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>
26 static unsigned pos(__isl_keep isl_dim
*dim
, enum isl_dim_type type
)
29 case isl_dim_param
: return 0;
30 case isl_dim_in
: return dim
->nparam
;
31 case isl_dim_out
: return dim
->nparam
+ dim
->n_in
;
36 int isl_upoly_is_cst(__isl_keep
struct isl_upoly
*up
)
44 __isl_keep
struct isl_upoly_cst
*isl_upoly_as_cst(__isl_keep
struct isl_upoly
*up
)
49 isl_assert(up
->ctx
, up
->var
< 0, return NULL
);
51 return (struct isl_upoly_cst
*)up
;
54 __isl_keep
struct isl_upoly_rec
*isl_upoly_as_rec(__isl_keep
struct isl_upoly
*up
)
59 isl_assert(up
->ctx
, up
->var
>= 0, return NULL
);
61 return (struct isl_upoly_rec
*)up
;
64 int isl_upoly_is_equal(__isl_keep
struct isl_upoly
*up1
,
65 __isl_keep
struct isl_upoly
*up2
)
68 struct isl_upoly_rec
*rec1
, *rec2
;
74 if (up1
->var
!= up2
->var
)
76 if (isl_upoly_is_cst(up1
)) {
77 struct isl_upoly_cst
*cst1
, *cst2
;
78 cst1
= isl_upoly_as_cst(up1
);
79 cst2
= isl_upoly_as_cst(up2
);
82 return isl_int_eq(cst1
->n
, cst2
->n
) &&
83 isl_int_eq(cst1
->d
, cst2
->d
);
86 rec1
= isl_upoly_as_rec(up1
);
87 rec2
= isl_upoly_as_rec(up2
);
91 if (rec1
->n
!= rec2
->n
)
94 for (i
= 0; i
< rec1
->n
; ++i
) {
95 int eq
= isl_upoly_is_equal(rec1
->p
[i
], rec2
->p
[i
]);
103 int isl_upoly_is_zero(__isl_keep
struct isl_upoly
*up
)
105 struct isl_upoly_cst
*cst
;
109 if (!isl_upoly_is_cst(up
))
112 cst
= isl_upoly_as_cst(up
);
116 return isl_int_is_zero(cst
->n
) && isl_int_is_pos(cst
->d
);
119 int isl_upoly_sgn(__isl_keep
struct isl_upoly
*up
)
121 struct isl_upoly_cst
*cst
;
125 if (!isl_upoly_is_cst(up
))
128 cst
= isl_upoly_as_cst(up
);
132 return isl_int_sgn(cst
->n
);
135 int isl_upoly_is_nan(__isl_keep
struct isl_upoly
*up
)
137 struct isl_upoly_cst
*cst
;
141 if (!isl_upoly_is_cst(up
))
144 cst
= isl_upoly_as_cst(up
);
148 return isl_int_is_zero(cst
->n
) && isl_int_is_zero(cst
->d
);
151 int isl_upoly_is_infty(__isl_keep
struct isl_upoly
*up
)
153 struct isl_upoly_cst
*cst
;
157 if (!isl_upoly_is_cst(up
))
160 cst
= isl_upoly_as_cst(up
);
164 return isl_int_is_pos(cst
->n
) && isl_int_is_zero(cst
->d
);
167 int isl_upoly_is_neginfty(__isl_keep
struct isl_upoly
*up
)
169 struct isl_upoly_cst
*cst
;
173 if (!isl_upoly_is_cst(up
))
176 cst
= isl_upoly_as_cst(up
);
180 return isl_int_is_neg(cst
->n
) && isl_int_is_zero(cst
->d
);
183 int isl_upoly_is_one(__isl_keep
struct isl_upoly
*up
)
185 struct isl_upoly_cst
*cst
;
189 if (!isl_upoly_is_cst(up
))
192 cst
= isl_upoly_as_cst(up
);
196 return isl_int_eq(cst
->n
, cst
->d
) && isl_int_is_pos(cst
->d
);
199 int isl_upoly_is_negone(__isl_keep
struct isl_upoly
*up
)
201 struct isl_upoly_cst
*cst
;
205 if (!isl_upoly_is_cst(up
))
208 cst
= isl_upoly_as_cst(up
);
212 return isl_int_is_negone(cst
->n
) && isl_int_is_one(cst
->d
);
215 __isl_give
struct isl_upoly_cst
*isl_upoly_cst_alloc(struct isl_ctx
*ctx
)
217 struct isl_upoly_cst
*cst
;
219 cst
= isl_alloc_type(ctx
, struct isl_upoly_cst
);
228 isl_int_init(cst
->n
);
229 isl_int_init(cst
->d
);
234 __isl_give
struct isl_upoly
*isl_upoly_zero(struct isl_ctx
*ctx
)
236 struct isl_upoly_cst
*cst
;
238 cst
= isl_upoly_cst_alloc(ctx
);
242 isl_int_set_si(cst
->n
, 0);
243 isl_int_set_si(cst
->d
, 1);
248 __isl_give
struct isl_upoly
*isl_upoly_one(struct isl_ctx
*ctx
)
250 struct isl_upoly_cst
*cst
;
252 cst
= isl_upoly_cst_alloc(ctx
);
256 isl_int_set_si(cst
->n
, 1);
257 isl_int_set_si(cst
->d
, 1);
262 __isl_give
struct isl_upoly
*isl_upoly_infty(struct isl_ctx
*ctx
)
264 struct isl_upoly_cst
*cst
;
266 cst
= isl_upoly_cst_alloc(ctx
);
270 isl_int_set_si(cst
->n
, 1);
271 isl_int_set_si(cst
->d
, 0);
276 __isl_give
struct isl_upoly
*isl_upoly_neginfty(struct isl_ctx
*ctx
)
278 struct isl_upoly_cst
*cst
;
280 cst
= isl_upoly_cst_alloc(ctx
);
284 isl_int_set_si(cst
->n
, -1);
285 isl_int_set_si(cst
->d
, 0);
290 __isl_give
struct isl_upoly
*isl_upoly_nan(struct isl_ctx
*ctx
)
292 struct isl_upoly_cst
*cst
;
294 cst
= isl_upoly_cst_alloc(ctx
);
298 isl_int_set_si(cst
->n
, 0);
299 isl_int_set_si(cst
->d
, 0);
304 __isl_give
struct isl_upoly
*isl_upoly_rat_cst(struct isl_ctx
*ctx
,
305 isl_int n
, isl_int d
)
307 struct isl_upoly_cst
*cst
;
309 cst
= isl_upoly_cst_alloc(ctx
);
313 isl_int_set(cst
->n
, n
);
314 isl_int_set(cst
->d
, d
);
319 __isl_give
struct isl_upoly_rec
*isl_upoly_alloc_rec(struct isl_ctx
*ctx
,
322 struct isl_upoly_rec
*rec
;
324 isl_assert(ctx
, var
>= 0, return NULL
);
325 isl_assert(ctx
, size
>= 0, return NULL
);
326 rec
= isl_calloc(ctx
, struct isl_upoly_rec
,
327 sizeof(struct isl_upoly_rec
) +
328 (size
- 1) * sizeof(struct isl_upoly
*));
343 __isl_give isl_qpolynomial
*isl_qpolynomial_reset_dim(
344 __isl_take isl_qpolynomial
*qp
, __isl_take isl_dim
*dim
)
346 qp
= isl_qpolynomial_cow(qp
);
350 isl_dim_free(qp
->dim
);
355 isl_qpolynomial_free(qp
);
360 isl_ctx
*isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial
*qp
)
362 return qp
? qp
->dim
->ctx
: NULL
;
365 __isl_give isl_dim
*isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial
*qp
)
367 return qp
? isl_dim_copy(qp
->dim
) : NULL
;
370 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial
*qp
,
371 enum isl_dim_type type
)
373 return qp
? isl_dim_size(qp
->dim
, type
) : 0;
376 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial
*qp
)
378 return qp
? isl_upoly_is_zero(qp
->upoly
) : -1;
381 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial
*qp
)
383 return qp
? isl_upoly_is_one(qp
->upoly
) : -1;
386 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial
*qp
)
388 return qp
? isl_upoly_is_nan(qp
->upoly
) : -1;
391 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial
*qp
)
393 return qp
? isl_upoly_is_infty(qp
->upoly
) : -1;
396 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial
*qp
)
398 return qp
? isl_upoly_is_neginfty(qp
->upoly
) : -1;
401 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial
*qp
)
403 return qp
? isl_upoly_sgn(qp
->upoly
) : 0;
406 static void upoly_free_cst(__isl_take
struct isl_upoly_cst
*cst
)
408 isl_int_clear(cst
->n
);
409 isl_int_clear(cst
->d
);
412 static void upoly_free_rec(__isl_take
struct isl_upoly_rec
*rec
)
416 for (i
= 0; i
< rec
->n
; ++i
)
417 isl_upoly_free(rec
->p
[i
]);
420 __isl_give
struct isl_upoly
*isl_upoly_copy(__isl_keep
struct isl_upoly
*up
)
429 __isl_give
struct isl_upoly
*isl_upoly_dup_cst(__isl_keep
struct isl_upoly
*up
)
431 struct isl_upoly_cst
*cst
;
432 struct isl_upoly_cst
*dup
;
434 cst
= isl_upoly_as_cst(up
);
438 dup
= isl_upoly_as_cst(isl_upoly_zero(up
->ctx
));
441 isl_int_set(dup
->n
, cst
->n
);
442 isl_int_set(dup
->d
, cst
->d
);
447 __isl_give
struct isl_upoly
*isl_upoly_dup_rec(__isl_keep
struct isl_upoly
*up
)
450 struct isl_upoly_rec
*rec
;
451 struct isl_upoly_rec
*dup
;
453 rec
= isl_upoly_as_rec(up
);
457 dup
= isl_upoly_alloc_rec(up
->ctx
, up
->var
, rec
->n
);
461 for (i
= 0; i
< rec
->n
; ++i
) {
462 dup
->p
[i
] = isl_upoly_copy(rec
->p
[i
]);
470 isl_upoly_free(&dup
->up
);
474 __isl_give
struct isl_upoly
*isl_upoly_dup(__isl_keep
struct isl_upoly
*up
)
476 struct isl_upoly
*dup
;
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
;
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
*up
;
1039 struct isl_upoly_rec
*rec
;
1040 struct isl_upoly_cst
*cst
;
1042 rec
= isl_upoly_alloc_rec(ctx
, pos
, 1 + power
);
1045 for (i
= 0; i
< 1 + power
; ++i
) {
1046 rec
->p
[i
] = isl_upoly_zero(ctx
);
1051 cst
= isl_upoly_as_cst(rec
->p
[power
]);
1052 isl_int_set_si(cst
->n
, 1);
1056 isl_upoly_free(&rec
->up
);
1060 /* r array maps original positions to new positions.
1062 static __isl_give
struct isl_upoly
*reorder(__isl_take
struct isl_upoly
*up
,
1066 struct isl_upoly_rec
*rec
;
1067 struct isl_upoly
*base
;
1068 struct isl_upoly
*res
;
1070 if (isl_upoly_is_cst(up
))
1073 rec
= isl_upoly_as_rec(up
);
1077 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
1079 base
= isl_upoly_var_pow(up
->ctx
, r
[up
->var
], 1);
1080 res
= reorder(isl_upoly_copy(rec
->p
[rec
->n
- 1]), r
);
1082 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1083 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
1084 res
= isl_upoly_sum(res
, reorder(isl_upoly_copy(rec
->p
[i
]), r
));
1087 isl_upoly_free(base
);
1096 static int compatible_divs(__isl_keep isl_mat
*div1
, __isl_keep isl_mat
*div2
)
1101 isl_assert(div1
->ctx
, div1
->n_row
>= div2
->n_row
&&
1102 div1
->n_col
>= div2
->n_col
, return -1);
1104 if (div1
->n_row
== div2
->n_row
)
1105 return isl_mat_is_equal(div1
, div2
);
1107 n_row
= div1
->n_row
;
1108 n_col
= div1
->n_col
;
1109 div1
->n_row
= div2
->n_row
;
1110 div1
->n_col
= div2
->n_col
;
1112 equal
= isl_mat_is_equal(div1
, div2
);
1114 div1
->n_row
= n_row
;
1115 div1
->n_col
= n_col
;
1120 static int cmp_row(__isl_keep isl_mat
*div
, int i
, int j
)
1124 li
= isl_seq_last_non_zero(div
->row
[i
], div
->n_col
);
1125 lj
= isl_seq_last_non_zero(div
->row
[j
], div
->n_col
);
1130 return isl_seq_cmp(div
->row
[i
], div
->row
[j
], div
->n_col
);
1133 struct isl_div_sort_info
{
1138 static int div_sort_cmp(const void *p1
, const void *p2
)
1140 const struct isl_div_sort_info
*i1
, *i2
;
1141 i1
= (const struct isl_div_sort_info
*) p1
;
1142 i2
= (const struct isl_div_sort_info
*) p2
;
1144 return cmp_row(i1
->div
, i1
->row
, i2
->row
);
1147 /* Sort divs and remove duplicates.
1149 static __isl_give isl_qpolynomial
*sort_divs(__isl_take isl_qpolynomial
*qp
)
1154 struct isl_div_sort_info
*array
= NULL
;
1155 int *pos
= NULL
, *at
= NULL
;
1156 int *reordering
= NULL
;
1161 if (qp
->div
->n_row
<= 1)
1164 div_pos
= isl_dim_total(qp
->dim
);
1166 array
= isl_alloc_array(qp
->div
->ctx
, struct isl_div_sort_info
,
1168 pos
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1169 at
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1170 len
= qp
->div
->n_col
- 2;
1171 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
1172 if (!array
|| !pos
|| !at
|| !reordering
)
1175 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1176 array
[i
].div
= qp
->div
;
1182 qsort(array
, qp
->div
->n_row
, sizeof(struct isl_div_sort_info
),
1185 for (i
= 0; i
< div_pos
; ++i
)
1188 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1189 if (pos
[array
[i
].row
] == i
)
1191 qp
->div
= isl_mat_swap_rows(qp
->div
, i
, pos
[array
[i
].row
]);
1192 pos
[at
[i
]] = pos
[array
[i
].row
];
1193 at
[pos
[array
[i
].row
]] = at
[i
];
1194 at
[i
] = array
[i
].row
;
1195 pos
[array
[i
].row
] = i
;
1199 for (i
= 0; i
< len
- div_pos
; ++i
) {
1201 isl_seq_eq(qp
->div
->row
[i
- skip
- 1],
1202 qp
->div
->row
[i
- skip
], qp
->div
->n_col
)) {
1203 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
1204 isl_mat_col_add(qp
->div
, 2 + div_pos
+ i
- skip
- 1,
1205 2 + div_pos
+ i
- skip
);
1206 qp
->div
= isl_mat_drop_cols(qp
->div
,
1207 2 + div_pos
+ i
- skip
, 1);
1210 reordering
[div_pos
+ array
[i
].row
] = div_pos
+ i
- skip
;
1213 qp
->upoly
= reorder(qp
->upoly
, reordering
);
1215 if (!qp
->upoly
|| !qp
->div
)
1229 isl_qpolynomial_free(qp
);
1233 static __isl_give
struct isl_upoly
*expand(__isl_take
struct isl_upoly
*up
,
1234 int *exp
, int first
)
1237 struct isl_upoly_rec
*rec
;
1239 if (isl_upoly_is_cst(up
))
1242 if (up
->var
< first
)
1245 if (exp
[up
->var
- first
] == up
->var
- first
)
1248 up
= isl_upoly_cow(up
);
1252 up
->var
= exp
[up
->var
- first
] + first
;
1254 rec
= isl_upoly_as_rec(up
);
1258 for (i
= 0; i
< rec
->n
; ++i
) {
1259 rec
->p
[i
] = expand(rec
->p
[i
], exp
, first
);
1270 static __isl_give isl_qpolynomial
*with_merged_divs(
1271 __isl_give isl_qpolynomial
*(*fn
)(__isl_take isl_qpolynomial
*qp1
,
1272 __isl_take isl_qpolynomial
*qp2
),
1273 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
1277 isl_mat
*div
= NULL
;
1279 qp1
= isl_qpolynomial_cow(qp1
);
1280 qp2
= isl_qpolynomial_cow(qp2
);
1285 isl_assert(qp1
->div
->ctx
, qp1
->div
->n_row
>= qp2
->div
->n_row
&&
1286 qp1
->div
->n_col
>= qp2
->div
->n_col
, goto error
);
1288 exp1
= isl_alloc_array(qp1
->div
->ctx
, int, qp1
->div
->n_row
);
1289 exp2
= isl_alloc_array(qp2
->div
->ctx
, int, qp2
->div
->n_row
);
1293 div
= isl_merge_divs(qp1
->div
, qp2
->div
, exp1
, exp2
);
1297 isl_mat_free(qp1
->div
);
1298 qp1
->div
= isl_mat_copy(div
);
1299 isl_mat_free(qp2
->div
);
1300 qp2
->div
= isl_mat_copy(div
);
1302 qp1
->upoly
= expand(qp1
->upoly
, exp1
, div
->n_col
- div
->n_row
- 2);
1303 qp2
->upoly
= expand(qp2
->upoly
, exp2
, div
->n_col
- div
->n_row
- 2);
1305 if (!qp1
->upoly
|| !qp2
->upoly
)
1312 return fn(qp1
, qp2
);
1317 isl_qpolynomial_free(qp1
);
1318 isl_qpolynomial_free(qp2
);
1322 __isl_give isl_qpolynomial
*isl_qpolynomial_add(__isl_take isl_qpolynomial
*qp1
,
1323 __isl_take isl_qpolynomial
*qp2
)
1325 qp1
= isl_qpolynomial_cow(qp1
);
1330 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1331 return isl_qpolynomial_add(qp2
, qp1
);
1333 isl_assert(qp1
->dim
->ctx
, isl_dim_equal(qp1
->dim
, qp2
->dim
), goto error
);
1334 if (!compatible_divs(qp1
->div
, qp2
->div
))
1335 return with_merged_divs(isl_qpolynomial_add
, qp1
, qp2
);
1337 qp1
->upoly
= isl_upoly_sum(qp1
->upoly
, isl_upoly_copy(qp2
->upoly
));
1341 isl_qpolynomial_free(qp2
);
1345 isl_qpolynomial_free(qp1
);
1346 isl_qpolynomial_free(qp2
);
1350 __isl_give isl_qpolynomial
*isl_qpolynomial_add_on_domain(
1351 __isl_keep isl_set
*dom
,
1352 __isl_take isl_qpolynomial
*qp1
,
1353 __isl_take isl_qpolynomial
*qp2
)
1355 qp1
= isl_qpolynomial_add(qp1
, qp2
);
1356 qp1
= isl_qpolynomial_gist(qp1
, isl_set_copy(dom
));
1360 __isl_give isl_qpolynomial
*isl_qpolynomial_sub(__isl_take isl_qpolynomial
*qp1
,
1361 __isl_take isl_qpolynomial
*qp2
)
1363 return isl_qpolynomial_add(qp1
, isl_qpolynomial_neg(qp2
));
1366 __isl_give isl_qpolynomial
*isl_qpolynomial_add_isl_int(
1367 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1369 if (isl_int_is_zero(v
))
1372 qp
= isl_qpolynomial_cow(qp
);
1376 qp
->upoly
= isl_upoly_add_isl_int(qp
->upoly
, v
);
1382 isl_qpolynomial_free(qp
);
1387 __isl_give isl_qpolynomial
*isl_qpolynomial_neg(__isl_take isl_qpolynomial
*qp
)
1392 return isl_qpolynomial_mul_isl_int(qp
, qp
->dim
->ctx
->negone
);
1395 __isl_give isl_qpolynomial
*isl_qpolynomial_mul_isl_int(
1396 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1398 if (isl_int_is_one(v
))
1401 if (qp
&& isl_int_is_zero(v
)) {
1402 isl_qpolynomial
*zero
;
1403 zero
= isl_qpolynomial_zero(isl_dim_copy(qp
->dim
));
1404 isl_qpolynomial_free(qp
);
1408 qp
= isl_qpolynomial_cow(qp
);
1412 qp
->upoly
= isl_upoly_mul_isl_int(qp
->upoly
, v
);
1418 isl_qpolynomial_free(qp
);
1422 __isl_give isl_qpolynomial
*isl_qpolynomial_mul(__isl_take isl_qpolynomial
*qp1
,
1423 __isl_take isl_qpolynomial
*qp2
)
1425 qp1
= isl_qpolynomial_cow(qp1
);
1430 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1431 return isl_qpolynomial_mul(qp2
, qp1
);
1433 isl_assert(qp1
->dim
->ctx
, isl_dim_equal(qp1
->dim
, qp2
->dim
), goto error
);
1434 if (!compatible_divs(qp1
->div
, qp2
->div
))
1435 return with_merged_divs(isl_qpolynomial_mul
, qp1
, qp2
);
1437 qp1
->upoly
= isl_upoly_mul(qp1
->upoly
, isl_upoly_copy(qp2
->upoly
));
1441 isl_qpolynomial_free(qp2
);
1445 isl_qpolynomial_free(qp1
);
1446 isl_qpolynomial_free(qp2
);
1450 __isl_give isl_qpolynomial
*isl_qpolynomial_pow(__isl_take isl_qpolynomial
*qp
,
1453 qp
= isl_qpolynomial_cow(qp
);
1458 qp
->upoly
= isl_upoly_pow(qp
->upoly
, power
);
1464 isl_qpolynomial_free(qp
);
1468 __isl_give isl_qpolynomial
*isl_qpolynomial_zero(__isl_take isl_dim
*dim
)
1470 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
1473 __isl_give isl_qpolynomial
*isl_qpolynomial_one(__isl_take isl_dim
*dim
)
1475 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_one(dim
->ctx
));
1478 __isl_give isl_qpolynomial
*isl_qpolynomial_infty(__isl_take isl_dim
*dim
)
1480 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_infty(dim
->ctx
));
1483 __isl_give isl_qpolynomial
*isl_qpolynomial_neginfty(__isl_take isl_dim
*dim
)
1485 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_neginfty(dim
->ctx
));
1488 __isl_give isl_qpolynomial
*isl_qpolynomial_nan(__isl_take isl_dim
*dim
)
1490 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_nan(dim
->ctx
));
1493 __isl_give isl_qpolynomial
*isl_qpolynomial_cst(__isl_take isl_dim
*dim
,
1496 struct isl_qpolynomial
*qp
;
1497 struct isl_upoly_cst
*cst
;
1499 qp
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
1503 cst
= isl_upoly_as_cst(qp
->upoly
);
1504 isl_int_set(cst
->n
, v
);
1509 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial
*qp
,
1510 isl_int
*n
, isl_int
*d
)
1512 struct isl_upoly_cst
*cst
;
1517 if (!isl_upoly_is_cst(qp
->upoly
))
1520 cst
= isl_upoly_as_cst(qp
->upoly
);
1525 isl_int_set(*n
, cst
->n
);
1527 isl_int_set(*d
, cst
->d
);
1532 int isl_upoly_is_affine(__isl_keep
struct isl_upoly
*up
)
1535 struct isl_upoly_rec
*rec
;
1543 rec
= isl_upoly_as_rec(up
);
1550 isl_assert(up
->ctx
, rec
->n
> 1, return -1);
1552 is_cst
= isl_upoly_is_cst(rec
->p
[1]);
1558 return isl_upoly_is_affine(rec
->p
[0]);
1561 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial
*qp
)
1566 if (qp
->div
->n_row
> 0)
1569 return isl_upoly_is_affine(qp
->upoly
);
1572 static void update_coeff(__isl_keep isl_vec
*aff
,
1573 __isl_keep
struct isl_upoly_cst
*cst
, int pos
)
1578 if (isl_int_is_zero(cst
->n
))
1583 isl_int_gcd(gcd
, cst
->d
, aff
->el
[0]);
1584 isl_int_divexact(f
, cst
->d
, gcd
);
1585 isl_int_divexact(gcd
, aff
->el
[0], gcd
);
1586 isl_seq_scale(aff
->el
, aff
->el
, f
, aff
->size
);
1587 isl_int_mul(aff
->el
[1 + pos
], gcd
, cst
->n
);
1592 int isl_upoly_update_affine(__isl_keep
struct isl_upoly
*up
,
1593 __isl_keep isl_vec
*aff
)
1595 struct isl_upoly_cst
*cst
;
1596 struct isl_upoly_rec
*rec
;
1602 struct isl_upoly_cst
*cst
;
1604 cst
= isl_upoly_as_cst(up
);
1607 update_coeff(aff
, cst
, 0);
1611 rec
= isl_upoly_as_rec(up
);
1614 isl_assert(up
->ctx
, rec
->n
== 2, return -1);
1616 cst
= isl_upoly_as_cst(rec
->p
[1]);
1619 update_coeff(aff
, cst
, 1 + up
->var
);
1621 return isl_upoly_update_affine(rec
->p
[0], aff
);
1624 __isl_give isl_vec
*isl_qpolynomial_extract_affine(
1625 __isl_keep isl_qpolynomial
*qp
)
1633 d
= isl_dim_total(qp
->dim
);
1634 aff
= isl_vec_alloc(qp
->div
->ctx
, 2 + d
+ qp
->div
->n_row
);
1638 isl_seq_clr(aff
->el
+ 1, 1 + d
+ qp
->div
->n_row
);
1639 isl_int_set_si(aff
->el
[0], 1);
1641 if (isl_upoly_update_affine(qp
->upoly
, aff
) < 0)
1650 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial
*qp1
,
1651 __isl_keep isl_qpolynomial
*qp2
)
1656 return isl_upoly_is_equal(qp1
->upoly
, qp2
->upoly
);
1659 static void upoly_update_den(__isl_keep
struct isl_upoly
*up
, isl_int
*d
)
1662 struct isl_upoly_rec
*rec
;
1664 if (isl_upoly_is_cst(up
)) {
1665 struct isl_upoly_cst
*cst
;
1666 cst
= isl_upoly_as_cst(up
);
1669 isl_int_lcm(*d
, *d
, cst
->d
);
1673 rec
= isl_upoly_as_rec(up
);
1677 for (i
= 0; i
< rec
->n
; ++i
)
1678 upoly_update_den(rec
->p
[i
], d
);
1681 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial
*qp
, isl_int
*d
)
1683 isl_int_set_si(*d
, 1);
1686 upoly_update_den(qp
->upoly
, d
);
1689 __isl_give isl_qpolynomial
*isl_qpolynomial_var_pow(__isl_take isl_dim
*dim
,
1692 struct isl_ctx
*ctx
;
1699 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_var_pow(ctx
, pos
, power
));
1702 __isl_give isl_qpolynomial
*isl_qpolynomial_var(__isl_take isl_dim
*dim
,
1703 enum isl_dim_type type
, unsigned pos
)
1708 isl_assert(dim
->ctx
, isl_dim_size(dim
, isl_dim_in
) == 0, goto error
);
1709 isl_assert(dim
->ctx
, pos
< isl_dim_size(dim
, type
), goto error
);
1711 if (type
== isl_dim_set
)
1712 pos
+= isl_dim_size(dim
, isl_dim_param
);
1714 return isl_qpolynomial_var_pow(dim
, pos
, 1);
1720 __isl_give
struct isl_upoly
*isl_upoly_subs(__isl_take
struct isl_upoly
*up
,
1721 unsigned first
, unsigned n
, __isl_keep
struct isl_upoly
**subs
)
1724 struct isl_upoly_rec
*rec
;
1725 struct isl_upoly
*base
, *res
;
1730 if (isl_upoly_is_cst(up
))
1733 if (up
->var
< first
)
1736 rec
= isl_upoly_as_rec(up
);
1740 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
1742 if (up
->var
>= first
+ n
)
1743 base
= isl_upoly_var_pow(up
->ctx
, up
->var
, 1);
1745 base
= isl_upoly_copy(subs
[up
->var
- first
]);
1747 res
= isl_upoly_subs(isl_upoly_copy(rec
->p
[rec
->n
- 1]), first
, n
, subs
);
1748 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1749 struct isl_upoly
*t
;
1750 t
= isl_upoly_subs(isl_upoly_copy(rec
->p
[i
]), first
, n
, subs
);
1751 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
1752 res
= isl_upoly_sum(res
, t
);
1755 isl_upoly_free(base
);
1764 __isl_give
struct isl_upoly
*isl_upoly_from_affine(isl_ctx
*ctx
, isl_int
*f
,
1765 isl_int denom
, unsigned len
)
1768 struct isl_upoly
*up
;
1770 isl_assert(ctx
, len
>= 1, return NULL
);
1772 up
= isl_upoly_rat_cst(ctx
, f
[0], denom
);
1773 for (i
= 0; i
< len
- 1; ++i
) {
1774 struct isl_upoly
*t
;
1775 struct isl_upoly
*c
;
1777 if (isl_int_is_zero(f
[1 + i
]))
1780 c
= isl_upoly_rat_cst(ctx
, f
[1 + i
], denom
);
1781 t
= isl_upoly_var_pow(ctx
, i
, 1);
1782 t
= isl_upoly_mul(c
, t
);
1783 up
= isl_upoly_sum(up
, t
);
1789 /* Remove common factor of non-constant terms and denominator.
1791 static void normalize_div(__isl_keep isl_qpolynomial
*qp
, int div
)
1793 isl_ctx
*ctx
= qp
->div
->ctx
;
1794 unsigned total
= qp
->div
->n_col
- 2;
1796 isl_seq_gcd(qp
->div
->row
[div
] + 2, total
, &ctx
->normalize_gcd
);
1797 isl_int_gcd(ctx
->normalize_gcd
,
1798 ctx
->normalize_gcd
, qp
->div
->row
[div
][0]);
1799 if (isl_int_is_one(ctx
->normalize_gcd
))
1802 isl_seq_scale_down(qp
->div
->row
[div
] + 2, qp
->div
->row
[div
] + 2,
1803 ctx
->normalize_gcd
, total
);
1804 isl_int_divexact(qp
->div
->row
[div
][0], qp
->div
->row
[div
][0],
1805 ctx
->normalize_gcd
);
1806 isl_int_fdiv_q(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1],
1807 ctx
->normalize_gcd
);
1810 /* Replace the integer division identified by "div" by the polynomial "s".
1811 * The integer division is assumed not to appear in the definition
1812 * of any other integer divisions.
1814 static __isl_give isl_qpolynomial
*substitute_div(
1815 __isl_take isl_qpolynomial
*qp
,
1816 int div
, __isl_take
struct isl_upoly
*s
)
1825 qp
= isl_qpolynomial_cow(qp
);
1829 total
= isl_dim_total(qp
->dim
);
1830 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ div
, 1, &s
);
1834 reordering
= isl_alloc_array(qp
->dim
->ctx
, int, total
+ qp
->div
->n_row
);
1837 for (i
= 0; i
< total
+ div
; ++i
)
1839 for (i
= total
+ div
+ 1; i
< total
+ qp
->div
->n_row
; ++i
)
1840 reordering
[i
] = i
- 1;
1841 qp
->div
= isl_mat_drop_rows(qp
->div
, div
, 1);
1842 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + total
+ div
, 1);
1843 qp
->upoly
= reorder(qp
->upoly
, reordering
);
1846 if (!qp
->upoly
|| !qp
->div
)
1852 isl_qpolynomial_free(qp
);
1857 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1858 * divisions because d is equal to 1 by their definition, i.e., e.
1860 static __isl_give isl_qpolynomial
*substitute_non_divs(
1861 __isl_take isl_qpolynomial
*qp
)
1865 struct isl_upoly
*s
;
1870 total
= isl_dim_total(qp
->dim
);
1871 for (i
= 0; qp
&& i
< qp
->div
->n_row
; ++i
) {
1872 if (!isl_int_is_one(qp
->div
->row
[i
][0]))
1874 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
1875 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
1877 isl_seq_combine(qp
->div
->row
[j
] + 1,
1878 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
1879 qp
->div
->row
[j
][2 + total
+ i
],
1880 qp
->div
->row
[i
] + 1, 1 + total
+ i
);
1881 isl_int_set_si(qp
->div
->row
[j
][2 + total
+ i
], 0);
1882 normalize_div(qp
, j
);
1884 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
1885 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
1886 qp
= substitute_div(qp
, i
, s
);
1893 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1894 * with d the denominator. When replacing the coefficient e of x by
1895 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1896 * inside the division, so we need to add floor(e/d) * x outside.
1897 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1898 * to adjust the coefficient of x in each later div that depends on the
1899 * current div "div" and also in the affine expression "aff"
1900 * (if it too depends on "div").
1902 static void reduce_div(__isl_keep isl_qpolynomial
*qp
, int div
,
1903 __isl_keep isl_vec
*aff
)
1907 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
1910 for (i
= 0; i
< 1 + total
+ div
; ++i
) {
1911 if (isl_int_is_nonneg(qp
->div
->row
[div
][1 + i
]) &&
1912 isl_int_lt(qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]))
1914 isl_int_fdiv_q(v
, qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
1915 isl_int_fdiv_r(qp
->div
->row
[div
][1 + i
],
1916 qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
1917 if (!isl_int_is_zero(aff
->el
[1 + total
+ div
]))
1918 isl_int_addmul(aff
->el
[i
], v
, aff
->el
[1 + total
+ div
]);
1919 for (j
= div
+ 1; j
< qp
->div
->n_row
; ++j
) {
1920 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ div
]))
1922 isl_int_addmul(qp
->div
->row
[j
][1 + i
],
1923 v
, qp
->div
->row
[j
][2 + total
+ div
]);
1929 /* Check if the last non-zero coefficient is bigger that half of the
1930 * denominator. If so, we will invert the div to further reduce the number
1931 * of distinct divs that may appear.
1932 * If the last non-zero coefficient is exactly half the denominator,
1933 * then we continue looking for earlier coefficients that are bigger
1934 * than half the denominator.
1936 static int needs_invert(__isl_keep isl_mat
*div
, int row
)
1941 for (i
= div
->n_col
- 1; i
>= 1; --i
) {
1942 if (isl_int_is_zero(div
->row
[row
][i
]))
1944 isl_int_mul_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
1945 cmp
= isl_int_cmp(div
->row
[row
][i
], div
->row
[row
][0]);
1946 isl_int_divexact_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
1956 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
1957 * We only invert the coefficients of e (and the coefficient of q in
1958 * later divs and in "aff"). After calling this function, the
1959 * coefficients of e should be reduced again.
1961 static void invert_div(__isl_keep isl_qpolynomial
*qp
, int div
,
1962 __isl_keep isl_vec
*aff
)
1964 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
1966 isl_seq_neg(qp
->div
->row
[div
] + 1,
1967 qp
->div
->row
[div
] + 1, qp
->div
->n_col
- 1);
1968 isl_int_sub_ui(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1], 1);
1969 isl_int_add(qp
->div
->row
[div
][1],
1970 qp
->div
->row
[div
][1], qp
->div
->row
[div
][0]);
1971 if (!isl_int_is_zero(aff
->el
[1 + total
+ div
]))
1972 isl_int_neg(aff
->el
[1 + total
+ div
], aff
->el
[1 + total
+ div
]);
1973 isl_mat_col_mul(qp
->div
, 2 + total
+ div
,
1974 qp
->div
->ctx
->negone
, 2 + total
+ div
);
1977 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
1978 * in the interval [0, d-1], with d the denominator and such that the
1979 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
1981 * After the reduction, some divs may have become redundant or identical,
1982 * so we call substitute_non_divs and sort_divs. If these functions
1983 * eliminate divs of merge * two or more divs into one, the coefficients
1984 * of the enclosing divs may have to be reduced again, so we call
1985 * ourselves recursively if the number of divs decreases.
1987 static __isl_give isl_qpolynomial
*reduce_divs(__isl_take isl_qpolynomial
*qp
)
1990 isl_vec
*aff
= NULL
;
1991 struct isl_upoly
*s
;
1997 aff
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
1998 aff
= isl_vec_clr(aff
);
2002 isl_int_set_si(aff
->el
[1 + qp
->upoly
->var
], 1);
2004 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2005 normalize_div(qp
, i
);
2006 reduce_div(qp
, i
, aff
);
2007 if (needs_invert(qp
->div
, i
)) {
2008 invert_div(qp
, i
, aff
);
2009 reduce_div(qp
, i
, aff
);
2013 s
= isl_upoly_from_affine(qp
->div
->ctx
, aff
->el
,
2014 qp
->div
->ctx
->one
, aff
->size
);
2015 qp
->upoly
= isl_upoly_subs(qp
->upoly
, qp
->upoly
->var
, 1, &s
);
2022 n_div
= qp
->div
->n_row
;
2023 qp
= substitute_non_divs(qp
);
2025 if (qp
&& qp
->div
->n_row
< n_div
)
2026 return reduce_divs(qp
);
2030 isl_qpolynomial_free(qp
);
2035 /* Assumes each div only depends on earlier divs.
2037 __isl_give isl_qpolynomial
*isl_qpolynomial_div_pow(__isl_take isl_div
*div
,
2040 struct isl_qpolynomial
*qp
= NULL
;
2041 struct isl_upoly_rec
*rec
;
2042 struct isl_upoly_cst
*cst
;
2049 d
= div
->line
- div
->bmap
->div
;
2051 pos
= isl_dim_total(div
->bmap
->dim
) + d
;
2052 rec
= isl_upoly_alloc_rec(div
->ctx
, pos
, 1 + power
);
2053 qp
= isl_qpolynomial_alloc(isl_basic_map_get_dim(div
->bmap
),
2054 div
->bmap
->n_div
, &rec
->up
);
2058 for (i
= 0; i
< div
->bmap
->n_div
; ++i
)
2059 isl_seq_cpy(qp
->div
->row
[i
], div
->bmap
->div
[i
], qp
->div
->n_col
);
2061 for (i
= 0; i
< 1 + power
; ++i
) {
2062 rec
->p
[i
] = isl_upoly_zero(div
->ctx
);
2067 cst
= isl_upoly_as_cst(rec
->p
[power
]);
2068 isl_int_set_si(cst
->n
, 1);
2072 qp
= reduce_divs(qp
);
2076 isl_qpolynomial_free(qp
);
2081 __isl_give isl_qpolynomial
*isl_qpolynomial_div(__isl_take isl_div
*div
)
2083 return isl_qpolynomial_div_pow(div
, 1);
2086 __isl_give isl_qpolynomial
*isl_qpolynomial_rat_cst(__isl_take isl_dim
*dim
,
2087 const isl_int n
, const isl_int d
)
2089 struct isl_qpolynomial
*qp
;
2090 struct isl_upoly_cst
*cst
;
2092 qp
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
2096 cst
= isl_upoly_as_cst(qp
->upoly
);
2097 isl_int_set(cst
->n
, n
);
2098 isl_int_set(cst
->d
, d
);
2103 static int up_set_active(__isl_keep
struct isl_upoly
*up
, int *active
, int d
)
2105 struct isl_upoly_rec
*rec
;
2111 if (isl_upoly_is_cst(up
))
2115 active
[up
->var
] = 1;
2117 rec
= isl_upoly_as_rec(up
);
2118 for (i
= 0; i
< rec
->n
; ++i
)
2119 if (up_set_active(rec
->p
[i
], active
, d
) < 0)
2125 static int set_active(__isl_keep isl_qpolynomial
*qp
, int *active
)
2128 int d
= isl_dim_total(qp
->dim
);
2133 for (i
= 0; i
< d
; ++i
)
2134 for (j
= 0; j
< qp
->div
->n_row
; ++j
) {
2135 if (isl_int_is_zero(qp
->div
->row
[j
][2 + i
]))
2141 return up_set_active(qp
->upoly
, active
, d
);
2144 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial
*qp
,
2145 enum isl_dim_type type
, unsigned first
, unsigned n
)
2156 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_dim_size(qp
->dim
, type
),
2158 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2159 type
== isl_dim_set
, return -1);
2161 active
= isl_calloc_array(set
->ctx
, int, isl_dim_total(qp
->dim
));
2162 if (set_active(qp
, active
) < 0)
2165 if (type
== isl_dim_set
)
2166 first
+= isl_dim_size(qp
->dim
, isl_dim_param
);
2167 for (i
= 0; i
< n
; ++i
)
2168 if (active
[first
+ i
]) {
2181 __isl_give
struct isl_upoly
*isl_upoly_drop(__isl_take
struct isl_upoly
*up
,
2182 unsigned first
, unsigned n
)
2185 struct isl_upoly_rec
*rec
;
2189 if (n
== 0 || up
->var
< 0 || up
->var
< first
)
2191 if (up
->var
< first
+ n
) {
2192 up
= replace_by_constant_term(up
);
2193 return isl_upoly_drop(up
, first
, n
);
2195 up
= isl_upoly_cow(up
);
2199 rec
= isl_upoly_as_rec(up
);
2203 for (i
= 0; i
< rec
->n
; ++i
) {
2204 rec
->p
[i
] = isl_upoly_drop(rec
->p
[i
], first
, n
);
2215 __isl_give isl_qpolynomial
*isl_qpolynomial_set_dim_name(
2216 __isl_take isl_qpolynomial
*qp
,
2217 enum isl_dim_type type
, unsigned pos
, const char *s
)
2219 qp
= isl_qpolynomial_cow(qp
);
2222 qp
->dim
= isl_dim_set_name(qp
->dim
, type
, pos
, s
);
2227 isl_qpolynomial_free(qp
);
2231 __isl_give isl_qpolynomial
*isl_qpolynomial_drop_dims(
2232 __isl_take isl_qpolynomial
*qp
,
2233 enum isl_dim_type type
, unsigned first
, unsigned n
)
2237 if (n
== 0 && !isl_dim_get_tuple_name(qp
->dim
, type
))
2240 qp
= isl_qpolynomial_cow(qp
);
2244 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_dim_size(qp
->dim
, type
),
2246 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2247 type
== isl_dim_set
, goto error
);
2249 qp
->dim
= isl_dim_drop(qp
->dim
, type
, first
, n
);
2253 if (type
== isl_dim_set
)
2254 first
+= isl_dim_size(qp
->dim
, isl_dim_param
);
2256 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + first
, n
);
2260 qp
->upoly
= isl_upoly_drop(qp
->upoly
, first
, n
);
2266 isl_qpolynomial_free(qp
);
2270 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities(
2271 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2277 struct isl_upoly
*up
;
2281 if (eq
->n_eq
== 0) {
2282 isl_basic_set_free(eq
);
2286 qp
= isl_qpolynomial_cow(qp
);
2289 qp
->div
= isl_mat_cow(qp
->div
);
2293 total
= 1 + isl_dim_total(eq
->dim
);
2295 isl_int_init(denom
);
2296 for (i
= 0; i
< eq
->n_eq
; ++i
) {
2297 j
= isl_seq_last_non_zero(eq
->eq
[i
], total
+ n_div
);
2298 if (j
< 0 || j
== 0 || j
>= total
)
2301 for (k
= 0; k
< qp
->div
->n_row
; ++k
) {
2302 if (isl_int_is_zero(qp
->div
->row
[k
][1 + j
]))
2304 isl_seq_elim(qp
->div
->row
[k
] + 1, eq
->eq
[i
], j
, total
,
2305 &qp
->div
->row
[k
][0]);
2306 normalize_div(qp
, k
);
2309 if (isl_int_is_pos(eq
->eq
[i
][j
]))
2310 isl_seq_neg(eq
->eq
[i
], eq
->eq
[i
], total
);
2311 isl_int_abs(denom
, eq
->eq
[i
][j
]);
2312 isl_int_set_si(eq
->eq
[i
][j
], 0);
2314 up
= isl_upoly_from_affine(qp
->dim
->ctx
,
2315 eq
->eq
[i
], denom
, total
);
2316 qp
->upoly
= isl_upoly_subs(qp
->upoly
, j
- 1, 1, &up
);
2319 isl_int_clear(denom
);
2324 isl_basic_set_free(eq
);
2326 qp
= substitute_non_divs(qp
);
2331 isl_basic_set_free(eq
);
2332 isl_qpolynomial_free(qp
);
2336 static __isl_give isl_basic_set
*add_div_constraints(
2337 __isl_take isl_basic_set
*bset
, __isl_take isl_mat
*div
)
2345 bset
= isl_basic_set_extend_constraints(bset
, 0, 2 * div
->n_row
);
2348 total
= isl_basic_set_total_dim(bset
);
2349 for (i
= 0; i
< div
->n_row
; ++i
)
2350 if (isl_basic_set_add_div_constraints_var(bset
,
2351 total
- div
->n_row
+ i
, div
->row
[i
]) < 0)
2358 isl_basic_set_free(bset
);
2362 /* Look for equalities among the variables shared by context and qp
2363 * and the integer divisions of qp, if any.
2364 * The equalities are then used to eliminate variables and/or integer
2365 * divisions from qp.
2367 __isl_give isl_qpolynomial
*isl_qpolynomial_gist(
2368 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
2374 if (qp
->div
->n_row
> 0) {
2375 isl_basic_set
*bset
;
2376 context
= isl_set_add_dims(context
, isl_dim_set
,
2378 bset
= isl_basic_set_universe(isl_set_get_dim(context
));
2379 bset
= add_div_constraints(bset
, isl_mat_copy(qp
->div
));
2380 context
= isl_set_intersect(context
,
2381 isl_set_from_basic_set(bset
));
2384 aff
= isl_set_affine_hull(context
);
2385 return isl_qpolynomial_substitute_equalities(qp
, aff
);
2387 isl_qpolynomial_free(qp
);
2388 isl_set_free(context
);
2393 #define PW isl_pw_qpolynomial
2395 #define EL isl_qpolynomial
2397 #define IS_ZERO is_zero
2401 #include <isl_pw_templ.c>
2404 #define UNION isl_union_pw_qpolynomial
2406 #define PART isl_pw_qpolynomial
2408 #define PARTS pw_qpolynomial
2410 #include <isl_union_templ.c>
2412 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial
*pwqp
)
2420 if (!isl_set_plain_is_universe(pwqp
->p
[0].set
))
2423 return isl_qpolynomial_is_one(pwqp
->p
[0].qp
);
2426 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_mul(
2427 __isl_take isl_pw_qpolynomial
*pwqp1
,
2428 __isl_take isl_pw_qpolynomial
*pwqp2
)
2431 struct isl_pw_qpolynomial
*res
;
2434 if (!pwqp1
|| !pwqp2
)
2437 isl_assert(pwqp1
->dim
->ctx
, isl_dim_equal(pwqp1
->dim
, pwqp2
->dim
),
2440 if (isl_pw_qpolynomial_is_zero(pwqp1
)) {
2441 isl_pw_qpolynomial_free(pwqp2
);
2445 if (isl_pw_qpolynomial_is_zero(pwqp2
)) {
2446 isl_pw_qpolynomial_free(pwqp1
);
2450 if (isl_pw_qpolynomial_is_one(pwqp1
)) {
2451 isl_pw_qpolynomial_free(pwqp1
);
2455 if (isl_pw_qpolynomial_is_one(pwqp2
)) {
2456 isl_pw_qpolynomial_free(pwqp2
);
2460 n
= pwqp1
->n
* pwqp2
->n
;
2461 res
= isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1
->dim
), n
);
2463 for (i
= 0; i
< pwqp1
->n
; ++i
) {
2464 for (j
= 0; j
< pwqp2
->n
; ++j
) {
2465 struct isl_set
*common
;
2466 struct isl_qpolynomial
*prod
;
2467 common
= isl_set_intersect(isl_set_copy(pwqp1
->p
[i
].set
),
2468 isl_set_copy(pwqp2
->p
[j
].set
));
2469 if (isl_set_plain_is_empty(common
)) {
2470 isl_set_free(common
);
2474 prod
= isl_qpolynomial_mul(
2475 isl_qpolynomial_copy(pwqp1
->p
[i
].qp
),
2476 isl_qpolynomial_copy(pwqp2
->p
[j
].qp
));
2478 res
= isl_pw_qpolynomial_add_piece(res
, common
, prod
);
2482 isl_pw_qpolynomial_free(pwqp1
);
2483 isl_pw_qpolynomial_free(pwqp2
);
2487 isl_pw_qpolynomial_free(pwqp1
);
2488 isl_pw_qpolynomial_free(pwqp2
);
2492 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_neg(
2493 __isl_take isl_pw_qpolynomial
*pwqp
)
2500 if (isl_pw_qpolynomial_is_zero(pwqp
))
2503 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
2507 for (i
= 0; i
< pwqp
->n
; ++i
) {
2508 pwqp
->p
[i
].qp
= isl_qpolynomial_neg(pwqp
->p
[i
].qp
);
2515 isl_pw_qpolynomial_free(pwqp
);
2519 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_sub(
2520 __isl_take isl_pw_qpolynomial
*pwqp1
,
2521 __isl_take isl_pw_qpolynomial
*pwqp2
)
2523 return isl_pw_qpolynomial_add(pwqp1
, isl_pw_qpolynomial_neg(pwqp2
));
2526 __isl_give
struct isl_upoly
*isl_upoly_eval(
2527 __isl_take
struct isl_upoly
*up
, __isl_take isl_vec
*vec
)
2530 struct isl_upoly_rec
*rec
;
2531 struct isl_upoly
*res
;
2532 struct isl_upoly
*base
;
2534 if (isl_upoly_is_cst(up
)) {
2539 rec
= isl_upoly_as_rec(up
);
2543 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
2545 base
= isl_upoly_rat_cst(up
->ctx
, vec
->el
[1 + up
->var
], vec
->el
[0]);
2547 res
= isl_upoly_eval(isl_upoly_copy(rec
->p
[rec
->n
- 1]),
2550 for (i
= rec
->n
- 2; i
>= 0; --i
) {
2551 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
2552 res
= isl_upoly_sum(res
,
2553 isl_upoly_eval(isl_upoly_copy(rec
->p
[i
]),
2554 isl_vec_copy(vec
)));
2557 isl_upoly_free(base
);
2567 __isl_give isl_qpolynomial
*isl_qpolynomial_eval(
2568 __isl_take isl_qpolynomial
*qp
, __isl_take isl_point
*pnt
)
2571 struct isl_upoly
*up
;
2576 isl_assert(pnt
->dim
->ctx
, isl_dim_equal(pnt
->dim
, qp
->dim
), goto error
);
2578 if (qp
->div
->n_row
== 0)
2579 ext
= isl_vec_copy(pnt
->vec
);
2582 unsigned dim
= isl_dim_total(qp
->dim
);
2583 ext
= isl_vec_alloc(qp
->dim
->ctx
, 1 + dim
+ qp
->div
->n_row
);
2587 isl_seq_cpy(ext
->el
, pnt
->vec
->el
, pnt
->vec
->size
);
2588 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2589 isl_seq_inner_product(qp
->div
->row
[i
] + 1, ext
->el
,
2590 1 + dim
+ i
, &ext
->el
[1+dim
+i
]);
2591 isl_int_fdiv_q(ext
->el
[1+dim
+i
], ext
->el
[1+dim
+i
],
2592 qp
->div
->row
[i
][0]);
2596 up
= isl_upoly_eval(isl_upoly_copy(qp
->upoly
), ext
);
2600 dim
= isl_dim_copy(qp
->dim
);
2601 isl_qpolynomial_free(qp
);
2602 isl_point_free(pnt
);
2604 return isl_qpolynomial_alloc(dim
, 0, up
);
2606 isl_qpolynomial_free(qp
);
2607 isl_point_free(pnt
);
2611 int isl_upoly_cmp(__isl_keep
struct isl_upoly_cst
*cst1
,
2612 __isl_keep
struct isl_upoly_cst
*cst2
)
2617 isl_int_mul(t
, cst1
->n
, cst2
->d
);
2618 isl_int_submul(t
, cst2
->n
, cst1
->d
);
2619 cmp
= isl_int_sgn(t
);
2624 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial
*qp1
,
2625 __isl_keep isl_qpolynomial
*qp2
)
2627 struct isl_upoly_cst
*cst1
, *cst2
;
2631 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), return -1);
2632 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), return -1);
2633 if (isl_qpolynomial_is_nan(qp1
))
2635 if (isl_qpolynomial_is_nan(qp2
))
2637 cst1
= isl_upoly_as_cst(qp1
->upoly
);
2638 cst2
= isl_upoly_as_cst(qp2
->upoly
);
2640 return isl_upoly_cmp(cst1
, cst2
) <= 0;
2643 __isl_give isl_qpolynomial
*isl_qpolynomial_min_cst(
2644 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
2646 struct isl_upoly_cst
*cst1
, *cst2
;
2651 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), goto error
);
2652 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), goto error
);
2653 cst1
= isl_upoly_as_cst(qp1
->upoly
);
2654 cst2
= isl_upoly_as_cst(qp2
->upoly
);
2655 cmp
= isl_upoly_cmp(cst1
, cst2
);
2658 isl_qpolynomial_free(qp2
);
2660 isl_qpolynomial_free(qp1
);
2665 isl_qpolynomial_free(qp1
);
2666 isl_qpolynomial_free(qp2
);
2670 __isl_give isl_qpolynomial
*isl_qpolynomial_max_cst(
2671 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
2673 struct isl_upoly_cst
*cst1
, *cst2
;
2678 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), goto error
);
2679 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), goto error
);
2680 cst1
= isl_upoly_as_cst(qp1
->upoly
);
2681 cst2
= isl_upoly_as_cst(qp2
->upoly
);
2682 cmp
= isl_upoly_cmp(cst1
, cst2
);
2685 isl_qpolynomial_free(qp2
);
2687 isl_qpolynomial_free(qp1
);
2692 isl_qpolynomial_free(qp1
);
2693 isl_qpolynomial_free(qp2
);
2697 __isl_give isl_qpolynomial
*isl_qpolynomial_insert_dims(
2698 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
,
2699 unsigned first
, unsigned n
)
2708 qp
= isl_qpolynomial_cow(qp
);
2712 isl_assert(qp
->div
->ctx
, first
<= isl_dim_size(qp
->dim
, type
),
2715 g_pos
= pos(qp
->dim
, type
) + first
;
2717 qp
->div
= isl_mat_insert_cols(qp
->div
, 2 + g_pos
, n
);
2721 total
= qp
->div
->n_col
- 2;
2722 if (total
> g_pos
) {
2724 exp
= isl_alloc_array(qp
->div
->ctx
, int, total
- g_pos
);
2727 for (i
= 0; i
< total
- g_pos
; ++i
)
2729 qp
->upoly
= expand(qp
->upoly
, exp
, g_pos
);
2735 qp
->dim
= isl_dim_insert(qp
->dim
, type
, first
, n
);
2741 isl_qpolynomial_free(qp
);
2745 __isl_give isl_qpolynomial
*isl_qpolynomial_add_dims(
2746 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
, unsigned n
)
2750 pos
= isl_qpolynomial_dim(qp
, type
);
2752 return isl_qpolynomial_insert_dims(qp
, type
, pos
, n
);
2755 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add_dims(
2756 __isl_take isl_pw_qpolynomial
*pwqp
,
2757 enum isl_dim_type type
, unsigned n
)
2761 pos
= isl_pw_qpolynomial_dim(pwqp
, type
);
2763 return isl_pw_qpolynomial_insert_dims(pwqp
, type
, pos
, n
);
2766 static int *reordering_move(isl_ctx
*ctx
,
2767 unsigned len
, unsigned dst
, unsigned src
, unsigned n
)
2772 reordering
= isl_alloc_array(ctx
, int, len
);
2777 for (i
= 0; i
< dst
; ++i
)
2779 for (i
= 0; i
< n
; ++i
)
2780 reordering
[src
+ i
] = dst
+ i
;
2781 for (i
= 0; i
< src
- dst
; ++i
)
2782 reordering
[dst
+ i
] = dst
+ n
+ i
;
2783 for (i
= 0; i
< len
- src
- n
; ++i
)
2784 reordering
[src
+ n
+ i
] = src
+ n
+ i
;
2786 for (i
= 0; i
< src
; ++i
)
2788 for (i
= 0; i
< n
; ++i
)
2789 reordering
[src
+ i
] = dst
+ i
;
2790 for (i
= 0; i
< dst
- src
; ++i
)
2791 reordering
[src
+ n
+ i
] = src
+ i
;
2792 for (i
= 0; i
< len
- dst
- n
; ++i
)
2793 reordering
[dst
+ n
+ i
] = dst
+ n
+ i
;
2799 __isl_give isl_qpolynomial
*isl_qpolynomial_move_dims(
2800 __isl_take isl_qpolynomial
*qp
,
2801 enum isl_dim_type dst_type
, unsigned dst_pos
,
2802 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
2808 qp
= isl_qpolynomial_cow(qp
);
2812 isl_assert(qp
->dim
->ctx
, src_pos
+ n
<= isl_dim_size(qp
->dim
, src_type
),
2815 g_dst_pos
= pos(qp
->dim
, dst_type
) + dst_pos
;
2816 g_src_pos
= pos(qp
->dim
, src_type
) + src_pos
;
2817 if (dst_type
> src_type
)
2820 qp
->div
= isl_mat_move_cols(qp
->div
, 2 + g_dst_pos
, 2 + g_src_pos
, n
);
2827 reordering
= reordering_move(qp
->dim
->ctx
,
2828 qp
->div
->n_col
- 2, g_dst_pos
, g_src_pos
, n
);
2832 qp
->upoly
= reorder(qp
->upoly
, reordering
);
2837 qp
->dim
= isl_dim_move(qp
->dim
, dst_type
, dst_pos
, src_type
, src_pos
, n
);
2843 isl_qpolynomial_free(qp
);
2847 __isl_give isl_qpolynomial
*isl_qpolynomial_from_affine(__isl_take isl_dim
*dim
,
2848 isl_int
*f
, isl_int denom
)
2850 struct isl_upoly
*up
;
2855 up
= isl_upoly_from_affine(dim
->ctx
, f
, denom
, 1 + isl_dim_total(dim
));
2857 return isl_qpolynomial_alloc(dim
, 0, up
);
2860 __isl_give isl_qpolynomial
*isl_qpolynomial_from_constraint(
2861 __isl_take isl_constraint
*c
, enum isl_dim_type type
, unsigned pos
)
2865 struct isl_upoly
*up
;
2866 isl_qpolynomial
*qp
;
2872 isl_int_init(denom
);
2874 isl_constraint_get_coefficient(c
, type
, pos
, &denom
);
2875 isl_constraint_set_coefficient(c
, type
, pos
, c
->ctx
->zero
);
2876 sgn
= isl_int_sgn(denom
);
2877 isl_int_abs(denom
, denom
);
2878 up
= isl_upoly_from_affine(c
->ctx
, c
->line
[0], denom
,
2879 1 + isl_constraint_dim(c
, isl_dim_all
));
2881 isl_int_neg(denom
, denom
);
2882 isl_constraint_set_coefficient(c
, type
, pos
, denom
);
2884 dim
= isl_dim_copy(c
->bmap
->dim
);
2886 isl_int_clear(denom
);
2887 isl_constraint_free(c
);
2889 qp
= isl_qpolynomial_alloc(dim
, 0, up
);
2891 qp
= isl_qpolynomial_neg(qp
);
2895 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
2896 * in "qp" by subs[i].
2898 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute(
2899 __isl_take isl_qpolynomial
*qp
,
2900 enum isl_dim_type type
, unsigned first
, unsigned n
,
2901 __isl_keep isl_qpolynomial
**subs
)
2904 struct isl_upoly
**ups
;
2909 qp
= isl_qpolynomial_cow(qp
);
2912 for (i
= 0; i
< n
; ++i
)
2916 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_dim_size(qp
->dim
, type
),
2919 for (i
= 0; i
< n
; ++i
)
2920 isl_assert(qp
->dim
->ctx
, isl_dim_equal(qp
->dim
, subs
[i
]->dim
),
2923 isl_assert(qp
->dim
->ctx
, qp
->div
->n_row
== 0, goto error
);
2924 for (i
= 0; i
< n
; ++i
)
2925 isl_assert(qp
->dim
->ctx
, subs
[i
]->div
->n_row
== 0, goto error
);
2927 first
+= pos(qp
->dim
, type
);
2929 ups
= isl_alloc_array(qp
->dim
->ctx
, struct isl_upoly
*, n
);
2932 for (i
= 0; i
< n
; ++i
)
2933 ups
[i
] = subs
[i
]->upoly
;
2935 qp
->upoly
= isl_upoly_subs(qp
->upoly
, first
, n
, ups
);
2944 isl_qpolynomial_free(qp
);
2948 /* Extend "bset" with extra set dimensions for each integer division
2949 * in "qp" and then call "fn" with the extended bset and the polynomial
2950 * that results from replacing each of the integer divisions by the
2951 * corresponding extra set dimension.
2953 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial
*qp
,
2954 __isl_keep isl_basic_set
*bset
,
2955 int (*fn
)(__isl_take isl_basic_set
*bset
,
2956 __isl_take isl_qpolynomial
*poly
, void *user
), void *user
)
2960 isl_qpolynomial
*poly
;
2964 if (qp
->div
->n_row
== 0)
2965 return fn(isl_basic_set_copy(bset
), isl_qpolynomial_copy(qp
),
2968 div
= isl_mat_copy(qp
->div
);
2969 dim
= isl_dim_copy(qp
->dim
);
2970 dim
= isl_dim_add(dim
, isl_dim_set
, qp
->div
->n_row
);
2971 poly
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_copy(qp
->upoly
));
2972 bset
= isl_basic_set_copy(bset
);
2973 bset
= isl_basic_set_add(bset
, isl_dim_set
, qp
->div
->n_row
);
2974 bset
= add_div_constraints(bset
, div
);
2976 return fn(bset
, poly
, user
);
2981 /* Return total degree in variables first (inclusive) up to last (exclusive).
2983 int isl_upoly_degree(__isl_keep
struct isl_upoly
*up
, int first
, int last
)
2987 struct isl_upoly_rec
*rec
;
2991 if (isl_upoly_is_zero(up
))
2993 if (isl_upoly_is_cst(up
) || up
->var
< first
)
2996 rec
= isl_upoly_as_rec(up
);
3000 for (i
= 0; i
< rec
->n
; ++i
) {
3003 if (isl_upoly_is_zero(rec
->p
[i
]))
3005 d
= isl_upoly_degree(rec
->p
[i
], first
, last
);
3015 /* Return total degree in set variables.
3017 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial
*poly
)
3025 ovar
= isl_dim_offset(poly
->dim
, isl_dim_set
);
3026 nvar
= isl_dim_size(poly
->dim
, isl_dim_set
);
3027 return isl_upoly_degree(poly
->upoly
, ovar
, ovar
+ nvar
);
3030 __isl_give
struct isl_upoly
*isl_upoly_coeff(__isl_keep
struct isl_upoly
*up
,
3031 unsigned pos
, int deg
)
3034 struct isl_upoly_rec
*rec
;
3039 if (isl_upoly_is_cst(up
) || up
->var
< pos
) {
3041 return isl_upoly_copy(up
);
3043 return isl_upoly_zero(up
->ctx
);
3046 rec
= isl_upoly_as_rec(up
);
3050 if (up
->var
== pos
) {
3052 return isl_upoly_copy(rec
->p
[deg
]);
3054 return isl_upoly_zero(up
->ctx
);
3057 up
= isl_upoly_copy(up
);
3058 up
= isl_upoly_cow(up
);
3059 rec
= isl_upoly_as_rec(up
);
3063 for (i
= 0; i
< rec
->n
; ++i
) {
3064 struct isl_upoly
*t
;
3065 t
= isl_upoly_coeff(rec
->p
[i
], pos
, deg
);
3068 isl_upoly_free(rec
->p
[i
]);
3078 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3080 __isl_give isl_qpolynomial
*isl_qpolynomial_coeff(
3081 __isl_keep isl_qpolynomial
*qp
,
3082 enum isl_dim_type type
, unsigned t_pos
, int deg
)
3085 struct isl_upoly
*up
;
3091 isl_assert(qp
->div
->ctx
, t_pos
< isl_dim_size(qp
->dim
, type
),
3094 g_pos
= pos(qp
->dim
, type
) + t_pos
;
3095 up
= isl_upoly_coeff(qp
->upoly
, g_pos
, deg
);
3097 c
= isl_qpolynomial_alloc(isl_dim_copy(qp
->dim
), qp
->div
->n_row
, up
);
3100 isl_mat_free(c
->div
);
3101 c
->div
= isl_mat_copy(qp
->div
);
3106 isl_qpolynomial_free(c
);
3110 /* Homogenize the polynomial in the variables first (inclusive) up to
3111 * last (exclusive) by inserting powers of variable first.
3112 * Variable first is assumed not to appear in the input.
3114 __isl_give
struct isl_upoly
*isl_upoly_homogenize(
3115 __isl_take
struct isl_upoly
*up
, int deg
, int target
,
3116 int first
, int last
)
3119 struct isl_upoly_rec
*rec
;
3123 if (isl_upoly_is_zero(up
))
3127 if (isl_upoly_is_cst(up
) || up
->var
< first
) {
3128 struct isl_upoly
*hom
;
3130 hom
= isl_upoly_var_pow(up
->ctx
, first
, target
- deg
);
3133 rec
= isl_upoly_as_rec(hom
);
3134 rec
->p
[target
- deg
] = isl_upoly_mul(rec
->p
[target
- deg
], up
);
3139 up
= isl_upoly_cow(up
);
3140 rec
= isl_upoly_as_rec(up
);
3144 for (i
= 0; i
< rec
->n
; ++i
) {
3145 if (isl_upoly_is_zero(rec
->p
[i
]))
3147 rec
->p
[i
] = isl_upoly_homogenize(rec
->p
[i
],
3148 up
->var
< last
? deg
+ i
: i
, target
,
3160 /* Homogenize the polynomial in the set variables by introducing
3161 * powers of an extra set variable at position 0.
3163 __isl_give isl_qpolynomial
*isl_qpolynomial_homogenize(
3164 __isl_take isl_qpolynomial
*poly
)
3168 int deg
= isl_qpolynomial_degree(poly
);
3173 poly
= isl_qpolynomial_insert_dims(poly
, isl_dim_set
, 0, 1);
3174 poly
= isl_qpolynomial_cow(poly
);
3178 ovar
= isl_dim_offset(poly
->dim
, isl_dim_set
);
3179 nvar
= isl_dim_size(poly
->dim
, isl_dim_set
);
3180 poly
->upoly
= isl_upoly_homogenize(poly
->upoly
, 0, deg
,
3187 isl_qpolynomial_free(poly
);
3191 __isl_give isl_term
*isl_term_alloc(__isl_take isl_dim
*dim
,
3192 __isl_take isl_mat
*div
)
3200 n
= isl_dim_total(dim
) + div
->n_row
;
3202 term
= isl_calloc(dim
->ctx
, struct isl_term
,
3203 sizeof(struct isl_term
) + (n
- 1) * sizeof(int));
3210 isl_int_init(term
->n
);
3211 isl_int_init(term
->d
);
3220 __isl_give isl_term
*isl_term_copy(__isl_keep isl_term
*term
)
3229 __isl_give isl_term
*isl_term_dup(__isl_keep isl_term
*term
)
3238 total
= isl_dim_total(term
->dim
) + term
->div
->n_row
;
3240 dup
= isl_term_alloc(isl_dim_copy(term
->dim
), isl_mat_copy(term
->div
));
3244 isl_int_set(dup
->n
, term
->n
);
3245 isl_int_set(dup
->d
, term
->d
);
3247 for (i
= 0; i
< total
; ++i
)
3248 dup
->pow
[i
] = term
->pow
[i
];
3253 __isl_give isl_term
*isl_term_cow(__isl_take isl_term
*term
)
3261 return isl_term_dup(term
);
3264 void isl_term_free(__isl_take isl_term
*term
)
3269 if (--term
->ref
> 0)
3272 isl_dim_free(term
->dim
);
3273 isl_mat_free(term
->div
);
3274 isl_int_clear(term
->n
);
3275 isl_int_clear(term
->d
);
3279 unsigned isl_term_dim(__isl_keep isl_term
*term
, enum isl_dim_type type
)
3287 case isl_dim_out
: return isl_dim_size(term
->dim
, type
);
3288 case isl_dim_div
: return term
->div
->n_row
;
3289 case isl_dim_all
: return isl_dim_total(term
->dim
) + term
->div
->n_row
;
3294 isl_ctx
*isl_term_get_ctx(__isl_keep isl_term
*term
)
3296 return term
? term
->dim
->ctx
: NULL
;
3299 void isl_term_get_num(__isl_keep isl_term
*term
, isl_int
*n
)
3303 isl_int_set(*n
, term
->n
);
3306 void isl_term_get_den(__isl_keep isl_term
*term
, isl_int
*d
)
3310 isl_int_set(*d
, term
->d
);
3313 int isl_term_get_exp(__isl_keep isl_term
*term
,
3314 enum isl_dim_type type
, unsigned pos
)
3319 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, type
), return -1);
3321 if (type
>= isl_dim_set
)
3322 pos
+= isl_dim_size(term
->dim
, isl_dim_param
);
3323 if (type
>= isl_dim_div
)
3324 pos
+= isl_dim_size(term
->dim
, isl_dim_set
);
3326 return term
->pow
[pos
];
3329 __isl_give isl_div
*isl_term_get_div(__isl_keep isl_term
*term
, unsigned pos
)
3331 isl_basic_map
*bmap
;
3338 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, isl_dim_div
),
3341 total
= term
->div
->n_col
- term
->div
->n_row
- 2;
3342 /* No nested divs for now */
3343 isl_assert(term
->dim
->ctx
,
3344 isl_seq_first_non_zero(term
->div
->row
[pos
] + 2 + total
,
3345 term
->div
->n_row
) == -1,
3348 bmap
= isl_basic_map_alloc_dim(isl_dim_copy(term
->dim
), 1, 0, 0);
3349 if ((k
= isl_basic_map_alloc_div(bmap
)) < 0)
3352 isl_seq_cpy(bmap
->div
[k
], term
->div
->row
[pos
], 2 + total
);
3354 return isl_basic_map_div(bmap
, k
);
3356 isl_basic_map_free(bmap
);
3360 __isl_give isl_term
*isl_upoly_foreach_term(__isl_keep
struct isl_upoly
*up
,
3361 int (*fn
)(__isl_take isl_term
*term
, void *user
),
3362 __isl_take isl_term
*term
, void *user
)
3365 struct isl_upoly_rec
*rec
;
3370 if (isl_upoly_is_zero(up
))
3373 isl_assert(up
->ctx
, !isl_upoly_is_nan(up
), goto error
);
3374 isl_assert(up
->ctx
, !isl_upoly_is_infty(up
), goto error
);
3375 isl_assert(up
->ctx
, !isl_upoly_is_neginfty(up
), goto error
);
3377 if (isl_upoly_is_cst(up
)) {
3378 struct isl_upoly_cst
*cst
;
3379 cst
= isl_upoly_as_cst(up
);
3382 term
= isl_term_cow(term
);
3385 isl_int_set(term
->n
, cst
->n
);
3386 isl_int_set(term
->d
, cst
->d
);
3387 if (fn(isl_term_copy(term
), user
) < 0)
3392 rec
= isl_upoly_as_rec(up
);
3396 for (i
= 0; i
< rec
->n
; ++i
) {
3397 term
= isl_term_cow(term
);
3400 term
->pow
[up
->var
] = i
;
3401 term
= isl_upoly_foreach_term(rec
->p
[i
], fn
, term
, user
);
3405 term
->pow
[up
->var
] = 0;
3409 isl_term_free(term
);
3413 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial
*qp
,
3414 int (*fn
)(__isl_take isl_term
*term
, void *user
), void *user
)
3421 term
= isl_term_alloc(isl_dim_copy(qp
->dim
), isl_mat_copy(qp
->div
));
3425 term
= isl_upoly_foreach_term(qp
->upoly
, fn
, term
, user
);
3427 isl_term_free(term
);
3429 return term
? 0 : -1;
3432 __isl_give isl_qpolynomial
*isl_qpolynomial_from_term(__isl_take isl_term
*term
)
3434 struct isl_upoly
*up
;
3435 isl_qpolynomial
*qp
;
3441 n
= isl_dim_total(term
->dim
) + term
->div
->n_row
;
3443 up
= isl_upoly_rat_cst(term
->dim
->ctx
, term
->n
, term
->d
);
3444 for (i
= 0; i
< n
; ++i
) {
3447 up
= isl_upoly_mul(up
,
3448 isl_upoly_var_pow(term
->dim
->ctx
, i
, term
->pow
[i
]));
3451 qp
= isl_qpolynomial_alloc(isl_dim_copy(term
->dim
), term
->div
->n_row
, up
);
3454 isl_mat_free(qp
->div
);
3455 qp
->div
= isl_mat_copy(term
->div
);
3459 isl_term_free(term
);
3462 isl_qpolynomial_free(qp
);
3463 isl_term_free(term
);
3467 __isl_give isl_qpolynomial
*isl_qpolynomial_lift(__isl_take isl_qpolynomial
*qp
,
3468 __isl_take isl_dim
*dim
)
3477 if (isl_dim_equal(qp
->dim
, dim
)) {
3482 qp
= isl_qpolynomial_cow(qp
);
3486 extra
= isl_dim_size(dim
, isl_dim_set
) -
3487 isl_dim_size(qp
->dim
, isl_dim_set
);
3488 total
= isl_dim_total(qp
->dim
);
3489 if (qp
->div
->n_row
) {
3492 exp
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
3495 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3497 qp
->upoly
= expand(qp
->upoly
, exp
, total
);
3502 qp
->div
= isl_mat_insert_cols(qp
->div
, 2 + total
, extra
);
3505 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3506 isl_seq_clr(qp
->div
->row
[i
] + 2 + total
, extra
);
3508 isl_dim_free(qp
->dim
);
3514 isl_qpolynomial_free(qp
);
3518 /* For each parameter or variable that does not appear in qp,
3519 * first eliminate the variable from all constraints and then set it to zero.
3521 static __isl_give isl_set
*fix_inactive(__isl_take isl_set
*set
,
3522 __isl_keep isl_qpolynomial
*qp
)
3533 d
= isl_dim_total(set
->dim
);
3534 active
= isl_calloc_array(set
->ctx
, int, d
);
3535 if (set_active(qp
, active
) < 0)
3538 for (i
= 0; i
< d
; ++i
)
3547 nparam
= isl_dim_size(set
->dim
, isl_dim_param
);
3548 nvar
= isl_dim_size(set
->dim
, isl_dim_set
);
3549 for (i
= 0; i
< nparam
; ++i
) {
3552 set
= isl_set_eliminate(set
, isl_dim_param
, i
, 1);
3553 set
= isl_set_fix_si(set
, isl_dim_param
, i
, 0);
3555 for (i
= 0; i
< nvar
; ++i
) {
3556 if (active
[nparam
+ i
])
3558 set
= isl_set_eliminate(set
, isl_dim_set
, i
, 1);
3559 set
= isl_set_fix_si(set
, isl_dim_set
, i
, 0);
3571 struct isl_opt_data
{
3572 isl_qpolynomial
*qp
;
3574 isl_qpolynomial
*opt
;
3578 static int opt_fn(__isl_take isl_point
*pnt
, void *user
)
3580 struct isl_opt_data
*data
= (struct isl_opt_data
*)user
;
3581 isl_qpolynomial
*val
;
3583 val
= isl_qpolynomial_eval(isl_qpolynomial_copy(data
->qp
), pnt
);
3587 } else if (data
->max
) {
3588 data
->opt
= isl_qpolynomial_max_cst(data
->opt
, val
);
3590 data
->opt
= isl_qpolynomial_min_cst(data
->opt
, val
);
3596 __isl_give isl_qpolynomial
*isl_qpolynomial_opt_on_domain(
3597 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*set
, int max
)
3599 struct isl_opt_data data
= { NULL
, 1, NULL
, max
};
3604 if (isl_upoly_is_cst(qp
->upoly
)) {
3609 set
= fix_inactive(set
, qp
);
3612 if (isl_set_foreach_point(set
, opt_fn
, &data
) < 0)
3616 data
.opt
= isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp
));
3619 isl_qpolynomial_free(qp
);
3623 isl_qpolynomial_free(qp
);
3624 isl_qpolynomial_free(data
.opt
);
3628 __isl_give isl_qpolynomial
*isl_qpolynomial_morph(__isl_take isl_qpolynomial
*qp
,
3629 __isl_take isl_morph
*morph
)
3634 struct isl_upoly
*up
;
3636 struct isl_upoly
**subs
;
3639 qp
= isl_qpolynomial_cow(qp
);
3644 isl_assert(ctx
, isl_dim_equal(qp
->dim
, morph
->dom
->dim
), goto error
);
3646 n_sub
= morph
->inv
->n_row
- 1;
3647 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
3648 n_sub
+= qp
->div
->n_row
;
3649 subs
= isl_calloc_array(ctx
, struct isl_upoly
*, n_sub
);
3653 for (i
= 0; 1 + i
< morph
->inv
->n_row
; ++i
)
3654 subs
[i
] = isl_upoly_from_affine(ctx
, morph
->inv
->row
[1 + i
],
3655 morph
->inv
->row
[0][0], morph
->inv
->n_col
);
3656 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
3657 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3658 subs
[morph
->inv
->n_row
- 1 + i
] =
3659 isl_upoly_var_pow(ctx
, morph
->inv
->n_col
- 1 + i
, 1);
3661 qp
->upoly
= isl_upoly_subs(qp
->upoly
, 0, n_sub
, subs
);
3663 for (i
= 0; i
< n_sub
; ++i
)
3664 isl_upoly_free(subs
[i
]);
3667 mat
= isl_mat_diagonal(isl_mat_identity(ctx
, 1), isl_mat_copy(morph
->inv
));
3668 mat
= isl_mat_diagonal(mat
, isl_mat_identity(ctx
, qp
->div
->n_row
));
3669 qp
->div
= isl_mat_product(qp
->div
, mat
);
3670 isl_dim_free(qp
->dim
);
3671 qp
->dim
= isl_dim_copy(morph
->ran
->dim
);
3673 if (!qp
->upoly
|| !qp
->div
|| !qp
->dim
)
3676 isl_morph_free(morph
);
3680 isl_qpolynomial_free(qp
);
3681 isl_morph_free(morph
);
3685 static int neg_entry(void **entry
, void *user
)
3687 isl_pw_qpolynomial
**pwqp
= (isl_pw_qpolynomial
**)entry
;
3689 *pwqp
= isl_pw_qpolynomial_neg(*pwqp
);
3691 return *pwqp
? 0 : -1;
3694 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_neg(
3695 __isl_take isl_union_pw_qpolynomial
*upwqp
)
3697 upwqp
= isl_union_pw_qpolynomial_cow(upwqp
);
3701 if (isl_hash_table_foreach(upwqp
->dim
->ctx
, &upwqp
->table
,
3702 &neg_entry
, NULL
) < 0)
3707 isl_union_pw_qpolynomial_free(upwqp
);
3711 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_sub(
3712 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
3713 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
3715 return isl_union_pw_qpolynomial_add(upwqp1
,
3716 isl_union_pw_qpolynomial_neg(upwqp2
));
3719 static int mul_entry(void **entry
, void *user
)
3721 struct isl_union_pw_qpolynomial_match_bin_data
*data
= user
;
3723 struct isl_hash_table_entry
*entry2
;
3724 isl_pw_qpolynomial
*pwpq
= *entry
;
3727 hash
= isl_dim_get_hash(pwpq
->dim
);
3728 entry2
= isl_hash_table_find(data
->u2
->dim
->ctx
, &data
->u2
->table
,
3729 hash
, &has_dim
, pwpq
->dim
, 0);
3733 pwpq
= isl_pw_qpolynomial_copy(pwpq
);
3734 pwpq
= isl_pw_qpolynomial_mul(pwpq
,
3735 isl_pw_qpolynomial_copy(entry2
->data
));
3737 empty
= isl_pw_qpolynomial_is_zero(pwpq
);
3739 isl_pw_qpolynomial_free(pwpq
);
3743 isl_pw_qpolynomial_free(pwpq
);
3747 data
->res
= isl_union_pw_qpolynomial_add_pw_qpolynomial(data
->res
, pwpq
);
3752 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_mul(
3753 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
3754 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
3756 return match_bin_op(upwqp1
, upwqp2
, &mul_entry
);
3759 /* Reorder the columns of the given div definitions according to the
3762 static __isl_give isl_mat
*reorder_divs(__isl_take isl_mat
*div
,
3763 __isl_take isl_reordering
*r
)
3772 extra
= isl_dim_total(r
->dim
) + div
->n_row
- r
->len
;
3773 mat
= isl_mat_alloc(div
->ctx
, div
->n_row
, div
->n_col
+ extra
);
3777 for (i
= 0; i
< div
->n_row
; ++i
) {
3778 isl_seq_cpy(mat
->row
[i
], div
->row
[i
], 2);
3779 isl_seq_clr(mat
->row
[i
] + 2, mat
->n_col
- 2);
3780 for (j
= 0; j
< r
->len
; ++j
)
3781 isl_int_set(mat
->row
[i
][2 + r
->pos
[j
]],
3782 div
->row
[i
][2 + j
]);
3785 isl_reordering_free(r
);
3789 isl_reordering_free(r
);
3794 /* Reorder the dimension of "qp" according to the given reordering.
3796 __isl_give isl_qpolynomial
*isl_qpolynomial_realign(
3797 __isl_take isl_qpolynomial
*qp
, __isl_take isl_reordering
*r
)
3799 qp
= isl_qpolynomial_cow(qp
);
3803 r
= isl_reordering_extend(r
, qp
->div
->n_row
);
3807 qp
->div
= reorder_divs(qp
->div
, isl_reordering_copy(r
));
3811 qp
->upoly
= reorder(qp
->upoly
, r
->pos
);
3815 qp
= isl_qpolynomial_reset_dim(qp
, isl_dim_copy(r
->dim
));
3817 isl_reordering_free(r
);
3820 isl_qpolynomial_free(qp
);
3821 isl_reordering_free(r
);
3825 __isl_give isl_qpolynomial
*isl_qpolynomial_align_params(
3826 __isl_take isl_qpolynomial
*qp
, __isl_take isl_dim
*model
)
3831 if (!isl_dim_match(qp
->dim
, isl_dim_param
, model
, isl_dim_param
)) {
3832 isl_reordering
*exp
;
3834 model
= isl_dim_drop(model
, isl_dim_in
,
3835 0, isl_dim_size(model
, isl_dim_in
));
3836 model
= isl_dim_drop(model
, isl_dim_out
,
3837 0, isl_dim_size(model
, isl_dim_out
));
3838 exp
= isl_parameter_alignment_reordering(qp
->dim
, model
);
3839 exp
= isl_reordering_extend_dim(exp
,
3840 isl_qpolynomial_get_dim(qp
));
3841 qp
= isl_qpolynomial_realign(qp
, exp
);
3844 isl_dim_free(model
);
3847 isl_dim_free(model
);
3848 isl_qpolynomial_free(qp
);
3852 struct isl_split_periods_data
{
3854 isl_pw_qpolynomial
*res
;
3857 /* Create a slice where the integer division "div" has the fixed value "v".
3858 * In particular, if "div" refers to floor(f/m), then create a slice
3860 * m v <= f <= m v + (m - 1)
3865 * -f + m v + (m - 1) >= 0
3867 static __isl_give isl_set
*set_div_slice(__isl_take isl_dim
*dim
,
3868 __isl_keep isl_qpolynomial
*qp
, int div
, isl_int v
)
3871 isl_basic_set
*bset
= NULL
;
3877 total
= isl_dim_total(dim
);
3878 bset
= isl_basic_set_alloc_dim(isl_dim_copy(dim
), 0, 0, 2);
3880 k
= isl_basic_set_alloc_inequality(bset
);
3883 isl_seq_cpy(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
3884 isl_int_submul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
3886 k
= isl_basic_set_alloc_inequality(bset
);
3889 isl_seq_neg(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
3890 isl_int_addmul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
3891 isl_int_add(bset
->ineq
[k
][0], bset
->ineq
[k
][0], qp
->div
->row
[div
][0]);
3892 isl_int_sub_ui(bset
->ineq
[k
][0], bset
->ineq
[k
][0], 1);
3895 return isl_set_from_basic_set(bset
);
3897 isl_basic_set_free(bset
);
3902 static int split_periods(__isl_take isl_set
*set
,
3903 __isl_take isl_qpolynomial
*qp
, void *user
);
3905 /* Create a slice of the domain "set" such that integer division "div"
3906 * has the fixed value "v" and add the results to data->res,
3907 * replacing the integer division by "v" in "qp".
3909 static int set_div(__isl_take isl_set
*set
,
3910 __isl_take isl_qpolynomial
*qp
, int div
, isl_int v
,
3911 struct isl_split_periods_data
*data
)
3916 struct isl_upoly
*cst
;
3918 slice
= set_div_slice(isl_set_get_dim(set
), qp
, div
, v
);
3919 set
= isl_set_intersect(set
, slice
);
3924 total
= isl_dim_total(qp
->dim
);
3926 for (i
= div
+ 1; i
< qp
->div
->n_row
; ++i
) {
3927 if (isl_int_is_zero(qp
->div
->row
[i
][2 + total
+ div
]))
3929 isl_int_addmul(qp
->div
->row
[i
][1],
3930 qp
->div
->row
[i
][2 + total
+ div
], v
);
3931 isl_int_set_si(qp
->div
->row
[i
][2 + total
+ div
], 0);
3934 cst
= isl_upoly_rat_cst(qp
->dim
->ctx
, v
, qp
->dim
->ctx
->one
);
3935 qp
= substitute_div(qp
, div
, cst
);
3937 return split_periods(set
, qp
, data
);
3940 isl_qpolynomial_free(qp
);
3944 /* Split the domain "set" such that integer division "div"
3945 * has a fixed value (ranging from "min" to "max") on each slice
3946 * and add the results to data->res.
3948 static int split_div(__isl_take isl_set
*set
,
3949 __isl_take isl_qpolynomial
*qp
, int div
, isl_int min
, isl_int max
,
3950 struct isl_split_periods_data
*data
)
3952 for (; isl_int_le(min
, max
); isl_int_add_ui(min
, min
, 1)) {
3953 isl_set
*set_i
= isl_set_copy(set
);
3954 isl_qpolynomial
*qp_i
= isl_qpolynomial_copy(qp
);
3956 if (set_div(set_i
, qp_i
, div
, min
, data
) < 0)
3960 isl_qpolynomial_free(qp
);
3964 isl_qpolynomial_free(qp
);
3968 /* If "qp" refers to any integer division
3969 * that can only attain "max_periods" distinct values on "set"
3970 * then split the domain along those distinct values.
3971 * Add the results (or the original if no splitting occurs)
3974 static int split_periods(__isl_take isl_set
*set
,
3975 __isl_take isl_qpolynomial
*qp
, void *user
)
3978 isl_pw_qpolynomial
*pwqp
;
3979 struct isl_split_periods_data
*data
;
3984 data
= (struct isl_split_periods_data
*)user
;
3989 if (qp
->div
->n_row
== 0) {
3990 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
3991 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
3997 total
= isl_dim_total(qp
->dim
);
3998 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
3999 enum isl_lp_result lp_res
;
4001 if (isl_seq_first_non_zero(qp
->div
->row
[i
] + 2 + total
,
4002 qp
->div
->n_row
) != -1)
4005 lp_res
= isl_set_solve_lp(set
, 0, qp
->div
->row
[i
] + 1,
4006 set
->ctx
->one
, &min
, NULL
, NULL
);
4007 if (lp_res
== isl_lp_error
)
4009 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4011 isl_int_fdiv_q(min
, min
, qp
->div
->row
[i
][0]);
4013 lp_res
= isl_set_solve_lp(set
, 1, qp
->div
->row
[i
] + 1,
4014 set
->ctx
->one
, &max
, NULL
, NULL
);
4015 if (lp_res
== isl_lp_error
)
4017 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4019 isl_int_fdiv_q(max
, max
, qp
->div
->row
[i
][0]);
4021 isl_int_sub(max
, max
, min
);
4022 if (isl_int_cmp_si(max
, data
->max_periods
) < 0) {
4023 isl_int_add(max
, max
, min
);
4028 if (i
< qp
->div
->n_row
) {
4029 r
= split_div(set
, qp
, i
, min
, max
, data
);
4031 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4032 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4044 isl_qpolynomial_free(qp
);
4048 /* If any quasi-polynomial in pwqp refers to any integer division
4049 * that can only attain "max_periods" distinct values on its domain
4050 * then split the domain along those distinct values.
4052 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_split_periods(
4053 __isl_take isl_pw_qpolynomial
*pwqp
, int max_periods
)
4055 struct isl_split_periods_data data
;
4057 data
.max_periods
= max_periods
;
4058 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp
));
4060 if (isl_pw_qpolynomial_foreach_piece(pwqp
, &split_periods
, &data
) < 0)
4063 isl_pw_qpolynomial_free(pwqp
);
4067 isl_pw_qpolynomial_free(data
.res
);
4068 isl_pw_qpolynomial_free(pwqp
);
4072 /* Construct a piecewise quasipolynomial that is constant on the given
4073 * domain. In particular, it is
4076 * infinity if cst == -1
4078 static __isl_give isl_pw_qpolynomial
*constant_on_domain(
4079 __isl_take isl_basic_set
*bset
, int cst
)
4082 isl_qpolynomial
*qp
;
4087 bset
= isl_basic_map_domain(isl_basic_map_from_range(bset
));
4088 dim
= isl_basic_set_get_dim(bset
);
4090 qp
= isl_qpolynomial_infty(dim
);
4092 qp
= isl_qpolynomial_zero(dim
);
4094 qp
= isl_qpolynomial_one(dim
);
4095 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset
), qp
);
4098 /* Factor bset, call fn on each of the factors and return the product.
4100 * If no factors can be found, simply call fn on the input.
4101 * Otherwise, construct the factors based on the factorizer,
4102 * call fn on each factor and compute the product.
4104 static __isl_give isl_pw_qpolynomial
*compressed_multiplicative_call(
4105 __isl_take isl_basic_set
*bset
,
4106 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4112 isl_qpolynomial
*qp
;
4113 isl_pw_qpolynomial
*pwqp
;
4117 f
= isl_basic_set_factorizer(bset
);
4120 if (f
->n_group
== 0) {
4121 isl_factorizer_free(f
);
4125 nparam
= isl_basic_set_dim(bset
, isl_dim_param
);
4126 nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
4128 dim
= isl_basic_set_get_dim(bset
);
4129 dim
= isl_dim_domain(dim
);
4130 set
= isl_set_universe(isl_dim_copy(dim
));
4131 qp
= isl_qpolynomial_one(dim
);
4132 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4134 bset
= isl_morph_basic_set(isl_morph_copy(f
->morph
), bset
);
4136 for (i
= 0, n
= 0; i
< f
->n_group
; ++i
) {
4137 isl_basic_set
*bset_i
;
4138 isl_pw_qpolynomial
*pwqp_i
;
4140 bset_i
= isl_basic_set_copy(bset
);
4141 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4142 nparam
+ n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4143 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4145 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
,
4146 n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4147 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
, 0, n
);
4149 pwqp_i
= fn(bset_i
);
4150 pwqp
= isl_pw_qpolynomial_mul(pwqp
, pwqp_i
);
4155 isl_basic_set_free(bset
);
4156 isl_factorizer_free(f
);
4160 isl_basic_set_free(bset
);
4164 /* Factor bset, call fn on each of the factors and return the product.
4165 * The function is assumed to evaluate to zero on empty domains,
4166 * to one on zero-dimensional domains and to infinity on unbounded domains
4167 * and will not be called explicitly on zero-dimensional or unbounded domains.
4169 * We first check for some special cases and remove all equalities.
4170 * Then we hand over control to compressed_multiplicative_call.
4172 __isl_give isl_pw_qpolynomial
*isl_basic_set_multiplicative_call(
4173 __isl_take isl_basic_set
*bset
,
4174 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4178 isl_pw_qpolynomial
*pwqp
;
4179 unsigned orig_nvar
, final_nvar
;
4184 if (isl_basic_set_plain_is_empty(bset
))
4185 return constant_on_domain(bset
, 0);
4187 orig_nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
4190 return constant_on_domain(bset
, 1);
4192 bounded
= isl_basic_set_is_bounded(bset
);
4196 return constant_on_domain(bset
, -1);
4198 if (bset
->n_eq
== 0)
4199 return compressed_multiplicative_call(bset
, fn
);
4201 morph
= isl_basic_set_full_compression(bset
);
4202 bset
= isl_morph_basic_set(isl_morph_copy(morph
), bset
);
4204 final_nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
4206 pwqp
= compressed_multiplicative_call(bset
, fn
);
4208 morph
= isl_morph_remove_dom_dims(morph
, isl_dim_set
, 0, orig_nvar
);
4209 morph
= isl_morph_remove_ran_dims(morph
, isl_dim_set
, 0, final_nvar
);
4210 morph
= isl_morph_inverse(morph
);
4212 pwqp
= isl_pw_qpolynomial_morph(pwqp
, morph
);
4216 isl_basic_set_free(bset
);
4220 /* Drop all floors in "qp", turning each integer division [a/m] into
4221 * a rational division a/m. If "down" is set, then the integer division
4222 * is replaces by (a-(m-1))/m instead.
4224 static __isl_give isl_qpolynomial
*qp_drop_floors(
4225 __isl_take isl_qpolynomial
*qp
, int down
)
4228 struct isl_upoly
*s
;
4232 if (qp
->div
->n_row
== 0)
4235 qp
= isl_qpolynomial_cow(qp
);
4239 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
4241 isl_int_sub(qp
->div
->row
[i
][1],
4242 qp
->div
->row
[i
][1], qp
->div
->row
[i
][0]);
4243 isl_int_add_ui(qp
->div
->row
[i
][1],
4244 qp
->div
->row
[i
][1], 1);
4246 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
4247 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
4248 qp
= substitute_div(qp
, i
, s
);
4256 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4257 * a rational division a/m.
4259 static __isl_give isl_pw_qpolynomial
*pwqp_drop_floors(
4260 __isl_take isl_pw_qpolynomial
*pwqp
)
4267 if (isl_pw_qpolynomial_is_zero(pwqp
))
4270 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
4274 for (i
= 0; i
< pwqp
->n
; ++i
) {
4275 pwqp
->p
[i
].qp
= qp_drop_floors(pwqp
->p
[i
].qp
, 0);
4282 isl_pw_qpolynomial_free(pwqp
);
4286 /* Adjust all the integer divisions in "qp" such that they are at least
4287 * one over the given orthant (identified by "signs"). This ensures
4288 * that they will still be non-negative even after subtracting (m-1)/m.
4290 * In particular, f is replaced by f' + v, changing f = [a/m]
4291 * to f' = [(a - m v)/m].
4292 * If the constant term k in a is smaller than m,
4293 * the constant term of v is set to floor(k/m) - 1.
4294 * For any other term, if the coefficient c and the variable x have
4295 * the same sign, then no changes are needed.
4296 * Otherwise, if the variable is positive (and c is negative),
4297 * then the coefficient of x in v is set to floor(c/m).
4298 * If the variable is negative (and c is positive),
4299 * then the coefficient of x in v is set to ceil(c/m).
4301 static __isl_give isl_qpolynomial
*make_divs_pos(__isl_take isl_qpolynomial
*qp
,
4307 struct isl_upoly
*s
;
4309 qp
= isl_qpolynomial_cow(qp
);
4312 qp
->div
= isl_mat_cow(qp
->div
);
4316 total
= isl_dim_total(qp
->dim
);
4317 v
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
4319 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4320 isl_int
*row
= qp
->div
->row
[i
];
4324 if (isl_int_lt(row
[1], row
[0])) {
4325 isl_int_fdiv_q(v
->el
[0], row
[1], row
[0]);
4326 isl_int_sub_ui(v
->el
[0], v
->el
[0], 1);
4327 isl_int_submul(row
[1], row
[0], v
->el
[0]);
4329 for (j
= 0; j
< total
; ++j
) {
4330 if (isl_int_sgn(row
[2 + j
]) * signs
[j
] >= 0)
4333 isl_int_cdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4335 isl_int_fdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4336 isl_int_submul(row
[2 + j
], row
[0], v
->el
[1 + j
]);
4338 for (j
= 0; j
< i
; ++j
) {
4339 if (isl_int_sgn(row
[2 + total
+ j
]) >= 0)
4341 isl_int_fdiv_q(v
->el
[1 + total
+ j
],
4342 row
[2 + total
+ j
], row
[0]);
4343 isl_int_submul(row
[2 + total
+ j
],
4344 row
[0], v
->el
[1 + total
+ j
]);
4346 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
4347 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
4349 isl_seq_combine(qp
->div
->row
[j
] + 1,
4350 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
4351 qp
->div
->row
[j
][2 + total
+ i
], v
->el
, v
->size
);
4353 isl_int_set_si(v
->el
[1 + total
+ i
], 1);
4354 s
= isl_upoly_from_affine(qp
->dim
->ctx
, v
->el
,
4355 qp
->div
->ctx
->one
, v
->size
);
4356 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ i
, 1, &s
);
4366 isl_qpolynomial_free(qp
);
4370 struct isl_to_poly_data
{
4372 isl_pw_qpolynomial
*res
;
4373 isl_qpolynomial
*qp
;
4376 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4377 * We first make all integer divisions positive and then split the
4378 * quasipolynomials into terms with sign data->sign (the direction
4379 * of the requested approximation) and terms with the opposite sign.
4380 * In the first set of terms, each integer division [a/m] is
4381 * overapproximated by a/m, while in the second it is underapproximated
4384 static int to_polynomial_on_orthant(__isl_take isl_set
*orthant
, int *signs
,
4387 struct isl_to_poly_data
*data
= user
;
4388 isl_pw_qpolynomial
*t
;
4389 isl_qpolynomial
*qp
, *up
, *down
;
4391 qp
= isl_qpolynomial_copy(data
->qp
);
4392 qp
= make_divs_pos(qp
, signs
);
4394 up
= isl_qpolynomial_terms_of_sign(qp
, signs
, data
->sign
);
4395 up
= qp_drop_floors(up
, 0);
4396 down
= isl_qpolynomial_terms_of_sign(qp
, signs
, -data
->sign
);
4397 down
= qp_drop_floors(down
, 1);
4399 isl_qpolynomial_free(qp
);
4400 qp
= isl_qpolynomial_add(up
, down
);
4402 t
= isl_pw_qpolynomial_alloc(orthant
, qp
);
4403 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, t
);
4408 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4409 * the polynomial will be an overapproximation. If "sign" is negative,
4410 * it will be an underapproximation. If "sign" is zero, the approximation
4411 * will lie somewhere in between.
4413 * In particular, is sign == 0, we simply drop the floors, turning
4414 * the integer divisions into rational divisions.
4415 * Otherwise, we split the domains into orthants, make all integer divisions
4416 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4417 * depending on the requested sign and the sign of the term in which
4418 * the integer division appears.
4420 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_to_polynomial(
4421 __isl_take isl_pw_qpolynomial
*pwqp
, int sign
)
4424 struct isl_to_poly_data data
;
4427 return pwqp_drop_floors(pwqp
);
4433 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp
));
4435 for (i
= 0; i
< pwqp
->n
; ++i
) {
4436 if (pwqp
->p
[i
].qp
->div
->n_row
== 0) {
4437 isl_pw_qpolynomial
*t
;
4438 t
= isl_pw_qpolynomial_alloc(
4439 isl_set_copy(pwqp
->p
[i
].set
),
4440 isl_qpolynomial_copy(pwqp
->p
[i
].qp
));
4441 data
.res
= isl_pw_qpolynomial_add_disjoint(data
.res
, t
);
4444 data
.qp
= pwqp
->p
[i
].qp
;
4445 if (isl_set_foreach_orthant(pwqp
->p
[i
].set
,
4446 &to_polynomial_on_orthant
, &data
) < 0)
4450 isl_pw_qpolynomial_free(pwqp
);
4454 isl_pw_qpolynomial_free(pwqp
);
4455 isl_pw_qpolynomial_free(data
.res
);
4459 static int poly_entry(void **entry
, void *user
)
4462 isl_pw_qpolynomial
**pwqp
= (isl_pw_qpolynomial
**)entry
;
4464 *pwqp
= isl_pw_qpolynomial_to_polynomial(*pwqp
, *sign
);
4466 return *pwqp
? 0 : -1;
4469 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_to_polynomial(
4470 __isl_take isl_union_pw_qpolynomial
*upwqp
, int sign
)
4472 upwqp
= isl_union_pw_qpolynomial_cow(upwqp
);
4476 if (isl_hash_table_foreach(upwqp
->dim
->ctx
, &upwqp
->table
,
4477 &poly_entry
, &sign
) < 0)
4482 isl_union_pw_qpolynomial_free(upwqp
);
4486 __isl_give isl_basic_map
*isl_basic_map_from_qpolynomial(
4487 __isl_take isl_qpolynomial
*qp
)
4491 isl_vec
*aff
= NULL
;
4492 isl_basic_map
*bmap
= NULL
;
4498 if (!isl_upoly_is_affine(qp
->upoly
))
4499 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
4500 "input quasi-polynomial not affine", goto error
);
4501 aff
= isl_qpolynomial_extract_affine(qp
);
4504 dim
= isl_qpolynomial_get_dim(qp
);
4505 dim
= isl_dim_from_domain(dim
);
4506 pos
= 1 + isl_dim_offset(dim
, isl_dim_out
);
4507 dim
= isl_dim_add(dim
, isl_dim_out
, 1);
4508 n_div
= qp
->div
->n_row
;
4509 bmap
= isl_basic_map_alloc_dim(dim
, n_div
, 1, 2 * n_div
);
4511 for (i
= 0; i
< n_div
; ++i
) {
4512 k
= isl_basic_map_alloc_div(bmap
);
4515 isl_seq_cpy(bmap
->div
[k
], qp
->div
->row
[i
], qp
->div
->n_col
);
4516 isl_int_set_si(bmap
->div
[k
][qp
->div
->n_col
], 0);
4517 if (isl_basic_map_add_div_constraints(bmap
, k
) < 0)
4520 k
= isl_basic_map_alloc_equality(bmap
);
4523 isl_int_neg(bmap
->eq
[k
][pos
], aff
->el
[0]);
4524 isl_seq_cpy(bmap
->eq
[k
], aff
->el
+ 1, pos
);
4525 isl_seq_cpy(bmap
->eq
[k
] + pos
+ 1, aff
->el
+ 1 + pos
, n_div
);
4528 isl_qpolynomial_free(qp
);
4529 bmap
= isl_basic_map_finalize(bmap
);
4533 isl_qpolynomial_free(qp
);
4534 isl_basic_map_free(bmap
);