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_scale(
1422 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1424 return isl_qpolynomial_mul_isl_int(qp
, v
);
1427 __isl_give isl_qpolynomial
*isl_qpolynomial_mul(__isl_take isl_qpolynomial
*qp1
,
1428 __isl_take isl_qpolynomial
*qp2
)
1430 qp1
= isl_qpolynomial_cow(qp1
);
1435 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1436 return isl_qpolynomial_mul(qp2
, qp1
);
1438 isl_assert(qp1
->dim
->ctx
, isl_dim_equal(qp1
->dim
, qp2
->dim
), goto error
);
1439 if (!compatible_divs(qp1
->div
, qp2
->div
))
1440 return with_merged_divs(isl_qpolynomial_mul
, qp1
, qp2
);
1442 qp1
->upoly
= isl_upoly_mul(qp1
->upoly
, isl_upoly_copy(qp2
->upoly
));
1446 isl_qpolynomial_free(qp2
);
1450 isl_qpolynomial_free(qp1
);
1451 isl_qpolynomial_free(qp2
);
1455 __isl_give isl_qpolynomial
*isl_qpolynomial_pow(__isl_take isl_qpolynomial
*qp
,
1458 qp
= isl_qpolynomial_cow(qp
);
1463 qp
->upoly
= isl_upoly_pow(qp
->upoly
, power
);
1469 isl_qpolynomial_free(qp
);
1473 __isl_give isl_qpolynomial
*isl_qpolynomial_zero(__isl_take isl_dim
*dim
)
1477 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
1480 __isl_give isl_qpolynomial
*isl_qpolynomial_one(__isl_take isl_dim
*dim
)
1484 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_one(dim
->ctx
));
1487 __isl_give isl_qpolynomial
*isl_qpolynomial_infty(__isl_take isl_dim
*dim
)
1491 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_infty(dim
->ctx
));
1494 __isl_give isl_qpolynomial
*isl_qpolynomial_neginfty(__isl_take isl_dim
*dim
)
1498 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_neginfty(dim
->ctx
));
1501 __isl_give isl_qpolynomial
*isl_qpolynomial_nan(__isl_take isl_dim
*dim
)
1505 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_nan(dim
->ctx
));
1508 __isl_give isl_qpolynomial
*isl_qpolynomial_cst(__isl_take isl_dim
*dim
,
1511 struct isl_qpolynomial
*qp
;
1512 struct isl_upoly_cst
*cst
;
1517 qp
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
1521 cst
= isl_upoly_as_cst(qp
->upoly
);
1522 isl_int_set(cst
->n
, v
);
1527 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial
*qp
,
1528 isl_int
*n
, isl_int
*d
)
1530 struct isl_upoly_cst
*cst
;
1535 if (!isl_upoly_is_cst(qp
->upoly
))
1538 cst
= isl_upoly_as_cst(qp
->upoly
);
1543 isl_int_set(*n
, cst
->n
);
1545 isl_int_set(*d
, cst
->d
);
1550 int isl_upoly_is_affine(__isl_keep
struct isl_upoly
*up
)
1553 struct isl_upoly_rec
*rec
;
1561 rec
= isl_upoly_as_rec(up
);
1568 isl_assert(up
->ctx
, rec
->n
> 1, return -1);
1570 is_cst
= isl_upoly_is_cst(rec
->p
[1]);
1576 return isl_upoly_is_affine(rec
->p
[0]);
1579 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial
*qp
)
1584 if (qp
->div
->n_row
> 0)
1587 return isl_upoly_is_affine(qp
->upoly
);
1590 static void update_coeff(__isl_keep isl_vec
*aff
,
1591 __isl_keep
struct isl_upoly_cst
*cst
, int pos
)
1596 if (isl_int_is_zero(cst
->n
))
1601 isl_int_gcd(gcd
, cst
->d
, aff
->el
[0]);
1602 isl_int_divexact(f
, cst
->d
, gcd
);
1603 isl_int_divexact(gcd
, aff
->el
[0], gcd
);
1604 isl_seq_scale(aff
->el
, aff
->el
, f
, aff
->size
);
1605 isl_int_mul(aff
->el
[1 + pos
], gcd
, cst
->n
);
1610 int isl_upoly_update_affine(__isl_keep
struct isl_upoly
*up
,
1611 __isl_keep isl_vec
*aff
)
1613 struct isl_upoly_cst
*cst
;
1614 struct isl_upoly_rec
*rec
;
1620 struct isl_upoly_cst
*cst
;
1622 cst
= isl_upoly_as_cst(up
);
1625 update_coeff(aff
, cst
, 0);
1629 rec
= isl_upoly_as_rec(up
);
1632 isl_assert(up
->ctx
, rec
->n
== 2, return -1);
1634 cst
= isl_upoly_as_cst(rec
->p
[1]);
1637 update_coeff(aff
, cst
, 1 + up
->var
);
1639 return isl_upoly_update_affine(rec
->p
[0], aff
);
1642 __isl_give isl_vec
*isl_qpolynomial_extract_affine(
1643 __isl_keep isl_qpolynomial
*qp
)
1651 d
= isl_dim_total(qp
->dim
);
1652 aff
= isl_vec_alloc(qp
->div
->ctx
, 2 + d
+ qp
->div
->n_row
);
1656 isl_seq_clr(aff
->el
+ 1, 1 + d
+ qp
->div
->n_row
);
1657 isl_int_set_si(aff
->el
[0], 1);
1659 if (isl_upoly_update_affine(qp
->upoly
, aff
) < 0)
1668 int isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial
*qp1
,
1669 __isl_keep isl_qpolynomial
*qp2
)
1676 equal
= isl_dim_equal(qp1
->dim
, qp2
->dim
);
1677 if (equal
< 0 || !equal
)
1680 equal
= isl_mat_is_equal(qp1
->div
, qp2
->div
);
1681 if (equal
< 0 || !equal
)
1684 return isl_upoly_is_equal(qp1
->upoly
, qp2
->upoly
);
1687 static void upoly_update_den(__isl_keep
struct isl_upoly
*up
, isl_int
*d
)
1690 struct isl_upoly_rec
*rec
;
1692 if (isl_upoly_is_cst(up
)) {
1693 struct isl_upoly_cst
*cst
;
1694 cst
= isl_upoly_as_cst(up
);
1697 isl_int_lcm(*d
, *d
, cst
->d
);
1701 rec
= isl_upoly_as_rec(up
);
1705 for (i
= 0; i
< rec
->n
; ++i
)
1706 upoly_update_den(rec
->p
[i
], d
);
1709 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial
*qp
, isl_int
*d
)
1711 isl_int_set_si(*d
, 1);
1714 upoly_update_den(qp
->upoly
, d
);
1717 __isl_give isl_qpolynomial
*isl_qpolynomial_var_pow(__isl_take isl_dim
*dim
,
1720 struct isl_ctx
*ctx
;
1727 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_var_pow(ctx
, pos
, power
));
1730 __isl_give isl_qpolynomial
*isl_qpolynomial_var(__isl_take isl_dim
*dim
,
1731 enum isl_dim_type type
, unsigned pos
)
1736 isl_assert(dim
->ctx
, isl_dim_size(dim
, isl_dim_in
) == 0, goto error
);
1737 isl_assert(dim
->ctx
, pos
< isl_dim_size(dim
, type
), goto error
);
1739 if (type
== isl_dim_set
)
1740 pos
+= isl_dim_size(dim
, isl_dim_param
);
1742 return isl_qpolynomial_var_pow(dim
, pos
, 1);
1748 __isl_give
struct isl_upoly
*isl_upoly_subs(__isl_take
struct isl_upoly
*up
,
1749 unsigned first
, unsigned n
, __isl_keep
struct isl_upoly
**subs
)
1752 struct isl_upoly_rec
*rec
;
1753 struct isl_upoly
*base
, *res
;
1758 if (isl_upoly_is_cst(up
))
1761 if (up
->var
< first
)
1764 rec
= isl_upoly_as_rec(up
);
1768 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
1770 if (up
->var
>= first
+ n
)
1771 base
= isl_upoly_var_pow(up
->ctx
, up
->var
, 1);
1773 base
= isl_upoly_copy(subs
[up
->var
- first
]);
1775 res
= isl_upoly_subs(isl_upoly_copy(rec
->p
[rec
->n
- 1]), first
, n
, subs
);
1776 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1777 struct isl_upoly
*t
;
1778 t
= isl_upoly_subs(isl_upoly_copy(rec
->p
[i
]), first
, n
, subs
);
1779 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
1780 res
= isl_upoly_sum(res
, t
);
1783 isl_upoly_free(base
);
1792 __isl_give
struct isl_upoly
*isl_upoly_from_affine(isl_ctx
*ctx
, isl_int
*f
,
1793 isl_int denom
, unsigned len
)
1796 struct isl_upoly
*up
;
1798 isl_assert(ctx
, len
>= 1, return NULL
);
1800 up
= isl_upoly_rat_cst(ctx
, f
[0], denom
);
1801 for (i
= 0; i
< len
- 1; ++i
) {
1802 struct isl_upoly
*t
;
1803 struct isl_upoly
*c
;
1805 if (isl_int_is_zero(f
[1 + i
]))
1808 c
= isl_upoly_rat_cst(ctx
, f
[1 + i
], denom
);
1809 t
= isl_upoly_var_pow(ctx
, i
, 1);
1810 t
= isl_upoly_mul(c
, t
);
1811 up
= isl_upoly_sum(up
, t
);
1817 /* Remove common factor of non-constant terms and denominator.
1819 static void normalize_div(__isl_keep isl_qpolynomial
*qp
, int div
)
1821 isl_ctx
*ctx
= qp
->div
->ctx
;
1822 unsigned total
= qp
->div
->n_col
- 2;
1824 isl_seq_gcd(qp
->div
->row
[div
] + 2, total
, &ctx
->normalize_gcd
);
1825 isl_int_gcd(ctx
->normalize_gcd
,
1826 ctx
->normalize_gcd
, qp
->div
->row
[div
][0]);
1827 if (isl_int_is_one(ctx
->normalize_gcd
))
1830 isl_seq_scale_down(qp
->div
->row
[div
] + 2, qp
->div
->row
[div
] + 2,
1831 ctx
->normalize_gcd
, total
);
1832 isl_int_divexact(qp
->div
->row
[div
][0], qp
->div
->row
[div
][0],
1833 ctx
->normalize_gcd
);
1834 isl_int_fdiv_q(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1],
1835 ctx
->normalize_gcd
);
1838 /* Replace the integer division identified by "div" by the polynomial "s".
1839 * The integer division is assumed not to appear in the definition
1840 * of any other integer divisions.
1842 static __isl_give isl_qpolynomial
*substitute_div(
1843 __isl_take isl_qpolynomial
*qp
,
1844 int div
, __isl_take
struct isl_upoly
*s
)
1853 qp
= isl_qpolynomial_cow(qp
);
1857 total
= isl_dim_total(qp
->dim
);
1858 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ div
, 1, &s
);
1862 reordering
= isl_alloc_array(qp
->dim
->ctx
, int, total
+ qp
->div
->n_row
);
1865 for (i
= 0; i
< total
+ div
; ++i
)
1867 for (i
= total
+ div
+ 1; i
< total
+ qp
->div
->n_row
; ++i
)
1868 reordering
[i
] = i
- 1;
1869 qp
->div
= isl_mat_drop_rows(qp
->div
, div
, 1);
1870 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + total
+ div
, 1);
1871 qp
->upoly
= reorder(qp
->upoly
, reordering
);
1874 if (!qp
->upoly
|| !qp
->div
)
1880 isl_qpolynomial_free(qp
);
1885 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1886 * divisions because d is equal to 1 by their definition, i.e., e.
1888 static __isl_give isl_qpolynomial
*substitute_non_divs(
1889 __isl_take isl_qpolynomial
*qp
)
1893 struct isl_upoly
*s
;
1898 total
= isl_dim_total(qp
->dim
);
1899 for (i
= 0; qp
&& i
< qp
->div
->n_row
; ++i
) {
1900 if (!isl_int_is_one(qp
->div
->row
[i
][0]))
1902 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
1903 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
1905 isl_seq_combine(qp
->div
->row
[j
] + 1,
1906 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
1907 qp
->div
->row
[j
][2 + total
+ i
],
1908 qp
->div
->row
[i
] + 1, 1 + total
+ i
);
1909 isl_int_set_si(qp
->div
->row
[j
][2 + total
+ i
], 0);
1910 normalize_div(qp
, j
);
1912 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
1913 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
1914 qp
= substitute_div(qp
, i
, s
);
1921 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1922 * with d the denominator. When replacing the coefficient e of x by
1923 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1924 * inside the division, so we need to add floor(e/d) * x outside.
1925 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1926 * to adjust the coefficient of x in each later div that depends on the
1927 * current div "div" and also in the affine expression "aff"
1928 * (if it too depends on "div").
1930 static void reduce_div(__isl_keep isl_qpolynomial
*qp
, int div
,
1931 __isl_keep isl_vec
*aff
)
1935 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
1938 for (i
= 0; i
< 1 + total
+ div
; ++i
) {
1939 if (isl_int_is_nonneg(qp
->div
->row
[div
][1 + i
]) &&
1940 isl_int_lt(qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]))
1942 isl_int_fdiv_q(v
, qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
1943 isl_int_fdiv_r(qp
->div
->row
[div
][1 + i
],
1944 qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
1945 if (!isl_int_is_zero(aff
->el
[1 + total
+ div
]))
1946 isl_int_addmul(aff
->el
[i
], v
, aff
->el
[1 + total
+ div
]);
1947 for (j
= div
+ 1; j
< qp
->div
->n_row
; ++j
) {
1948 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ div
]))
1950 isl_int_addmul(qp
->div
->row
[j
][1 + i
],
1951 v
, qp
->div
->row
[j
][2 + total
+ div
]);
1957 /* Check if the last non-zero coefficient is bigger that half of the
1958 * denominator. If so, we will invert the div to further reduce the number
1959 * of distinct divs that may appear.
1960 * If the last non-zero coefficient is exactly half the denominator,
1961 * then we continue looking for earlier coefficients that are bigger
1962 * than half the denominator.
1964 static int needs_invert(__isl_keep isl_mat
*div
, int row
)
1969 for (i
= div
->n_col
- 1; i
>= 1; --i
) {
1970 if (isl_int_is_zero(div
->row
[row
][i
]))
1972 isl_int_mul_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
1973 cmp
= isl_int_cmp(div
->row
[row
][i
], div
->row
[row
][0]);
1974 isl_int_divexact_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
1984 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
1985 * We only invert the coefficients of e (and the coefficient of q in
1986 * later divs and in "aff"). After calling this function, the
1987 * coefficients of e should be reduced again.
1989 static void invert_div(__isl_keep isl_qpolynomial
*qp
, int div
,
1990 __isl_keep isl_vec
*aff
)
1992 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
1994 isl_seq_neg(qp
->div
->row
[div
] + 1,
1995 qp
->div
->row
[div
] + 1, qp
->div
->n_col
- 1);
1996 isl_int_sub_ui(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1], 1);
1997 isl_int_add(qp
->div
->row
[div
][1],
1998 qp
->div
->row
[div
][1], qp
->div
->row
[div
][0]);
1999 if (!isl_int_is_zero(aff
->el
[1 + total
+ div
]))
2000 isl_int_neg(aff
->el
[1 + total
+ div
], aff
->el
[1 + total
+ div
]);
2001 isl_mat_col_mul(qp
->div
, 2 + total
+ div
,
2002 qp
->div
->ctx
->negone
, 2 + total
+ div
);
2005 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2006 * in the interval [0, d-1], with d the denominator and such that the
2007 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2009 * After the reduction, some divs may have become redundant or identical,
2010 * so we call substitute_non_divs and sort_divs. If these functions
2011 * eliminate divs or merge two or more divs into one, the coefficients
2012 * of the enclosing divs may have to be reduced again, so we call
2013 * ourselves recursively if the number of divs decreases.
2015 static __isl_give isl_qpolynomial
*reduce_divs(__isl_take isl_qpolynomial
*qp
)
2018 isl_vec
*aff
= NULL
;
2019 struct isl_upoly
*s
;
2025 aff
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
2026 aff
= isl_vec_clr(aff
);
2030 isl_int_set_si(aff
->el
[1 + qp
->upoly
->var
], 1);
2032 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2033 normalize_div(qp
, i
);
2034 reduce_div(qp
, i
, aff
);
2035 if (needs_invert(qp
->div
, i
)) {
2036 invert_div(qp
, i
, aff
);
2037 reduce_div(qp
, i
, aff
);
2041 s
= isl_upoly_from_affine(qp
->div
->ctx
, aff
->el
,
2042 qp
->div
->ctx
->one
, aff
->size
);
2043 qp
->upoly
= isl_upoly_subs(qp
->upoly
, qp
->upoly
->var
, 1, &s
);
2050 n_div
= qp
->div
->n_row
;
2051 qp
= substitute_non_divs(qp
);
2053 if (qp
&& qp
->div
->n_row
< n_div
)
2054 return reduce_divs(qp
);
2058 isl_qpolynomial_free(qp
);
2063 /* Assumes each div only depends on earlier divs.
2065 __isl_give isl_qpolynomial
*isl_qpolynomial_div_pow(__isl_take isl_div
*div
,
2068 struct isl_qpolynomial
*qp
= NULL
;
2069 struct isl_upoly_rec
*rec
;
2070 struct isl_upoly_cst
*cst
;
2077 d
= div
->line
- div
->bmap
->div
;
2079 pos
= isl_dim_total(div
->bmap
->dim
) + d
;
2080 rec
= isl_upoly_alloc_rec(div
->ctx
, pos
, 1 + power
);
2081 qp
= isl_qpolynomial_alloc(isl_basic_map_get_dim(div
->bmap
),
2082 div
->bmap
->n_div
, &rec
->up
);
2086 for (i
= 0; i
< div
->bmap
->n_div
; ++i
)
2087 isl_seq_cpy(qp
->div
->row
[i
], div
->bmap
->div
[i
], qp
->div
->n_col
);
2089 for (i
= 0; i
< 1 + power
; ++i
) {
2090 rec
->p
[i
] = isl_upoly_zero(div
->ctx
);
2095 cst
= isl_upoly_as_cst(rec
->p
[power
]);
2096 isl_int_set_si(cst
->n
, 1);
2100 qp
= reduce_divs(qp
);
2104 isl_qpolynomial_free(qp
);
2109 __isl_give isl_qpolynomial
*isl_qpolynomial_div(__isl_take isl_div
*div
)
2111 return isl_qpolynomial_div_pow(div
, 1);
2114 __isl_give isl_qpolynomial
*isl_qpolynomial_rat_cst(__isl_take isl_dim
*dim
,
2115 const isl_int n
, const isl_int d
)
2117 struct isl_qpolynomial
*qp
;
2118 struct isl_upoly_cst
*cst
;
2120 qp
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
2124 cst
= isl_upoly_as_cst(qp
->upoly
);
2125 isl_int_set(cst
->n
, n
);
2126 isl_int_set(cst
->d
, d
);
2131 static int up_set_active(__isl_keep
struct isl_upoly
*up
, int *active
, int d
)
2133 struct isl_upoly_rec
*rec
;
2139 if (isl_upoly_is_cst(up
))
2143 active
[up
->var
] = 1;
2145 rec
= isl_upoly_as_rec(up
);
2146 for (i
= 0; i
< rec
->n
; ++i
)
2147 if (up_set_active(rec
->p
[i
], active
, d
) < 0)
2153 static int set_active(__isl_keep isl_qpolynomial
*qp
, int *active
)
2156 int d
= isl_dim_total(qp
->dim
);
2161 for (i
= 0; i
< d
; ++i
)
2162 for (j
= 0; j
< qp
->div
->n_row
; ++j
) {
2163 if (isl_int_is_zero(qp
->div
->row
[j
][2 + i
]))
2169 return up_set_active(qp
->upoly
, active
, d
);
2172 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial
*qp
,
2173 enum isl_dim_type type
, unsigned first
, unsigned n
)
2184 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_dim_size(qp
->dim
, type
),
2186 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2187 type
== isl_dim_set
, return -1);
2189 active
= isl_calloc_array(qp
->dim
->ctx
, int, isl_dim_total(qp
->dim
));
2190 if (set_active(qp
, active
) < 0)
2193 if (type
== isl_dim_set
)
2194 first
+= isl_dim_size(qp
->dim
, isl_dim_param
);
2195 for (i
= 0; i
< n
; ++i
)
2196 if (active
[first
+ i
]) {
2209 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2210 * of the divs that do appear in the quasi-polynomial.
2212 static __isl_give isl_qpolynomial
*remove_redundant_divs(
2213 __isl_take isl_qpolynomial
*qp
)
2220 int *reordering
= NULL
;
2227 if (qp
->div
->n_row
== 0)
2230 d
= isl_dim_total(qp
->dim
);
2231 len
= qp
->div
->n_col
- 2;
2232 ctx
= isl_qpolynomial_get_ctx(qp
);
2233 active
= isl_calloc_array(ctx
, int, len
);
2237 if (up_set_active(qp
->upoly
, active
, len
) < 0)
2240 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
2241 if (!active
[d
+ i
]) {
2245 for (j
= 0; j
< i
; ++j
) {
2246 if (isl_int_is_zero(qp
->div
->row
[i
][2 + d
+ j
]))
2258 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
2262 for (i
= 0; i
< d
; ++i
)
2266 n_div
= qp
->div
->n_row
;
2267 for (i
= 0; i
< n_div
; ++i
) {
2268 if (!active
[d
+ i
]) {
2269 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
2270 qp
->div
= isl_mat_drop_cols(qp
->div
,
2271 2 + d
+ i
- skip
, 1);
2274 reordering
[d
+ i
] = d
+ i
- skip
;
2277 qp
->upoly
= reorder(qp
->upoly
, reordering
);
2279 if (!qp
->upoly
|| !qp
->div
)
2289 isl_qpolynomial_free(qp
);
2293 __isl_give
struct isl_upoly
*isl_upoly_drop(__isl_take
struct isl_upoly
*up
,
2294 unsigned first
, unsigned n
)
2297 struct isl_upoly_rec
*rec
;
2301 if (n
== 0 || up
->var
< 0 || up
->var
< first
)
2303 if (up
->var
< first
+ n
) {
2304 up
= replace_by_constant_term(up
);
2305 return isl_upoly_drop(up
, first
, n
);
2307 up
= isl_upoly_cow(up
);
2311 rec
= isl_upoly_as_rec(up
);
2315 for (i
= 0; i
< rec
->n
; ++i
) {
2316 rec
->p
[i
] = isl_upoly_drop(rec
->p
[i
], first
, n
);
2327 __isl_give isl_qpolynomial
*isl_qpolynomial_set_dim_name(
2328 __isl_take isl_qpolynomial
*qp
,
2329 enum isl_dim_type type
, unsigned pos
, const char *s
)
2331 qp
= isl_qpolynomial_cow(qp
);
2334 qp
->dim
= isl_dim_set_name(qp
->dim
, type
, pos
, s
);
2339 isl_qpolynomial_free(qp
);
2343 __isl_give isl_qpolynomial
*isl_qpolynomial_drop_dims(
2344 __isl_take isl_qpolynomial
*qp
,
2345 enum isl_dim_type type
, unsigned first
, unsigned n
)
2349 if (n
== 0 && !isl_dim_is_named_or_nested(qp
->dim
, type
))
2352 qp
= isl_qpolynomial_cow(qp
);
2356 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_dim_size(qp
->dim
, type
),
2358 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2359 type
== isl_dim_set
, goto error
);
2361 qp
->dim
= isl_dim_drop(qp
->dim
, type
, first
, n
);
2365 if (type
== isl_dim_set
)
2366 first
+= isl_dim_size(qp
->dim
, isl_dim_param
);
2368 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + first
, n
);
2372 qp
->upoly
= isl_upoly_drop(qp
->upoly
, first
, n
);
2378 isl_qpolynomial_free(qp
);
2382 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities(
2383 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2389 struct isl_upoly
*up
;
2393 if (eq
->n_eq
== 0) {
2394 isl_basic_set_free(eq
);
2398 qp
= isl_qpolynomial_cow(qp
);
2401 qp
->div
= isl_mat_cow(qp
->div
);
2405 total
= 1 + isl_dim_total(eq
->dim
);
2407 isl_int_init(denom
);
2408 for (i
= 0; i
< eq
->n_eq
; ++i
) {
2409 j
= isl_seq_last_non_zero(eq
->eq
[i
], total
+ n_div
);
2410 if (j
< 0 || j
== 0 || j
>= total
)
2413 for (k
= 0; k
< qp
->div
->n_row
; ++k
) {
2414 if (isl_int_is_zero(qp
->div
->row
[k
][1 + j
]))
2416 isl_seq_elim(qp
->div
->row
[k
] + 1, eq
->eq
[i
], j
, total
,
2417 &qp
->div
->row
[k
][0]);
2418 normalize_div(qp
, k
);
2421 if (isl_int_is_pos(eq
->eq
[i
][j
]))
2422 isl_seq_neg(eq
->eq
[i
], eq
->eq
[i
], total
);
2423 isl_int_abs(denom
, eq
->eq
[i
][j
]);
2424 isl_int_set_si(eq
->eq
[i
][j
], 0);
2426 up
= isl_upoly_from_affine(qp
->dim
->ctx
,
2427 eq
->eq
[i
], denom
, total
);
2428 qp
->upoly
= isl_upoly_subs(qp
->upoly
, j
- 1, 1, &up
);
2431 isl_int_clear(denom
);
2436 isl_basic_set_free(eq
);
2438 qp
= substitute_non_divs(qp
);
2443 isl_basic_set_free(eq
);
2444 isl_qpolynomial_free(qp
);
2448 static __isl_give isl_basic_set
*add_div_constraints(
2449 __isl_take isl_basic_set
*bset
, __isl_take isl_mat
*div
)
2457 bset
= isl_basic_set_extend_constraints(bset
, 0, 2 * div
->n_row
);
2460 total
= isl_basic_set_total_dim(bset
);
2461 for (i
= 0; i
< div
->n_row
; ++i
)
2462 if (isl_basic_set_add_div_constraints_var(bset
,
2463 total
- div
->n_row
+ i
, div
->row
[i
]) < 0)
2470 isl_basic_set_free(bset
);
2474 /* Look for equalities among the variables shared by context and qp
2475 * and the integer divisions of qp, if any.
2476 * The equalities are then used to eliminate variables and/or integer
2477 * divisions from qp.
2479 __isl_give isl_qpolynomial
*isl_qpolynomial_gist(
2480 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
2486 if (qp
->div
->n_row
> 0) {
2487 isl_basic_set
*bset
;
2488 context
= isl_set_add_dims(context
, isl_dim_set
,
2490 bset
= isl_basic_set_universe(isl_set_get_dim(context
));
2491 bset
= add_div_constraints(bset
, isl_mat_copy(qp
->div
));
2492 context
= isl_set_intersect(context
,
2493 isl_set_from_basic_set(bset
));
2496 aff
= isl_set_affine_hull(context
);
2497 return isl_qpolynomial_substitute_equalities(qp
, aff
);
2499 isl_qpolynomial_free(qp
);
2500 isl_set_free(context
);
2505 #define PW isl_pw_qpolynomial
2507 #define EL isl_qpolynomial
2509 #define EL_IS_ZERO is_zero
2513 #define IS_ZERO is_zero
2517 #include <isl_pw_templ.c>
2520 #define UNION isl_union_pw_qpolynomial
2522 #define PART isl_pw_qpolynomial
2524 #define PARTS pw_qpolynomial
2526 #include <isl_union_templ.c>
2528 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial
*pwqp
)
2536 if (!isl_set_plain_is_universe(pwqp
->p
[0].set
))
2539 return isl_qpolynomial_is_one(pwqp
->p
[0].qp
);
2542 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_mul(
2543 __isl_take isl_pw_qpolynomial
*pwqp1
,
2544 __isl_take isl_pw_qpolynomial
*pwqp2
)
2547 struct isl_pw_qpolynomial
*res
;
2549 if (!pwqp1
|| !pwqp2
)
2552 isl_assert(pwqp1
->dim
->ctx
, isl_dim_equal(pwqp1
->dim
, pwqp2
->dim
),
2555 if (isl_pw_qpolynomial_is_zero(pwqp1
)) {
2556 isl_pw_qpolynomial_free(pwqp2
);
2560 if (isl_pw_qpolynomial_is_zero(pwqp2
)) {
2561 isl_pw_qpolynomial_free(pwqp1
);
2565 if (isl_pw_qpolynomial_is_one(pwqp1
)) {
2566 isl_pw_qpolynomial_free(pwqp1
);
2570 if (isl_pw_qpolynomial_is_one(pwqp2
)) {
2571 isl_pw_qpolynomial_free(pwqp2
);
2575 n
= pwqp1
->n
* pwqp2
->n
;
2576 res
= isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1
->dim
), n
);
2578 for (i
= 0; i
< pwqp1
->n
; ++i
) {
2579 for (j
= 0; j
< pwqp2
->n
; ++j
) {
2580 struct isl_set
*common
;
2581 struct isl_qpolynomial
*prod
;
2582 common
= isl_set_intersect(isl_set_copy(pwqp1
->p
[i
].set
),
2583 isl_set_copy(pwqp2
->p
[j
].set
));
2584 if (isl_set_plain_is_empty(common
)) {
2585 isl_set_free(common
);
2589 prod
= isl_qpolynomial_mul(
2590 isl_qpolynomial_copy(pwqp1
->p
[i
].qp
),
2591 isl_qpolynomial_copy(pwqp2
->p
[j
].qp
));
2593 res
= isl_pw_qpolynomial_add_piece(res
, common
, prod
);
2597 isl_pw_qpolynomial_free(pwqp1
);
2598 isl_pw_qpolynomial_free(pwqp2
);
2602 isl_pw_qpolynomial_free(pwqp1
);
2603 isl_pw_qpolynomial_free(pwqp2
);
2607 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_sub(
2608 __isl_take isl_pw_qpolynomial
*pwqp1
,
2609 __isl_take isl_pw_qpolynomial
*pwqp2
)
2611 return isl_pw_qpolynomial_add(pwqp1
, isl_pw_qpolynomial_neg(pwqp2
));
2614 __isl_give
struct isl_upoly
*isl_upoly_eval(
2615 __isl_take
struct isl_upoly
*up
, __isl_take isl_vec
*vec
)
2618 struct isl_upoly_rec
*rec
;
2619 struct isl_upoly
*res
;
2620 struct isl_upoly
*base
;
2622 if (isl_upoly_is_cst(up
)) {
2627 rec
= isl_upoly_as_rec(up
);
2631 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
2633 base
= isl_upoly_rat_cst(up
->ctx
, vec
->el
[1 + up
->var
], vec
->el
[0]);
2635 res
= isl_upoly_eval(isl_upoly_copy(rec
->p
[rec
->n
- 1]),
2638 for (i
= rec
->n
- 2; i
>= 0; --i
) {
2639 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
2640 res
= isl_upoly_sum(res
,
2641 isl_upoly_eval(isl_upoly_copy(rec
->p
[i
]),
2642 isl_vec_copy(vec
)));
2645 isl_upoly_free(base
);
2655 __isl_give isl_qpolynomial
*isl_qpolynomial_eval(
2656 __isl_take isl_qpolynomial
*qp
, __isl_take isl_point
*pnt
)
2659 struct isl_upoly
*up
;
2664 isl_assert(pnt
->dim
->ctx
, isl_dim_equal(pnt
->dim
, qp
->dim
), goto error
);
2666 if (qp
->div
->n_row
== 0)
2667 ext
= isl_vec_copy(pnt
->vec
);
2670 unsigned dim
= isl_dim_total(qp
->dim
);
2671 ext
= isl_vec_alloc(qp
->dim
->ctx
, 1 + dim
+ qp
->div
->n_row
);
2675 isl_seq_cpy(ext
->el
, pnt
->vec
->el
, pnt
->vec
->size
);
2676 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2677 isl_seq_inner_product(qp
->div
->row
[i
] + 1, ext
->el
,
2678 1 + dim
+ i
, &ext
->el
[1+dim
+i
]);
2679 isl_int_fdiv_q(ext
->el
[1+dim
+i
], ext
->el
[1+dim
+i
],
2680 qp
->div
->row
[i
][0]);
2684 up
= isl_upoly_eval(isl_upoly_copy(qp
->upoly
), ext
);
2688 dim
= isl_dim_copy(qp
->dim
);
2689 isl_qpolynomial_free(qp
);
2690 isl_point_free(pnt
);
2692 return isl_qpolynomial_alloc(dim
, 0, up
);
2694 isl_qpolynomial_free(qp
);
2695 isl_point_free(pnt
);
2699 int isl_upoly_cmp(__isl_keep
struct isl_upoly_cst
*cst1
,
2700 __isl_keep
struct isl_upoly_cst
*cst2
)
2705 isl_int_mul(t
, cst1
->n
, cst2
->d
);
2706 isl_int_submul(t
, cst2
->n
, cst1
->d
);
2707 cmp
= isl_int_sgn(t
);
2712 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial
*qp1
,
2713 __isl_keep isl_qpolynomial
*qp2
)
2715 struct isl_upoly_cst
*cst1
, *cst2
;
2719 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), return -1);
2720 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), return -1);
2721 if (isl_qpolynomial_is_nan(qp1
))
2723 if (isl_qpolynomial_is_nan(qp2
))
2725 cst1
= isl_upoly_as_cst(qp1
->upoly
);
2726 cst2
= isl_upoly_as_cst(qp2
->upoly
);
2728 return isl_upoly_cmp(cst1
, cst2
) <= 0;
2731 __isl_give isl_qpolynomial
*isl_qpolynomial_min_cst(
2732 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
2734 struct isl_upoly_cst
*cst1
, *cst2
;
2739 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), goto error
);
2740 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), goto error
);
2741 cst1
= isl_upoly_as_cst(qp1
->upoly
);
2742 cst2
= isl_upoly_as_cst(qp2
->upoly
);
2743 cmp
= isl_upoly_cmp(cst1
, cst2
);
2746 isl_qpolynomial_free(qp2
);
2748 isl_qpolynomial_free(qp1
);
2753 isl_qpolynomial_free(qp1
);
2754 isl_qpolynomial_free(qp2
);
2758 __isl_give isl_qpolynomial
*isl_qpolynomial_max_cst(
2759 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
2761 struct isl_upoly_cst
*cst1
, *cst2
;
2766 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), goto error
);
2767 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), goto error
);
2768 cst1
= isl_upoly_as_cst(qp1
->upoly
);
2769 cst2
= isl_upoly_as_cst(qp2
->upoly
);
2770 cmp
= isl_upoly_cmp(cst1
, cst2
);
2773 isl_qpolynomial_free(qp2
);
2775 isl_qpolynomial_free(qp1
);
2780 isl_qpolynomial_free(qp1
);
2781 isl_qpolynomial_free(qp2
);
2785 __isl_give isl_qpolynomial
*isl_qpolynomial_insert_dims(
2786 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
,
2787 unsigned first
, unsigned n
)
2793 if (n
== 0 && !isl_dim_is_named_or_nested(qp
->dim
, type
))
2796 qp
= isl_qpolynomial_cow(qp
);
2800 isl_assert(qp
->div
->ctx
, first
<= isl_dim_size(qp
->dim
, type
),
2803 g_pos
= pos(qp
->dim
, type
) + first
;
2805 qp
->div
= isl_mat_insert_zero_cols(qp
->div
, 2 + g_pos
, n
);
2809 total
= qp
->div
->n_col
- 2;
2810 if (total
> g_pos
) {
2812 exp
= isl_alloc_array(qp
->div
->ctx
, int, total
- g_pos
);
2815 for (i
= 0; i
< total
- g_pos
; ++i
)
2817 qp
->upoly
= expand(qp
->upoly
, exp
, g_pos
);
2823 qp
->dim
= isl_dim_insert(qp
->dim
, type
, first
, n
);
2829 isl_qpolynomial_free(qp
);
2833 __isl_give isl_qpolynomial
*isl_qpolynomial_add_dims(
2834 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
, unsigned n
)
2838 pos
= isl_qpolynomial_dim(qp
, type
);
2840 return isl_qpolynomial_insert_dims(qp
, type
, pos
, n
);
2843 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add_dims(
2844 __isl_take isl_pw_qpolynomial
*pwqp
,
2845 enum isl_dim_type type
, unsigned n
)
2849 pos
= isl_pw_qpolynomial_dim(pwqp
, type
);
2851 return isl_pw_qpolynomial_insert_dims(pwqp
, type
, pos
, n
);
2854 static int *reordering_move(isl_ctx
*ctx
,
2855 unsigned len
, unsigned dst
, unsigned src
, unsigned n
)
2860 reordering
= isl_alloc_array(ctx
, int, len
);
2865 for (i
= 0; i
< dst
; ++i
)
2867 for (i
= 0; i
< n
; ++i
)
2868 reordering
[src
+ i
] = dst
+ i
;
2869 for (i
= 0; i
< src
- dst
; ++i
)
2870 reordering
[dst
+ i
] = dst
+ n
+ i
;
2871 for (i
= 0; i
< len
- src
- n
; ++i
)
2872 reordering
[src
+ n
+ i
] = src
+ n
+ i
;
2874 for (i
= 0; i
< src
; ++i
)
2876 for (i
= 0; i
< n
; ++i
)
2877 reordering
[src
+ i
] = dst
+ i
;
2878 for (i
= 0; i
< dst
- src
; ++i
)
2879 reordering
[src
+ n
+ i
] = src
+ i
;
2880 for (i
= 0; i
< len
- dst
- n
; ++i
)
2881 reordering
[dst
+ n
+ i
] = dst
+ n
+ i
;
2887 __isl_give isl_qpolynomial
*isl_qpolynomial_move_dims(
2888 __isl_take isl_qpolynomial
*qp
,
2889 enum isl_dim_type dst_type
, unsigned dst_pos
,
2890 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
2896 qp
= isl_qpolynomial_cow(qp
);
2900 isl_assert(qp
->dim
->ctx
, src_pos
+ n
<= isl_dim_size(qp
->dim
, src_type
),
2903 g_dst_pos
= pos(qp
->dim
, dst_type
) + dst_pos
;
2904 g_src_pos
= pos(qp
->dim
, src_type
) + src_pos
;
2905 if (dst_type
> src_type
)
2908 qp
->div
= isl_mat_move_cols(qp
->div
, 2 + g_dst_pos
, 2 + g_src_pos
, n
);
2915 reordering
= reordering_move(qp
->dim
->ctx
,
2916 qp
->div
->n_col
- 2, g_dst_pos
, g_src_pos
, n
);
2920 qp
->upoly
= reorder(qp
->upoly
, reordering
);
2925 qp
->dim
= isl_dim_move(qp
->dim
, dst_type
, dst_pos
, src_type
, src_pos
, n
);
2931 isl_qpolynomial_free(qp
);
2935 __isl_give isl_qpolynomial
*isl_qpolynomial_from_affine(__isl_take isl_dim
*dim
,
2936 isl_int
*f
, isl_int denom
)
2938 struct isl_upoly
*up
;
2943 up
= isl_upoly_from_affine(dim
->ctx
, f
, denom
, 1 + isl_dim_total(dim
));
2945 return isl_qpolynomial_alloc(dim
, 0, up
);
2948 __isl_give isl_qpolynomial
*isl_qpolynomial_from_aff(__isl_take isl_aff
*aff
)
2951 struct isl_upoly
*up
;
2952 isl_qpolynomial
*qp
;
2957 ctx
= isl_aff_get_ctx(aff
);
2958 up
= isl_upoly_from_affine(ctx
, aff
->v
->el
+ 1, aff
->v
->el
[0],
2961 qp
= isl_qpolynomial_alloc(isl_aff_get_dim(aff
),
2962 aff
->ls
->div
->n_row
, up
);
2966 isl_mat_free(qp
->div
);
2967 qp
->div
= isl_mat_copy(aff
->ls
->div
);
2968 qp
->div
= isl_mat_cow(qp
->div
);
2973 qp
= reduce_divs(qp
);
2974 qp
= remove_redundant_divs(qp
);
2981 __isl_give isl_qpolynomial
*isl_qpolynomial_from_constraint(
2982 __isl_take isl_constraint
*c
, enum isl_dim_type type
, unsigned pos
)
2986 aff
= isl_constraint_get_bound(c
, type
, pos
);
2987 isl_constraint_free(c
);
2988 return isl_qpolynomial_from_aff(aff
);
2991 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
2992 * in "qp" by subs[i].
2994 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute(
2995 __isl_take isl_qpolynomial
*qp
,
2996 enum isl_dim_type type
, unsigned first
, unsigned n
,
2997 __isl_keep isl_qpolynomial
**subs
)
3000 struct isl_upoly
**ups
;
3005 qp
= isl_qpolynomial_cow(qp
);
3008 for (i
= 0; i
< n
; ++i
)
3012 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_dim_size(qp
->dim
, type
),
3015 for (i
= 0; i
< n
; ++i
)
3016 isl_assert(qp
->dim
->ctx
, isl_dim_equal(qp
->dim
, subs
[i
]->dim
),
3019 isl_assert(qp
->dim
->ctx
, qp
->div
->n_row
== 0, goto error
);
3020 for (i
= 0; i
< n
; ++i
)
3021 isl_assert(qp
->dim
->ctx
, subs
[i
]->div
->n_row
== 0, goto error
);
3023 first
+= pos(qp
->dim
, type
);
3025 ups
= isl_alloc_array(qp
->dim
->ctx
, struct isl_upoly
*, n
);
3028 for (i
= 0; i
< n
; ++i
)
3029 ups
[i
] = subs
[i
]->upoly
;
3031 qp
->upoly
= isl_upoly_subs(qp
->upoly
, first
, n
, ups
);
3040 isl_qpolynomial_free(qp
);
3044 /* Extend "bset" with extra set dimensions for each integer division
3045 * in "qp" and then call "fn" with the extended bset and the polynomial
3046 * that results from replacing each of the integer divisions by the
3047 * corresponding extra set dimension.
3049 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial
*qp
,
3050 __isl_keep isl_basic_set
*bset
,
3051 int (*fn
)(__isl_take isl_basic_set
*bset
,
3052 __isl_take isl_qpolynomial
*poly
, void *user
), void *user
)
3056 isl_qpolynomial
*poly
;
3060 if (qp
->div
->n_row
== 0)
3061 return fn(isl_basic_set_copy(bset
), isl_qpolynomial_copy(qp
),
3064 div
= isl_mat_copy(qp
->div
);
3065 dim
= isl_dim_copy(qp
->dim
);
3066 dim
= isl_dim_add(dim
, isl_dim_set
, qp
->div
->n_row
);
3067 poly
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_copy(qp
->upoly
));
3068 bset
= isl_basic_set_copy(bset
);
3069 bset
= isl_basic_set_add(bset
, isl_dim_set
, qp
->div
->n_row
);
3070 bset
= add_div_constraints(bset
, div
);
3072 return fn(bset
, poly
, user
);
3077 /* Return total degree in variables first (inclusive) up to last (exclusive).
3079 int isl_upoly_degree(__isl_keep
struct isl_upoly
*up
, int first
, int last
)
3083 struct isl_upoly_rec
*rec
;
3087 if (isl_upoly_is_zero(up
))
3089 if (isl_upoly_is_cst(up
) || up
->var
< first
)
3092 rec
= isl_upoly_as_rec(up
);
3096 for (i
= 0; i
< rec
->n
; ++i
) {
3099 if (isl_upoly_is_zero(rec
->p
[i
]))
3101 d
= isl_upoly_degree(rec
->p
[i
], first
, last
);
3111 /* Return total degree in set variables.
3113 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial
*poly
)
3121 ovar
= isl_dim_offset(poly
->dim
, isl_dim_set
);
3122 nvar
= isl_dim_size(poly
->dim
, isl_dim_set
);
3123 return isl_upoly_degree(poly
->upoly
, ovar
, ovar
+ nvar
);
3126 __isl_give
struct isl_upoly
*isl_upoly_coeff(__isl_keep
struct isl_upoly
*up
,
3127 unsigned pos
, int deg
)
3130 struct isl_upoly_rec
*rec
;
3135 if (isl_upoly_is_cst(up
) || up
->var
< pos
) {
3137 return isl_upoly_copy(up
);
3139 return isl_upoly_zero(up
->ctx
);
3142 rec
= isl_upoly_as_rec(up
);
3146 if (up
->var
== pos
) {
3148 return isl_upoly_copy(rec
->p
[deg
]);
3150 return isl_upoly_zero(up
->ctx
);
3153 up
= isl_upoly_copy(up
);
3154 up
= isl_upoly_cow(up
);
3155 rec
= isl_upoly_as_rec(up
);
3159 for (i
= 0; i
< rec
->n
; ++i
) {
3160 struct isl_upoly
*t
;
3161 t
= isl_upoly_coeff(rec
->p
[i
], pos
, deg
);
3164 isl_upoly_free(rec
->p
[i
]);
3174 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3176 __isl_give isl_qpolynomial
*isl_qpolynomial_coeff(
3177 __isl_keep isl_qpolynomial
*qp
,
3178 enum isl_dim_type type
, unsigned t_pos
, int deg
)
3181 struct isl_upoly
*up
;
3187 isl_assert(qp
->div
->ctx
, t_pos
< isl_dim_size(qp
->dim
, type
),
3190 g_pos
= pos(qp
->dim
, type
) + t_pos
;
3191 up
= isl_upoly_coeff(qp
->upoly
, g_pos
, deg
);
3193 c
= isl_qpolynomial_alloc(isl_dim_copy(qp
->dim
), qp
->div
->n_row
, up
);
3196 isl_mat_free(c
->div
);
3197 c
->div
= isl_mat_copy(qp
->div
);
3202 isl_qpolynomial_free(c
);
3206 /* Homogenize the polynomial in the variables first (inclusive) up to
3207 * last (exclusive) by inserting powers of variable first.
3208 * Variable first is assumed not to appear in the input.
3210 __isl_give
struct isl_upoly
*isl_upoly_homogenize(
3211 __isl_take
struct isl_upoly
*up
, int deg
, int target
,
3212 int first
, int last
)
3215 struct isl_upoly_rec
*rec
;
3219 if (isl_upoly_is_zero(up
))
3223 if (isl_upoly_is_cst(up
) || up
->var
< first
) {
3224 struct isl_upoly
*hom
;
3226 hom
= isl_upoly_var_pow(up
->ctx
, first
, target
- deg
);
3229 rec
= isl_upoly_as_rec(hom
);
3230 rec
->p
[target
- deg
] = isl_upoly_mul(rec
->p
[target
- deg
], up
);
3235 up
= isl_upoly_cow(up
);
3236 rec
= isl_upoly_as_rec(up
);
3240 for (i
= 0; i
< rec
->n
; ++i
) {
3241 if (isl_upoly_is_zero(rec
->p
[i
]))
3243 rec
->p
[i
] = isl_upoly_homogenize(rec
->p
[i
],
3244 up
->var
< last
? deg
+ i
: i
, target
,
3256 /* Homogenize the polynomial in the set variables by introducing
3257 * powers of an extra set variable at position 0.
3259 __isl_give isl_qpolynomial
*isl_qpolynomial_homogenize(
3260 __isl_take isl_qpolynomial
*poly
)
3264 int deg
= isl_qpolynomial_degree(poly
);
3269 poly
= isl_qpolynomial_insert_dims(poly
, isl_dim_set
, 0, 1);
3270 poly
= isl_qpolynomial_cow(poly
);
3274 ovar
= isl_dim_offset(poly
->dim
, isl_dim_set
);
3275 nvar
= isl_dim_size(poly
->dim
, isl_dim_set
);
3276 poly
->upoly
= isl_upoly_homogenize(poly
->upoly
, 0, deg
,
3283 isl_qpolynomial_free(poly
);
3287 __isl_give isl_term
*isl_term_alloc(__isl_take isl_dim
*dim
,
3288 __isl_take isl_mat
*div
)
3296 n
= isl_dim_total(dim
) + div
->n_row
;
3298 term
= isl_calloc(dim
->ctx
, struct isl_term
,
3299 sizeof(struct isl_term
) + (n
- 1) * sizeof(int));
3306 isl_int_init(term
->n
);
3307 isl_int_init(term
->d
);
3316 __isl_give isl_term
*isl_term_copy(__isl_keep isl_term
*term
)
3325 __isl_give isl_term
*isl_term_dup(__isl_keep isl_term
*term
)
3334 total
= isl_dim_total(term
->dim
) + term
->div
->n_row
;
3336 dup
= isl_term_alloc(isl_dim_copy(term
->dim
), isl_mat_copy(term
->div
));
3340 isl_int_set(dup
->n
, term
->n
);
3341 isl_int_set(dup
->d
, term
->d
);
3343 for (i
= 0; i
< total
; ++i
)
3344 dup
->pow
[i
] = term
->pow
[i
];
3349 __isl_give isl_term
*isl_term_cow(__isl_take isl_term
*term
)
3357 return isl_term_dup(term
);
3360 void isl_term_free(__isl_take isl_term
*term
)
3365 if (--term
->ref
> 0)
3368 isl_dim_free(term
->dim
);
3369 isl_mat_free(term
->div
);
3370 isl_int_clear(term
->n
);
3371 isl_int_clear(term
->d
);
3375 unsigned isl_term_dim(__isl_keep isl_term
*term
, enum isl_dim_type type
)
3383 case isl_dim_out
: return isl_dim_size(term
->dim
, type
);
3384 case isl_dim_div
: return term
->div
->n_row
;
3385 case isl_dim_all
: return isl_dim_total(term
->dim
) + term
->div
->n_row
;
3390 isl_ctx
*isl_term_get_ctx(__isl_keep isl_term
*term
)
3392 return term
? term
->dim
->ctx
: NULL
;
3395 void isl_term_get_num(__isl_keep isl_term
*term
, isl_int
*n
)
3399 isl_int_set(*n
, term
->n
);
3402 void isl_term_get_den(__isl_keep isl_term
*term
, isl_int
*d
)
3406 isl_int_set(*d
, term
->d
);
3409 int isl_term_get_exp(__isl_keep isl_term
*term
,
3410 enum isl_dim_type type
, unsigned pos
)
3415 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, type
), return -1);
3417 if (type
>= isl_dim_set
)
3418 pos
+= isl_dim_size(term
->dim
, isl_dim_param
);
3419 if (type
>= isl_dim_div
)
3420 pos
+= isl_dim_size(term
->dim
, isl_dim_set
);
3422 return term
->pow
[pos
];
3425 __isl_give isl_div
*isl_term_get_div(__isl_keep isl_term
*term
, unsigned pos
)
3427 isl_basic_map
*bmap
;
3434 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, isl_dim_div
),
3437 total
= term
->div
->n_col
- term
->div
->n_row
- 2;
3438 /* No nested divs for now */
3439 isl_assert(term
->dim
->ctx
,
3440 isl_seq_first_non_zero(term
->div
->row
[pos
] + 2 + total
,
3441 term
->div
->n_row
) == -1,
3444 bmap
= isl_basic_map_alloc_dim(isl_dim_copy(term
->dim
), 1, 0, 0);
3445 if ((k
= isl_basic_map_alloc_div(bmap
)) < 0)
3448 isl_seq_cpy(bmap
->div
[k
], term
->div
->row
[pos
], 2 + total
);
3450 return isl_basic_map_div(bmap
, k
);
3452 isl_basic_map_free(bmap
);
3456 __isl_give isl_term
*isl_upoly_foreach_term(__isl_keep
struct isl_upoly
*up
,
3457 int (*fn
)(__isl_take isl_term
*term
, void *user
),
3458 __isl_take isl_term
*term
, void *user
)
3461 struct isl_upoly_rec
*rec
;
3466 if (isl_upoly_is_zero(up
))
3469 isl_assert(up
->ctx
, !isl_upoly_is_nan(up
), goto error
);
3470 isl_assert(up
->ctx
, !isl_upoly_is_infty(up
), goto error
);
3471 isl_assert(up
->ctx
, !isl_upoly_is_neginfty(up
), goto error
);
3473 if (isl_upoly_is_cst(up
)) {
3474 struct isl_upoly_cst
*cst
;
3475 cst
= isl_upoly_as_cst(up
);
3478 term
= isl_term_cow(term
);
3481 isl_int_set(term
->n
, cst
->n
);
3482 isl_int_set(term
->d
, cst
->d
);
3483 if (fn(isl_term_copy(term
), user
) < 0)
3488 rec
= isl_upoly_as_rec(up
);
3492 for (i
= 0; i
< rec
->n
; ++i
) {
3493 term
= isl_term_cow(term
);
3496 term
->pow
[up
->var
] = i
;
3497 term
= isl_upoly_foreach_term(rec
->p
[i
], fn
, term
, user
);
3501 term
->pow
[up
->var
] = 0;
3505 isl_term_free(term
);
3509 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial
*qp
,
3510 int (*fn
)(__isl_take isl_term
*term
, void *user
), void *user
)
3517 term
= isl_term_alloc(isl_dim_copy(qp
->dim
), isl_mat_copy(qp
->div
));
3521 term
= isl_upoly_foreach_term(qp
->upoly
, fn
, term
, user
);
3523 isl_term_free(term
);
3525 return term
? 0 : -1;
3528 __isl_give isl_qpolynomial
*isl_qpolynomial_from_term(__isl_take isl_term
*term
)
3530 struct isl_upoly
*up
;
3531 isl_qpolynomial
*qp
;
3537 n
= isl_dim_total(term
->dim
) + term
->div
->n_row
;
3539 up
= isl_upoly_rat_cst(term
->dim
->ctx
, term
->n
, term
->d
);
3540 for (i
= 0; i
< n
; ++i
) {
3543 up
= isl_upoly_mul(up
,
3544 isl_upoly_var_pow(term
->dim
->ctx
, i
, term
->pow
[i
]));
3547 qp
= isl_qpolynomial_alloc(isl_dim_copy(term
->dim
), term
->div
->n_row
, up
);
3550 isl_mat_free(qp
->div
);
3551 qp
->div
= isl_mat_copy(term
->div
);
3555 isl_term_free(term
);
3558 isl_qpolynomial_free(qp
);
3559 isl_term_free(term
);
3563 __isl_give isl_qpolynomial
*isl_qpolynomial_lift(__isl_take isl_qpolynomial
*qp
,
3564 __isl_take isl_dim
*dim
)
3573 if (isl_dim_equal(qp
->dim
, dim
)) {
3578 qp
= isl_qpolynomial_cow(qp
);
3582 extra
= isl_dim_size(dim
, isl_dim_set
) -
3583 isl_dim_size(qp
->dim
, isl_dim_set
);
3584 total
= isl_dim_total(qp
->dim
);
3585 if (qp
->div
->n_row
) {
3588 exp
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
3591 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3593 qp
->upoly
= expand(qp
->upoly
, exp
, total
);
3598 qp
->div
= isl_mat_insert_cols(qp
->div
, 2 + total
, extra
);
3601 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3602 isl_seq_clr(qp
->div
->row
[i
] + 2 + total
, extra
);
3604 isl_dim_free(qp
->dim
);
3610 isl_qpolynomial_free(qp
);
3614 /* For each parameter or variable that does not appear in qp,
3615 * first eliminate the variable from all constraints and then set it to zero.
3617 static __isl_give isl_set
*fix_inactive(__isl_take isl_set
*set
,
3618 __isl_keep isl_qpolynomial
*qp
)
3629 d
= isl_dim_total(set
->dim
);
3630 active
= isl_calloc_array(set
->ctx
, int, d
);
3631 if (set_active(qp
, active
) < 0)
3634 for (i
= 0; i
< d
; ++i
)
3643 nparam
= isl_dim_size(set
->dim
, isl_dim_param
);
3644 nvar
= isl_dim_size(set
->dim
, isl_dim_set
);
3645 for (i
= 0; i
< nparam
; ++i
) {
3648 set
= isl_set_eliminate(set
, isl_dim_param
, i
, 1);
3649 set
= isl_set_fix_si(set
, isl_dim_param
, i
, 0);
3651 for (i
= 0; i
< nvar
; ++i
) {
3652 if (active
[nparam
+ i
])
3654 set
= isl_set_eliminate(set
, isl_dim_set
, i
, 1);
3655 set
= isl_set_fix_si(set
, isl_dim_set
, i
, 0);
3667 struct isl_opt_data
{
3668 isl_qpolynomial
*qp
;
3670 isl_qpolynomial
*opt
;
3674 static int opt_fn(__isl_take isl_point
*pnt
, void *user
)
3676 struct isl_opt_data
*data
= (struct isl_opt_data
*)user
;
3677 isl_qpolynomial
*val
;
3679 val
= isl_qpolynomial_eval(isl_qpolynomial_copy(data
->qp
), pnt
);
3683 } else if (data
->max
) {
3684 data
->opt
= isl_qpolynomial_max_cst(data
->opt
, val
);
3686 data
->opt
= isl_qpolynomial_min_cst(data
->opt
, val
);
3692 __isl_give isl_qpolynomial
*isl_qpolynomial_opt_on_domain(
3693 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*set
, int max
)
3695 struct isl_opt_data data
= { NULL
, 1, NULL
, max
};
3700 if (isl_upoly_is_cst(qp
->upoly
)) {
3705 set
= fix_inactive(set
, qp
);
3708 if (isl_set_foreach_point(set
, opt_fn
, &data
) < 0)
3712 data
.opt
= isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp
));
3715 isl_qpolynomial_free(qp
);
3719 isl_qpolynomial_free(qp
);
3720 isl_qpolynomial_free(data
.opt
);
3724 __isl_give isl_qpolynomial
*isl_qpolynomial_morph(__isl_take isl_qpolynomial
*qp
,
3725 __isl_take isl_morph
*morph
)
3730 struct isl_upoly
**subs
;
3733 qp
= isl_qpolynomial_cow(qp
);
3738 isl_assert(ctx
, isl_dim_equal(qp
->dim
, morph
->dom
->dim
), goto error
);
3740 n_sub
= morph
->inv
->n_row
- 1;
3741 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
3742 n_sub
+= qp
->div
->n_row
;
3743 subs
= isl_calloc_array(ctx
, struct isl_upoly
*, n_sub
);
3747 for (i
= 0; 1 + i
< morph
->inv
->n_row
; ++i
)
3748 subs
[i
] = isl_upoly_from_affine(ctx
, morph
->inv
->row
[1 + i
],
3749 morph
->inv
->row
[0][0], morph
->inv
->n_col
);
3750 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
3751 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3752 subs
[morph
->inv
->n_row
- 1 + i
] =
3753 isl_upoly_var_pow(ctx
, morph
->inv
->n_col
- 1 + i
, 1);
3755 qp
->upoly
= isl_upoly_subs(qp
->upoly
, 0, n_sub
, subs
);
3757 for (i
= 0; i
< n_sub
; ++i
)
3758 isl_upoly_free(subs
[i
]);
3761 mat
= isl_mat_diagonal(isl_mat_identity(ctx
, 1), isl_mat_copy(morph
->inv
));
3762 mat
= isl_mat_diagonal(mat
, isl_mat_identity(ctx
, qp
->div
->n_row
));
3763 qp
->div
= isl_mat_product(qp
->div
, mat
);
3764 isl_dim_free(qp
->dim
);
3765 qp
->dim
= isl_dim_copy(morph
->ran
->dim
);
3767 if (!qp
->upoly
|| !qp
->div
|| !qp
->dim
)
3770 isl_morph_free(morph
);
3774 isl_qpolynomial_free(qp
);
3775 isl_morph_free(morph
);
3779 static int neg_entry(void **entry
, void *user
)
3781 isl_pw_qpolynomial
**pwqp
= (isl_pw_qpolynomial
**)entry
;
3783 *pwqp
= isl_pw_qpolynomial_neg(*pwqp
);
3785 return *pwqp
? 0 : -1;
3788 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_neg(
3789 __isl_take isl_union_pw_qpolynomial
*upwqp
)
3791 upwqp
= isl_union_pw_qpolynomial_cow(upwqp
);
3795 if (isl_hash_table_foreach(upwqp
->dim
->ctx
, &upwqp
->table
,
3796 &neg_entry
, NULL
) < 0)
3801 isl_union_pw_qpolynomial_free(upwqp
);
3805 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_sub(
3806 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
3807 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
3809 return isl_union_pw_qpolynomial_add(upwqp1
,
3810 isl_union_pw_qpolynomial_neg(upwqp2
));
3813 static int mul_entry(void **entry
, void *user
)
3815 struct isl_union_pw_qpolynomial_match_bin_data
*data
= user
;
3817 struct isl_hash_table_entry
*entry2
;
3818 isl_pw_qpolynomial
*pwpq
= *entry
;
3821 hash
= isl_dim_get_hash(pwpq
->dim
);
3822 entry2
= isl_hash_table_find(data
->u2
->dim
->ctx
, &data
->u2
->table
,
3823 hash
, &has_dim
, pwpq
->dim
, 0);
3827 pwpq
= isl_pw_qpolynomial_copy(pwpq
);
3828 pwpq
= isl_pw_qpolynomial_mul(pwpq
,
3829 isl_pw_qpolynomial_copy(entry2
->data
));
3831 empty
= isl_pw_qpolynomial_is_zero(pwpq
);
3833 isl_pw_qpolynomial_free(pwpq
);
3837 isl_pw_qpolynomial_free(pwpq
);
3841 data
->res
= isl_union_pw_qpolynomial_add_pw_qpolynomial(data
->res
, pwpq
);
3846 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_mul(
3847 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
3848 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
3850 return match_bin_op(upwqp1
, upwqp2
, &mul_entry
);
3853 /* Reorder the columns of the given div definitions according to the
3856 static __isl_give isl_mat
*reorder_divs(__isl_take isl_mat
*div
,
3857 __isl_take isl_reordering
*r
)
3866 extra
= isl_dim_total(r
->dim
) + div
->n_row
- r
->len
;
3867 mat
= isl_mat_alloc(div
->ctx
, div
->n_row
, div
->n_col
+ extra
);
3871 for (i
= 0; i
< div
->n_row
; ++i
) {
3872 isl_seq_cpy(mat
->row
[i
], div
->row
[i
], 2);
3873 isl_seq_clr(mat
->row
[i
] + 2, mat
->n_col
- 2);
3874 for (j
= 0; j
< r
->len
; ++j
)
3875 isl_int_set(mat
->row
[i
][2 + r
->pos
[j
]],
3876 div
->row
[i
][2 + j
]);
3879 isl_reordering_free(r
);
3883 isl_reordering_free(r
);
3888 /* Reorder the dimension of "qp" according to the given reordering.
3890 __isl_give isl_qpolynomial
*isl_qpolynomial_realign(
3891 __isl_take isl_qpolynomial
*qp
, __isl_take isl_reordering
*r
)
3893 qp
= isl_qpolynomial_cow(qp
);
3897 r
= isl_reordering_extend(r
, qp
->div
->n_row
);
3901 qp
->div
= reorder_divs(qp
->div
, isl_reordering_copy(r
));
3905 qp
->upoly
= reorder(qp
->upoly
, r
->pos
);
3909 qp
= isl_qpolynomial_reset_dim(qp
, isl_dim_copy(r
->dim
));
3911 isl_reordering_free(r
);
3914 isl_qpolynomial_free(qp
);
3915 isl_reordering_free(r
);
3919 __isl_give isl_qpolynomial
*isl_qpolynomial_align_params(
3920 __isl_take isl_qpolynomial
*qp
, __isl_take isl_dim
*model
)
3925 if (!isl_dim_match(qp
->dim
, isl_dim_param
, model
, isl_dim_param
)) {
3926 isl_reordering
*exp
;
3928 model
= isl_dim_drop(model
, isl_dim_in
,
3929 0, isl_dim_size(model
, isl_dim_in
));
3930 model
= isl_dim_drop(model
, isl_dim_out
,
3931 0, isl_dim_size(model
, isl_dim_out
));
3932 exp
= isl_parameter_alignment_reordering(qp
->dim
, model
);
3933 exp
= isl_reordering_extend_dim(exp
,
3934 isl_qpolynomial_get_dim(qp
));
3935 qp
= isl_qpolynomial_realign(qp
, exp
);
3938 isl_dim_free(model
);
3941 isl_dim_free(model
);
3942 isl_qpolynomial_free(qp
);
3946 struct isl_split_periods_data
{
3948 isl_pw_qpolynomial
*res
;
3951 /* Create a slice where the integer division "div" has the fixed value "v".
3952 * In particular, if "div" refers to floor(f/m), then create a slice
3954 * m v <= f <= m v + (m - 1)
3959 * -f + m v + (m - 1) >= 0
3961 static __isl_give isl_set
*set_div_slice(__isl_take isl_dim
*dim
,
3962 __isl_keep isl_qpolynomial
*qp
, int div
, isl_int v
)
3965 isl_basic_set
*bset
= NULL
;
3971 total
= isl_dim_total(dim
);
3972 bset
= isl_basic_set_alloc_dim(isl_dim_copy(dim
), 0, 0, 2);
3974 k
= isl_basic_set_alloc_inequality(bset
);
3977 isl_seq_cpy(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
3978 isl_int_submul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
3980 k
= isl_basic_set_alloc_inequality(bset
);
3983 isl_seq_neg(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
3984 isl_int_addmul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
3985 isl_int_add(bset
->ineq
[k
][0], bset
->ineq
[k
][0], qp
->div
->row
[div
][0]);
3986 isl_int_sub_ui(bset
->ineq
[k
][0], bset
->ineq
[k
][0], 1);
3989 return isl_set_from_basic_set(bset
);
3991 isl_basic_set_free(bset
);
3996 static int split_periods(__isl_take isl_set
*set
,
3997 __isl_take isl_qpolynomial
*qp
, void *user
);
3999 /* Create a slice of the domain "set" such that integer division "div"
4000 * has the fixed value "v" and add the results to data->res,
4001 * replacing the integer division by "v" in "qp".
4003 static int set_div(__isl_take isl_set
*set
,
4004 __isl_take isl_qpolynomial
*qp
, int div
, isl_int v
,
4005 struct isl_split_periods_data
*data
)
4010 struct isl_upoly
*cst
;
4012 slice
= set_div_slice(isl_set_get_dim(set
), qp
, div
, v
);
4013 set
= isl_set_intersect(set
, slice
);
4018 total
= isl_dim_total(qp
->dim
);
4020 for (i
= div
+ 1; i
< qp
->div
->n_row
; ++i
) {
4021 if (isl_int_is_zero(qp
->div
->row
[i
][2 + total
+ div
]))
4023 isl_int_addmul(qp
->div
->row
[i
][1],
4024 qp
->div
->row
[i
][2 + total
+ div
], v
);
4025 isl_int_set_si(qp
->div
->row
[i
][2 + total
+ div
], 0);
4028 cst
= isl_upoly_rat_cst(qp
->dim
->ctx
, v
, qp
->dim
->ctx
->one
);
4029 qp
= substitute_div(qp
, div
, cst
);
4031 return split_periods(set
, qp
, data
);
4034 isl_qpolynomial_free(qp
);
4038 /* Split the domain "set" such that integer division "div"
4039 * has a fixed value (ranging from "min" to "max") on each slice
4040 * and add the results to data->res.
4042 static int split_div(__isl_take isl_set
*set
,
4043 __isl_take isl_qpolynomial
*qp
, int div
, isl_int min
, isl_int max
,
4044 struct isl_split_periods_data
*data
)
4046 for (; isl_int_le(min
, max
); isl_int_add_ui(min
, min
, 1)) {
4047 isl_set
*set_i
= isl_set_copy(set
);
4048 isl_qpolynomial
*qp_i
= isl_qpolynomial_copy(qp
);
4050 if (set_div(set_i
, qp_i
, div
, min
, data
) < 0)
4054 isl_qpolynomial_free(qp
);
4058 isl_qpolynomial_free(qp
);
4062 /* If "qp" refers to any integer division
4063 * that can only attain "max_periods" distinct values on "set"
4064 * then split the domain along those distinct values.
4065 * Add the results (or the original if no splitting occurs)
4068 static int split_periods(__isl_take isl_set
*set
,
4069 __isl_take isl_qpolynomial
*qp
, void *user
)
4072 isl_pw_qpolynomial
*pwqp
;
4073 struct isl_split_periods_data
*data
;
4078 data
= (struct isl_split_periods_data
*)user
;
4083 if (qp
->div
->n_row
== 0) {
4084 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4085 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4091 total
= isl_dim_total(qp
->dim
);
4092 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4093 enum isl_lp_result lp_res
;
4095 if (isl_seq_first_non_zero(qp
->div
->row
[i
] + 2 + total
,
4096 qp
->div
->n_row
) != -1)
4099 lp_res
= isl_set_solve_lp(set
, 0, qp
->div
->row
[i
] + 1,
4100 set
->ctx
->one
, &min
, NULL
, NULL
);
4101 if (lp_res
== isl_lp_error
)
4103 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4105 isl_int_fdiv_q(min
, min
, qp
->div
->row
[i
][0]);
4107 lp_res
= isl_set_solve_lp(set
, 1, qp
->div
->row
[i
] + 1,
4108 set
->ctx
->one
, &max
, NULL
, NULL
);
4109 if (lp_res
== isl_lp_error
)
4111 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4113 isl_int_fdiv_q(max
, max
, qp
->div
->row
[i
][0]);
4115 isl_int_sub(max
, max
, min
);
4116 if (isl_int_cmp_si(max
, data
->max_periods
) < 0) {
4117 isl_int_add(max
, max
, min
);
4122 if (i
< qp
->div
->n_row
) {
4123 r
= split_div(set
, qp
, i
, min
, max
, data
);
4125 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4126 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4138 isl_qpolynomial_free(qp
);
4142 /* If any quasi-polynomial in pwqp refers to any integer division
4143 * that can only attain "max_periods" distinct values on its domain
4144 * then split the domain along those distinct values.
4146 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_split_periods(
4147 __isl_take isl_pw_qpolynomial
*pwqp
, int max_periods
)
4149 struct isl_split_periods_data data
;
4151 data
.max_periods
= max_periods
;
4152 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp
));
4154 if (isl_pw_qpolynomial_foreach_piece(pwqp
, &split_periods
, &data
) < 0)
4157 isl_pw_qpolynomial_free(pwqp
);
4161 isl_pw_qpolynomial_free(data
.res
);
4162 isl_pw_qpolynomial_free(pwqp
);
4166 /* Construct a piecewise quasipolynomial that is constant on the given
4167 * domain. In particular, it is
4170 * infinity if cst == -1
4172 static __isl_give isl_pw_qpolynomial
*constant_on_domain(
4173 __isl_take isl_basic_set
*bset
, int cst
)
4176 isl_qpolynomial
*qp
;
4181 bset
= isl_basic_map_domain(isl_basic_map_from_range(bset
));
4182 dim
= isl_basic_set_get_dim(bset
);
4184 qp
= isl_qpolynomial_infty(dim
);
4186 qp
= isl_qpolynomial_zero(dim
);
4188 qp
= isl_qpolynomial_one(dim
);
4189 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset
), qp
);
4192 /* Factor bset, call fn on each of the factors and return the product.
4194 * If no factors can be found, simply call fn on the input.
4195 * Otherwise, construct the factors based on the factorizer,
4196 * call fn on each factor and compute the product.
4198 static __isl_give isl_pw_qpolynomial
*compressed_multiplicative_call(
4199 __isl_take isl_basic_set
*bset
,
4200 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4206 isl_qpolynomial
*qp
;
4207 isl_pw_qpolynomial
*pwqp
;
4211 f
= isl_basic_set_factorizer(bset
);
4214 if (f
->n_group
== 0) {
4215 isl_factorizer_free(f
);
4219 nparam
= isl_basic_set_dim(bset
, isl_dim_param
);
4220 nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
4222 dim
= isl_basic_set_get_dim(bset
);
4223 dim
= isl_dim_domain(dim
);
4224 set
= isl_set_universe(isl_dim_copy(dim
));
4225 qp
= isl_qpolynomial_one(dim
);
4226 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4228 bset
= isl_morph_basic_set(isl_morph_copy(f
->morph
), bset
);
4230 for (i
= 0, n
= 0; i
< f
->n_group
; ++i
) {
4231 isl_basic_set
*bset_i
;
4232 isl_pw_qpolynomial
*pwqp_i
;
4234 bset_i
= isl_basic_set_copy(bset
);
4235 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4236 nparam
+ n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4237 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4239 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
,
4240 n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4241 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
, 0, n
);
4243 pwqp_i
= fn(bset_i
);
4244 pwqp
= isl_pw_qpolynomial_mul(pwqp
, pwqp_i
);
4249 isl_basic_set_free(bset
);
4250 isl_factorizer_free(f
);
4254 isl_basic_set_free(bset
);
4258 /* Factor bset, call fn on each of the factors and return the product.
4259 * The function is assumed to evaluate to zero on empty domains,
4260 * to one on zero-dimensional domains and to infinity on unbounded domains
4261 * and will not be called explicitly on zero-dimensional or unbounded domains.
4263 * We first check for some special cases and remove all equalities.
4264 * Then we hand over control to compressed_multiplicative_call.
4266 __isl_give isl_pw_qpolynomial
*isl_basic_set_multiplicative_call(
4267 __isl_take isl_basic_set
*bset
,
4268 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4272 isl_pw_qpolynomial
*pwqp
;
4273 unsigned orig_nvar
, final_nvar
;
4278 if (isl_basic_set_plain_is_empty(bset
))
4279 return constant_on_domain(bset
, 0);
4281 orig_nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
4284 return constant_on_domain(bset
, 1);
4286 bounded
= isl_basic_set_is_bounded(bset
);
4290 return constant_on_domain(bset
, -1);
4292 if (bset
->n_eq
== 0)
4293 return compressed_multiplicative_call(bset
, fn
);
4295 morph
= isl_basic_set_full_compression(bset
);
4296 bset
= isl_morph_basic_set(isl_morph_copy(morph
), bset
);
4298 final_nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
4300 pwqp
= compressed_multiplicative_call(bset
, fn
);
4302 morph
= isl_morph_remove_dom_dims(morph
, isl_dim_set
, 0, orig_nvar
);
4303 morph
= isl_morph_remove_ran_dims(morph
, isl_dim_set
, 0, final_nvar
);
4304 morph
= isl_morph_inverse(morph
);
4306 pwqp
= isl_pw_qpolynomial_morph(pwqp
, morph
);
4310 isl_basic_set_free(bset
);
4314 /* Drop all floors in "qp", turning each integer division [a/m] into
4315 * a rational division a/m. If "down" is set, then the integer division
4316 * is replaces by (a-(m-1))/m instead.
4318 static __isl_give isl_qpolynomial
*qp_drop_floors(
4319 __isl_take isl_qpolynomial
*qp
, int down
)
4322 struct isl_upoly
*s
;
4326 if (qp
->div
->n_row
== 0)
4329 qp
= isl_qpolynomial_cow(qp
);
4333 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
4335 isl_int_sub(qp
->div
->row
[i
][1],
4336 qp
->div
->row
[i
][1], qp
->div
->row
[i
][0]);
4337 isl_int_add_ui(qp
->div
->row
[i
][1],
4338 qp
->div
->row
[i
][1], 1);
4340 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
4341 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
4342 qp
= substitute_div(qp
, i
, s
);
4350 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4351 * a rational division a/m.
4353 static __isl_give isl_pw_qpolynomial
*pwqp_drop_floors(
4354 __isl_take isl_pw_qpolynomial
*pwqp
)
4361 if (isl_pw_qpolynomial_is_zero(pwqp
))
4364 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
4368 for (i
= 0; i
< pwqp
->n
; ++i
) {
4369 pwqp
->p
[i
].qp
= qp_drop_floors(pwqp
->p
[i
].qp
, 0);
4376 isl_pw_qpolynomial_free(pwqp
);
4380 /* Adjust all the integer divisions in "qp" such that they are at least
4381 * one over the given orthant (identified by "signs"). This ensures
4382 * that they will still be non-negative even after subtracting (m-1)/m.
4384 * In particular, f is replaced by f' + v, changing f = [a/m]
4385 * to f' = [(a - m v)/m].
4386 * If the constant term k in a is smaller than m,
4387 * the constant term of v is set to floor(k/m) - 1.
4388 * For any other term, if the coefficient c and the variable x have
4389 * the same sign, then no changes are needed.
4390 * Otherwise, if the variable is positive (and c is negative),
4391 * then the coefficient of x in v is set to floor(c/m).
4392 * If the variable is negative (and c is positive),
4393 * then the coefficient of x in v is set to ceil(c/m).
4395 static __isl_give isl_qpolynomial
*make_divs_pos(__isl_take isl_qpolynomial
*qp
,
4401 struct isl_upoly
*s
;
4403 qp
= isl_qpolynomial_cow(qp
);
4406 qp
->div
= isl_mat_cow(qp
->div
);
4410 total
= isl_dim_total(qp
->dim
);
4411 v
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
4413 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4414 isl_int
*row
= qp
->div
->row
[i
];
4418 if (isl_int_lt(row
[1], row
[0])) {
4419 isl_int_fdiv_q(v
->el
[0], row
[1], row
[0]);
4420 isl_int_sub_ui(v
->el
[0], v
->el
[0], 1);
4421 isl_int_submul(row
[1], row
[0], v
->el
[0]);
4423 for (j
= 0; j
< total
; ++j
) {
4424 if (isl_int_sgn(row
[2 + j
]) * signs
[j
] >= 0)
4427 isl_int_cdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4429 isl_int_fdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4430 isl_int_submul(row
[2 + j
], row
[0], v
->el
[1 + j
]);
4432 for (j
= 0; j
< i
; ++j
) {
4433 if (isl_int_sgn(row
[2 + total
+ j
]) >= 0)
4435 isl_int_fdiv_q(v
->el
[1 + total
+ j
],
4436 row
[2 + total
+ j
], row
[0]);
4437 isl_int_submul(row
[2 + total
+ j
],
4438 row
[0], v
->el
[1 + total
+ j
]);
4440 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
4441 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
4443 isl_seq_combine(qp
->div
->row
[j
] + 1,
4444 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
4445 qp
->div
->row
[j
][2 + total
+ i
], v
->el
, v
->size
);
4447 isl_int_set_si(v
->el
[1 + total
+ i
], 1);
4448 s
= isl_upoly_from_affine(qp
->dim
->ctx
, v
->el
,
4449 qp
->div
->ctx
->one
, v
->size
);
4450 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ i
, 1, &s
);
4460 isl_qpolynomial_free(qp
);
4464 struct isl_to_poly_data
{
4466 isl_pw_qpolynomial
*res
;
4467 isl_qpolynomial
*qp
;
4470 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4471 * We first make all integer divisions positive and then split the
4472 * quasipolynomials into terms with sign data->sign (the direction
4473 * of the requested approximation) and terms with the opposite sign.
4474 * In the first set of terms, each integer division [a/m] is
4475 * overapproximated by a/m, while in the second it is underapproximated
4478 static int to_polynomial_on_orthant(__isl_take isl_set
*orthant
, int *signs
,
4481 struct isl_to_poly_data
*data
= user
;
4482 isl_pw_qpolynomial
*t
;
4483 isl_qpolynomial
*qp
, *up
, *down
;
4485 qp
= isl_qpolynomial_copy(data
->qp
);
4486 qp
= make_divs_pos(qp
, signs
);
4488 up
= isl_qpolynomial_terms_of_sign(qp
, signs
, data
->sign
);
4489 up
= qp_drop_floors(up
, 0);
4490 down
= isl_qpolynomial_terms_of_sign(qp
, signs
, -data
->sign
);
4491 down
= qp_drop_floors(down
, 1);
4493 isl_qpolynomial_free(qp
);
4494 qp
= isl_qpolynomial_add(up
, down
);
4496 t
= isl_pw_qpolynomial_alloc(orthant
, qp
);
4497 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, t
);
4502 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4503 * the polynomial will be an overapproximation. If "sign" is negative,
4504 * it will be an underapproximation. If "sign" is zero, the approximation
4505 * will lie somewhere in between.
4507 * In particular, is sign == 0, we simply drop the floors, turning
4508 * the integer divisions into rational divisions.
4509 * Otherwise, we split the domains into orthants, make all integer divisions
4510 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4511 * depending on the requested sign and the sign of the term in which
4512 * the integer division appears.
4514 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_to_polynomial(
4515 __isl_take isl_pw_qpolynomial
*pwqp
, int sign
)
4518 struct isl_to_poly_data data
;
4521 return pwqp_drop_floors(pwqp
);
4527 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp
));
4529 for (i
= 0; i
< pwqp
->n
; ++i
) {
4530 if (pwqp
->p
[i
].qp
->div
->n_row
== 0) {
4531 isl_pw_qpolynomial
*t
;
4532 t
= isl_pw_qpolynomial_alloc(
4533 isl_set_copy(pwqp
->p
[i
].set
),
4534 isl_qpolynomial_copy(pwqp
->p
[i
].qp
));
4535 data
.res
= isl_pw_qpolynomial_add_disjoint(data
.res
, t
);
4538 data
.qp
= pwqp
->p
[i
].qp
;
4539 if (isl_set_foreach_orthant(pwqp
->p
[i
].set
,
4540 &to_polynomial_on_orthant
, &data
) < 0)
4544 isl_pw_qpolynomial_free(pwqp
);
4548 isl_pw_qpolynomial_free(pwqp
);
4549 isl_pw_qpolynomial_free(data
.res
);
4553 static int poly_entry(void **entry
, void *user
)
4556 isl_pw_qpolynomial
**pwqp
= (isl_pw_qpolynomial
**)entry
;
4558 *pwqp
= isl_pw_qpolynomial_to_polynomial(*pwqp
, *sign
);
4560 return *pwqp
? 0 : -1;
4563 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_to_polynomial(
4564 __isl_take isl_union_pw_qpolynomial
*upwqp
, int sign
)
4566 upwqp
= isl_union_pw_qpolynomial_cow(upwqp
);
4570 if (isl_hash_table_foreach(upwqp
->dim
->ctx
, &upwqp
->table
,
4571 &poly_entry
, &sign
) < 0)
4576 isl_union_pw_qpolynomial_free(upwqp
);
4580 __isl_give isl_basic_map
*isl_basic_map_from_qpolynomial(
4581 __isl_take isl_qpolynomial
*qp
)
4585 isl_vec
*aff
= NULL
;
4586 isl_basic_map
*bmap
= NULL
;
4592 if (!isl_upoly_is_affine(qp
->upoly
))
4593 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
4594 "input quasi-polynomial not affine", goto error
);
4595 aff
= isl_qpolynomial_extract_affine(qp
);
4598 dim
= isl_qpolynomial_get_dim(qp
);
4599 dim
= isl_dim_from_domain(dim
);
4600 pos
= 1 + isl_dim_offset(dim
, isl_dim_out
);
4601 dim
= isl_dim_add(dim
, isl_dim_out
, 1);
4602 n_div
= qp
->div
->n_row
;
4603 bmap
= isl_basic_map_alloc_dim(dim
, n_div
, 1, 2 * n_div
);
4605 for (i
= 0; i
< n_div
; ++i
) {
4606 k
= isl_basic_map_alloc_div(bmap
);
4609 isl_seq_cpy(bmap
->div
[k
], qp
->div
->row
[i
], qp
->div
->n_col
);
4610 isl_int_set_si(bmap
->div
[k
][qp
->div
->n_col
], 0);
4611 if (isl_basic_map_add_div_constraints(bmap
, k
) < 0)
4614 k
= isl_basic_map_alloc_equality(bmap
);
4617 isl_int_neg(bmap
->eq
[k
][pos
], aff
->el
[0]);
4618 isl_seq_cpy(bmap
->eq
[k
], aff
->el
+ 1, pos
);
4619 isl_seq_cpy(bmap
->eq
[k
] + pos
+ 1, aff
->el
+ 1 + pos
, n_div
);
4622 isl_qpolynomial_free(qp
);
4623 bmap
= isl_basic_map_finalize(bmap
);
4627 isl_qpolynomial_free(qp
);
4628 isl_basic_map_free(bmap
);