)
380 return qp
? isl_upoly_is_zero(qp
->upoly
) : -1;
383 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial
*qp
)
385 return qp
? isl_upoly_is_one(qp
->upoly
) : -1;
388 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial
*qp
)
390 return qp
? isl_upoly_is_nan(qp
->upoly
) : -1;
393 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial
*qp
)
395 return qp
? isl_upoly_is_infty(qp
->upoly
) : -1;
398 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial
*qp
)
400 return qp
? isl_upoly_is_neginfty(qp
->upoly
) : -1;
403 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial
*qp
)
405 return qp
? isl_upoly_sgn(qp
->upoly
) : 0;
408 static void upoly_free_cst(__isl_take
struct isl_upoly_cst
*cst
)
410 isl_int_clear(cst
->n
);
411 isl_int_clear(cst
->d
);
414 static void upoly_free_rec(__isl_take
struct isl_upoly_rec
*rec
)
418 for (i
= 0; i
< rec
->n
; ++i
)
419 isl_upoly_free(rec
->p
[i
]);
422 __isl_give
struct isl_upoly
*isl_upoly_copy(__isl_keep
struct isl_upoly
*up
)
431 __isl_give
struct isl_upoly
*isl_upoly_dup_cst(__isl_keep
struct isl_upoly
*up
)
433 struct isl_upoly_cst
*cst
;
434 struct isl_upoly_cst
*dup
;
436 cst
= isl_upoly_as_cst(up
);
440 dup
= isl_upoly_as_cst(isl_upoly_zero(up
->ctx
));
443 isl_int_set(dup
->n
, cst
->n
);
444 isl_int_set(dup
->d
, cst
->d
);
449 __isl_give
struct isl_upoly
*isl_upoly_dup_rec(__isl_keep
struct isl_upoly
*up
)
452 struct isl_upoly_rec
*rec
;
453 struct isl_upoly_rec
*dup
;
455 rec
= isl_upoly_as_rec(up
);
459 dup
= isl_upoly_alloc_rec(up
->ctx
, up
->var
, rec
->n
);
463 for (i
= 0; i
< rec
->n
; ++i
) {
464 dup
->p
[i
] = isl_upoly_copy(rec
->p
[i
]);
472 isl_upoly_free(&dup
->up
);
476 __isl_give
struct isl_upoly
*isl_upoly_dup(__isl_keep
struct isl_upoly
*up
)
481 if (isl_upoly_is_cst(up
))
482 return isl_upoly_dup_cst(up
);
484 return isl_upoly_dup_rec(up
);
487 __isl_give
struct isl_upoly
*isl_upoly_cow(__isl_take
struct isl_upoly
*up
)
495 return isl_upoly_dup(up
);
498 void isl_upoly_free(__isl_take
struct isl_upoly
*up
)
507 upoly_free_cst((struct isl_upoly_cst
*)up
);
509 upoly_free_rec((struct isl_upoly_rec
*)up
);
511 isl_ctx_deref(up
->ctx
);
515 static void isl_upoly_cst_reduce(__isl_keep
struct isl_upoly_cst
*cst
)
520 isl_int_gcd(gcd
, cst
->n
, cst
->d
);
521 if (!isl_int_is_zero(gcd
) && !isl_int_is_one(gcd
)) {
522 isl_int_divexact(cst
->n
, cst
->n
, gcd
);
523 isl_int_divexact(cst
->d
, cst
->d
, gcd
);
528 __isl_give
struct isl_upoly
*isl_upoly_sum_cst(__isl_take
struct isl_upoly
*up1
,
529 __isl_take
struct isl_upoly
*up2
)
531 struct isl_upoly_cst
*cst1
;
532 struct isl_upoly_cst
*cst2
;
534 up1
= isl_upoly_cow(up1
);
538 cst1
= isl_upoly_as_cst(up1
);
539 cst2
= isl_upoly_as_cst(up2
);
541 if (isl_int_eq(cst1
->d
, cst2
->d
))
542 isl_int_add(cst1
->n
, cst1
->n
, cst2
->n
);
544 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->d
);
545 isl_int_addmul(cst1
->n
, cst2
->n
, cst1
->d
);
546 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
549 isl_upoly_cst_reduce(cst1
);
559 static __isl_give
struct isl_upoly
*replace_by_zero(
560 __isl_take
struct isl_upoly
*up
)
568 return isl_upoly_zero(ctx
);
571 static __isl_give
struct isl_upoly
*replace_by_constant_term(
572 __isl_take
struct isl_upoly
*up
)
574 struct isl_upoly_rec
*rec
;
575 struct isl_upoly
*cst
;
580 rec
= isl_upoly_as_rec(up
);
583 cst
= isl_upoly_copy(rec
->p
[0]);
591 __isl_give
struct isl_upoly
*isl_upoly_sum(__isl_take
struct isl_upoly
*up1
,
592 __isl_take
struct isl_upoly
*up2
)
595 struct isl_upoly_rec
*rec1
, *rec2
;
600 if (isl_upoly_is_nan(up1
)) {
605 if (isl_upoly_is_nan(up2
)) {
610 if (isl_upoly_is_zero(up1
)) {
615 if (isl_upoly_is_zero(up2
)) {
620 if (up1
->var
< up2
->var
)
621 return isl_upoly_sum(up2
, up1
);
623 if (up2
->var
< up1
->var
) {
624 struct isl_upoly_rec
*rec
;
625 if (isl_upoly_is_infty(up2
) || isl_upoly_is_neginfty(up2
)) {
629 up1
= isl_upoly_cow(up1
);
630 rec
= isl_upoly_as_rec(up1
);
633 rec
->p
[0] = isl_upoly_sum(rec
->p
[0], up2
);
635 up1
= replace_by_constant_term(up1
);
639 if (isl_upoly_is_cst(up1
))
640 return isl_upoly_sum_cst(up1
, up2
);
642 rec1
= isl_upoly_as_rec(up1
);
643 rec2
= isl_upoly_as_rec(up2
);
647 if (rec1
->n
< rec2
->n
)
648 return isl_upoly_sum(up2
, up1
);
650 up1
= isl_upoly_cow(up1
);
651 rec1
= isl_upoly_as_rec(up1
);
655 for (i
= rec2
->n
- 1; i
>= 0; --i
) {
656 rec1
->p
[i
] = isl_upoly_sum(rec1
->p
[i
],
657 isl_upoly_copy(rec2
->p
[i
]));
660 if (i
== rec1
->n
- 1 && isl_upoly_is_zero(rec1
->p
[i
])) {
661 isl_upoly_free(rec1
->p
[i
]);
667 up1
= replace_by_zero(up1
);
668 else if (rec1
->n
== 1)
669 up1
= replace_by_constant_term(up1
);
680 __isl_give
struct isl_upoly
*isl_upoly_cst_add_isl_int(
681 __isl_take
struct isl_upoly
*up
, isl_int v
)
683 struct isl_upoly_cst
*cst
;
685 up
= isl_upoly_cow(up
);
689 cst
= isl_upoly_as_cst(up
);
691 isl_int_addmul(cst
->n
, cst
->d
, v
);
696 __isl_give
struct isl_upoly
*isl_upoly_add_isl_int(
697 __isl_take
struct isl_upoly
*up
, isl_int v
)
699 struct isl_upoly_rec
*rec
;
704 if (isl_upoly_is_cst(up
))
705 return isl_upoly_cst_add_isl_int(up
, v
);
707 up
= isl_upoly_cow(up
);
708 rec
= isl_upoly_as_rec(up
);
712 rec
->p
[0] = isl_upoly_add_isl_int(rec
->p
[0], v
);
722 __isl_give
struct isl_upoly
*isl_upoly_cst_mul_isl_int(
723 __isl_take
struct isl_upoly
*up
, isl_int v
)
725 struct isl_upoly_cst
*cst
;
727 if (isl_upoly_is_zero(up
))
730 up
= isl_upoly_cow(up
);
734 cst
= isl_upoly_as_cst(up
);
736 isl_int_mul(cst
->n
, cst
->n
, v
);
741 __isl_give
struct isl_upoly
*isl_upoly_mul_isl_int(
742 __isl_take
struct isl_upoly
*up
, isl_int v
)
745 struct isl_upoly_rec
*rec
;
750 if (isl_upoly_is_cst(up
))
751 return isl_upoly_cst_mul_isl_int(up
, v
);
753 up
= isl_upoly_cow(up
);
754 rec
= isl_upoly_as_rec(up
);
758 for (i
= 0; i
< rec
->n
; ++i
) {
759 rec
->p
[i
] = isl_upoly_mul_isl_int(rec
->p
[i
], v
);
770 __isl_give
struct isl_upoly
*isl_upoly_mul_cst(__isl_take
struct isl_upoly
*up1
,
771 __isl_take
struct isl_upoly
*up2
)
773 struct isl_upoly_cst
*cst1
;
774 struct isl_upoly_cst
*cst2
;
776 up1
= isl_upoly_cow(up1
);
780 cst1
= isl_upoly_as_cst(up1
);
781 cst2
= isl_upoly_as_cst(up2
);
783 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->n
);
784 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
786 isl_upoly_cst_reduce(cst1
);
796 __isl_give
struct isl_upoly
*isl_upoly_mul_rec(__isl_take
struct isl_upoly
*up1
,
797 __isl_take
struct isl_upoly
*up2
)
799 struct isl_upoly_rec
*rec1
;
800 struct isl_upoly_rec
*rec2
;
801 struct isl_upoly_rec
*res
= NULL
;
805 rec1
= isl_upoly_as_rec(up1
);
806 rec2
= isl_upoly_as_rec(up2
);
809 size
= rec1
->n
+ rec2
->n
- 1;
810 res
= isl_upoly_alloc_rec(up1
->ctx
, up1
->var
, size
);
814 for (i
= 0; i
< rec1
->n
; ++i
) {
815 res
->p
[i
] = isl_upoly_mul(isl_upoly_copy(rec2
->p
[0]),
816 isl_upoly_copy(rec1
->p
[i
]));
821 for (; i
< size
; ++i
) {
822 res
->p
[i
] = isl_upoly_zero(up1
->ctx
);
827 for (i
= 0; i
< rec1
->n
; ++i
) {
828 for (j
= 1; j
< rec2
->n
; ++j
) {
829 struct isl_upoly
*up
;
830 up
= isl_upoly_mul(isl_upoly_copy(rec2
->p
[j
]),
831 isl_upoly_copy(rec1
->p
[i
]));
832 res
->p
[i
+ j
] = isl_upoly_sum(res
->p
[i
+ j
], up
);
845 isl_upoly_free(&res
->up
);
849 __isl_give
struct isl_upoly
*isl_upoly_mul(__isl_take
struct isl_upoly
*up1
,
850 __isl_take
struct isl_upoly
*up2
)
855 if (isl_upoly_is_nan(up1
)) {
860 if (isl_upoly_is_nan(up2
)) {
865 if (isl_upoly_is_zero(up1
)) {
870 if (isl_upoly_is_zero(up2
)) {
875 if (isl_upoly_is_one(up1
)) {
880 if (isl_upoly_is_one(up2
)) {
885 if (up1
->var
< up2
->var
)
886 return isl_upoly_mul(up2
, up1
);
888 if (up2
->var
< up1
->var
) {
890 struct isl_upoly_rec
*rec
;
891 if (isl_upoly_is_infty(up2
) || isl_upoly_is_neginfty(up2
)) {
892 isl_ctx
*ctx
= up1
->ctx
;
895 return isl_upoly_nan(ctx
);
897 up1
= isl_upoly_cow(up1
);
898 rec
= isl_upoly_as_rec(up1
);
902 for (i
= 0; i
< rec
->n
; ++i
) {
903 rec
->p
[i
] = isl_upoly_mul(rec
->p
[i
],
904 isl_upoly_copy(up2
));
912 if (isl_upoly_is_cst(up1
))
913 return isl_upoly_mul_cst(up1
, up2
);
915 return isl_upoly_mul_rec(up1
, up2
);
922 __isl_give
struct isl_upoly
*isl_upoly_pow(__isl_take
struct isl_upoly
*up
,
925 struct isl_upoly
*res
;
933 res
= isl_upoly_copy(up
);
935 res
= isl_upoly_one(up
->ctx
);
937 while (power
>>= 1) {
938 up
= isl_upoly_mul(up
, isl_upoly_copy(up
));
940 res
= isl_upoly_mul(res
, isl_upoly_copy(up
));
947 __isl_give isl_qpolynomial
*isl_qpolynomial_alloc(__isl_take isl_dim
*dim
,
948 unsigned n_div
, __isl_take
struct isl_upoly
*up
)
950 struct isl_qpolynomial
*qp
= NULL
;
956 total
= isl_dim_total(dim
);
958 qp
= isl_calloc_type(dim
->ctx
, struct isl_qpolynomial
);
963 qp
->div
= isl_mat_alloc(dim
->ctx
, n_div
, 1 + 1 + total
+ n_div
);
974 isl_qpolynomial_free(qp
);
978 __isl_give isl_qpolynomial
*isl_qpolynomial_copy(__isl_keep isl_qpolynomial
*qp
)
987 __isl_give isl_qpolynomial
*isl_qpolynomial_dup(__isl_keep isl_qpolynomial
*qp
)
989 struct isl_qpolynomial
*dup
;
994 dup
= isl_qpolynomial_alloc(isl_dim_copy(qp
->dim
), qp
->div
->n_row
,
995 isl_upoly_copy(qp
->upoly
));
998 isl_mat_free(dup
->div
);
999 dup
->div
= isl_mat_copy(qp
->div
);
1005 isl_qpolynomial_free(dup
);
1009 __isl_give isl_qpolynomial
*isl_qpolynomial_cow(__isl_take isl_qpolynomial
*qp
)
1017 return isl_qpolynomial_dup(qp
);
1020 void isl_qpolynomial_free(__isl_take isl_qpolynomial
*qp
)
1028 isl_dim_free(qp
->dim
);
1029 isl_mat_free(qp
->div
);
1030 isl_upoly_free(qp
->upoly
);
1035 __isl_give
struct isl_upoly
*isl_upoly_var_pow(isl_ctx
*ctx
, int pos
, int power
)
1038 struct isl_upoly_rec
*rec
;
1039 struct isl_upoly_cst
*cst
;
1041 rec
= isl_upoly_alloc_rec(ctx
, pos
, 1 + power
);
1044 for (i
= 0; i
< 1 + power
; ++i
) {
1045 rec
->p
[i
] = isl_upoly_zero(ctx
);
1050 cst
= isl_upoly_as_cst(rec
->p
[power
]);
1051 isl_int_set_si(cst
->n
, 1);
1055 isl_upoly_free(&rec
->up
);
1059 /* r array maps original positions to new positions.
1061 static __isl_give
struct isl_upoly
*reorder(__isl_take
struct isl_upoly
*up
,
1065 struct isl_upoly_rec
*rec
;
1066 struct isl_upoly
*base
;
1067 struct isl_upoly
*res
;
1069 if (isl_upoly_is_cst(up
))
1072 rec
= isl_upoly_as_rec(up
);
1076 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
1078 base
= isl_upoly_var_pow(up
->ctx
, r
[up
->var
], 1);
1079 res
= reorder(isl_upoly_copy(rec
->p
[rec
->n
- 1]), r
);
1081 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1082 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
1083 res
= isl_upoly_sum(res
, reorder(isl_upoly_copy(rec
->p
[i
]), r
));
1086 isl_upoly_free(base
);
1095 static int compatible_divs(__isl_keep isl_mat
*div1
, __isl_keep isl_mat
*div2
)
1100 isl_assert(div1
->ctx
, div1
->n_row
>= div2
->n_row
&&
1101 div1
->n_col
>= div2
->n_col
, return -1);
1103 if (div1
->n_row
== div2
->n_row
)
1104 return isl_mat_is_equal(div1
, div2
);
1106 n_row
= div1
->n_row
;
1107 n_col
= div1
->n_col
;
1108 div1
->n_row
= div2
->n_row
;
1109 div1
->n_col
= div2
->n_col
;
1111 equal
= isl_mat_is_equal(div1
, div2
);
1113 div1
->n_row
= n_row
;
1114 div1
->n_col
= n_col
;
1119 static int cmp_row(__isl_keep isl_mat
*div
, int i
, int j
)
1123 li
= isl_seq_last_non_zero(div
->row
[i
], div
->n_col
);
1124 lj
= isl_seq_last_non_zero(div
->row
[j
], div
->n_col
);
1129 return isl_seq_cmp(div
->row
[i
], div
->row
[j
], div
->n_col
);
1132 struct isl_div_sort_info
{
1137 static int div_sort_cmp(const void *p1
, const void *p2
)
1139 const struct isl_div_sort_info
*i1
, *i2
;
1140 i1
= (const struct isl_div_sort_info
*) p1
;
1141 i2
= (const struct isl_div_sort_info
*) p2
;
1143 return cmp_row(i1
->div
, i1
->row
, i2
->row
);
1146 /* Sort divs and remove duplicates.
1148 static __isl_give isl_qpolynomial
*sort_divs(__isl_take isl_qpolynomial
*qp
)
1153 struct isl_div_sort_info
*array
= NULL
;
1154 int *pos
= NULL
, *at
= NULL
;
1155 int *reordering
= NULL
;
1160 if (qp
->div
->n_row
<= 1)
1163 div_pos
= isl_dim_total(qp
->dim
);
1165 array
= isl_alloc_array(qp
->div
->ctx
, struct isl_div_sort_info
,
1167 pos
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1168 at
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1169 len
= qp
->div
->n_col
- 2;
1170 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
1171 if (!array
|| !pos
|| !at
|| !reordering
)
1174 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1175 array
[i
].div
= qp
->div
;
1181 qsort(array
, qp
->div
->n_row
, sizeof(struct isl_div_sort_info
),
1184 for (i
= 0; i
< div_pos
; ++i
)
1187 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1188 if (pos
[array
[i
].row
] == i
)
1190 qp
->div
= isl_mat_swap_rows(qp
->div
, i
, pos
[array
[i
].row
]);
1191 pos
[at
[i
]] = pos
[array
[i
].row
];
1192 at
[pos
[array
[i
].row
]] = at
[i
];
1193 at
[i
] = array
[i
].row
;
1194 pos
[array
[i
].row
] = i
;
1198 for (i
= 0; i
< len
- div_pos
; ++i
) {
1200 isl_seq_eq(qp
->div
->row
[i
- skip
- 1],
1201 qp
->div
->row
[i
- skip
], qp
->div
->n_col
)) {
1202 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
1203 isl_mat_col_add(qp
->div
, 2 + div_pos
+ i
- skip
- 1,
1204 2 + div_pos
+ i
- skip
);
1205 qp
->div
= isl_mat_drop_cols(qp
->div
,
1206 2 + div_pos
+ i
- skip
, 1);
1209 reordering
[div_pos
+ array
[i
].row
] = div_pos
+ i
- skip
;
1212 qp
->upoly
= reorder(qp
->upoly
, reordering
);
1214 if (!qp
->upoly
|| !qp
->div
)
1228 isl_qpolynomial_free(qp
);
1232 static __isl_give
struct isl_upoly
*expand(__isl_take
struct isl_upoly
*up
,
1233 int *exp
, int first
)
1236 struct isl_upoly_rec
*rec
;
1238 if (isl_upoly_is_cst(up
))
1241 if (up
->var
< first
)
1244 if (exp
[up
->var
- first
] == up
->var
- first
)
1247 up
= isl_upoly_cow(up
);
1251 up
->var
= exp
[up
->var
- first
] + first
;
1253 rec
= isl_upoly_as_rec(up
);
1257 for (i
= 0; i
< rec
->n
; ++i
) {
1258 rec
->p
[i
] = expand(rec
->p
[i
], exp
, first
);
1269 static __isl_give isl_qpolynomial
*with_merged_divs(
1270 __isl_give isl_qpolynomial
*(*fn
)(__isl_take isl_qpolynomial
*qp1
,
1271 __isl_take isl_qpolynomial
*qp2
),
1272 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
1276 isl_mat
*div
= NULL
;
1278 qp1
= isl_qpolynomial_cow(qp1
);
1279 qp2
= isl_qpolynomial_cow(qp2
);
1284 isl_assert(qp1
->div
->ctx
, qp1
->div
->n_row
>= qp2
->div
->n_row
&&
1285 qp1
->div
->n_col
>= qp2
->div
->n_col
, goto error
);
1287 exp1
= isl_alloc_array(qp1
->div
->ctx
, int, qp1
->div
->n_row
);
1288 exp2
= isl_alloc_array(qp2
->div
->ctx
, int, qp2
->div
->n_row
);
1292 div
= isl_merge_divs(qp1
->div
, qp2
->div
, exp1
, exp2
);
1296 isl_mat_free(qp1
->div
);
1297 qp1
->div
= isl_mat_copy(div
);
1298 isl_mat_free(qp2
->div
);
1299 qp2
->div
= isl_mat_copy(div
);
1301 qp1
->upoly
= expand(qp1
->upoly
, exp1
, div
->n_col
- div
->n_row
- 2);
1302 qp2
->upoly
= expand(qp2
->upoly
, exp2
, div
->n_col
- div
->n_row
- 2);
1304 if (!qp1
->upoly
|| !qp2
->upoly
)
1311 return fn(qp1
, qp2
);
1316 isl_qpolynomial_free(qp1
);
1317 isl_qpolynomial_free(qp2
);
1321 __isl_give isl_qpolynomial
*isl_qpolynomial_add(__isl_take isl_qpolynomial
*qp1
,
1322 __isl_take isl_qpolynomial
*qp2
)
1324 qp1
= isl_qpolynomial_cow(qp1
);
1329 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1330 return isl_qpolynomial_add(qp2
, qp1
);
1332 isl_assert(qp1
->dim
->ctx
, isl_dim_equal(qp1
->dim
, qp2
->dim
), goto error
);
1333 if (!compatible_divs(qp1
->div
, qp2
->div
))
1334 return with_merged_divs(isl_qpolynomial_add
, qp1
, qp2
);
1336 qp1
->upoly
= isl_upoly_sum(qp1
->upoly
, isl_upoly_copy(qp2
->upoly
));
1340 isl_qpolynomial_free(qp2
);
1344 isl_qpolynomial_free(qp1
);
1345 isl_qpolynomial_free(qp2
);
1349 __isl_give isl_qpolynomial
*isl_qpolynomial_add_on_domain(
1350 __isl_keep isl_set
*dom
,
1351 __isl_take isl_qpolynomial
*qp1
,
1352 __isl_take isl_qpolynomial
*qp2
)
1354 qp1
= isl_qpolynomial_add(qp1
, qp2
);
1355 qp1
= isl_qpolynomial_gist(qp1
, isl_set_copy(dom
));
1359 __isl_give isl_qpolynomial
*isl_qpolynomial_sub(__isl_take isl_qpolynomial
*qp1
,
1360 __isl_take isl_qpolynomial
*qp2
)
1362 return isl_qpolynomial_add(qp1
, isl_qpolynomial_neg(qp2
));
1365 __isl_give isl_qpolynomial
*isl_qpolynomial_add_isl_int(
1366 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1368 if (isl_int_is_zero(v
))
1371 qp
= isl_qpolynomial_cow(qp
);
1375 qp
->upoly
= isl_upoly_add_isl_int(qp
->upoly
, v
);
1381 isl_qpolynomial_free(qp
);
1386 __isl_give isl_qpolynomial
*isl_qpolynomial_neg(__isl_take isl_qpolynomial
*qp
)
1391 return isl_qpolynomial_mul_isl_int(qp
, qp
->dim
->ctx
->negone
);
1394 __isl_give isl_qpolynomial
*isl_qpolynomial_mul_isl_int(
1395 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1397 if (isl_int_is_one(v
))
1400 if (qp
&& isl_int_is_zero(v
)) {
1401 isl_qpolynomial
*zero
;
1402 zero
= isl_qpolynomial_zero(isl_dim_copy(qp
->dim
));
1403 isl_qpolynomial_free(qp
);
1407 qp
= isl_qpolynomial_cow(qp
);
1411 qp
->upoly
= isl_upoly_mul_isl_int(qp
->upoly
, v
);
1417 isl_qpolynomial_free(qp
);
1421 __isl_give isl_qpolynomial
*isl_qpolynomial_mul(__isl_take isl_qpolynomial
*qp1
,
1422 __isl_take isl_qpolynomial
*qp2
)
1424 qp1
= isl_qpolynomial_cow(qp1
);
1429 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1430 return isl_qpolynomial_mul(qp2
, qp1
);
1432 isl_assert(qp1
->dim
->ctx
, isl_dim_equal(qp1
->dim
, qp2
->dim
), goto error
);
1433 if (!compatible_divs(qp1
->div
, qp2
->div
))
1434 return with_merged_divs(isl_qpolynomial_mul
, qp1
, qp2
);
1436 qp1
->upoly
= isl_upoly_mul(qp1
->upoly
, isl_upoly_copy(qp2
->upoly
));
1440 isl_qpolynomial_free(qp2
);
1444 isl_qpolynomial_free(qp1
);
1445 isl_qpolynomial_free(qp2
);
1449 __isl_give isl_qpolynomial
*isl_qpolynomial_pow(__isl_take isl_qpolynomial
*qp
,
1452 qp
= isl_qpolynomial_cow(qp
);
1457 qp
->upoly
= isl_upoly_pow(qp
->upoly
, power
);
1463 isl_qpolynomial_free(qp
);
1467 __isl_give isl_qpolynomial
*isl_qpolynomial_zero(__isl_take isl_dim
*dim
)
1471 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
1474 __isl_give isl_qpolynomial
*isl_qpolynomial_one(__isl_take isl_dim
*dim
)
1478 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_one(dim
->ctx
));
1481 __isl_give isl_qpolynomial
*isl_qpolynomial_infty(__isl_take isl_dim
*dim
)
1485 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_infty(dim
->ctx
));
1488 __isl_give isl_qpolynomial
*isl_qpolynomial_neginfty(__isl_take isl_dim
*dim
)
1492 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_neginfty(dim
->ctx
));
1495 __isl_give isl_qpolynomial
*isl_qpolynomial_nan(__isl_take isl_dim
*dim
)
1499 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_nan(dim
->ctx
));
1502 __isl_give isl_qpolynomial
*isl_qpolynomial_cst(__isl_take isl_dim
*dim
,
1505 struct isl_qpolynomial
*qp
;
1506 struct isl_upoly_cst
*cst
;
1511 qp
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
1515 cst
= isl_upoly_as_cst(qp
->upoly
);
1516 isl_int_set(cst
->n
, v
);
1521 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial
*qp
,
1522 isl_int
*n
, isl_int
*d
)
1524 struct isl_upoly_cst
*cst
;
1529 if (!isl_upoly_is_cst(qp
->upoly
))
1532 cst
= isl_upoly_as_cst(qp
->upoly
);
1537 isl_int_set(*n
, cst
->n
);
1539 isl_int_set(*d
, cst
->d
);
1544 int isl_upoly_is_affine(__isl_keep
struct isl_upoly
*up
)
1547 struct isl_upoly_rec
*rec
;
1555 rec
= isl_upoly_as_rec(up
);
1562 isl_assert(up
->ctx
, rec
->n
> 1, return -1);
1564 is_cst
= isl_upoly_is_cst(rec
->p
[1]);
1570 return isl_upoly_is_affine(rec
->p
[0]);
1573 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial
*qp
)
1578 if (qp
->div
->n_row
> 0)
1581 return isl_upoly_is_affine(qp
->upoly
);
1584 static void update_coeff(__isl_keep isl_vec
*aff
,
1585 __isl_keep
struct isl_upoly_cst
*cst
, int pos
)
1590 if (isl_int_is_zero(cst
->n
))
1595 isl_int_gcd(gcd
, cst
->d
, aff
->el
[0]);
1596 isl_int_divexact(f
, cst
->d
, gcd
);
1597 isl_int_divexact(gcd
, aff
->el
[0], gcd
);
1598 isl_seq_scale(aff
->el
, aff
->el
, f
, aff
->size
);
1599 isl_int_mul(aff
->el
[1 + pos
], gcd
, cst
->n
);
1604 int isl_upoly_update_affine(__isl_keep
struct isl_upoly
*up
,
1605 __isl_keep isl_vec
*aff
)
1607 struct isl_upoly_cst
*cst
;
1608 struct isl_upoly_rec
*rec
;
1614 struct isl_upoly_cst
*cst
;
1616 cst
= isl_upoly_as_cst(up
);
1619 update_coeff(aff
, cst
, 0);
1623 rec
= isl_upoly_as_rec(up
);
1626 isl_assert(up
->ctx
, rec
->n
== 2, return -1);
1628 cst
= isl_upoly_as_cst(rec
->p
[1]);
1631 update_coeff(aff
, cst
, 1 + up
->var
);
1633 return isl_upoly_update_affine(rec
->p
[0], aff
);
1636 __isl_give isl_vec
*isl_qpolynomial_extract_affine(
1637 __isl_keep isl_qpolynomial
*qp
)
1645 d
= isl_dim_total(qp
->dim
);
1646 aff
= isl_vec_alloc(qp
->div
->ctx
, 2 + d
+ qp
->div
->n_row
);
1650 isl_seq_clr(aff
->el
+ 1, 1 + d
+ qp
->div
->n_row
);
1651 isl_int_set_si(aff
->el
[0], 1);
1653 if (isl_upoly_update_affine(qp
->upoly
, aff
) < 0)
1662 int isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial
*qp1
,
1663 __isl_keep isl_qpolynomial
*qp2
)
1670 equal
= isl_dim_equal(qp1
->dim
, qp2
->dim
);
1671 if (equal
< 0 || !equal
)
1674 equal
= isl_mat_is_equal(qp1
->div
, qp2
->div
);
1675 if (equal
< 0 || !equal
)
1678 return isl_upoly_is_equal(qp1
->upoly
, qp2
->upoly
);
1681 static void upoly_update_den(__isl_keep
struct isl_upoly
*up
, isl_int
*d
)
1684 struct isl_upoly_rec
*rec
;
1686 if (isl_upoly_is_cst(up
)) {
1687 struct isl_upoly_cst
*cst
;
1688 cst
= isl_upoly_as_cst(up
);
1691 isl_int_lcm(*d
, *d
, cst
->d
);
1695 rec
= isl_upoly_as_rec(up
);
1699 for (i
= 0; i
< rec
->n
; ++i
)
1700 upoly_update_den(rec
->p
[i
], d
);
1703 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial
*qp
, isl_int
*d
)
1705 isl_int_set_si(*d
, 1);
1708 upoly_update_den(qp
->upoly
, d
);
1711 __isl_give isl_qpolynomial
*isl_qpolynomial_var_pow(__isl_take isl_dim
*dim
,
1714 struct isl_ctx
*ctx
;
1721 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_var_pow(ctx
, pos
, power
));
1724 __isl_give isl_qpolynomial
*isl_qpolynomial_var(__isl_take isl_dim
*dim
,
1725 enum isl_dim_type type
, unsigned pos
)
1730 isl_assert(dim
->ctx
, isl_dim_size(dim
, isl_dim_in
) == 0, goto error
);
1731 isl_assert(dim
->ctx
, pos
< isl_dim_size(dim
, type
), goto error
);
1733 if (type
== isl_dim_set
)
1734 pos
+= isl_dim_size(dim
, isl_dim_param
);
1736 return isl_qpolynomial_var_pow(dim
, pos
, 1);
1742 __isl_give
struct isl_upoly
*isl_upoly_subs(__isl_take
struct isl_upoly
*up
,
1743 unsigned first
, unsigned n
, __isl_keep
struct isl_upoly
**subs
)
1746 struct isl_upoly_rec
*rec
;
1747 struct isl_upoly
*base
, *res
;
1752 if (isl_upoly_is_cst(up
))
1755 if (up
->var
< first
)
1758 rec
= isl_upoly_as_rec(up
);
1762 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
1764 if (up
->var
>= first
+ n
)
1765 base
= isl_upoly_var_pow(up
->ctx
, up
->var
, 1);
1767 base
= isl_upoly_copy(subs
[up
->var
- first
]);
1769 res
= isl_upoly_subs(isl_upoly_copy(rec
->p
[rec
->n
- 1]), first
, n
, subs
);
1770 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1771 struct isl_upoly
*t
;
1772 t
= isl_upoly_subs(isl_upoly_copy(rec
->p
[i
]), first
, n
, subs
);
1773 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
1774 res
= isl_upoly_sum(res
, t
);
1777 isl_upoly_free(base
);
1786 __isl_give
struct isl_upoly
*isl_upoly_from_affine(isl_ctx
*ctx
, isl_int
*f
,
1787 isl_int denom
, unsigned len
)
1790 struct isl_upoly
*up
;
1792 isl_assert(ctx
, len
>= 1, return NULL
);
1794 up
= isl_upoly_rat_cst(ctx
, f
[0], denom
);
1795 for (i
= 0; i
< len
- 1; ++i
) {
1796 struct isl_upoly
*t
;
1797 struct isl_upoly
*c
;
1799 if (isl_int_is_zero(f
[1 + i
]))
1802 c
= isl_upoly_rat_cst(ctx
, f
[1 + i
], denom
);
1803 t
= isl_upoly_var_pow(ctx
, i
, 1);
1804 t
= isl_upoly_mul(c
, t
);
1805 up
= isl_upoly_sum(up
, t
);
1811 /* Remove common factor of non-constant terms and denominator.
1813 static void normalize_div(__isl_keep isl_qpolynomial
*qp
, int div
)
1815 isl_ctx
*ctx
= qp
->div
->ctx
;
1816 unsigned total
= qp
->div
->n_col
- 2;
1818 isl_seq_gcd(qp
->div
->row
[div
] + 2, total
, &ctx
->normalize_gcd
);
1819 isl_int_gcd(ctx
->normalize_gcd
,
1820 ctx
->normalize_gcd
, qp
->div
->row
[div
][0]);
1821 if (isl_int_is_one(ctx
->normalize_gcd
))
1824 isl_seq_scale_down(qp
->div
->row
[div
] + 2, qp
->div
->row
[div
] + 2,
1825 ctx
->normalize_gcd
, total
);
1826 isl_int_divexact(qp
->div
->row
[div
][0], qp
->div
->row
[div
][0],
1827 ctx
->normalize_gcd
);
1828 isl_int_fdiv_q(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1],
1829 ctx
->normalize_gcd
);
1832 /* Replace the integer division identified by "div" by the polynomial "s".
1833 * The integer division is assumed not to appear in the definition
1834 * of any other integer divisions.
1836 static __isl_give isl_qpolynomial
*substitute_div(
1837 __isl_take isl_qpolynomial
*qp
,
1838 int div
, __isl_take
struct isl_upoly
*s
)
1847 qp
= isl_qpolynomial_cow(qp
);
1851 total
= isl_dim_total(qp
->dim
);
1852 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ div
, 1, &s
);
1856 reordering
= isl_alloc_array(qp
->dim
->ctx
, int, total
+ qp
->div
->n_row
);
1859 for (i
= 0; i
< total
+ div
; ++i
)
1861 for (i
= total
+ div
+ 1; i
< total
+ qp
->div
->n_row
; ++i
)
1862 reordering
[i
] = i
- 1;
1863 qp
->div
= isl_mat_drop_rows(qp
->div
, div
, 1);
1864 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + total
+ div
, 1);
1865 qp
->upoly
= reorder(qp
->upoly
, reordering
);
1868 if (!qp
->upoly
|| !qp
->div
)
1874 isl_qpolynomial_free(qp
);
1879 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1880 * divisions because d is equal to 1 by their definition, i.e., e.
1882 static __isl_give isl_qpolynomial
*substitute_non_divs(
1883 __isl_take isl_qpolynomial
*qp
)
1887 struct isl_upoly
*s
;
1892 total
= isl_dim_total(qp
->dim
);
1893 for (i
= 0; qp
&& i
< qp
->div
->n_row
; ++i
) {
1894 if (!isl_int_is_one(qp
->div
->row
[i
][0]))
1896 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
1897 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
1899 isl_seq_combine(qp
->div
->row
[j
] + 1,
1900 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
1901 qp
->div
->row
[j
][2 + total
+ i
],
1902 qp
->div
->row
[i
] + 1, 1 + total
+ i
);
1903 isl_int_set_si(qp
->div
->row
[j
][2 + total
+ i
], 0);
1904 normalize_div(qp
, j
);
1906 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
1907 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
1908 qp
= substitute_div(qp
, i
, s
);
1915 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1916 * with d the denominator. When replacing the coefficient e of x by
1917 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1918 * inside the division, so we need to add floor(e/d) * x outside.
1919 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1920 * to adjust the coefficient of x in each later div that depends on the
1921 * current div "div" and also in the affine expression "aff"
1922 * (if it too depends on "div").
1924 static void reduce_div(__isl_keep isl_qpolynomial
*qp
, int div
,
1925 __isl_keep isl_vec
*aff
)
1929 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
1932 for (i
= 0; i
< 1 + total
+ div
; ++i
) {
1933 if (isl_int_is_nonneg(qp
->div
->row
[div
][1 + i
]) &&
1934 isl_int_lt(qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]))
1936 isl_int_fdiv_q(v
, qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
1937 isl_int_fdiv_r(qp
->div
->row
[div
][1 + i
],
1938 qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
1939 if (!isl_int_is_zero(aff
->el
[1 + total
+ div
]))
1940 isl_int_addmul(aff
->el
[i
], v
, aff
->el
[1 + total
+ div
]);
1941 for (j
= div
+ 1; j
< qp
->div
->n_row
; ++j
) {
1942 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ div
]))
1944 isl_int_addmul(qp
->div
->row
[j
][1 + i
],
1945 v
, qp
->div
->row
[j
][2 + total
+ div
]);
1951 /* Check if the last non-zero coefficient is bigger that half of the
1952 * denominator. If so, we will invert the div to further reduce the number
1953 * of distinct divs that may appear.
1954 * If the last non-zero coefficient is exactly half the denominator,
1955 * then we continue looking for earlier coefficients that are bigger
1956 * than half the denominator.
1958 static int needs_invert(__isl_keep isl_mat
*div
, int row
)
1963 for (i
= div
->n_col
- 1; i
>= 1; --i
) {
1964 if (isl_int_is_zero(div
->row
[row
][i
]))
1966 isl_int_mul_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
1967 cmp
= isl_int_cmp(div
->row
[row
][i
], div
->row
[row
][0]);
1968 isl_int_divexact_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
1978 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
1979 * We only invert the coefficients of e (and the coefficient of q in
1980 * later divs and in "aff"). After calling this function, the
1981 * coefficients of e should be reduced again.
1983 static void invert_div(__isl_keep isl_qpolynomial
*qp
, int div
,
1984 __isl_keep isl_vec
*aff
)
1986 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
1988 isl_seq_neg(qp
->div
->row
[div
] + 1,
1989 qp
->div
->row
[div
] + 1, qp
->div
->n_col
- 1);
1990 isl_int_sub_ui(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1], 1);
1991 isl_int_add(qp
->div
->row
[div
][1],
1992 qp
->div
->row
[div
][1], qp
->div
->row
[div
][0]);
1993 if (!isl_int_is_zero(aff
->el
[1 + total
+ div
]))
1994 isl_int_neg(aff
->el
[1 + total
+ div
], aff
->el
[1 + total
+ div
]);
1995 isl_mat_col_mul(qp
->div
, 2 + total
+ div
,
1996 qp
->div
->ctx
->negone
, 2 + total
+ div
);
1999 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2000 * in the interval [0, d-1], with d the denominator and such that the
2001 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2003 * After the reduction, some divs may have become redundant or identical,
2004 * so we call substitute_non_divs and sort_divs. If these functions
2005 * eliminate divs or merge two or more divs into one, the coefficients
2006 * of the enclosing divs may have to be reduced again, so we call
2007 * ourselves recursively if the number of divs decreases.
2009 static __isl_give isl_qpolynomial
*reduce_divs(__isl_take isl_qpolynomial
*qp
)
2012 isl_vec
*aff
= NULL
;
2013 struct isl_upoly
*s
;
2019 aff
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
2020 aff
= isl_vec_clr(aff
);
2024 isl_int_set_si(aff
->el
[1 + qp
->upoly
->var
], 1);
2026 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2027 normalize_div(qp
, i
);
2028 reduce_div(qp
, i
, aff
);
2029 if (needs_invert(qp
->div
, i
)) {
2030 invert_div(qp
, i
, aff
);
2031 reduce_div(qp
, i
, aff
);
2035 s
= isl_upoly_from_affine(qp
->div
->ctx
, aff
->el
,
2036 qp
->div
->ctx
->one
, aff
->size
);
2037 qp
->upoly
= isl_upoly_subs(qp
->upoly
, qp
->upoly
->var
, 1, &s
);
2044 n_div
= qp
->div
->n_row
;
2045 qp
= substitute_non_divs(qp
);
2047 if (qp
&& qp
->div
->n_row
< n_div
)
2048 return reduce_divs(qp
);
2052 isl_qpolynomial_free(qp
);
2057 /* Assumes each div only depends on earlier divs.
2059 __isl_give isl_qpolynomial
*isl_qpolynomial_div_pow(__isl_take isl_div
*div
,
2062 struct isl_qpolynomial
*qp
= NULL
;
2063 struct isl_upoly_rec
*rec
;
2064 struct isl_upoly_cst
*cst
;
2071 d
= div
->line
- div
->bmap
->div
;
2073 pos
= isl_dim_total(div
->bmap
->dim
) + d
;
2074 rec
= isl_upoly_alloc_rec(div
->ctx
, pos
, 1 + power
);
2075 qp
= isl_qpolynomial_alloc(isl_basic_map_get_dim(div
->bmap
),
2076 div
->bmap
->n_div
, &rec
->up
);
2080 for (i
= 0; i
< div
->bmap
->n_div
; ++i
)
2081 isl_seq_cpy(qp
->div
->row
[i
], div
->bmap
->div
[i
], qp
->div
->n_col
);
2083 for (i
= 0; i
< 1 + power
; ++i
) {
2084 rec
->p
[i
] = isl_upoly_zero(div
->ctx
);
2089 cst
= isl_upoly_as_cst(rec
->p
[power
]);
2090 isl_int_set_si(cst
->n
, 1);
2094 qp
= reduce_divs(qp
);
2098 isl_qpolynomial_free(qp
);
2103 __isl_give isl_qpolynomial
*isl_qpolynomial_div(__isl_take isl_div
*div
)
2105 return isl_qpolynomial_div_pow(div
, 1);
2108 __isl_give isl_qpolynomial
*isl_qpolynomial_rat_cst(__isl_take isl_dim
*dim
,
2109 const isl_int n
, const isl_int d
)
2111 struct isl_qpolynomial
*qp
;
2112 struct isl_upoly_cst
*cst
;
2114 qp
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
2118 cst
= isl_upoly_as_cst(qp
->upoly
);
2119 isl_int_set(cst
->n
, n
);
2120 isl_int_set(cst
->d
, d
);
2125 static int up_set_active(__isl_keep
struct isl_upoly
*up
, int *active
, int d
)
2127 struct isl_upoly_rec
*rec
;
2133 if (isl_upoly_is_cst(up
))
2137 active
[up
->var
] = 1;
2139 rec
= isl_upoly_as_rec(up
);
2140 for (i
= 0; i
< rec
->n
; ++i
)
2141 if (up_set_active(rec
->p
[i
], active
, d
) < 0)
2147 static int set_active(__isl_keep isl_qpolynomial
*qp
, int *active
)
2150 int d
= isl_dim_total(qp
->dim
);
2155 for (i
= 0; i
< d
; ++i
)
2156 for (j
= 0; j
< qp
->div
->n_row
; ++j
) {
2157 if (isl_int_is_zero(qp
->div
->row
[j
][2 + i
]))
2163 return up_set_active(qp
->upoly
, active
, d
);
2166 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial
*qp
,
2167 enum isl_dim_type type
, unsigned first
, unsigned n
)
2178 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_dim_size(qp
->dim
, type
),
2180 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2181 type
== isl_dim_set
, return -1);
2183 active
= isl_calloc_array(qp
->dim
->ctx
, int, isl_dim_total(qp
->dim
));
2184 if (set_active(qp
, active
) < 0)
2187 if (type
== isl_dim_set
)
2188 first
+= isl_dim_size(qp
->dim
, isl_dim_param
);
2189 for (i
= 0; i
< n
; ++i
)
2190 if (active
[first
+ i
]) {
2203 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2204 * of the divs that do appear in the quasi-polynomial.
2206 static __isl_give isl_qpolynomial
*remove_redundant_divs(
2207 __isl_take isl_qpolynomial
*qp
)
2214 int *reordering
= NULL
;
2221 if (qp
->div
->n_row
== 0)
2224 d
= isl_dim_total(qp
->dim
);
2225 len
= qp
->div
->n_col
- 2;
2226 ctx
= isl_qpolynomial_get_ctx(qp
);
2227 active
= isl_calloc_array(ctx
, int, len
);
2231 if (up_set_active(qp
->upoly
, active
, len
) < 0)
2234 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
2235 if (!active
[d
+ i
]) {
2239 for (j
= 0; j
< i
; ++j
) {
2240 if (isl_int_is_zero(qp
->div
->row
[i
][2 + d
+ j
]))
2252 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
2256 for (i
= 0; i
< d
; ++i
)
2260 n_div
= qp
->div
->n_row
;
2261 for (i
= 0; i
< n_div
; ++i
) {
2262 if (!active
[d
+ i
]) {
2263 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
2264 qp
->div
= isl_mat_drop_cols(qp
->div
,
2265 2 + d
+ i
- skip
, 1);
2268 reordering
[d
+ i
] = d
+ i
- skip
;
2271 qp
->upoly
= reorder(qp
->upoly
, reordering
);
2273 if (!qp
->upoly
|| !qp
->div
)
2283 isl_qpolynomial_free(qp
);
2287 __isl_give
struct isl_upoly
*isl_upoly_drop(__isl_take
struct isl_upoly
*up
,
2288 unsigned first
, unsigned n
)
2291 struct isl_upoly_rec
*rec
;
2295 if (n
== 0 || up
->var
< 0 || up
->var
< first
)
2297 if (up
->var
< first
+ n
) {
2298 up
= replace_by_constant_term(up
);
2299 return isl_upoly_drop(up
, first
, n
);
2301 up
= isl_upoly_cow(up
);
2305 rec
= isl_upoly_as_rec(up
);
2309 for (i
= 0; i
< rec
->n
; ++i
) {
2310 rec
->p
[i
] = isl_upoly_drop(rec
->p
[i
], first
, n
);
2321 __isl_give isl_qpolynomial
*isl_qpolynomial_set_dim_name(
2322 __isl_take isl_qpolynomial
*qp
,
2323 enum isl_dim_type type
, unsigned pos
, const char *s
)
2325 qp
= isl_qpolynomial_cow(qp
);
2328 qp
->dim
= isl_dim_set_name(qp
->dim
, type
, pos
, s
);
2333 isl_qpolynomial_free(qp
);
2337 __isl_give isl_qpolynomial
*isl_qpolynomial_drop_dims(
2338 __isl_take isl_qpolynomial
*qp
,
2339 enum isl_dim_type type
, unsigned first
, unsigned n
)
2343 if (n
== 0 && !isl_dim_get_tuple_name(qp
->dim
, type
))
2346 qp
= isl_qpolynomial_cow(qp
);
2350 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_dim_size(qp
->dim
, type
),
2352 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2353 type
== isl_dim_set
, goto error
);
2355 qp
->dim
= isl_dim_drop(qp
->dim
, type
, first
, n
);
2359 if (type
== isl_dim_set
)
2360 first
+= isl_dim_size(qp
->dim
, isl_dim_param
);
2362 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + first
, n
);
2366 qp
->upoly
= isl_upoly_drop(qp
->upoly
, first
, n
);
2372 isl_qpolynomial_free(qp
);
2376 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities(
2377 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2383 struct isl_upoly
*up
;
2387 if (eq
->n_eq
== 0) {
2388 isl_basic_set_free(eq
);
2392 qp
= isl_qpolynomial_cow(qp
);
2395 qp
->div
= isl_mat_cow(qp
->div
);
2399 total
= 1 + isl_dim_total(eq
->dim
);
2401 isl_int_init(denom
);
2402 for (i
= 0; i
< eq
->n_eq
; ++i
) {
2403 j
= isl_seq_last_non_zero(eq
->eq
[i
], total
+ n_div
);
2404 if (j
< 0 || j
== 0 || j
>= total
)
2407 for (k
= 0; k
< qp
->div
->n_row
; ++k
) {
2408 if (isl_int_is_zero(qp
->div
->row
[k
][1 + j
]))
2410 isl_seq_elim(qp
->div
->row
[k
] + 1, eq
->eq
[i
], j
, total
,
2411 &qp
->div
->row
[k
][0]);
2412 normalize_div(qp
, k
);
2415 if (isl_int_is_pos(eq
->eq
[i
][j
]))
2416 isl_seq_neg(eq
->eq
[i
], eq
->eq
[i
], total
);
2417 isl_int_abs(denom
, eq
->eq
[i
][j
]);
2418 isl_int_set_si(eq
->eq
[i
][j
], 0);
2420 up
= isl_upoly_from_affine(qp
->dim
->ctx
,
2421 eq
->eq
[i
], denom
, total
);
2422 qp
->upoly
= isl_upoly_subs(qp
->upoly
, j
- 1, 1, &up
);
2425 isl_int_clear(denom
);
2430 isl_basic_set_free(eq
);
2432 qp
= substitute_non_divs(qp
);
2437 isl_basic_set_free(eq
);
2438 isl_qpolynomial_free(qp
);
2442 static __isl_give isl_basic_set
*add_div_constraints(
2443 __isl_take isl_basic_set
*bset
, __isl_take isl_mat
*div
)
2451 bset
= isl_basic_set_extend_constraints(bset
, 0, 2 * div
->n_row
);
2454 total
= isl_basic_set_total_dim(bset
);
2455 for (i
= 0; i
< div
->n_row
; ++i
)
2456 if (isl_basic_set_add_div_constraints_var(bset
,
2457 total
- div
->n_row
+ i
, div
->row
[i
]) < 0)
2464 isl_basic_set_free(bset
);
2468 /* Look for equalities among the variables shared by context and qp
2469 * and the integer divisions of qp, if any.
2470 * The equalities are then used to eliminate variables and/or integer
2471 * divisions from qp.
2473 __isl_give isl_qpolynomial
*isl_qpolynomial_gist(
2474 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
2480 if (qp
->div
->n_row
> 0) {
2481 isl_basic_set
*bset
;
2482 context
= isl_set_add_dims(context
, isl_dim_set
,
2484 bset
= isl_basic_set_universe(isl_set_get_dim(context
));
2485 bset
= add_div_constraints(bset
, isl_mat_copy(qp
->div
));
2486 context
= isl_set_intersect(context
,
2487 isl_set_from_basic_set(bset
));
2490 aff
= isl_set_affine_hull(context
);
2491 return isl_qpolynomial_substitute_equalities(qp
, aff
);
2493 isl_qpolynomial_free(qp
);
2494 isl_set_free(context
);
2499 #define PW isl_pw_qpolynomial
2501 #define EL isl_qpolynomial
2503 #define IS_ZERO is_zero
2507 #include <isl_pw_templ.c>
2510 #define UNION isl_union_pw_qpolynomial
2512 #define PART isl_pw_qpolynomial
2514 #define PARTS pw_qpolynomial
2516 #include <isl_union_templ.c>
2518 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial
*pwqp
)
2526 if (!isl_set_plain_is_universe(pwqp
->p
[0].set
))
2529 return isl_qpolynomial_is_one(pwqp
->p
[0].qp
);
2532 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_mul(
2533 __isl_take isl_pw_qpolynomial
*pwqp1
,
2534 __isl_take isl_pw_qpolynomial
*pwqp2
)
2537 struct isl_pw_qpolynomial
*res
;
2539 if (!pwqp1
|| !pwqp2
)
2542 isl_assert(pwqp1
->dim
->ctx
, isl_dim_equal(pwqp1
->dim
, pwqp2
->dim
),
2545 if (isl_pw_qpolynomial_is_zero(pwqp1
)) {
2546 isl_pw_qpolynomial_free(pwqp2
);
2550 if (isl_pw_qpolynomial_is_zero(pwqp2
)) {
2551 isl_pw_qpolynomial_free(pwqp1
);
2555 if (isl_pw_qpolynomial_is_one(pwqp1
)) {
2556 isl_pw_qpolynomial_free(pwqp1
);
2560 if (isl_pw_qpolynomial_is_one(pwqp2
)) {
2561 isl_pw_qpolynomial_free(pwqp2
);
2565 n
= pwqp1
->n
* pwqp2
->n
;
2566 res
= isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1
->dim
), n
);
2568 for (i
= 0; i
< pwqp1
->n
; ++i
) {
2569 for (j
= 0; j
< pwqp2
->n
; ++j
) {
2570 struct isl_set
*common
;
2571 struct isl_qpolynomial
*prod
;
2572 common
= isl_set_intersect(isl_set_copy(pwqp1
->p
[i
].set
),
2573 isl_set_copy(pwqp2
->p
[j
].set
));
2574 if (isl_set_plain_is_empty(common
)) {
2575 isl_set_free(common
);
2579 prod
= isl_qpolynomial_mul(
2580 isl_qpolynomial_copy(pwqp1
->p
[i
].qp
),
2581 isl_qpolynomial_copy(pwqp2
->p
[j
].qp
));
2583 res
= isl_pw_qpolynomial_add_piece(res
, common
, prod
);
2587 isl_pw_qpolynomial_free(pwqp1
);
2588 isl_pw_qpolynomial_free(pwqp2
);
2592 isl_pw_qpolynomial_free(pwqp1
);
2593 isl_pw_qpolynomial_free(pwqp2
);
2597 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_neg(
2598 __isl_take isl_pw_qpolynomial
*pwqp
)
2605 if (isl_pw_qpolynomial_is_zero(pwqp
))
2608 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
2612 for (i
= 0; i
< pwqp
->n
; ++i
) {
2613 pwqp
->p
[i
].qp
= isl_qpolynomial_neg(pwqp
->p
[i
].qp
);
2620 isl_pw_qpolynomial_free(pwqp
);
2624 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_sub(
2625 __isl_take isl_pw_qpolynomial
*pwqp1
,
2626 __isl_take isl_pw_qpolynomial
*pwqp2
)
2628 return isl_pw_qpolynomial_add(pwqp1
, isl_pw_qpolynomial_neg(pwqp2
));
2631 __isl_give
struct isl_upoly
*isl_upoly_eval(
2632 __isl_take
struct isl_upoly
*up
, __isl_take isl_vec
*vec
)
2635 struct isl_upoly_rec
*rec
;
2636 struct isl_upoly
*res
;
2637 struct isl_upoly
*base
;
2639 if (isl_upoly_is_cst(up
)) {
2644 rec
= isl_upoly_as_rec(up
);
2648 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
2650 base
= isl_upoly_rat_cst(up
->ctx
, vec
->el
[1 + up
->var
], vec
->el
[0]);
2652 res
= isl_upoly_eval(isl_upoly_copy(rec
->p
[rec
->n
- 1]),
2655 for (i
= rec
->n
- 2; i
>= 0; --i
) {
2656 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
2657 res
= isl_upoly_sum(res
,
2658 isl_upoly_eval(isl_upoly_copy(rec
->p
[i
]),
2659 isl_vec_copy(vec
)));
2662 isl_upoly_free(base
);
2672 __isl_give isl_qpolynomial
*isl_qpolynomial_eval(
2673 __isl_take isl_qpolynomial
*qp
, __isl_take isl_point
*pnt
)
2676 struct isl_upoly
*up
;
2681 isl_assert(pnt
->dim
->ctx
, isl_dim_equal(pnt
->dim
, qp
->dim
), goto error
);
2683 if (qp
->div
->n_row
== 0)
2684 ext
= isl_vec_copy(pnt
->vec
);
2687 unsigned dim
= isl_dim_total(qp
->dim
);
2688 ext
= isl_vec_alloc(qp
->dim
->ctx
, 1 + dim
+ qp
->div
->n_row
);
2692 isl_seq_cpy(ext
->el
, pnt
->vec
->el
, pnt
->vec
->size
);
2693 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2694 isl_seq_inner_product(qp
->div
->row
[i
] + 1, ext
->el
,
2695 1 + dim
+ i
, &ext
->el
[1+dim
+i
]);
2696 isl_int_fdiv_q(ext
->el
[1+dim
+i
], ext
->el
[1+dim
+i
],
2697 qp
->div
->row
[i
][0]);
2701 up
= isl_upoly_eval(isl_upoly_copy(qp
->upoly
), ext
);
2705 dim
= isl_dim_copy(qp
->dim
);
2706 isl_qpolynomial_free(qp
);
2707 isl_point_free(pnt
);
2709 return isl_qpolynomial_alloc(dim
, 0, up
);
2711 isl_qpolynomial_free(qp
);
2712 isl_point_free(pnt
);
2716 int isl_upoly_cmp(__isl_keep
struct isl_upoly_cst
*cst1
,
2717 __isl_keep
struct isl_upoly_cst
*cst2
)
2722 isl_int_mul(t
, cst1
->n
, cst2
->d
);
2723 isl_int_submul(t
, cst2
->n
, cst1
->d
);
2724 cmp
= isl_int_sgn(t
);
2729 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial
*qp1
,
2730 __isl_keep isl_qpolynomial
*qp2
)
2732 struct isl_upoly_cst
*cst1
, *cst2
;
2736 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), return -1);
2737 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), return -1);
2738 if (isl_qpolynomial_is_nan(qp1
))
2740 if (isl_qpolynomial_is_nan(qp2
))
2742 cst1
= isl_upoly_as_cst(qp1
->upoly
);
2743 cst2
= isl_upoly_as_cst(qp2
->upoly
);
2745 return isl_upoly_cmp(cst1
, cst2
) <= 0;
2748 __isl_give isl_qpolynomial
*isl_qpolynomial_min_cst(
2749 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
2751 struct isl_upoly_cst
*cst1
, *cst2
;
2756 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), goto error
);
2757 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), goto error
);
2758 cst1
= isl_upoly_as_cst(qp1
->upoly
);
2759 cst2
= isl_upoly_as_cst(qp2
->upoly
);
2760 cmp
= isl_upoly_cmp(cst1
, cst2
);
2763 isl_qpolynomial_free(qp2
);
2765 isl_qpolynomial_free(qp1
);
2770 isl_qpolynomial_free(qp1
);
2771 isl_qpolynomial_free(qp2
);
2775 __isl_give isl_qpolynomial
*isl_qpolynomial_max_cst(
2776 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
2778 struct isl_upoly_cst
*cst1
, *cst2
;
2783 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), goto error
);
2784 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), goto error
);
2785 cst1
= isl_upoly_as_cst(qp1
->upoly
);
2786 cst2
= isl_upoly_as_cst(qp2
->upoly
);
2787 cmp
= isl_upoly_cmp(cst1
, cst2
);
2790 isl_qpolynomial_free(qp2
);
2792 isl_qpolynomial_free(qp1
);
2797 isl_qpolynomial_free(qp1
);
2798 isl_qpolynomial_free(qp2
);
2802 __isl_give isl_qpolynomial
*isl_qpolynomial_insert_dims(
2803 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
,
2804 unsigned first
, unsigned n
)
2813 qp
= isl_qpolynomial_cow(qp
);
2817 isl_assert(qp
->div
->ctx
, first
<= isl_dim_size(qp
->dim
, type
),
2820 g_pos
= pos(qp
->dim
, type
) + first
;
2822 qp
->div
= isl_mat_insert_cols(qp
->div
, 2 + g_pos
, n
);
2826 total
= qp
->div
->n_col
- 2;
2827 if (total
> g_pos
) {
2829 exp
= isl_alloc_array(qp
->div
->ctx
, int, total
- g_pos
);
2832 for (i
= 0; i
< total
- g_pos
; ++i
)
2834 qp
->upoly
= expand(qp
->upoly
, exp
, g_pos
);
2840 qp
->dim
= isl_dim_insert(qp
->dim
, type
, first
, n
);
2846 isl_qpolynomial_free(qp
);
2850 __isl_give isl_qpolynomial
*isl_qpolynomial_add_dims(
2851 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
, unsigned n
)
2855 pos
= isl_qpolynomial_dim(qp
, type
);
2857 return isl_qpolynomial_insert_dims(qp
, type
, pos
, n
);
2860 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add_dims(
2861 __isl_take isl_pw_qpolynomial
*pwqp
,
2862 enum isl_dim_type type
, unsigned n
)
2866 pos
= isl_pw_qpolynomial_dim(pwqp
, type
);
2868 return isl_pw_qpolynomial_insert_dims(pwqp
, type
, pos
, n
);
2871 static int *reordering_move(isl_ctx
*ctx
,
2872 unsigned len
, unsigned dst
, unsigned src
, unsigned n
)
2877 reordering
= isl_alloc_array(ctx
, int, len
);
2882 for (i
= 0; i
< dst
; ++i
)
2884 for (i
= 0; i
< n
; ++i
)
2885 reordering
[src
+ i
] = dst
+ i
;
2886 for (i
= 0; i
< src
- dst
; ++i
)
2887 reordering
[dst
+ i
] = dst
+ n
+ i
;
2888 for (i
= 0; i
< len
- src
- n
; ++i
)
2889 reordering
[src
+ n
+ i
] = src
+ n
+ i
;
2891 for (i
= 0; i
< src
; ++i
)
2893 for (i
= 0; i
< n
; ++i
)
2894 reordering
[src
+ i
] = dst
+ i
;
2895 for (i
= 0; i
< dst
- src
; ++i
)
2896 reordering
[src
+ n
+ i
] = src
+ i
;
2897 for (i
= 0; i
< len
- dst
- n
; ++i
)
2898 reordering
[dst
+ n
+ i
] = dst
+ n
+ i
;
2904 __isl_give isl_qpolynomial
*isl_qpolynomial_move_dims(
2905 __isl_take isl_qpolynomial
*qp
,
2906 enum isl_dim_type dst_type
, unsigned dst_pos
,
2907 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
2913 qp
= isl_qpolynomial_cow(qp
);
2917 isl_assert(qp
->dim
->ctx
, src_pos
+ n
<= isl_dim_size(qp
->dim
, src_type
),
2920 g_dst_pos
= pos(qp
->dim
, dst_type
) + dst_pos
;
2921 g_src_pos
= pos(qp
->dim
, src_type
) + src_pos
;
2922 if (dst_type
> src_type
)
2925 qp
->div
= isl_mat_move_cols(qp
->div
, 2 + g_dst_pos
, 2 + g_src_pos
, n
);
2932 reordering
= reordering_move(qp
->dim
->ctx
,
2933 qp
->div
->n_col
- 2, g_dst_pos
, g_src_pos
, n
);
2937 qp
->upoly
= reorder(qp
->upoly
, reordering
);
2942 qp
->dim
= isl_dim_move(qp
->dim
, dst_type
, dst_pos
, src_type
, src_pos
, n
);
2948 isl_qpolynomial_free(qp
);
2952 __isl_give isl_qpolynomial
*isl_qpolynomial_from_affine(__isl_take isl_dim
*dim
,
2953 isl_int
*f
, isl_int denom
)
2955 struct isl_upoly
*up
;
2960 up
= isl_upoly_from_affine(dim
->ctx
, f
, denom
, 1 + isl_dim_total(dim
));
2962 return isl_qpolynomial_alloc(dim
, 0, up
);
2965 __isl_give isl_qpolynomial
*isl_qpolynomial_from_aff(__isl_take isl_aff
*aff
)
2968 struct isl_upoly
*up
;
2969 isl_qpolynomial
*qp
;
2974 ctx
= isl_aff_get_ctx(aff
);
2975 up
= isl_upoly_from_affine(ctx
, aff
->v
->el
+ 1, aff
->v
->el
[0],
2978 qp
= isl_qpolynomial_alloc(isl_aff_get_dim(aff
),
2979 aff
->ls
->div
->n_row
, up
);
2983 isl_mat_free(qp
->div
);
2984 qp
->div
= isl_mat_copy(aff
->ls
->div
);
2985 qp
->div
= isl_mat_cow(qp
->div
);
2990 qp
= reduce_divs(qp
);
2991 qp
= remove_redundant_divs(qp
);
2998 __isl_give isl_qpolynomial
*isl_qpolynomial_from_constraint(
2999 __isl_take isl_constraint
*c
, enum isl_dim_type type
, unsigned pos
)
3003 struct isl_upoly
*up
;
3004 isl_qpolynomial
*qp
;
3010 isl_int_init(denom
);
3012 isl_constraint_get_coefficient(c
, type
, pos
, &denom
);
3013 isl_constraint_set_coefficient(c
, type
, pos
, c
->ctx
->zero
);
3014 sgn
= isl_int_sgn(denom
);
3015 isl_int_abs(denom
, denom
);
3016 up
= isl_upoly_from_affine(c
->ctx
, c
->line
[0], denom
,
3017 1 + isl_constraint_dim(c
, isl_dim_all
));
3019 isl_int_neg(denom
, denom
);
3020 isl_constraint_set_coefficient(c
, type
, pos
, denom
);
3022 dim
= isl_dim_copy(c
->bmap
->dim
);
3024 isl_int_clear(denom
);
3025 isl_constraint_free(c
);
3027 qp
= isl_qpolynomial_alloc(dim
, 0, up
);
3029 qp
= isl_qpolynomial_neg(qp
);
3033 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3034 * in "qp" by subs[i].
3036 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute(
3037 __isl_take isl_qpolynomial
*qp
,
3038 enum isl_dim_type type
, unsigned first
, unsigned n
,
3039 __isl_keep isl_qpolynomial
**subs
)
3042 struct isl_upoly
**ups
;
3047 qp
= isl_qpolynomial_cow(qp
);
3050 for (i
= 0; i
< n
; ++i
)
3054 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_dim_size(qp
->dim
, type
),
3057 for (i
= 0; i
< n
; ++i
)
3058 isl_assert(qp
->dim
->ctx
, isl_dim_equal(qp
->dim
, subs
[i
]->dim
),
3061 isl_assert(qp
->dim
->ctx
, qp
->div
->n_row
== 0, goto error
);
3062 for (i
= 0; i
< n
; ++i
)
3063 isl_assert(qp
->dim
->ctx
, subs
[i
]->div
->n_row
== 0, goto error
);
3065 first
+= pos(qp
->dim
, type
);
3067 ups
= isl_alloc_array(qp
->dim
->ctx
, struct isl_upoly
*, n
);
3070 for (i
= 0; i
< n
; ++i
)
3071 ups
[i
] = subs
[i
]->upoly
;
3073 qp
->upoly
= isl_upoly_subs(qp
->upoly
, first
, n
, ups
);
3082 isl_qpolynomial_free(qp
);
3086 /* Extend "bset" with extra set dimensions for each integer division
3087 * in "qp" and then call "fn" with the extended bset and the polynomial
3088 * that results from replacing each of the integer divisions by the
3089 * corresponding extra set dimension.
3091 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial
*qp
,
3092 __isl_keep isl_basic_set
*bset
,
3093 int (*fn
)(__isl_take isl_basic_set
*bset
,
3094 __isl_take isl_qpolynomial
*poly
, void *user
), void *user
)
3098 isl_qpolynomial
*poly
;
3102 if (qp
->div
->n_row
== 0)
3103 return fn(isl_basic_set_copy(bset
), isl_qpolynomial_copy(qp
),
3106 div
= isl_mat_copy(qp
->div
);
3107 dim
= isl_dim_copy(qp
->dim
);
3108 dim
= isl_dim_add(dim
, isl_dim_set
, qp
->div
->n_row
);
3109 poly
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_copy(qp
->upoly
));
3110 bset
= isl_basic_set_copy(bset
);
3111 bset
= isl_basic_set_add(bset
, isl_dim_set
, qp
->div
->n_row
);
3112 bset
= add_div_constraints(bset
, div
);
3114 return fn(bset
, poly
, user
);
3119 /* Return total degree in variables first (inclusive) up to last (exclusive).
3121 int isl_upoly_degree(__isl_keep
struct isl_upoly
*up
, int first
, int last
)
3125 struct isl_upoly_rec
*rec
;
3129 if (isl_upoly_is_zero(up
))
3131 if (isl_upoly_is_cst(up
) || up
->var
< first
)
3134 rec
= isl_upoly_as_rec(up
);
3138 for (i
= 0; i
< rec
->n
; ++i
) {
3141 if (isl_upoly_is_zero(rec
->p
[i
]))
3143 d
= isl_upoly_degree(rec
->p
[i
], first
, last
);
3153 /* Return total degree in set variables.
3155 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial
*poly
)
3163 ovar
= isl_dim_offset(poly
->dim
, isl_dim_set
);
3164 nvar
= isl_dim_size(poly
->dim
, isl_dim_set
);
3165 return isl_upoly_degree(poly
->upoly
, ovar
, ovar
+ nvar
);
3168 __isl_give
struct isl_upoly
*isl_upoly_coeff(__isl_keep
struct isl_upoly
*up
,
3169 unsigned pos
, int deg
)
3172 struct isl_upoly_rec
*rec
;
3177 if (isl_upoly_is_cst(up
) || up
->var
< pos
) {
3179 return isl_upoly_copy(up
);
3181 return isl_upoly_zero(up
->ctx
);
3184 rec
= isl_upoly_as_rec(up
);
3188 if (up
->var
== pos
) {
3190 return isl_upoly_copy(rec
->p
[deg
]);
3192 return isl_upoly_zero(up
->ctx
);
3195 up
= isl_upoly_copy(up
);
3196 up
= isl_upoly_cow(up
);
3197 rec
= isl_upoly_as_rec(up
);
3201 for (i
= 0; i
< rec
->n
; ++i
) {
3202 struct isl_upoly
*t
;
3203 t
= isl_upoly_coeff(rec
->p
[i
], pos
, deg
);
3206 isl_upoly_free(rec
->p
[i
]);
3216 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3218 __isl_give isl_qpolynomial
*isl_qpolynomial_coeff(
3219 __isl_keep isl_qpolynomial
*qp
,
3220 enum isl_dim_type type
, unsigned t_pos
, int deg
)
3223 struct isl_upoly
*up
;
3229 isl_assert(qp
->div
->ctx
, t_pos
< isl_dim_size(qp
->dim
, type
),
3232 g_pos
= pos(qp
->dim
, type
) + t_pos
;
3233 up
= isl_upoly_coeff(qp
->upoly
, g_pos
, deg
);
3235 c
= isl_qpolynomial_alloc(isl_dim_copy(qp
->dim
), qp
->div
->n_row
, up
);
3238 isl_mat_free(c
->div
);
3239 c
->div
= isl_mat_copy(qp
->div
);
3244 isl_qpolynomial_free(c
);
3248 /* Homogenize the polynomial in the variables first (inclusive) up to
3249 * last (exclusive) by inserting powers of variable first.
3250 * Variable first is assumed not to appear in the input.
3252 __isl_give
struct isl_upoly
*isl_upoly_homogenize(
3253 __isl_take
struct isl_upoly
*up
, int deg
, int target
,
3254 int first
, int last
)
3257 struct isl_upoly_rec
*rec
;
3261 if (isl_upoly_is_zero(up
))
3265 if (isl_upoly_is_cst(up
) || up
->var
< first
) {
3266 struct isl_upoly
*hom
;
3268 hom
= isl_upoly_var_pow(up
->ctx
, first
, target
- deg
);
3271 rec
= isl_upoly_as_rec(hom
);
3272 rec
->p
[target
- deg
] = isl_upoly_mul(rec
->p
[target
- deg
], up
);
3277 up
= isl_upoly_cow(up
);
3278 rec
= isl_upoly_as_rec(up
);
3282 for (i
= 0; i
< rec
->n
; ++i
) {
3283 if (isl_upoly_is_zero(rec
->p
[i
]))
3285 rec
->p
[i
] = isl_upoly_homogenize(rec
->p
[i
],
3286 up
->var
< last
? deg
+ i
: i
, target
,
3298 /* Homogenize the polynomial in the set variables by introducing
3299 * powers of an extra set variable at position 0.
3301 __isl_give isl_qpolynomial
*isl_qpolynomial_homogenize(
3302 __isl_take isl_qpolynomial
*poly
)
3306 int deg
= isl_qpolynomial_degree(poly
);
3311 poly
= isl_qpolynomial_insert_dims(poly
, isl_dim_set
, 0, 1);
3312 poly
= isl_qpolynomial_cow(poly
);
3316 ovar
= isl_dim_offset(poly
->dim
, isl_dim_set
);
3317 nvar
= isl_dim_size(poly
->dim
, isl_dim_set
);
3318 poly
->upoly
= isl_upoly_homogenize(poly
->upoly
, 0, deg
,
3325 isl_qpolynomial_free(poly
);
3329 __isl_give isl_term
*isl_term_alloc(__isl_take isl_dim
*dim
,
3330 __isl_take isl_mat
*div
)
3338 n
= isl_dim_total(dim
) + div
->n_row
;
3340 term
= isl_calloc(dim
->ctx
, struct isl_term
,
3341 sizeof(struct isl_term
) + (n
- 1) * sizeof(int));
3348 isl_int_init(term
->n
);
3349 isl_int_init(term
->d
);
3358 __isl_give isl_term
*isl_term_copy(__isl_keep isl_term
*term
)
3367 __isl_give isl_term
*isl_term_dup(__isl_keep isl_term
*term
)
3376 total
= isl_dim_total(term
->dim
) + term
->div
->n_row
;
3378 dup
= isl_term_alloc(isl_dim_copy(term
->dim
), isl_mat_copy(term
->div
));
3382 isl_int_set(dup
->n
, term
->n
);
3383 isl_int_set(dup
->d
, term
->d
);
3385 for (i
= 0; i
< total
; ++i
)
3386 dup
->pow
[i
] = term
->pow
[i
];
3391 __isl_give isl_term
*isl_term_cow(__isl_take isl_term
*term
)
3399 return isl_term_dup(term
);
3402 void isl_term_free(__isl_take isl_term
*term
)
3407 if (--term
->ref
> 0)
3410 isl_dim_free(term
->dim
);
3411 isl_mat_free(term
->div
);
3412 isl_int_clear(term
->n
);
3413 isl_int_clear(term
->d
);
3417 unsigned isl_term_dim(__isl_keep isl_term
*term
, enum isl_dim_type type
)
3425 case isl_dim_out
: return isl_dim_size(term
->dim
, type
);
3426 case isl_dim_div
: return term
->div
->n_row
;
3427 case isl_dim_all
: return isl_dim_total(term
->dim
) + term
->div
->n_row
;
3432 isl_ctx
*isl_term_get_ctx(__isl_keep isl_term
*term
)
3434 return term
? term
->dim
->ctx
: NULL
;
3437 void isl_term_get_num(__isl_keep isl_term
*term
, isl_int
*n
)
3441 isl_int_set(*n
, term
->n
);
3444 void isl_term_get_den(__isl_keep isl_term
*term
, isl_int
*d
)
3448 isl_int_set(*d
, term
->d
);
3451 int isl_term_get_exp(__isl_keep isl_term
*term
,
3452 enum isl_dim_type type
, unsigned pos
)
3457 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, type
), return -1);
3459 if (type
>= isl_dim_set
)
3460 pos
+= isl_dim_size(term
->dim
, isl_dim_param
);
3461 if (type
>= isl_dim_div
)
3462 pos
+= isl_dim_size(term
->dim
, isl_dim_set
);
3464 return term
->pow
[pos
];
3467 __isl_give isl_div
*isl_term_get_div(__isl_keep isl_term
*term
, unsigned pos
)
3469 isl_basic_map
*bmap
;
3476 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, isl_dim_div
),
3479 total
= term
->div
->n_col
- term
->div
->n_row
- 2;
3480 /* No nested divs for now */
3481 isl_assert(term
->dim
->ctx
,
3482 isl_seq_first_non_zero(term
->div
->row
[pos
] + 2 + total
,
3483 term
->div
->n_row
) == -1,
3486 bmap
= isl_basic_map_alloc_dim(isl_dim_copy(term
->dim
), 1, 0, 0);
3487 if ((k
= isl_basic_map_alloc_div(bmap
)) < 0)
3490 isl_seq_cpy(bmap
->div
[k
], term
->div
->row
[pos
], 2 + total
);
3492 return isl_basic_map_div(bmap
, k
);
3494 isl_basic_map_free(bmap
);
3498 __isl_give isl_term
*isl_upoly_foreach_term(__isl_keep
struct isl_upoly
*up
,
3499 int (*fn
)(__isl_take isl_term
*term
, void *user
),
3500 __isl_take isl_term
*term
, void *user
)
3503 struct isl_upoly_rec
*rec
;
3508 if (isl_upoly_is_zero(up
))
3511 isl_assert(up
->ctx
, !isl_upoly_is_nan(up
), goto error
);
3512 isl_assert(up
->ctx
, !isl_upoly_is_infty(up
), goto error
);
3513 isl_assert(up
->ctx
, !isl_upoly_is_neginfty(up
), goto error
);
3515 if (isl_upoly_is_cst(up
)) {
3516 struct isl_upoly_cst
*cst
;
3517 cst
= isl_upoly_as_cst(up
);
3520 term
= isl_term_cow(term
);
3523 isl_int_set(term
->n
, cst
->n
);
3524 isl_int_set(term
->d
, cst
->d
);
3525 if (fn(isl_term_copy(term
), user
) < 0)
3530 rec
= isl_upoly_as_rec(up
);
3534 for (i
= 0; i
< rec
->n
; ++i
) {
3535 term
= isl_term_cow(term
);
3538 term
->pow
[up
->var
] = i
;
3539 term
= isl_upoly_foreach_term(rec
->p
[i
], fn
, term
, user
);
3543 term
->pow
[up
->var
] = 0;
3547 isl_term_free(term
);
3551 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial
*qp
,
3552 int (*fn
)(__isl_take isl_term
*term
, void *user
), void *user
)
3559 term
= isl_term_alloc(isl_dim_copy(qp
->dim
), isl_mat_copy(qp
->div
));
3563 term
= isl_upoly_foreach_term(qp
->upoly
, fn
, term
, user
);
3565 isl_term_free(term
);
3567 return term
? 0 : -1;
3570 __isl_give isl_qpolynomial
*isl_qpolynomial_from_term(__isl_take isl_term
*term
)
3572 struct isl_upoly
*up
;
3573 isl_qpolynomial
*qp
;
3579 n
= isl_dim_total(term
->dim
) + term
->div
->n_row
;
3581 up
= isl_upoly_rat_cst(term
->dim
->ctx
, term
->n
, term
->d
);
3582 for (i
= 0; i
< n
; ++i
) {
3585 up
= isl_upoly_mul(up
,
3586 isl_upoly_var_pow(term
->dim
->ctx
, i
, term
->pow
[i
]));
3589 qp
= isl_qpolynomial_alloc(isl_dim_copy(term
->dim
), term
->div
->n_row
, up
);
3592 isl_mat_free(qp
->div
);
3593 qp
->div
= isl_mat_copy(term
->div
);
3597 isl_term_free(term
);
3600 isl_qpolynomial_free(qp
);
3601 isl_term_free(term
);
3605 __isl_give isl_qpolynomial
*isl_qpolynomial_lift(__isl_take isl_qpolynomial
*qp
,
3606 __isl_take isl_dim
*dim
)
3615 if (isl_dim_equal(qp
->dim
, dim
)) {
3620 qp
= isl_qpolynomial_cow(qp
);
3624 extra
= isl_dim_size(dim
, isl_dim_set
) -
3625 isl_dim_size(qp
->dim
, isl_dim_set
);
3626 total
= isl_dim_total(qp
->dim
);
3627 if (qp
->div
->n_row
) {
3630 exp
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
3633 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3635 qp
->upoly
= expand(qp
->upoly
, exp
, total
);
3640 qp
->div
= isl_mat_insert_cols(qp
->div
, 2 + total
, extra
);
3643 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3644 isl_seq_clr(qp
->div
->row
[i
] + 2 + total
, extra
);
3646 isl_dim_free(qp
->dim
);
3652 isl_qpolynomial_free(qp
);
3656 /* For each parameter or variable that does not appear in qp,
3657 * first eliminate the variable from all constraints and then set it to zero.
3659 static __isl_give isl_set
*fix_inactive(__isl_take isl_set
*set
,
3660 __isl_keep isl_qpolynomial
*qp
)
3671 d
= isl_dim_total(set
->dim
);
3672 active
= isl_calloc_array(set
->ctx
, int, d
);
3673 if (set_active(qp
, active
) < 0)
3676 for (i
= 0; i
< d
; ++i
)
3685 nparam
= isl_dim_size(set
->dim
, isl_dim_param
);
3686 nvar
= isl_dim_size(set
->dim
, isl_dim_set
);
3687 for (i
= 0; i
< nparam
; ++i
) {
3690 set
= isl_set_eliminate(set
, isl_dim_param
, i
, 1);
3691 set
= isl_set_fix_si(set
, isl_dim_param
, i
, 0);
3693 for (i
= 0; i
< nvar
; ++i
) {
3694 if (active
[nparam
+ i
])
3696 set
= isl_set_eliminate(set
, isl_dim_set
, i
, 1);
3697 set
= isl_set_fix_si(set
, isl_dim_set
, i
, 0);
3709 struct isl_opt_data
{
3710 isl_qpolynomial
*qp
;
3712 isl_qpolynomial
*opt
;
3716 static int opt_fn(__isl_take isl_point
*pnt
, void *user
)
3718 struct isl_opt_data
*data
= (struct isl_opt_data
*)user
;
3719 isl_qpolynomial
*val
;
3721 val
= isl_qpolynomial_eval(isl_qpolynomial_copy(data
->qp
), pnt
);
3725 } else if (data
->max
) {
3726 data
->opt
= isl_qpolynomial_max_cst(data
->opt
, val
);
3728 data
->opt
= isl_qpolynomial_min_cst(data
->opt
, val
);
3734 __isl_give isl_qpolynomial
*isl_qpolynomial_opt_on_domain(
3735 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*set
, int max
)
3737 struct isl_opt_data data
= { NULL
, 1, NULL
, max
};
3742 if (isl_upoly_is_cst(qp
->upoly
)) {
3747 set
= fix_inactive(set
, qp
);
3750 if (isl_set_foreach_point(set
, opt_fn
, &data
) < 0)
3754 data
.opt
= isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp
));
3757 isl_qpolynomial_free(qp
);
3761 isl_qpolynomial_free(qp
);
3762 isl_qpolynomial_free(data
.opt
);
3766 __isl_give isl_qpolynomial
*isl_qpolynomial_morph(__isl_take isl_qpolynomial
*qp
,
3767 __isl_take isl_morph
*morph
)
3772 struct isl_upoly
**subs
;
3775 qp
= isl_qpolynomial_cow(qp
);
3780 isl_assert(ctx
, isl_dim_equal(qp
->dim
, morph
->dom
->dim
), goto error
);
3782 n_sub
= morph
->inv
->n_row
- 1;
3783 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
3784 n_sub
+= qp
->div
->n_row
;
3785 subs
= isl_calloc_array(ctx
, struct isl_upoly
*, n_sub
);
3789 for (i
= 0; 1 + i
< morph
->inv
->n_row
; ++i
)
3790 subs
[i
] = isl_upoly_from_affine(ctx
, morph
->inv
->row
[1 + i
],
3791 morph
->inv
->row
[0][0], morph
->inv
->n_col
);
3792 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
3793 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3794 subs
[morph
->inv
->n_row
- 1 + i
] =
3795 isl_upoly_var_pow(ctx
, morph
->inv
->n_col
- 1 + i
, 1);
3797 qp
->upoly
= isl_upoly_subs(qp
->upoly
, 0, n_sub
, subs
);
3799 for (i
= 0; i
< n_sub
; ++i
)
3800 isl_upoly_free(subs
[i
]);
3803 mat
= isl_mat_diagonal(isl_mat_identity(ctx
, 1), isl_mat_copy(morph
->inv
));
3804 mat
= isl_mat_diagonal(mat
, isl_mat_identity(ctx
, qp
->div
->n_row
));
3805 qp
->div
= isl_mat_product(qp
->div
, mat
);
3806 isl_dim_free(qp
->dim
);
3807 qp
->dim
= isl_dim_copy(morph
->ran
->dim
);
3809 if (!qp
->upoly
|| !qp
->div
|| !qp
->dim
)
3812 isl_morph_free(morph
);
3816 isl_qpolynomial_free(qp
);
3817 isl_morph_free(morph
);
3821 static int neg_entry(void **entry
, void *user
)
3823 isl_pw_qpolynomial
**pwqp
= (isl_pw_qpolynomial
**)entry
;
3825 *pwqp
= isl_pw_qpolynomial_neg(*pwqp
);
3827 return *pwqp
? 0 : -1;
3830 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_neg(
3831 __isl_take isl_union_pw_qpolynomial
*upwqp
)
3833 upwqp
= isl_union_pw_qpolynomial_cow(upwqp
);
3837 if (isl_hash_table_foreach(upwqp
->dim
->ctx
, &upwqp
->table
,
3838 &neg_entry
, NULL
) < 0)
3843 isl_union_pw_qpolynomial_free(upwqp
);
3847 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_sub(
3848 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
3849 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
3851 return isl_union_pw_qpolynomial_add(upwqp1
,
3852 isl_union_pw_qpolynomial_neg(upwqp2
));
3855 static int mul_entry(void **entry
, void *user
)
3857 struct isl_union_pw_qpolynomial_match_bin_data
*data
= user
;
3859 struct isl_hash_table_entry
*entry2
;
3860 isl_pw_qpolynomial
*pwpq
= *entry
;
3863 hash
= isl_dim_get_hash(pwpq
->dim
);
3864 entry2
= isl_hash_table_find(data
->u2
->dim
->ctx
, &data
->u2
->table
,
3865 hash
, &has_dim
, pwpq
->dim
, 0);
3869 pwpq
= isl_pw_qpolynomial_copy(pwpq
);
3870 pwpq
= isl_pw_qpolynomial_mul(pwpq
,
3871 isl_pw_qpolynomial_copy(entry2
->data
));
3873 empty
= isl_pw_qpolynomial_is_zero(pwpq
);
3875 isl_pw_qpolynomial_free(pwpq
);
3879 isl_pw_qpolynomial_free(pwpq
);
3883 data
->res
= isl_union_pw_qpolynomial_add_pw_qpolynomial(data
->res
, pwpq
);
3888 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_mul(
3889 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
3890 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
3892 return match_bin_op(upwqp1
, upwqp2
, &mul_entry
);
3895 /* Reorder the columns of the given div definitions according to the
3898 static __isl_give isl_mat
*reorder_divs(__isl_take isl_mat
*div
,
3899 __isl_take isl_reordering
*r
)
3908 extra
= isl_dim_total(r
->dim
) + div
->n_row
- r
->len
;
3909 mat
= isl_mat_alloc(div
->ctx
, div
->n_row
, div
->n_col
+ extra
);
3913 for (i
= 0; i
< div
->n_row
; ++i
) {
3914 isl_seq_cpy(mat
->row
[i
], div
->row
[i
], 2);
3915 isl_seq_clr(mat
->row
[i
] + 2, mat
->n_col
- 2);
3916 for (j
= 0; j
< r
->len
; ++j
)
3917 isl_int_set(mat
->row
[i
][2 + r
->pos
[j
]],
3918 div
->row
[i
][2 + j
]);
3921 isl_reordering_free(r
);
3925 isl_reordering_free(r
);
3930 /* Reorder the dimension of "qp" according to the given reordering.
3932 __isl_give isl_qpolynomial
*isl_qpolynomial_realign(
3933 __isl_take isl_qpolynomial
*qp
, __isl_take isl_reordering
*r
)
3935 qp
= isl_qpolynomial_cow(qp
);
3939 r
= isl_reordering_extend(r
, qp
->div
->n_row
);
3943 qp
->div
= reorder_divs(qp
->div
, isl_reordering_copy(r
));
3947 qp
->upoly
= reorder(qp
->upoly
, r
->pos
);
3951 qp
= isl_qpolynomial_reset_dim(qp
, isl_dim_copy(r
->dim
));
3953 isl_reordering_free(r
);
3956 isl_qpolynomial_free(qp
);
3957 isl_reordering_free(r
);
3961 __isl_give isl_qpolynomial
*isl_qpolynomial_align_params(
3962 __isl_take isl_qpolynomial
*qp
, __isl_take isl_dim
*model
)
3967 if (!isl_dim_match(qp
->dim
, isl_dim_param
, model
, isl_dim_param
)) {
3968 isl_reordering
*exp
;
3970 model
= isl_dim_drop(model
, isl_dim_in
,
3971 0, isl_dim_size(model
, isl_dim_in
));
3972 model
= isl_dim_drop(model
, isl_dim_out
,
3973 0, isl_dim_size(model
, isl_dim_out
));
3974 exp
= isl_parameter_alignment_reordering(qp
->dim
, model
);
3975 exp
= isl_reordering_extend_dim(exp
,
3976 isl_qpolynomial_get_dim(qp
));
3977 qp
= isl_qpolynomial_realign(qp
, exp
);
3980 isl_dim_free(model
);
3983 isl_dim_free(model
);
3984 isl_qpolynomial_free(qp
);
3988 struct isl_split_periods_data
{
3990 isl_pw_qpolynomial
*res
;
3993 /* Create a slice where the integer division "div" has the fixed value "v".
3994 * In particular, if "div" refers to floor(f/m), then create a slice
3996 * m v <= f <= m v + (m - 1)
4001 * -f + m v + (m - 1) >= 0
4003 static __isl_give isl_set
*set_div_slice(__isl_take isl_dim
*dim
,
4004 __isl_keep isl_qpolynomial
*qp
, int div
, isl_int v
)
4007 isl_basic_set
*bset
= NULL
;
4013 total
= isl_dim_total(dim
);
4014 bset
= isl_basic_set_alloc_dim(isl_dim_copy(dim
), 0, 0, 2);
4016 k
= isl_basic_set_alloc_inequality(bset
);
4019 isl_seq_cpy(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4020 isl_int_submul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4022 k
= isl_basic_set_alloc_inequality(bset
);
4025 isl_seq_neg(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4026 isl_int_addmul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4027 isl_int_add(bset
->ineq
[k
][0], bset
->ineq
[k
][0], qp
->div
->row
[div
][0]);
4028 isl_int_sub_ui(bset
->ineq
[k
][0], bset
->ineq
[k
][0], 1);
4031 return isl_set_from_basic_set(bset
);
4033 isl_basic_set_free(bset
);
4038 static int split_periods(__isl_take isl_set
*set
,
4039 __isl_take isl_qpolynomial
*qp
, void *user
);
4041 /* Create a slice of the domain "set" such that integer division "div"
4042 * has the fixed value "v" and add the results to data->res,
4043 * replacing the integer division by "v" in "qp".
4045 static int set_div(__isl_take isl_set
*set
,
4046 __isl_take isl_qpolynomial
*qp
, int div
, isl_int v
,
4047 struct isl_split_periods_data
*data
)
4052 struct isl_upoly
*cst
;
4054 slice
= set_div_slice(isl_set_get_dim(set
), qp
, div
, v
);
4055 set
= isl_set_intersect(set
, slice
);
4060 total
= isl_dim_total(qp
->dim
);
4062 for (i
= div
+ 1; i
< qp
->div
->n_row
; ++i
) {
4063 if (isl_int_is_zero(qp
->div
->row
[i
][2 + total
+ div
]))
4065 isl_int_addmul(qp
->div
->row
[i
][1],
4066 qp
->div
->row
[i
][2 + total
+ div
], v
);
4067 isl_int_set_si(qp
->div
->row
[i
][2 + total
+ div
], 0);
4070 cst
= isl_upoly_rat_cst(qp
->dim
->ctx
, v
, qp
->dim
->ctx
->one
);
4071 qp
= substitute_div(qp
, div
, cst
);
4073 return split_periods(set
, qp
, data
);
4076 isl_qpolynomial_free(qp
);
4080 /* Split the domain "set" such that integer division "div"
4081 * has a fixed value (ranging from "min" to "max") on each slice
4082 * and add the results to data->res.
4084 static int split_div(__isl_take isl_set
*set
,
4085 __isl_take isl_qpolynomial
*qp
, int div
, isl_int min
, isl_int max
,
4086 struct isl_split_periods_data
*data
)
4088 for (; isl_int_le(min
, max
); isl_int_add_ui(min
, min
, 1)) {
4089 isl_set
*set_i
= isl_set_copy(set
);
4090 isl_qpolynomial
*qp_i
= isl_qpolynomial_copy(qp
);
4092 if (set_div(set_i
, qp_i
, div
, min
, data
) < 0)
4096 isl_qpolynomial_free(qp
);
4100 isl_qpolynomial_free(qp
);
4104 /* If "qp" refers to any integer division
4105 * that can only attain "max_periods" distinct values on "set"
4106 * then split the domain along those distinct values.
4107 * Add the results (or the original if no splitting occurs)
4110 static int split_periods(__isl_take isl_set
*set
,
4111 __isl_take isl_qpolynomial
*qp
, void *user
)
4114 isl_pw_qpolynomial
*pwqp
;
4115 struct isl_split_periods_data
*data
;
4120 data
= (struct isl_split_periods_data
*)user
;
4125 if (qp
->div
->n_row
== 0) {
4126 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4127 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4133 total
= isl_dim_total(qp
->dim
);
4134 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4135 enum isl_lp_result lp_res
;
4137 if (isl_seq_first_non_zero(qp
->div
->row
[i
] + 2 + total
,
4138 qp
->div
->n_row
) != -1)
4141 lp_res
= isl_set_solve_lp(set
, 0, qp
->div
->row
[i
] + 1,
4142 set
->ctx
->one
, &min
, NULL
, NULL
);
4143 if (lp_res
== isl_lp_error
)
4145 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4147 isl_int_fdiv_q(min
, min
, qp
->div
->row
[i
][0]);
4149 lp_res
= isl_set_solve_lp(set
, 1, qp
->div
->row
[i
] + 1,
4150 set
->ctx
->one
, &max
, NULL
, NULL
);
4151 if (lp_res
== isl_lp_error
)
4153 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4155 isl_int_fdiv_q(max
, max
, qp
->div
->row
[i
][0]);
4157 isl_int_sub(max
, max
, min
);
4158 if (isl_int_cmp_si(max
, data
->max_periods
) < 0) {
4159 isl_int_add(max
, max
, min
);
4164 if (i
< qp
->div
->n_row
) {
4165 r
= split_div(set
, qp
, i
, min
, max
, data
);
4167 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4168 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4180 isl_qpolynomial_free(qp
);
4184 /* If any quasi-polynomial in pwqp refers to any integer division
4185 * that can only attain "max_periods" distinct values on its domain
4186 * then split the domain along those distinct values.
4188 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_split_periods(
4189 __isl_take isl_pw_qpolynomial
*pwqp
, int max_periods
)
4191 struct isl_split_periods_data data
;
4193 data
.max_periods
= max_periods
;
4194 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp
));
4196 if (isl_pw_qpolynomial_foreach_piece(pwqp
, &split_periods
, &data
) < 0)
4199 isl_pw_qpolynomial_free(pwqp
);
4203 isl_pw_qpolynomial_free(data
.res
);
4204 isl_pw_qpolynomial_free(pwqp
);
4208 /* Construct a piecewise quasipolynomial that is constant on the given
4209 * domain. In particular, it is
4212 * infinity if cst == -1
4214 static __isl_give isl_pw_qpolynomial
*constant_on_domain(
4215 __isl_take isl_basic_set
*bset
, int cst
)
4218 isl_qpolynomial
*qp
;
4223 bset
= isl_basic_map_domain(isl_basic_map_from_range(bset
));
4224 dim
= isl_basic_set_get_dim(bset
);
4226 qp
= isl_qpolynomial_infty(dim
);
4228 qp
= isl_qpolynomial_zero(dim
);
4230 qp
= isl_qpolynomial_one(dim
);
4231 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset
), qp
);
4234 /* Factor bset, call fn on each of the factors and return the product.
4236 * If no factors can be found, simply call fn on the input.
4237 * Otherwise, construct the factors based on the factorizer,
4238 * call fn on each factor and compute the product.
4240 static __isl_give isl_pw_qpolynomial
*compressed_multiplicative_call(
4241 __isl_take isl_basic_set
*bset
,
4242 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4248 isl_qpolynomial
*qp
;
4249 isl_pw_qpolynomial
*pwqp
;
4253 f
= isl_basic_set_factorizer(bset
);
4256 if (f
->n_group
== 0) {
4257 isl_factorizer_free(f
);
4261 nparam
= isl_basic_set_dim(bset
, isl_dim_param
);
4262 nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
4264 dim
= isl_basic_set_get_dim(bset
);
4265 dim
= isl_dim_domain(dim
);
4266 set
= isl_set_universe(isl_dim_copy(dim
));
4267 qp
= isl_qpolynomial_one(dim
);
4268 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4270 bset
= isl_morph_basic_set(isl_morph_copy(f
->morph
), bset
);
4272 for (i
= 0, n
= 0; i
< f
->n_group
; ++i
) {
4273 isl_basic_set
*bset_i
;
4274 isl_pw_qpolynomial
*pwqp_i
;
4276 bset_i
= isl_basic_set_copy(bset
);
4277 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4278 nparam
+ n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4279 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4281 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
,
4282 n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4283 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
, 0, n
);
4285 pwqp_i
= fn(bset_i
);
4286 pwqp
= isl_pw_qpolynomial_mul(pwqp
, pwqp_i
);
4291 isl_basic_set_free(bset
);
4292 isl_factorizer_free(f
);
4296 isl_basic_set_free(bset
);
4300 /* Factor bset, call fn on each of the factors and return the product.
4301 * The function is assumed to evaluate to zero on empty domains,
4302 * to one on zero-dimensional domains and to infinity on unbounded domains
4303 * and will not be called explicitly on zero-dimensional or unbounded domains.
4305 * We first check for some special cases and remove all equalities.
4306 * Then we hand over control to compressed_multiplicative_call.
4308 __isl_give isl_pw_qpolynomial
*isl_basic_set_multiplicative_call(
4309 __isl_take isl_basic_set
*bset
,
4310 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4314 isl_pw_qpolynomial
*pwqp
;
4315 unsigned orig_nvar
, final_nvar
;
4320 if (isl_basic_set_plain_is_empty(bset
))
4321 return constant_on_domain(bset
, 0);
4323 orig_nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
4326 return constant_on_domain(bset
, 1);
4328 bounded
= isl_basic_set_is_bounded(bset
);
4332 return constant_on_domain(bset
, -1);
4334 if (bset
->n_eq
== 0)
4335 return compressed_multiplicative_call(bset
, fn
);
4337 morph
= isl_basic_set_full_compression(bset
);
4338 bset
= isl_morph_basic_set(isl_morph_copy(morph
), bset
);
4340 final_nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
4342 pwqp
= compressed_multiplicative_call(bset
, fn
);
4344 morph
= isl_morph_remove_dom_dims(morph
, isl_dim_set
, 0, orig_nvar
);
4345 morph
= isl_morph_remove_ran_dims(morph
, isl_dim_set
, 0, final_nvar
);
4346 morph
= isl_morph_inverse(morph
);
4348 pwqp
= isl_pw_qpolynomial_morph(pwqp
, morph
);
4352 isl_basic_set_free(bset
);
4356 /* Drop all floors in "qp", turning each integer division [a/m] into
4357 * a rational division a/m. If "down" is set, then the integer division
4358 * is replaces by (a-(m-1))/m instead.
4360 static __isl_give isl_qpolynomial
*qp_drop_floors(
4361 __isl_take isl_qpolynomial
*qp
, int down
)
4364 struct isl_upoly
*s
;
4368 if (qp
->div
->n_row
== 0)
4371 qp
= isl_qpolynomial_cow(qp
);
4375 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
4377 isl_int_sub(qp
->div
->row
[i
][1],
4378 qp
->div
->row
[i
][1], qp
->div
->row
[i
][0]);
4379 isl_int_add_ui(qp
->div
->row
[i
][1],
4380 qp
->div
->row
[i
][1], 1);
4382 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
4383 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
4384 qp
= substitute_div(qp
, i
, s
);
4392 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4393 * a rational division a/m.
4395 static __isl_give isl_pw_qpolynomial
*pwqp_drop_floors(
4396 __isl_take isl_pw_qpolynomial
*pwqp
)
4403 if (isl_pw_qpolynomial_is_zero(pwqp
))
4406 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
4410 for (i
= 0; i
< pwqp
->n
; ++i
) {
4411 pwqp
->p
[i
].qp
= qp_drop_floors(pwqp
->p
[i
].qp
, 0);
4418 isl_pw_qpolynomial_free(pwqp
);
4422 /* Adjust all the integer divisions in "qp" such that they are at least
4423 * one over the given orthant (identified by "signs"). This ensures
4424 * that they will still be non-negative even after subtracting (m-1)/m.
4426 * In particular, f is replaced by f' + v, changing f = [a/m]
4427 * to f' = [(a - m v)/m].
4428 * If the constant term k in a is smaller than m,
4429 * the constant term of v is set to floor(k/m) - 1.
4430 * For any other term, if the coefficient c and the variable x have
4431 * the same sign, then no changes are needed.
4432 * Otherwise, if the variable is positive (and c is negative),
4433 * then the coefficient of x in v is set to floor(c/m).
4434 * If the variable is negative (and c is positive),
4435 * then the coefficient of x in v is set to ceil(c/m).
4437 static __isl_give isl_qpolynomial
*make_divs_pos(__isl_take isl_qpolynomial
*qp
,
4443 struct isl_upoly
*s
;
4445 qp
= isl_qpolynomial_cow(qp
);
4448 qp
->div
= isl_mat_cow(qp
->div
);
4452 total
= isl_dim_total(qp
->dim
);
4453 v
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
4455 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4456 isl_int
*row
= qp
->div
->row
[i
];
4460 if (isl_int_lt(row
[1], row
[0])) {
4461 isl_int_fdiv_q(v
->el
[0], row
[1], row
[0]);
4462 isl_int_sub_ui(v
->el
[0], v
->el
[0], 1);
4463 isl_int_submul(row
[1], row
[0], v
->el
[0]);
4465 for (j
= 0; j
< total
; ++j
) {
4466 if (isl_int_sgn(row
[2 + j
]) * signs
[j
] >= 0)
4469 isl_int_cdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4471 isl_int_fdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4472 isl_int_submul(row
[2 + j
], row
[0], v
->el
[1 + j
]);
4474 for (j
= 0; j
< i
; ++j
) {
4475 if (isl_int_sgn(row
[2 + total
+ j
]) >= 0)
4477 isl_int_fdiv_q(v
->el
[1 + total
+ j
],
4478 row
[2 + total
+ j
], row
[0]);
4479 isl_int_submul(row
[2 + total
+ j
],
4480 row
[0], v
->el
[1 + total
+ j
]);
4482 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
4483 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
4485 isl_seq_combine(qp
->div
->row
[j
] + 1,
4486 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
4487 qp
->div
->row
[j
][2 + total
+ i
], v
->el
, v
->size
);
4489 isl_int_set_si(v
->el
[1 + total
+ i
], 1);
4490 s
= isl_upoly_from_affine(qp
->dim
->ctx
, v
->el
,
4491 qp
->div
->ctx
->one
, v
->size
);
4492 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ i
, 1, &s
);
4502 isl_qpolynomial_free(qp
);
4506 struct isl_to_poly_data
{
4508 isl_pw_qpolynomial
*res
;
4509 isl_qpolynomial
*qp
;
4512 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4513 * We first make all integer divisions positive and then split the
4514 * quasipolynomials into terms with sign data->sign (the direction
4515 * of the requested approximation) and terms with the opposite sign.
4516 * In the first set of terms, each integer division [a/m] is
4517 * overapproximated by a/m, while in the second it is underapproximated
4520 static int to_polynomial_on_orthant(__isl_take isl_set
*orthant
, int *signs
,
4523 struct isl_to_poly_data
*data
= user
;
4524 isl_pw_qpolynomial
*t
;
4525 isl_qpolynomial
*qp
, *up
, *down
;
4527 qp
= isl_qpolynomial_copy(data
->qp
);
4528 qp
= make_divs_pos(qp
, signs
);
4530 up
= isl_qpolynomial_terms_of_sign(qp
, signs
, data
->sign
);
4531 up
= qp_drop_floors(up
, 0);
4532 down
= isl_qpolynomial_terms_of_sign(qp
, signs
, -data
->sign
);
4533 down
= qp_drop_floors(down
, 1);
4535 isl_qpolynomial_free(qp
);
4536 qp
= isl_qpolynomial_add(up
, down
);
4538 t
= isl_pw_qpolynomial_alloc(orthant
, qp
);
4539 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, t
);
4544 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4545 * the polynomial will be an overapproximation. If "sign" is negative,
4546 * it will be an underapproximation. If "sign" is zero, the approximation
4547 * will lie somewhere in between.
4549 * In particular, is sign == 0, we simply drop the floors, turning
4550 * the integer divisions into rational divisions.
4551 * Otherwise, we split the domains into orthants, make all integer divisions
4552 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4553 * depending on the requested sign and the sign of the term in which
4554 * the integer division appears.
4556 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_to_polynomial(
4557 __isl_take isl_pw_qpolynomial
*pwqp
, int sign
)
4560 struct isl_to_poly_data data
;
4563 return pwqp_drop_floors(pwqp
);
4569 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp
));
4571 for (i
= 0; i
< pwqp
->n
; ++i
) {
4572 if (pwqp
->p
[i
].qp
->div
->n_row
== 0) {
4573 isl_pw_qpolynomial
*t
;
4574 t
= isl_pw_qpolynomial_alloc(
4575 isl_set_copy(pwqp
->p
[i
].set
),
4576 isl_qpolynomial_copy(pwqp
->p
[i
].qp
));
4577 data
.res
= isl_pw_qpolynomial_add_disjoint(data
.res
, t
);
4580 data
.qp
= pwqp
->p
[i
].qp
;
4581 if (isl_set_foreach_orthant(pwqp
->p
[i
].set
,
4582 &to_polynomial_on_orthant
, &data
) < 0)
4586 isl_pw_qpolynomial_free(pwqp
);
4590 isl_pw_qpolynomial_free(pwqp
);
4591 isl_pw_qpolynomial_free(data
.res
);
4595 static int poly_entry(void **entry
, void *user
)
4598 isl_pw_qpolynomial
**pwqp
= (isl_pw_qpolynomial
**)entry
;
4600 *pwqp
= isl_pw_qpolynomial_to_polynomial(*pwqp
, *sign
);
4602 return *pwqp
? 0 : -1;
4605 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_to_polynomial(
4606 __isl_take isl_union_pw_qpolynomial
*upwqp
, int sign
)
4608 upwqp
= isl_union_pw_qpolynomial_cow(upwqp
);
4612 if (isl_hash_table_foreach(upwqp
->dim
->ctx
, &upwqp
->table
,
4613 &poly_entry
, &sign
) < 0)
4618 isl_union_pw_qpolynomial_free(upwqp
);
4622 __isl_give isl_basic_map
*isl_basic_map_from_qpolynomial(
4623 __isl_take isl_qpolynomial
*qp
)
4627 isl_vec
*aff
= NULL
;
4628 isl_basic_map
*bmap
= NULL
;
4634 if (!isl_upoly_is_affine(qp
->upoly
))
4635 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
4636 "input quasi-polynomial not affine", goto error
);
4637 aff
= isl_qpolynomial_extract_affine(qp
);
4640 dim
= isl_qpolynomial_get_dim(qp
);
4641 dim
= isl_dim_from_domain(dim
);
4642 pos
= 1 + isl_dim_offset(dim
, isl_dim_out
);
4643 dim
= isl_dim_add(dim
, isl_dim_out
, 1);
4644 n_div
= qp
->div
->n_row
;
4645 bmap
= isl_basic_map_alloc_dim(dim
, n_div
, 1, 2 * n_div
);
4647 for (i
= 0; i
< n_div
; ++i
) {
4648 k
= isl_basic_map_alloc_div(bmap
);
4651 isl_seq_cpy(bmap
->div
[k
], qp
->div
->row
[i
], qp
->div
->n_col
);
4652 isl_int_set_si(bmap
->div
[k
][qp
->div
->n_col
], 0);
4653 if (isl_basic_map_add_div_constraints(bmap
, k
) < 0)
4656 k
= isl_basic_map_alloc_equality(bmap
);
4659 isl_int_neg(bmap
->eq
[k
][pos
], aff
->el
[0]);
4660 isl_seq_cpy(bmap
->eq
[k
], aff
->el
+ 1, pos
);
4661 isl_seq_cpy(bmap
->eq
[k
] + pos
+ 1, aff
->el
+ 1 + pos
, n_div
);
4664 isl_qpolynomial_free(qp
);
4665 bmap
= isl_basic_map_finalize(bmap
);
4669 isl_qpolynomial_free(qp
);
4670 isl_basic_map_free(bmap
);