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,
13 #include <isl_ctx_private.h>
14 #include <isl_map_private.h>
15 #include <isl_factorization.h>
18 #include <isl_union_map_private.h>
19 #include <isl_constraint_private.h>
20 #include <isl_polynomial_private.h>
21 #include <isl_point_private.h>
22 #include <isl_space_private.h>
23 #include <isl_div_private.h>
24 #include <isl_mat_private.h>
25 #include <isl_range.h>
26 #include <isl_local_space_private.h>
27 #include <isl_aff_private.h>
28 #include <isl_config.h>
30 static unsigned pos(__isl_keep isl_space
*dim
, enum isl_dim_type type
)
33 case isl_dim_param
: return 0;
34 case isl_dim_in
: return dim
->nparam
;
35 case isl_dim_out
: return dim
->nparam
+ dim
->n_in
;
40 int isl_upoly_is_cst(__isl_keep
struct isl_upoly
*up
)
48 __isl_keep
struct isl_upoly_cst
*isl_upoly_as_cst(__isl_keep
struct isl_upoly
*up
)
53 isl_assert(up
->ctx
, up
->var
< 0, return NULL
);
55 return (struct isl_upoly_cst
*)up
;
58 __isl_keep
struct isl_upoly_rec
*isl_upoly_as_rec(__isl_keep
struct isl_upoly
*up
)
63 isl_assert(up
->ctx
, up
->var
>= 0, return NULL
);
65 return (struct isl_upoly_rec
*)up
;
68 int isl_upoly_is_equal(__isl_keep
struct isl_upoly
*up1
,
69 __isl_keep
struct isl_upoly
*up2
)
72 struct isl_upoly_rec
*rec1
, *rec2
;
78 if (up1
->var
!= up2
->var
)
80 if (isl_upoly_is_cst(up1
)) {
81 struct isl_upoly_cst
*cst1
, *cst2
;
82 cst1
= isl_upoly_as_cst(up1
);
83 cst2
= isl_upoly_as_cst(up2
);
86 return isl_int_eq(cst1
->n
, cst2
->n
) &&
87 isl_int_eq(cst1
->d
, cst2
->d
);
90 rec1
= isl_upoly_as_rec(up1
);
91 rec2
= isl_upoly_as_rec(up2
);
95 if (rec1
->n
!= rec2
->n
)
98 for (i
= 0; i
< rec1
->n
; ++i
) {
99 int eq
= isl_upoly_is_equal(rec1
->p
[i
], rec2
->p
[i
]);
107 int isl_upoly_is_zero(__isl_keep
struct isl_upoly
*up
)
109 struct isl_upoly_cst
*cst
;
113 if (!isl_upoly_is_cst(up
))
116 cst
= isl_upoly_as_cst(up
);
120 return isl_int_is_zero(cst
->n
) && isl_int_is_pos(cst
->d
);
123 int isl_upoly_sgn(__isl_keep
struct isl_upoly
*up
)
125 struct isl_upoly_cst
*cst
;
129 if (!isl_upoly_is_cst(up
))
132 cst
= isl_upoly_as_cst(up
);
136 return isl_int_sgn(cst
->n
);
139 int isl_upoly_is_nan(__isl_keep
struct isl_upoly
*up
)
141 struct isl_upoly_cst
*cst
;
145 if (!isl_upoly_is_cst(up
))
148 cst
= isl_upoly_as_cst(up
);
152 return isl_int_is_zero(cst
->n
) && isl_int_is_zero(cst
->d
);
155 int isl_upoly_is_infty(__isl_keep
struct isl_upoly
*up
)
157 struct isl_upoly_cst
*cst
;
161 if (!isl_upoly_is_cst(up
))
164 cst
= isl_upoly_as_cst(up
);
168 return isl_int_is_pos(cst
->n
) && isl_int_is_zero(cst
->d
);
171 int isl_upoly_is_neginfty(__isl_keep
struct isl_upoly
*up
)
173 struct isl_upoly_cst
*cst
;
177 if (!isl_upoly_is_cst(up
))
180 cst
= isl_upoly_as_cst(up
);
184 return isl_int_is_neg(cst
->n
) && isl_int_is_zero(cst
->d
);
187 int isl_upoly_is_one(__isl_keep
struct isl_upoly
*up
)
189 struct isl_upoly_cst
*cst
;
193 if (!isl_upoly_is_cst(up
))
196 cst
= isl_upoly_as_cst(up
);
200 return isl_int_eq(cst
->n
, cst
->d
) && isl_int_is_pos(cst
->d
);
203 int isl_upoly_is_negone(__isl_keep
struct isl_upoly
*up
)
205 struct isl_upoly_cst
*cst
;
209 if (!isl_upoly_is_cst(up
))
212 cst
= isl_upoly_as_cst(up
);
216 return isl_int_is_negone(cst
->n
) && isl_int_is_one(cst
->d
);
219 __isl_give
struct isl_upoly_cst
*isl_upoly_cst_alloc(struct isl_ctx
*ctx
)
221 struct isl_upoly_cst
*cst
;
223 cst
= isl_alloc_type(ctx
, struct isl_upoly_cst
);
232 isl_int_init(cst
->n
);
233 isl_int_init(cst
->d
);
238 __isl_give
struct isl_upoly
*isl_upoly_zero(struct isl_ctx
*ctx
)
240 struct isl_upoly_cst
*cst
;
242 cst
= isl_upoly_cst_alloc(ctx
);
246 isl_int_set_si(cst
->n
, 0);
247 isl_int_set_si(cst
->d
, 1);
252 __isl_give
struct isl_upoly
*isl_upoly_one(struct isl_ctx
*ctx
)
254 struct isl_upoly_cst
*cst
;
256 cst
= isl_upoly_cst_alloc(ctx
);
260 isl_int_set_si(cst
->n
, 1);
261 isl_int_set_si(cst
->d
, 1);
266 __isl_give
struct isl_upoly
*isl_upoly_infty(struct isl_ctx
*ctx
)
268 struct isl_upoly_cst
*cst
;
270 cst
= isl_upoly_cst_alloc(ctx
);
274 isl_int_set_si(cst
->n
, 1);
275 isl_int_set_si(cst
->d
, 0);
280 __isl_give
struct isl_upoly
*isl_upoly_neginfty(struct isl_ctx
*ctx
)
282 struct isl_upoly_cst
*cst
;
284 cst
= isl_upoly_cst_alloc(ctx
);
288 isl_int_set_si(cst
->n
, -1);
289 isl_int_set_si(cst
->d
, 0);
294 __isl_give
struct isl_upoly
*isl_upoly_nan(struct isl_ctx
*ctx
)
296 struct isl_upoly_cst
*cst
;
298 cst
= isl_upoly_cst_alloc(ctx
);
302 isl_int_set_si(cst
->n
, 0);
303 isl_int_set_si(cst
->d
, 0);
308 __isl_give
struct isl_upoly
*isl_upoly_rat_cst(struct isl_ctx
*ctx
,
309 isl_int n
, isl_int d
)
311 struct isl_upoly_cst
*cst
;
313 cst
= isl_upoly_cst_alloc(ctx
);
317 isl_int_set(cst
->n
, n
);
318 isl_int_set(cst
->d
, d
);
323 __isl_give
struct isl_upoly_rec
*isl_upoly_alloc_rec(struct isl_ctx
*ctx
,
326 struct isl_upoly_rec
*rec
;
328 isl_assert(ctx
, var
>= 0, return NULL
);
329 isl_assert(ctx
, size
>= 0, return NULL
);
330 rec
= isl_calloc(ctx
, struct isl_upoly_rec
,
331 sizeof(struct isl_upoly_rec
) +
332 size
* sizeof(struct isl_upoly
*));
347 __isl_give isl_qpolynomial
*isl_qpolynomial_reset_domain_space(
348 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*dim
)
350 qp
= isl_qpolynomial_cow(qp
);
354 isl_space_free(qp
->dim
);
359 isl_qpolynomial_free(qp
);
364 /* Reset the space of "qp". This function is called from isl_pw_templ.c
365 * and doesn't know if the space of an element object is represented
366 * directly or through its domain. It therefore passes along both.
368 __isl_give isl_qpolynomial
*isl_qpolynomial_reset_space_and_domain(
369 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*space
,
370 __isl_take isl_space
*domain
)
372 isl_space_free(space
);
373 return isl_qpolynomial_reset_domain_space(qp
, domain
);
376 isl_ctx
*isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial
*qp
)
378 return qp
? qp
->dim
->ctx
: NULL
;
381 __isl_give isl_space
*isl_qpolynomial_get_domain_space(
382 __isl_keep isl_qpolynomial
*qp
)
384 return qp
? isl_space_copy(qp
->dim
) : NULL
;
387 __isl_give isl_space
*isl_qpolynomial_get_space(__isl_keep isl_qpolynomial
*qp
)
392 space
= isl_space_copy(qp
->dim
);
393 space
= isl_space_from_domain(space
);
394 space
= isl_space_add_dims(space
, isl_dim_out
, 1);
398 /* Externally, an isl_qpolynomial has a map space, but internally, the
399 * ls field corresponds to the domain of that space.
401 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial
*qp
,
402 enum isl_dim_type type
)
406 if (type
== isl_dim_out
)
408 if (type
== isl_dim_in
)
410 return isl_space_dim(qp
->dim
, type
);
413 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial
*qp
)
415 return qp
? isl_upoly_is_zero(qp
->upoly
) : -1;
418 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial
*qp
)
420 return qp
? isl_upoly_is_one(qp
->upoly
) : -1;
423 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial
*qp
)
425 return qp
? isl_upoly_is_nan(qp
->upoly
) : -1;
428 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial
*qp
)
430 return qp
? isl_upoly_is_infty(qp
->upoly
) : -1;
433 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial
*qp
)
435 return qp
? isl_upoly_is_neginfty(qp
->upoly
) : -1;
438 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial
*qp
)
440 return qp
? isl_upoly_sgn(qp
->upoly
) : 0;
443 static void upoly_free_cst(__isl_take
struct isl_upoly_cst
*cst
)
445 isl_int_clear(cst
->n
);
446 isl_int_clear(cst
->d
);
449 static void upoly_free_rec(__isl_take
struct isl_upoly_rec
*rec
)
453 for (i
= 0; i
< rec
->n
; ++i
)
454 isl_upoly_free(rec
->p
[i
]);
457 __isl_give
struct isl_upoly
*isl_upoly_copy(__isl_keep
struct isl_upoly
*up
)
466 __isl_give
struct isl_upoly
*isl_upoly_dup_cst(__isl_keep
struct isl_upoly
*up
)
468 struct isl_upoly_cst
*cst
;
469 struct isl_upoly_cst
*dup
;
471 cst
= isl_upoly_as_cst(up
);
475 dup
= isl_upoly_as_cst(isl_upoly_zero(up
->ctx
));
478 isl_int_set(dup
->n
, cst
->n
);
479 isl_int_set(dup
->d
, cst
->d
);
484 __isl_give
struct isl_upoly
*isl_upoly_dup_rec(__isl_keep
struct isl_upoly
*up
)
487 struct isl_upoly_rec
*rec
;
488 struct isl_upoly_rec
*dup
;
490 rec
= isl_upoly_as_rec(up
);
494 dup
= isl_upoly_alloc_rec(up
->ctx
, up
->var
, rec
->n
);
498 for (i
= 0; i
< rec
->n
; ++i
) {
499 dup
->p
[i
] = isl_upoly_copy(rec
->p
[i
]);
507 isl_upoly_free(&dup
->up
);
511 __isl_give
struct isl_upoly
*isl_upoly_dup(__isl_keep
struct isl_upoly
*up
)
516 if (isl_upoly_is_cst(up
))
517 return isl_upoly_dup_cst(up
);
519 return isl_upoly_dup_rec(up
);
522 __isl_give
struct isl_upoly
*isl_upoly_cow(__isl_take
struct isl_upoly
*up
)
530 return isl_upoly_dup(up
);
533 void isl_upoly_free(__isl_take
struct isl_upoly
*up
)
542 upoly_free_cst((struct isl_upoly_cst
*)up
);
544 upoly_free_rec((struct isl_upoly_rec
*)up
);
546 isl_ctx_deref(up
->ctx
);
550 static void isl_upoly_cst_reduce(__isl_keep
struct isl_upoly_cst
*cst
)
555 isl_int_gcd(gcd
, cst
->n
, cst
->d
);
556 if (!isl_int_is_zero(gcd
) && !isl_int_is_one(gcd
)) {
557 isl_int_divexact(cst
->n
, cst
->n
, gcd
);
558 isl_int_divexact(cst
->d
, cst
->d
, gcd
);
563 __isl_give
struct isl_upoly
*isl_upoly_sum_cst(__isl_take
struct isl_upoly
*up1
,
564 __isl_take
struct isl_upoly
*up2
)
566 struct isl_upoly_cst
*cst1
;
567 struct isl_upoly_cst
*cst2
;
569 up1
= isl_upoly_cow(up1
);
573 cst1
= isl_upoly_as_cst(up1
);
574 cst2
= isl_upoly_as_cst(up2
);
576 if (isl_int_eq(cst1
->d
, cst2
->d
))
577 isl_int_add(cst1
->n
, cst1
->n
, cst2
->n
);
579 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->d
);
580 isl_int_addmul(cst1
->n
, cst2
->n
, cst1
->d
);
581 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
584 isl_upoly_cst_reduce(cst1
);
594 static __isl_give
struct isl_upoly
*replace_by_zero(
595 __isl_take
struct isl_upoly
*up
)
603 return isl_upoly_zero(ctx
);
606 static __isl_give
struct isl_upoly
*replace_by_constant_term(
607 __isl_take
struct isl_upoly
*up
)
609 struct isl_upoly_rec
*rec
;
610 struct isl_upoly
*cst
;
615 rec
= isl_upoly_as_rec(up
);
618 cst
= isl_upoly_copy(rec
->p
[0]);
626 __isl_give
struct isl_upoly
*isl_upoly_sum(__isl_take
struct isl_upoly
*up1
,
627 __isl_take
struct isl_upoly
*up2
)
630 struct isl_upoly_rec
*rec1
, *rec2
;
635 if (isl_upoly_is_nan(up1
)) {
640 if (isl_upoly_is_nan(up2
)) {
645 if (isl_upoly_is_zero(up1
)) {
650 if (isl_upoly_is_zero(up2
)) {
655 if (up1
->var
< up2
->var
)
656 return isl_upoly_sum(up2
, up1
);
658 if (up2
->var
< up1
->var
) {
659 struct isl_upoly_rec
*rec
;
660 if (isl_upoly_is_infty(up2
) || isl_upoly_is_neginfty(up2
)) {
664 up1
= isl_upoly_cow(up1
);
665 rec
= isl_upoly_as_rec(up1
);
668 rec
->p
[0] = isl_upoly_sum(rec
->p
[0], up2
);
670 up1
= replace_by_constant_term(up1
);
674 if (isl_upoly_is_cst(up1
))
675 return isl_upoly_sum_cst(up1
, up2
);
677 rec1
= isl_upoly_as_rec(up1
);
678 rec2
= isl_upoly_as_rec(up2
);
682 if (rec1
->n
< rec2
->n
)
683 return isl_upoly_sum(up2
, up1
);
685 up1
= isl_upoly_cow(up1
);
686 rec1
= isl_upoly_as_rec(up1
);
690 for (i
= rec2
->n
- 1; i
>= 0; --i
) {
691 rec1
->p
[i
] = isl_upoly_sum(rec1
->p
[i
],
692 isl_upoly_copy(rec2
->p
[i
]));
695 if (i
== rec1
->n
- 1 && isl_upoly_is_zero(rec1
->p
[i
])) {
696 isl_upoly_free(rec1
->p
[i
]);
702 up1
= replace_by_zero(up1
);
703 else if (rec1
->n
== 1)
704 up1
= replace_by_constant_term(up1
);
715 __isl_give
struct isl_upoly
*isl_upoly_cst_add_isl_int(
716 __isl_take
struct isl_upoly
*up
, isl_int v
)
718 struct isl_upoly_cst
*cst
;
720 up
= isl_upoly_cow(up
);
724 cst
= isl_upoly_as_cst(up
);
726 isl_int_addmul(cst
->n
, cst
->d
, v
);
731 __isl_give
struct isl_upoly
*isl_upoly_add_isl_int(
732 __isl_take
struct isl_upoly
*up
, isl_int v
)
734 struct isl_upoly_rec
*rec
;
739 if (isl_upoly_is_cst(up
))
740 return isl_upoly_cst_add_isl_int(up
, v
);
742 up
= isl_upoly_cow(up
);
743 rec
= isl_upoly_as_rec(up
);
747 rec
->p
[0] = isl_upoly_add_isl_int(rec
->p
[0], v
);
757 __isl_give
struct isl_upoly
*isl_upoly_cst_mul_isl_int(
758 __isl_take
struct isl_upoly
*up
, isl_int v
)
760 struct isl_upoly_cst
*cst
;
762 if (isl_upoly_is_zero(up
))
765 up
= isl_upoly_cow(up
);
769 cst
= isl_upoly_as_cst(up
);
771 isl_int_mul(cst
->n
, cst
->n
, v
);
776 __isl_give
struct isl_upoly
*isl_upoly_mul_isl_int(
777 __isl_take
struct isl_upoly
*up
, isl_int v
)
780 struct isl_upoly_rec
*rec
;
785 if (isl_upoly_is_cst(up
))
786 return isl_upoly_cst_mul_isl_int(up
, v
);
788 up
= isl_upoly_cow(up
);
789 rec
= isl_upoly_as_rec(up
);
793 for (i
= 0; i
< rec
->n
; ++i
) {
794 rec
->p
[i
] = isl_upoly_mul_isl_int(rec
->p
[i
], v
);
805 __isl_give
struct isl_upoly
*isl_upoly_mul_cst(__isl_take
struct isl_upoly
*up1
,
806 __isl_take
struct isl_upoly
*up2
)
808 struct isl_upoly_cst
*cst1
;
809 struct isl_upoly_cst
*cst2
;
811 up1
= isl_upoly_cow(up1
);
815 cst1
= isl_upoly_as_cst(up1
);
816 cst2
= isl_upoly_as_cst(up2
);
818 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->n
);
819 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
821 isl_upoly_cst_reduce(cst1
);
831 __isl_give
struct isl_upoly
*isl_upoly_mul_rec(__isl_take
struct isl_upoly
*up1
,
832 __isl_take
struct isl_upoly
*up2
)
834 struct isl_upoly_rec
*rec1
;
835 struct isl_upoly_rec
*rec2
;
836 struct isl_upoly_rec
*res
= NULL
;
840 rec1
= isl_upoly_as_rec(up1
);
841 rec2
= isl_upoly_as_rec(up2
);
844 size
= rec1
->n
+ rec2
->n
- 1;
845 res
= isl_upoly_alloc_rec(up1
->ctx
, up1
->var
, size
);
849 for (i
= 0; i
< rec1
->n
; ++i
) {
850 res
->p
[i
] = isl_upoly_mul(isl_upoly_copy(rec2
->p
[0]),
851 isl_upoly_copy(rec1
->p
[i
]));
856 for (; i
< size
; ++i
) {
857 res
->p
[i
] = isl_upoly_zero(up1
->ctx
);
862 for (i
= 0; i
< rec1
->n
; ++i
) {
863 for (j
= 1; j
< rec2
->n
; ++j
) {
864 struct isl_upoly
*up
;
865 up
= isl_upoly_mul(isl_upoly_copy(rec2
->p
[j
]),
866 isl_upoly_copy(rec1
->p
[i
]));
867 res
->p
[i
+ j
] = isl_upoly_sum(res
->p
[i
+ j
], up
);
880 isl_upoly_free(&res
->up
);
884 __isl_give
struct isl_upoly
*isl_upoly_mul(__isl_take
struct isl_upoly
*up1
,
885 __isl_take
struct isl_upoly
*up2
)
890 if (isl_upoly_is_nan(up1
)) {
895 if (isl_upoly_is_nan(up2
)) {
900 if (isl_upoly_is_zero(up1
)) {
905 if (isl_upoly_is_zero(up2
)) {
910 if (isl_upoly_is_one(up1
)) {
915 if (isl_upoly_is_one(up2
)) {
920 if (up1
->var
< up2
->var
)
921 return isl_upoly_mul(up2
, up1
);
923 if (up2
->var
< up1
->var
) {
925 struct isl_upoly_rec
*rec
;
926 if (isl_upoly_is_infty(up2
) || isl_upoly_is_neginfty(up2
)) {
927 isl_ctx
*ctx
= up1
->ctx
;
930 return isl_upoly_nan(ctx
);
932 up1
= isl_upoly_cow(up1
);
933 rec
= isl_upoly_as_rec(up1
);
937 for (i
= 0; i
< rec
->n
; ++i
) {
938 rec
->p
[i
] = isl_upoly_mul(rec
->p
[i
],
939 isl_upoly_copy(up2
));
947 if (isl_upoly_is_cst(up1
))
948 return isl_upoly_mul_cst(up1
, up2
);
950 return isl_upoly_mul_rec(up1
, up2
);
957 __isl_give
struct isl_upoly
*isl_upoly_pow(__isl_take
struct isl_upoly
*up
,
960 struct isl_upoly
*res
;
968 res
= isl_upoly_copy(up
);
970 res
= isl_upoly_one(up
->ctx
);
972 while (power
>>= 1) {
973 up
= isl_upoly_mul(up
, isl_upoly_copy(up
));
975 res
= isl_upoly_mul(res
, isl_upoly_copy(up
));
982 __isl_give isl_qpolynomial
*isl_qpolynomial_alloc(__isl_take isl_space
*dim
,
983 unsigned n_div
, __isl_take
struct isl_upoly
*up
)
985 struct isl_qpolynomial
*qp
= NULL
;
991 if (!isl_space_is_set(dim
))
992 isl_die(isl_space_get_ctx(dim
), isl_error_invalid
,
993 "domain of polynomial should be a set", goto error
);
995 total
= isl_space_dim(dim
, isl_dim_all
);
997 qp
= isl_calloc_type(dim
->ctx
, struct isl_qpolynomial
);
1002 qp
->div
= isl_mat_alloc(dim
->ctx
, n_div
, 1 + 1 + total
+ n_div
);
1011 isl_space_free(dim
);
1013 isl_qpolynomial_free(qp
);
1017 __isl_give isl_qpolynomial
*isl_qpolynomial_copy(__isl_keep isl_qpolynomial
*qp
)
1026 __isl_give isl_qpolynomial
*isl_qpolynomial_dup(__isl_keep isl_qpolynomial
*qp
)
1028 struct isl_qpolynomial
*dup
;
1033 dup
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
), qp
->div
->n_row
,
1034 isl_upoly_copy(qp
->upoly
));
1037 isl_mat_free(dup
->div
);
1038 dup
->div
= isl_mat_copy(qp
->div
);
1044 isl_qpolynomial_free(dup
);
1048 __isl_give isl_qpolynomial
*isl_qpolynomial_cow(__isl_take isl_qpolynomial
*qp
)
1056 return isl_qpolynomial_dup(qp
);
1059 void *isl_qpolynomial_free(__isl_take isl_qpolynomial
*qp
)
1067 isl_space_free(qp
->dim
);
1068 isl_mat_free(qp
->div
);
1069 isl_upoly_free(qp
->upoly
);
1075 __isl_give
struct isl_upoly
*isl_upoly_var_pow(isl_ctx
*ctx
, int pos
, int power
)
1078 struct isl_upoly_rec
*rec
;
1079 struct isl_upoly_cst
*cst
;
1081 rec
= isl_upoly_alloc_rec(ctx
, pos
, 1 + power
);
1084 for (i
= 0; i
< 1 + power
; ++i
) {
1085 rec
->p
[i
] = isl_upoly_zero(ctx
);
1090 cst
= isl_upoly_as_cst(rec
->p
[power
]);
1091 isl_int_set_si(cst
->n
, 1);
1095 isl_upoly_free(&rec
->up
);
1099 /* r array maps original positions to new positions.
1101 static __isl_give
struct isl_upoly
*reorder(__isl_take
struct isl_upoly
*up
,
1105 struct isl_upoly_rec
*rec
;
1106 struct isl_upoly
*base
;
1107 struct isl_upoly
*res
;
1109 if (isl_upoly_is_cst(up
))
1112 rec
= isl_upoly_as_rec(up
);
1116 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
1118 base
= isl_upoly_var_pow(up
->ctx
, r
[up
->var
], 1);
1119 res
= reorder(isl_upoly_copy(rec
->p
[rec
->n
- 1]), r
);
1121 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1122 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
1123 res
= isl_upoly_sum(res
, reorder(isl_upoly_copy(rec
->p
[i
]), r
));
1126 isl_upoly_free(base
);
1135 static int compatible_divs(__isl_keep isl_mat
*div1
, __isl_keep isl_mat
*div2
)
1140 isl_assert(div1
->ctx
, div1
->n_row
>= div2
->n_row
&&
1141 div1
->n_col
>= div2
->n_col
, return -1);
1143 if (div1
->n_row
== div2
->n_row
)
1144 return isl_mat_is_equal(div1
, div2
);
1146 n_row
= div1
->n_row
;
1147 n_col
= div1
->n_col
;
1148 div1
->n_row
= div2
->n_row
;
1149 div1
->n_col
= div2
->n_col
;
1151 equal
= isl_mat_is_equal(div1
, div2
);
1153 div1
->n_row
= n_row
;
1154 div1
->n_col
= n_col
;
1159 static int cmp_row(__isl_keep isl_mat
*div
, int i
, int j
)
1163 li
= isl_seq_last_non_zero(div
->row
[i
], div
->n_col
);
1164 lj
= isl_seq_last_non_zero(div
->row
[j
], div
->n_col
);
1169 return isl_seq_cmp(div
->row
[i
], div
->row
[j
], div
->n_col
);
1172 struct isl_div_sort_info
{
1177 static int div_sort_cmp(const void *p1
, const void *p2
)
1179 const struct isl_div_sort_info
*i1
, *i2
;
1180 i1
= (const struct isl_div_sort_info
*) p1
;
1181 i2
= (const struct isl_div_sort_info
*) p2
;
1183 return cmp_row(i1
->div
, i1
->row
, i2
->row
);
1186 /* Sort divs and remove duplicates.
1188 static __isl_give isl_qpolynomial
*sort_divs(__isl_take isl_qpolynomial
*qp
)
1193 struct isl_div_sort_info
*array
= NULL
;
1194 int *pos
= NULL
, *at
= NULL
;
1195 int *reordering
= NULL
;
1200 if (qp
->div
->n_row
<= 1)
1203 div_pos
= isl_space_dim(qp
->dim
, isl_dim_all
);
1205 array
= isl_alloc_array(qp
->div
->ctx
, struct isl_div_sort_info
,
1207 pos
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1208 at
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1209 len
= qp
->div
->n_col
- 2;
1210 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
1211 if (!array
|| !pos
|| !at
|| !reordering
)
1214 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1215 array
[i
].div
= qp
->div
;
1221 qsort(array
, qp
->div
->n_row
, sizeof(struct isl_div_sort_info
),
1224 for (i
= 0; i
< div_pos
; ++i
)
1227 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1228 if (pos
[array
[i
].row
] == i
)
1230 qp
->div
= isl_mat_swap_rows(qp
->div
, i
, pos
[array
[i
].row
]);
1231 pos
[at
[i
]] = pos
[array
[i
].row
];
1232 at
[pos
[array
[i
].row
]] = at
[i
];
1233 at
[i
] = array
[i
].row
;
1234 pos
[array
[i
].row
] = i
;
1238 for (i
= 0; i
< len
- div_pos
; ++i
) {
1240 isl_seq_eq(qp
->div
->row
[i
- skip
- 1],
1241 qp
->div
->row
[i
- skip
], qp
->div
->n_col
)) {
1242 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
1243 isl_mat_col_add(qp
->div
, 2 + div_pos
+ i
- skip
- 1,
1244 2 + div_pos
+ i
- skip
);
1245 qp
->div
= isl_mat_drop_cols(qp
->div
,
1246 2 + div_pos
+ i
- skip
, 1);
1249 reordering
[div_pos
+ array
[i
].row
] = div_pos
+ i
- skip
;
1252 qp
->upoly
= reorder(qp
->upoly
, reordering
);
1254 if (!qp
->upoly
|| !qp
->div
)
1268 isl_qpolynomial_free(qp
);
1272 static __isl_give
struct isl_upoly
*expand(__isl_take
struct isl_upoly
*up
,
1273 int *exp
, int first
)
1276 struct isl_upoly_rec
*rec
;
1278 if (isl_upoly_is_cst(up
))
1281 if (up
->var
< first
)
1284 if (exp
[up
->var
- first
] == up
->var
- first
)
1287 up
= isl_upoly_cow(up
);
1291 up
->var
= exp
[up
->var
- first
] + first
;
1293 rec
= isl_upoly_as_rec(up
);
1297 for (i
= 0; i
< rec
->n
; ++i
) {
1298 rec
->p
[i
] = expand(rec
->p
[i
], exp
, first
);
1309 static __isl_give isl_qpolynomial
*with_merged_divs(
1310 __isl_give isl_qpolynomial
*(*fn
)(__isl_take isl_qpolynomial
*qp1
,
1311 __isl_take isl_qpolynomial
*qp2
),
1312 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
1316 isl_mat
*div
= NULL
;
1318 qp1
= isl_qpolynomial_cow(qp1
);
1319 qp2
= isl_qpolynomial_cow(qp2
);
1324 isl_assert(qp1
->div
->ctx
, qp1
->div
->n_row
>= qp2
->div
->n_row
&&
1325 qp1
->div
->n_col
>= qp2
->div
->n_col
, goto error
);
1327 exp1
= isl_alloc_array(qp1
->div
->ctx
, int, qp1
->div
->n_row
);
1328 exp2
= isl_alloc_array(qp2
->div
->ctx
, int, qp2
->div
->n_row
);
1332 div
= isl_merge_divs(qp1
->div
, qp2
->div
, exp1
, exp2
);
1336 isl_mat_free(qp1
->div
);
1337 qp1
->div
= isl_mat_copy(div
);
1338 isl_mat_free(qp2
->div
);
1339 qp2
->div
= isl_mat_copy(div
);
1341 qp1
->upoly
= expand(qp1
->upoly
, exp1
, div
->n_col
- div
->n_row
- 2);
1342 qp2
->upoly
= expand(qp2
->upoly
, exp2
, div
->n_col
- div
->n_row
- 2);
1344 if (!qp1
->upoly
|| !qp2
->upoly
)
1351 return fn(qp1
, qp2
);
1356 isl_qpolynomial_free(qp1
);
1357 isl_qpolynomial_free(qp2
);
1361 __isl_give isl_qpolynomial
*isl_qpolynomial_add(__isl_take isl_qpolynomial
*qp1
,
1362 __isl_take isl_qpolynomial
*qp2
)
1364 qp1
= isl_qpolynomial_cow(qp1
);
1369 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1370 return isl_qpolynomial_add(qp2
, qp1
);
1372 isl_assert(qp1
->dim
->ctx
, isl_space_is_equal(qp1
->dim
, qp2
->dim
), goto error
);
1373 if (!compatible_divs(qp1
->div
, qp2
->div
))
1374 return with_merged_divs(isl_qpolynomial_add
, qp1
, qp2
);
1376 qp1
->upoly
= isl_upoly_sum(qp1
->upoly
, isl_upoly_copy(qp2
->upoly
));
1380 isl_qpolynomial_free(qp2
);
1384 isl_qpolynomial_free(qp1
);
1385 isl_qpolynomial_free(qp2
);
1389 __isl_give isl_qpolynomial
*isl_qpolynomial_add_on_domain(
1390 __isl_keep isl_set
*dom
,
1391 __isl_take isl_qpolynomial
*qp1
,
1392 __isl_take isl_qpolynomial
*qp2
)
1394 qp1
= isl_qpolynomial_add(qp1
, qp2
);
1395 qp1
= isl_qpolynomial_gist(qp1
, isl_set_copy(dom
));
1399 __isl_give isl_qpolynomial
*isl_qpolynomial_sub(__isl_take isl_qpolynomial
*qp1
,
1400 __isl_take isl_qpolynomial
*qp2
)
1402 return isl_qpolynomial_add(qp1
, isl_qpolynomial_neg(qp2
));
1405 __isl_give isl_qpolynomial
*isl_qpolynomial_add_isl_int(
1406 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1408 if (isl_int_is_zero(v
))
1411 qp
= isl_qpolynomial_cow(qp
);
1415 qp
->upoly
= isl_upoly_add_isl_int(qp
->upoly
, v
);
1421 isl_qpolynomial_free(qp
);
1426 __isl_give isl_qpolynomial
*isl_qpolynomial_neg(__isl_take isl_qpolynomial
*qp
)
1431 return isl_qpolynomial_mul_isl_int(qp
, qp
->dim
->ctx
->negone
);
1434 __isl_give isl_qpolynomial
*isl_qpolynomial_mul_isl_int(
1435 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1437 if (isl_int_is_one(v
))
1440 if (qp
&& isl_int_is_zero(v
)) {
1441 isl_qpolynomial
*zero
;
1442 zero
= isl_qpolynomial_zero_on_domain(isl_space_copy(qp
->dim
));
1443 isl_qpolynomial_free(qp
);
1447 qp
= isl_qpolynomial_cow(qp
);
1451 qp
->upoly
= isl_upoly_mul_isl_int(qp
->upoly
, v
);
1457 isl_qpolynomial_free(qp
);
1461 __isl_give isl_qpolynomial
*isl_qpolynomial_scale(
1462 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1464 return isl_qpolynomial_mul_isl_int(qp
, v
);
1467 __isl_give isl_qpolynomial
*isl_qpolynomial_mul(__isl_take isl_qpolynomial
*qp1
,
1468 __isl_take isl_qpolynomial
*qp2
)
1470 qp1
= isl_qpolynomial_cow(qp1
);
1475 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1476 return isl_qpolynomial_mul(qp2
, qp1
);
1478 isl_assert(qp1
->dim
->ctx
, isl_space_is_equal(qp1
->dim
, qp2
->dim
), goto error
);
1479 if (!compatible_divs(qp1
->div
, qp2
->div
))
1480 return with_merged_divs(isl_qpolynomial_mul
, qp1
, qp2
);
1482 qp1
->upoly
= isl_upoly_mul(qp1
->upoly
, isl_upoly_copy(qp2
->upoly
));
1486 isl_qpolynomial_free(qp2
);
1490 isl_qpolynomial_free(qp1
);
1491 isl_qpolynomial_free(qp2
);
1495 __isl_give isl_qpolynomial
*isl_qpolynomial_pow(__isl_take isl_qpolynomial
*qp
,
1498 qp
= isl_qpolynomial_cow(qp
);
1503 qp
->upoly
= isl_upoly_pow(qp
->upoly
, power
);
1509 isl_qpolynomial_free(qp
);
1513 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_pow(
1514 __isl_take isl_pw_qpolynomial
*pwqp
, unsigned power
)
1521 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
1525 for (i
= 0; i
< pwqp
->n
; ++i
) {
1526 pwqp
->p
[i
].qp
= isl_qpolynomial_pow(pwqp
->p
[i
].qp
, power
);
1528 return isl_pw_qpolynomial_free(pwqp
);
1534 __isl_give isl_qpolynomial
*isl_qpolynomial_zero_on_domain(
1535 __isl_take isl_space
*dim
)
1539 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
1542 __isl_give isl_qpolynomial
*isl_qpolynomial_one_on_domain(
1543 __isl_take isl_space
*dim
)
1547 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_one(dim
->ctx
));
1550 __isl_give isl_qpolynomial
*isl_qpolynomial_infty_on_domain(
1551 __isl_take isl_space
*dim
)
1555 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_infty(dim
->ctx
));
1558 __isl_give isl_qpolynomial
*isl_qpolynomial_neginfty_on_domain(
1559 __isl_take isl_space
*dim
)
1563 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_neginfty(dim
->ctx
));
1566 __isl_give isl_qpolynomial
*isl_qpolynomial_nan_on_domain(
1567 __isl_take isl_space
*dim
)
1571 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_nan(dim
->ctx
));
1574 __isl_give isl_qpolynomial
*isl_qpolynomial_cst_on_domain(
1575 __isl_take isl_space
*dim
,
1578 struct isl_qpolynomial
*qp
;
1579 struct isl_upoly_cst
*cst
;
1584 qp
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
1588 cst
= isl_upoly_as_cst(qp
->upoly
);
1589 isl_int_set(cst
->n
, v
);
1594 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial
*qp
,
1595 isl_int
*n
, isl_int
*d
)
1597 struct isl_upoly_cst
*cst
;
1602 if (!isl_upoly_is_cst(qp
->upoly
))
1605 cst
= isl_upoly_as_cst(qp
->upoly
);
1610 isl_int_set(*n
, cst
->n
);
1612 isl_int_set(*d
, cst
->d
);
1617 int isl_upoly_is_affine(__isl_keep
struct isl_upoly
*up
)
1620 struct isl_upoly_rec
*rec
;
1628 rec
= isl_upoly_as_rec(up
);
1635 isl_assert(up
->ctx
, rec
->n
> 1, return -1);
1637 is_cst
= isl_upoly_is_cst(rec
->p
[1]);
1643 return isl_upoly_is_affine(rec
->p
[0]);
1646 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial
*qp
)
1651 if (qp
->div
->n_row
> 0)
1654 return isl_upoly_is_affine(qp
->upoly
);
1657 static void update_coeff(__isl_keep isl_vec
*aff
,
1658 __isl_keep
struct isl_upoly_cst
*cst
, int pos
)
1663 if (isl_int_is_zero(cst
->n
))
1668 isl_int_gcd(gcd
, cst
->d
, aff
->el
[0]);
1669 isl_int_divexact(f
, cst
->d
, gcd
);
1670 isl_int_divexact(gcd
, aff
->el
[0], gcd
);
1671 isl_seq_scale(aff
->el
, aff
->el
, f
, aff
->size
);
1672 isl_int_mul(aff
->el
[1 + pos
], gcd
, cst
->n
);
1677 int isl_upoly_update_affine(__isl_keep
struct isl_upoly
*up
,
1678 __isl_keep isl_vec
*aff
)
1680 struct isl_upoly_cst
*cst
;
1681 struct isl_upoly_rec
*rec
;
1687 struct isl_upoly_cst
*cst
;
1689 cst
= isl_upoly_as_cst(up
);
1692 update_coeff(aff
, cst
, 0);
1696 rec
= isl_upoly_as_rec(up
);
1699 isl_assert(up
->ctx
, rec
->n
== 2, return -1);
1701 cst
= isl_upoly_as_cst(rec
->p
[1]);
1704 update_coeff(aff
, cst
, 1 + up
->var
);
1706 return isl_upoly_update_affine(rec
->p
[0], aff
);
1709 __isl_give isl_vec
*isl_qpolynomial_extract_affine(
1710 __isl_keep isl_qpolynomial
*qp
)
1718 d
= isl_space_dim(qp
->dim
, isl_dim_all
);
1719 aff
= isl_vec_alloc(qp
->div
->ctx
, 2 + d
+ qp
->div
->n_row
);
1723 isl_seq_clr(aff
->el
+ 1, 1 + d
+ qp
->div
->n_row
);
1724 isl_int_set_si(aff
->el
[0], 1);
1726 if (isl_upoly_update_affine(qp
->upoly
, aff
) < 0)
1735 int isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial
*qp1
,
1736 __isl_keep isl_qpolynomial
*qp2
)
1743 equal
= isl_space_is_equal(qp1
->dim
, qp2
->dim
);
1744 if (equal
< 0 || !equal
)
1747 equal
= isl_mat_is_equal(qp1
->div
, qp2
->div
);
1748 if (equal
< 0 || !equal
)
1751 return isl_upoly_is_equal(qp1
->upoly
, qp2
->upoly
);
1754 static void upoly_update_den(__isl_keep
struct isl_upoly
*up
, isl_int
*d
)
1757 struct isl_upoly_rec
*rec
;
1759 if (isl_upoly_is_cst(up
)) {
1760 struct isl_upoly_cst
*cst
;
1761 cst
= isl_upoly_as_cst(up
);
1764 isl_int_lcm(*d
, *d
, cst
->d
);
1768 rec
= isl_upoly_as_rec(up
);
1772 for (i
= 0; i
< rec
->n
; ++i
)
1773 upoly_update_den(rec
->p
[i
], d
);
1776 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial
*qp
, isl_int
*d
)
1778 isl_int_set_si(*d
, 1);
1781 upoly_update_den(qp
->upoly
, d
);
1784 __isl_give isl_qpolynomial
*isl_qpolynomial_var_pow_on_domain(
1785 __isl_take isl_space
*dim
, int pos
, int power
)
1787 struct isl_ctx
*ctx
;
1794 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_var_pow(ctx
, pos
, power
));
1797 __isl_give isl_qpolynomial
*isl_qpolynomial_var_on_domain(__isl_take isl_space
*dim
,
1798 enum isl_dim_type type
, unsigned pos
)
1803 isl_assert(dim
->ctx
, isl_space_dim(dim
, isl_dim_in
) == 0, goto error
);
1804 isl_assert(dim
->ctx
, pos
< isl_space_dim(dim
, type
), goto error
);
1806 if (type
== isl_dim_set
)
1807 pos
+= isl_space_dim(dim
, isl_dim_param
);
1809 return isl_qpolynomial_var_pow_on_domain(dim
, pos
, 1);
1811 isl_space_free(dim
);
1815 __isl_give
struct isl_upoly
*isl_upoly_subs(__isl_take
struct isl_upoly
*up
,
1816 unsigned first
, unsigned n
, __isl_keep
struct isl_upoly
**subs
)
1819 struct isl_upoly_rec
*rec
;
1820 struct isl_upoly
*base
, *res
;
1825 if (isl_upoly_is_cst(up
))
1828 if (up
->var
< first
)
1831 rec
= isl_upoly_as_rec(up
);
1835 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
1837 if (up
->var
>= first
+ n
)
1838 base
= isl_upoly_var_pow(up
->ctx
, up
->var
, 1);
1840 base
= isl_upoly_copy(subs
[up
->var
- first
]);
1842 res
= isl_upoly_subs(isl_upoly_copy(rec
->p
[rec
->n
- 1]), first
, n
, subs
);
1843 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1844 struct isl_upoly
*t
;
1845 t
= isl_upoly_subs(isl_upoly_copy(rec
->p
[i
]), first
, n
, subs
);
1846 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
1847 res
= isl_upoly_sum(res
, t
);
1850 isl_upoly_free(base
);
1859 __isl_give
struct isl_upoly
*isl_upoly_from_affine(isl_ctx
*ctx
, isl_int
*f
,
1860 isl_int denom
, unsigned len
)
1863 struct isl_upoly
*up
;
1865 isl_assert(ctx
, len
>= 1, return NULL
);
1867 up
= isl_upoly_rat_cst(ctx
, f
[0], denom
);
1868 for (i
= 0; i
< len
- 1; ++i
) {
1869 struct isl_upoly
*t
;
1870 struct isl_upoly
*c
;
1872 if (isl_int_is_zero(f
[1 + i
]))
1875 c
= isl_upoly_rat_cst(ctx
, f
[1 + i
], denom
);
1876 t
= isl_upoly_var_pow(ctx
, i
, 1);
1877 t
= isl_upoly_mul(c
, t
);
1878 up
= isl_upoly_sum(up
, t
);
1884 /* Remove common factor of non-constant terms and denominator.
1886 static void normalize_div(__isl_keep isl_qpolynomial
*qp
, int div
)
1888 isl_ctx
*ctx
= qp
->div
->ctx
;
1889 unsigned total
= qp
->div
->n_col
- 2;
1891 isl_seq_gcd(qp
->div
->row
[div
] + 2, total
, &ctx
->normalize_gcd
);
1892 isl_int_gcd(ctx
->normalize_gcd
,
1893 ctx
->normalize_gcd
, qp
->div
->row
[div
][0]);
1894 if (isl_int_is_one(ctx
->normalize_gcd
))
1897 isl_seq_scale_down(qp
->div
->row
[div
] + 2, qp
->div
->row
[div
] + 2,
1898 ctx
->normalize_gcd
, total
);
1899 isl_int_divexact(qp
->div
->row
[div
][0], qp
->div
->row
[div
][0],
1900 ctx
->normalize_gcd
);
1901 isl_int_fdiv_q(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1],
1902 ctx
->normalize_gcd
);
1905 /* Replace the integer division identified by "div" by the polynomial "s".
1906 * The integer division is assumed not to appear in the definition
1907 * of any other integer divisions.
1909 static __isl_give isl_qpolynomial
*substitute_div(
1910 __isl_take isl_qpolynomial
*qp
,
1911 int div
, __isl_take
struct isl_upoly
*s
)
1920 qp
= isl_qpolynomial_cow(qp
);
1924 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
1925 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ div
, 1, &s
);
1929 reordering
= isl_alloc_array(qp
->dim
->ctx
, int, total
+ qp
->div
->n_row
);
1932 for (i
= 0; i
< total
+ div
; ++i
)
1934 for (i
= total
+ div
+ 1; i
< total
+ qp
->div
->n_row
; ++i
)
1935 reordering
[i
] = i
- 1;
1936 qp
->div
= isl_mat_drop_rows(qp
->div
, div
, 1);
1937 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + total
+ div
, 1);
1938 qp
->upoly
= reorder(qp
->upoly
, reordering
);
1941 if (!qp
->upoly
|| !qp
->div
)
1947 isl_qpolynomial_free(qp
);
1952 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1953 * divisions because d is equal to 1 by their definition, i.e., e.
1955 static __isl_give isl_qpolynomial
*substitute_non_divs(
1956 __isl_take isl_qpolynomial
*qp
)
1960 struct isl_upoly
*s
;
1965 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
1966 for (i
= 0; qp
&& i
< qp
->div
->n_row
; ++i
) {
1967 if (!isl_int_is_one(qp
->div
->row
[i
][0]))
1969 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
1970 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
1972 isl_seq_combine(qp
->div
->row
[j
] + 1,
1973 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
1974 qp
->div
->row
[j
][2 + total
+ i
],
1975 qp
->div
->row
[i
] + 1, 1 + total
+ i
);
1976 isl_int_set_si(qp
->div
->row
[j
][2 + total
+ i
], 0);
1977 normalize_div(qp
, j
);
1979 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
1980 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
1981 qp
= substitute_div(qp
, i
, s
);
1988 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1989 * with d the denominator. When replacing the coefficient e of x by
1990 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1991 * inside the division, so we need to add floor(e/d) * x outside.
1992 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1993 * to adjust the coefficient of x in each later div that depends on the
1994 * current div "div" and also in the affine expression "aff"
1995 * (if it too depends on "div").
1997 static void reduce_div(__isl_keep isl_qpolynomial
*qp
, int div
,
1998 __isl_keep isl_vec
*aff
)
2002 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
2005 for (i
= 0; i
< 1 + total
+ div
; ++i
) {
2006 if (isl_int_is_nonneg(qp
->div
->row
[div
][1 + i
]) &&
2007 isl_int_lt(qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]))
2009 isl_int_fdiv_q(v
, qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
2010 isl_int_fdiv_r(qp
->div
->row
[div
][1 + i
],
2011 qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
2012 if (!isl_int_is_zero(aff
->el
[1 + total
+ div
]))
2013 isl_int_addmul(aff
->el
[i
], v
, aff
->el
[1 + total
+ div
]);
2014 for (j
= div
+ 1; j
< qp
->div
->n_row
; ++j
) {
2015 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ div
]))
2017 isl_int_addmul(qp
->div
->row
[j
][1 + i
],
2018 v
, qp
->div
->row
[j
][2 + total
+ div
]);
2024 /* Check if the last non-zero coefficient is bigger that half of the
2025 * denominator. If so, we will invert the div to further reduce the number
2026 * of distinct divs that may appear.
2027 * If the last non-zero coefficient is exactly half the denominator,
2028 * then we continue looking for earlier coefficients that are bigger
2029 * than half the denominator.
2031 static int needs_invert(__isl_keep isl_mat
*div
, int row
)
2036 for (i
= div
->n_col
- 1; i
>= 1; --i
) {
2037 if (isl_int_is_zero(div
->row
[row
][i
]))
2039 isl_int_mul_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
2040 cmp
= isl_int_cmp(div
->row
[row
][i
], div
->row
[row
][0]);
2041 isl_int_divexact_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
2051 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
2052 * We only invert the coefficients of e (and the coefficient of q in
2053 * later divs and in "aff"). After calling this function, the
2054 * coefficients of e should be reduced again.
2056 static void invert_div(__isl_keep isl_qpolynomial
*qp
, int div
,
2057 __isl_keep isl_vec
*aff
)
2059 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
2061 isl_seq_neg(qp
->div
->row
[div
] + 1,
2062 qp
->div
->row
[div
] + 1, qp
->div
->n_col
- 1);
2063 isl_int_sub_ui(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1], 1);
2064 isl_int_add(qp
->div
->row
[div
][1],
2065 qp
->div
->row
[div
][1], qp
->div
->row
[div
][0]);
2066 if (!isl_int_is_zero(aff
->el
[1 + total
+ div
]))
2067 isl_int_neg(aff
->el
[1 + total
+ div
], aff
->el
[1 + total
+ div
]);
2068 isl_mat_col_mul(qp
->div
, 2 + total
+ div
,
2069 qp
->div
->ctx
->negone
, 2 + total
+ div
);
2072 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2073 * in the interval [0, d-1], with d the denominator and such that the
2074 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2076 * After the reduction, some divs may have become redundant or identical,
2077 * so we call substitute_non_divs and sort_divs. If these functions
2078 * eliminate divs or merge two or more divs into one, the coefficients
2079 * of the enclosing divs may have to be reduced again, so we call
2080 * ourselves recursively if the number of divs decreases.
2082 static __isl_give isl_qpolynomial
*reduce_divs(__isl_take isl_qpolynomial
*qp
)
2085 isl_vec
*aff
= NULL
;
2086 struct isl_upoly
*s
;
2092 aff
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
2093 aff
= isl_vec_clr(aff
);
2097 isl_int_set_si(aff
->el
[1 + qp
->upoly
->var
], 1);
2099 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2100 normalize_div(qp
, i
);
2101 reduce_div(qp
, i
, aff
);
2102 if (needs_invert(qp
->div
, i
)) {
2103 invert_div(qp
, i
, aff
);
2104 reduce_div(qp
, i
, aff
);
2108 s
= isl_upoly_from_affine(qp
->div
->ctx
, aff
->el
,
2109 qp
->div
->ctx
->one
, aff
->size
);
2110 qp
->upoly
= isl_upoly_subs(qp
->upoly
, qp
->upoly
->var
, 1, &s
);
2117 n_div
= qp
->div
->n_row
;
2118 qp
= substitute_non_divs(qp
);
2120 if (qp
&& qp
->div
->n_row
< n_div
)
2121 return reduce_divs(qp
);
2125 isl_qpolynomial_free(qp
);
2130 /* Assumes each div only depends on earlier divs.
2132 __isl_give isl_qpolynomial
*isl_qpolynomial_div_pow(__isl_take isl_div
*div
,
2135 struct isl_qpolynomial
*qp
= NULL
;
2136 struct isl_upoly_rec
*rec
;
2137 struct isl_upoly_cst
*cst
;
2144 d
= div
->line
- div
->bmap
->div
;
2146 pos
= isl_space_dim(div
->bmap
->dim
, isl_dim_all
) + d
;
2147 rec
= isl_upoly_alloc_rec(div
->ctx
, pos
, 1 + power
);
2148 qp
= isl_qpolynomial_alloc(isl_basic_map_get_space(div
->bmap
),
2149 div
->bmap
->n_div
, &rec
->up
);
2153 for (i
= 0; i
< div
->bmap
->n_div
; ++i
)
2154 isl_seq_cpy(qp
->div
->row
[i
], div
->bmap
->div
[i
], qp
->div
->n_col
);
2156 for (i
= 0; i
< 1 + power
; ++i
) {
2157 rec
->p
[i
] = isl_upoly_zero(div
->ctx
);
2162 cst
= isl_upoly_as_cst(rec
->p
[power
]);
2163 isl_int_set_si(cst
->n
, 1);
2167 qp
= reduce_divs(qp
);
2171 isl_qpolynomial_free(qp
);
2176 __isl_give isl_qpolynomial
*isl_qpolynomial_div(__isl_take isl_div
*div
)
2178 return isl_qpolynomial_div_pow(div
, 1);
2181 __isl_give isl_qpolynomial
*isl_qpolynomial_rat_cst_on_domain(
2182 __isl_take isl_space
*dim
, const isl_int n
, const isl_int d
)
2184 struct isl_qpolynomial
*qp
;
2185 struct isl_upoly_cst
*cst
;
2190 qp
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
2194 cst
= isl_upoly_as_cst(qp
->upoly
);
2195 isl_int_set(cst
->n
, n
);
2196 isl_int_set(cst
->d
, d
);
2201 static int up_set_active(__isl_keep
struct isl_upoly
*up
, int *active
, int d
)
2203 struct isl_upoly_rec
*rec
;
2209 if (isl_upoly_is_cst(up
))
2213 active
[up
->var
] = 1;
2215 rec
= isl_upoly_as_rec(up
);
2216 for (i
= 0; i
< rec
->n
; ++i
)
2217 if (up_set_active(rec
->p
[i
], active
, d
) < 0)
2223 static int set_active(__isl_keep isl_qpolynomial
*qp
, int *active
)
2226 int d
= isl_space_dim(qp
->dim
, isl_dim_all
);
2231 for (i
= 0; i
< d
; ++i
)
2232 for (j
= 0; j
< qp
->div
->n_row
; ++j
) {
2233 if (isl_int_is_zero(qp
->div
->row
[j
][2 + i
]))
2239 return up_set_active(qp
->upoly
, active
, d
);
2242 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial
*qp
,
2243 enum isl_dim_type type
, unsigned first
, unsigned n
)
2254 isl_assert(qp
->dim
->ctx
,
2255 first
+ n
<= isl_qpolynomial_dim(qp
, type
), return -1);
2256 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2257 type
== isl_dim_in
, return -1);
2259 active
= isl_calloc_array(qp
->dim
->ctx
, int,
2260 isl_space_dim(qp
->dim
, isl_dim_all
));
2261 if (set_active(qp
, active
) < 0)
2264 if (type
== isl_dim_in
)
2265 first
+= isl_space_dim(qp
->dim
, isl_dim_param
);
2266 for (i
= 0; i
< n
; ++i
)
2267 if (active
[first
+ i
]) {
2280 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2281 * of the divs that do appear in the quasi-polynomial.
2283 static __isl_give isl_qpolynomial
*remove_redundant_divs(
2284 __isl_take isl_qpolynomial
*qp
)
2291 int *reordering
= NULL
;
2298 if (qp
->div
->n_row
== 0)
2301 d
= isl_space_dim(qp
->dim
, isl_dim_all
);
2302 len
= qp
->div
->n_col
- 2;
2303 ctx
= isl_qpolynomial_get_ctx(qp
);
2304 active
= isl_calloc_array(ctx
, int, len
);
2308 if (up_set_active(qp
->upoly
, active
, len
) < 0)
2311 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
2312 if (!active
[d
+ i
]) {
2316 for (j
= 0; j
< i
; ++j
) {
2317 if (isl_int_is_zero(qp
->div
->row
[i
][2 + d
+ j
]))
2329 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
2333 for (i
= 0; i
< d
; ++i
)
2337 n_div
= qp
->div
->n_row
;
2338 for (i
= 0; i
< n_div
; ++i
) {
2339 if (!active
[d
+ i
]) {
2340 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
2341 qp
->div
= isl_mat_drop_cols(qp
->div
,
2342 2 + d
+ i
- skip
, 1);
2345 reordering
[d
+ i
] = d
+ i
- skip
;
2348 qp
->upoly
= reorder(qp
->upoly
, reordering
);
2350 if (!qp
->upoly
|| !qp
->div
)
2360 isl_qpolynomial_free(qp
);
2364 __isl_give
struct isl_upoly
*isl_upoly_drop(__isl_take
struct isl_upoly
*up
,
2365 unsigned first
, unsigned n
)
2368 struct isl_upoly_rec
*rec
;
2372 if (n
== 0 || up
->var
< 0 || up
->var
< first
)
2374 if (up
->var
< first
+ n
) {
2375 up
= replace_by_constant_term(up
);
2376 return isl_upoly_drop(up
, first
, n
);
2378 up
= isl_upoly_cow(up
);
2382 rec
= isl_upoly_as_rec(up
);
2386 for (i
= 0; i
< rec
->n
; ++i
) {
2387 rec
->p
[i
] = isl_upoly_drop(rec
->p
[i
], first
, n
);
2398 __isl_give isl_qpolynomial
*isl_qpolynomial_set_dim_name(
2399 __isl_take isl_qpolynomial
*qp
,
2400 enum isl_dim_type type
, unsigned pos
, const char *s
)
2402 qp
= isl_qpolynomial_cow(qp
);
2405 qp
->dim
= isl_space_set_dim_name(qp
->dim
, type
, pos
, s
);
2410 isl_qpolynomial_free(qp
);
2414 __isl_give isl_qpolynomial
*isl_qpolynomial_drop_dims(
2415 __isl_take isl_qpolynomial
*qp
,
2416 enum isl_dim_type type
, unsigned first
, unsigned n
)
2420 if (type
== isl_dim_out
)
2421 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
2422 "cannot drop output/set dimension",
2424 if (type
== isl_dim_in
)
2426 if (n
== 0 && !isl_space_is_named_or_nested(qp
->dim
, type
))
2429 qp
= isl_qpolynomial_cow(qp
);
2433 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_space_dim(qp
->dim
, type
),
2435 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2436 type
== isl_dim_set
, goto error
);
2438 qp
->dim
= isl_space_drop_dims(qp
->dim
, type
, first
, n
);
2442 if (type
== isl_dim_set
)
2443 first
+= isl_space_dim(qp
->dim
, isl_dim_param
);
2445 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + first
, n
);
2449 qp
->upoly
= isl_upoly_drop(qp
->upoly
, first
, n
);
2455 isl_qpolynomial_free(qp
);
2459 /* Project the domain of the quasi-polynomial onto its parameter space.
2460 * The quasi-polynomial may not involve any of the domain dimensions.
2462 __isl_give isl_qpolynomial
*isl_qpolynomial_project_domain_on_params(
2463 __isl_take isl_qpolynomial
*qp
)
2469 n
= isl_qpolynomial_dim(qp
, isl_dim_in
);
2470 involves
= isl_qpolynomial_involves_dims(qp
, isl_dim_in
, 0, n
);
2472 return isl_qpolynomial_free(qp
);
2474 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
2475 "polynomial involves some of the domain dimensions",
2476 return isl_qpolynomial_free(qp
));
2477 qp
= isl_qpolynomial_drop_dims(qp
, isl_dim_in
, 0, n
);
2478 space
= isl_qpolynomial_get_domain_space(qp
);
2479 space
= isl_space_params(space
);
2480 qp
= isl_qpolynomial_reset_domain_space(qp
, space
);
2484 static __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities_lifted(
2485 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2491 struct isl_upoly
*up
;
2495 if (eq
->n_eq
== 0) {
2496 isl_basic_set_free(eq
);
2500 qp
= isl_qpolynomial_cow(qp
);
2503 qp
->div
= isl_mat_cow(qp
->div
);
2507 total
= 1 + isl_space_dim(eq
->dim
, isl_dim_all
);
2509 isl_int_init(denom
);
2510 for (i
= 0; i
< eq
->n_eq
; ++i
) {
2511 j
= isl_seq_last_non_zero(eq
->eq
[i
], total
+ n_div
);
2512 if (j
< 0 || j
== 0 || j
>= total
)
2515 for (k
= 0; k
< qp
->div
->n_row
; ++k
) {
2516 if (isl_int_is_zero(qp
->div
->row
[k
][1 + j
]))
2518 isl_seq_elim(qp
->div
->row
[k
] + 1, eq
->eq
[i
], j
, total
,
2519 &qp
->div
->row
[k
][0]);
2520 normalize_div(qp
, k
);
2523 if (isl_int_is_pos(eq
->eq
[i
][j
]))
2524 isl_seq_neg(eq
->eq
[i
], eq
->eq
[i
], total
);
2525 isl_int_abs(denom
, eq
->eq
[i
][j
]);
2526 isl_int_set_si(eq
->eq
[i
][j
], 0);
2528 up
= isl_upoly_from_affine(qp
->dim
->ctx
,
2529 eq
->eq
[i
], denom
, total
);
2530 qp
->upoly
= isl_upoly_subs(qp
->upoly
, j
- 1, 1, &up
);
2533 isl_int_clear(denom
);
2538 isl_basic_set_free(eq
);
2540 qp
= substitute_non_divs(qp
);
2545 isl_basic_set_free(eq
);
2546 isl_qpolynomial_free(qp
);
2550 /* Exploit the equalities in "eq" to simplify the quasi-polynomial.
2552 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities(
2553 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2557 if (qp
->div
->n_row
> 0)
2558 eq
= isl_basic_set_add(eq
, isl_dim_set
, qp
->div
->n_row
);
2559 return isl_qpolynomial_substitute_equalities_lifted(qp
, eq
);
2561 isl_basic_set_free(eq
);
2562 isl_qpolynomial_free(qp
);
2566 static __isl_give isl_basic_set
*add_div_constraints(
2567 __isl_take isl_basic_set
*bset
, __isl_take isl_mat
*div
)
2575 bset
= isl_basic_set_extend_constraints(bset
, 0, 2 * div
->n_row
);
2578 total
= isl_basic_set_total_dim(bset
);
2579 for (i
= 0; i
< div
->n_row
; ++i
)
2580 if (isl_basic_set_add_div_constraints_var(bset
,
2581 total
- div
->n_row
+ i
, div
->row
[i
]) < 0)
2588 isl_basic_set_free(bset
);
2592 /* Look for equalities among the variables shared by context and qp
2593 * and the integer divisions of qp, if any.
2594 * The equalities are then used to eliminate variables and/or integer
2595 * divisions from qp.
2597 __isl_give isl_qpolynomial
*isl_qpolynomial_gist(
2598 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
2604 if (qp
->div
->n_row
> 0) {
2605 isl_basic_set
*bset
;
2606 context
= isl_set_add_dims(context
, isl_dim_set
,
2608 bset
= isl_basic_set_universe(isl_set_get_space(context
));
2609 bset
= add_div_constraints(bset
, isl_mat_copy(qp
->div
));
2610 context
= isl_set_intersect(context
,
2611 isl_set_from_basic_set(bset
));
2614 aff
= isl_set_affine_hull(context
);
2615 return isl_qpolynomial_substitute_equalities_lifted(qp
, aff
);
2617 isl_qpolynomial_free(qp
);
2618 isl_set_free(context
);
2622 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_from_qpolynomial(
2623 __isl_take isl_qpolynomial
*qp
)
2629 if (isl_qpolynomial_is_zero(qp
)) {
2630 isl_space
*dim
= isl_qpolynomial_get_space(qp
);
2631 isl_qpolynomial_free(qp
);
2632 return isl_pw_qpolynomial_zero(dim
);
2635 dom
= isl_set_universe(isl_qpolynomial_get_domain_space(qp
));
2636 return isl_pw_qpolynomial_alloc(dom
, qp
);
2640 #define PW isl_pw_qpolynomial
2642 #define EL isl_qpolynomial
2644 #define EL_IS_ZERO is_zero
2648 #define IS_ZERO is_zero
2652 #include <isl_pw_templ.c>
2655 #define UNION isl_union_pw_qpolynomial
2657 #define PART isl_pw_qpolynomial
2659 #define PARTS pw_qpolynomial
2660 #define ALIGN_DOMAIN
2662 #include <isl_union_templ.c>
2664 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial
*pwqp
)
2672 if (!isl_set_plain_is_universe(pwqp
->p
[0].set
))
2675 return isl_qpolynomial_is_one(pwqp
->p
[0].qp
);
2678 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_mul(
2679 __isl_take isl_pw_qpolynomial
*pwqp1
,
2680 __isl_take isl_pw_qpolynomial
*pwqp2
)
2683 struct isl_pw_qpolynomial
*res
;
2685 if (!pwqp1
|| !pwqp2
)
2688 isl_assert(pwqp1
->dim
->ctx
, isl_space_is_equal(pwqp1
->dim
, pwqp2
->dim
),
2691 if (isl_pw_qpolynomial_is_zero(pwqp1
)) {
2692 isl_pw_qpolynomial_free(pwqp2
);
2696 if (isl_pw_qpolynomial_is_zero(pwqp2
)) {
2697 isl_pw_qpolynomial_free(pwqp1
);
2701 if (isl_pw_qpolynomial_is_one(pwqp1
)) {
2702 isl_pw_qpolynomial_free(pwqp1
);
2706 if (isl_pw_qpolynomial_is_one(pwqp2
)) {
2707 isl_pw_qpolynomial_free(pwqp2
);
2711 n
= pwqp1
->n
* pwqp2
->n
;
2712 res
= isl_pw_qpolynomial_alloc_size(isl_space_copy(pwqp1
->dim
), n
);
2714 for (i
= 0; i
< pwqp1
->n
; ++i
) {
2715 for (j
= 0; j
< pwqp2
->n
; ++j
) {
2716 struct isl_set
*common
;
2717 struct isl_qpolynomial
*prod
;
2718 common
= isl_set_intersect(isl_set_copy(pwqp1
->p
[i
].set
),
2719 isl_set_copy(pwqp2
->p
[j
].set
));
2720 if (isl_set_plain_is_empty(common
)) {
2721 isl_set_free(common
);
2725 prod
= isl_qpolynomial_mul(
2726 isl_qpolynomial_copy(pwqp1
->p
[i
].qp
),
2727 isl_qpolynomial_copy(pwqp2
->p
[j
].qp
));
2729 res
= isl_pw_qpolynomial_add_piece(res
, common
, prod
);
2733 isl_pw_qpolynomial_free(pwqp1
);
2734 isl_pw_qpolynomial_free(pwqp2
);
2738 isl_pw_qpolynomial_free(pwqp1
);
2739 isl_pw_qpolynomial_free(pwqp2
);
2743 __isl_give
struct isl_upoly
*isl_upoly_eval(
2744 __isl_take
struct isl_upoly
*up
, __isl_take isl_vec
*vec
)
2747 struct isl_upoly_rec
*rec
;
2748 struct isl_upoly
*res
;
2749 struct isl_upoly
*base
;
2751 if (isl_upoly_is_cst(up
)) {
2756 rec
= isl_upoly_as_rec(up
);
2760 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
2762 base
= isl_upoly_rat_cst(up
->ctx
, vec
->el
[1 + up
->var
], vec
->el
[0]);
2764 res
= isl_upoly_eval(isl_upoly_copy(rec
->p
[rec
->n
- 1]),
2767 for (i
= rec
->n
- 2; i
>= 0; --i
) {
2768 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
2769 res
= isl_upoly_sum(res
,
2770 isl_upoly_eval(isl_upoly_copy(rec
->p
[i
]),
2771 isl_vec_copy(vec
)));
2774 isl_upoly_free(base
);
2784 __isl_give isl_qpolynomial
*isl_qpolynomial_eval(
2785 __isl_take isl_qpolynomial
*qp
, __isl_take isl_point
*pnt
)
2788 struct isl_upoly
*up
;
2793 isl_assert(pnt
->dim
->ctx
, isl_space_is_equal(pnt
->dim
, qp
->dim
), goto error
);
2795 if (qp
->div
->n_row
== 0)
2796 ext
= isl_vec_copy(pnt
->vec
);
2799 unsigned dim
= isl_space_dim(qp
->dim
, isl_dim_all
);
2800 ext
= isl_vec_alloc(qp
->dim
->ctx
, 1 + dim
+ qp
->div
->n_row
);
2804 isl_seq_cpy(ext
->el
, pnt
->vec
->el
, pnt
->vec
->size
);
2805 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2806 isl_seq_inner_product(qp
->div
->row
[i
] + 1, ext
->el
,
2807 1 + dim
+ i
, &ext
->el
[1+dim
+i
]);
2808 isl_int_fdiv_q(ext
->el
[1+dim
+i
], ext
->el
[1+dim
+i
],
2809 qp
->div
->row
[i
][0]);
2813 up
= isl_upoly_eval(isl_upoly_copy(qp
->upoly
), ext
);
2817 dim
= isl_space_copy(qp
->dim
);
2818 isl_qpolynomial_free(qp
);
2819 isl_point_free(pnt
);
2821 return isl_qpolynomial_alloc(dim
, 0, up
);
2823 isl_qpolynomial_free(qp
);
2824 isl_point_free(pnt
);
2828 int isl_upoly_cmp(__isl_keep
struct isl_upoly_cst
*cst1
,
2829 __isl_keep
struct isl_upoly_cst
*cst2
)
2834 isl_int_mul(t
, cst1
->n
, cst2
->d
);
2835 isl_int_submul(t
, cst2
->n
, cst1
->d
);
2836 cmp
= isl_int_sgn(t
);
2841 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial
*qp1
,
2842 __isl_keep isl_qpolynomial
*qp2
)
2844 struct isl_upoly_cst
*cst1
, *cst2
;
2848 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), return -1);
2849 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), return -1);
2850 if (isl_qpolynomial_is_nan(qp1
))
2852 if (isl_qpolynomial_is_nan(qp2
))
2854 cst1
= isl_upoly_as_cst(qp1
->upoly
);
2855 cst2
= isl_upoly_as_cst(qp2
->upoly
);
2857 return isl_upoly_cmp(cst1
, cst2
) <= 0;
2860 __isl_give isl_qpolynomial
*isl_qpolynomial_min_cst(
2861 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
2863 struct isl_upoly_cst
*cst1
, *cst2
;
2868 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), goto error
);
2869 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), goto error
);
2870 cst1
= isl_upoly_as_cst(qp1
->upoly
);
2871 cst2
= isl_upoly_as_cst(qp2
->upoly
);
2872 cmp
= isl_upoly_cmp(cst1
, cst2
);
2875 isl_qpolynomial_free(qp2
);
2877 isl_qpolynomial_free(qp1
);
2882 isl_qpolynomial_free(qp1
);
2883 isl_qpolynomial_free(qp2
);
2887 __isl_give isl_qpolynomial
*isl_qpolynomial_max_cst(
2888 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
2890 struct isl_upoly_cst
*cst1
, *cst2
;
2895 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), goto error
);
2896 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), goto error
);
2897 cst1
= isl_upoly_as_cst(qp1
->upoly
);
2898 cst2
= isl_upoly_as_cst(qp2
->upoly
);
2899 cmp
= isl_upoly_cmp(cst1
, cst2
);
2902 isl_qpolynomial_free(qp2
);
2904 isl_qpolynomial_free(qp1
);
2909 isl_qpolynomial_free(qp1
);
2910 isl_qpolynomial_free(qp2
);
2914 __isl_give isl_qpolynomial
*isl_qpolynomial_insert_dims(
2915 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
,
2916 unsigned first
, unsigned n
)
2924 if (type
== isl_dim_out
)
2925 isl_die(qp
->div
->ctx
, isl_error_invalid
,
2926 "cannot insert output/set dimensions",
2928 if (type
== isl_dim_in
)
2930 if (n
== 0 && !isl_space_is_named_or_nested(qp
->dim
, type
))
2933 qp
= isl_qpolynomial_cow(qp
);
2937 isl_assert(qp
->div
->ctx
, first
<= isl_space_dim(qp
->dim
, type
),
2940 g_pos
= pos(qp
->dim
, type
) + first
;
2942 qp
->div
= isl_mat_insert_zero_cols(qp
->div
, 2 + g_pos
, n
);
2946 total
= qp
->div
->n_col
- 2;
2947 if (total
> g_pos
) {
2949 exp
= isl_alloc_array(qp
->div
->ctx
, int, total
- g_pos
);
2952 for (i
= 0; i
< total
- g_pos
; ++i
)
2954 qp
->upoly
= expand(qp
->upoly
, exp
, g_pos
);
2960 qp
->dim
= isl_space_insert_dims(qp
->dim
, type
, first
, n
);
2966 isl_qpolynomial_free(qp
);
2970 __isl_give isl_qpolynomial
*isl_qpolynomial_add_dims(
2971 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
, unsigned n
)
2975 pos
= isl_qpolynomial_dim(qp
, type
);
2977 return isl_qpolynomial_insert_dims(qp
, type
, pos
, n
);
2980 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add_dims(
2981 __isl_take isl_pw_qpolynomial
*pwqp
,
2982 enum isl_dim_type type
, unsigned n
)
2986 pos
= isl_pw_qpolynomial_dim(pwqp
, type
);
2988 return isl_pw_qpolynomial_insert_dims(pwqp
, type
, pos
, n
);
2991 static int *reordering_move(isl_ctx
*ctx
,
2992 unsigned len
, unsigned dst
, unsigned src
, unsigned n
)
2997 reordering
= isl_alloc_array(ctx
, int, len
);
3002 for (i
= 0; i
< dst
; ++i
)
3004 for (i
= 0; i
< n
; ++i
)
3005 reordering
[src
+ i
] = dst
+ i
;
3006 for (i
= 0; i
< src
- dst
; ++i
)
3007 reordering
[dst
+ i
] = dst
+ n
+ i
;
3008 for (i
= 0; i
< len
- src
- n
; ++i
)
3009 reordering
[src
+ n
+ i
] = src
+ n
+ i
;
3011 for (i
= 0; i
< src
; ++i
)
3013 for (i
= 0; i
< n
; ++i
)
3014 reordering
[src
+ i
] = dst
+ i
;
3015 for (i
= 0; i
< dst
- src
; ++i
)
3016 reordering
[src
+ n
+ i
] = src
+ i
;
3017 for (i
= 0; i
< len
- dst
- n
; ++i
)
3018 reordering
[dst
+ n
+ i
] = dst
+ n
+ i
;
3024 __isl_give isl_qpolynomial
*isl_qpolynomial_move_dims(
3025 __isl_take isl_qpolynomial
*qp
,
3026 enum isl_dim_type dst_type
, unsigned dst_pos
,
3027 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
3033 qp
= isl_qpolynomial_cow(qp
);
3037 if (dst_type
== isl_dim_out
|| src_type
== isl_dim_out
)
3038 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
3039 "cannot move output/set dimension",
3041 if (dst_type
== isl_dim_in
)
3042 dst_type
= isl_dim_set
;
3043 if (src_type
== isl_dim_in
)
3044 src_type
= isl_dim_set
;
3046 isl_assert(qp
->dim
->ctx
, src_pos
+ n
<= isl_space_dim(qp
->dim
, src_type
),
3049 g_dst_pos
= pos(qp
->dim
, dst_type
) + dst_pos
;
3050 g_src_pos
= pos(qp
->dim
, src_type
) + src_pos
;
3051 if (dst_type
> src_type
)
3054 qp
->div
= isl_mat_move_cols(qp
->div
, 2 + g_dst_pos
, 2 + g_src_pos
, n
);
3061 reordering
= reordering_move(qp
->dim
->ctx
,
3062 qp
->div
->n_col
- 2, g_dst_pos
, g_src_pos
, n
);
3066 qp
->upoly
= reorder(qp
->upoly
, reordering
);
3071 qp
->dim
= isl_space_move_dims(qp
->dim
, dst_type
, dst_pos
, src_type
, src_pos
, n
);
3077 isl_qpolynomial_free(qp
);
3081 __isl_give isl_qpolynomial
*isl_qpolynomial_from_affine(__isl_take isl_space
*dim
,
3082 isl_int
*f
, isl_int denom
)
3084 struct isl_upoly
*up
;
3086 dim
= isl_space_domain(dim
);
3090 up
= isl_upoly_from_affine(dim
->ctx
, f
, denom
,
3091 1 + isl_space_dim(dim
, isl_dim_all
));
3093 return isl_qpolynomial_alloc(dim
, 0, up
);
3096 __isl_give isl_qpolynomial
*isl_qpolynomial_from_aff(__isl_take isl_aff
*aff
)
3099 struct isl_upoly
*up
;
3100 isl_qpolynomial
*qp
;
3105 ctx
= isl_aff_get_ctx(aff
);
3106 up
= isl_upoly_from_affine(ctx
, aff
->v
->el
+ 1, aff
->v
->el
[0],
3109 qp
= isl_qpolynomial_alloc(isl_aff_get_domain_space(aff
),
3110 aff
->ls
->div
->n_row
, up
);
3114 isl_mat_free(qp
->div
);
3115 qp
->div
= isl_mat_copy(aff
->ls
->div
);
3116 qp
->div
= isl_mat_cow(qp
->div
);
3121 qp
= reduce_divs(qp
);
3122 qp
= remove_redundant_divs(qp
);
3129 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_from_pw_aff(
3130 __isl_take isl_pw_aff
*pwaff
)
3133 isl_pw_qpolynomial
*pwqp
;
3138 pwqp
= isl_pw_qpolynomial_alloc_size(isl_pw_aff_get_space(pwaff
),
3141 for (i
= 0; i
< pwaff
->n
; ++i
) {
3143 isl_qpolynomial
*qp
;
3145 dom
= isl_set_copy(pwaff
->p
[i
].set
);
3146 qp
= isl_qpolynomial_from_aff(isl_aff_copy(pwaff
->p
[i
].aff
));
3147 pwqp
= isl_pw_qpolynomial_add_piece(pwqp
, dom
, qp
);
3150 isl_pw_aff_free(pwaff
);
3154 __isl_give isl_qpolynomial
*isl_qpolynomial_from_constraint(
3155 __isl_take isl_constraint
*c
, enum isl_dim_type type
, unsigned pos
)
3159 aff
= isl_constraint_get_bound(c
, type
, pos
);
3160 isl_constraint_free(c
);
3161 return isl_qpolynomial_from_aff(aff
);
3164 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3165 * in "qp" by subs[i].
3167 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute(
3168 __isl_take isl_qpolynomial
*qp
,
3169 enum isl_dim_type type
, unsigned first
, unsigned n
,
3170 __isl_keep isl_qpolynomial
**subs
)
3173 struct isl_upoly
**ups
;
3178 qp
= isl_qpolynomial_cow(qp
);
3182 if (type
== isl_dim_out
)
3183 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
3184 "cannot substitute output/set dimension",
3186 if (type
== isl_dim_in
)
3189 for (i
= 0; i
< n
; ++i
)
3193 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_space_dim(qp
->dim
, type
),
3196 for (i
= 0; i
< n
; ++i
)
3197 isl_assert(qp
->dim
->ctx
, isl_space_is_equal(qp
->dim
, subs
[i
]->dim
),
3200 isl_assert(qp
->dim
->ctx
, qp
->div
->n_row
== 0, goto error
);
3201 for (i
= 0; i
< n
; ++i
)
3202 isl_assert(qp
->dim
->ctx
, subs
[i
]->div
->n_row
== 0, goto error
);
3204 first
+= pos(qp
->dim
, type
);
3206 ups
= isl_alloc_array(qp
->dim
->ctx
, struct isl_upoly
*, n
);
3209 for (i
= 0; i
< n
; ++i
)
3210 ups
[i
] = subs
[i
]->upoly
;
3212 qp
->upoly
= isl_upoly_subs(qp
->upoly
, first
, n
, ups
);
3221 isl_qpolynomial_free(qp
);
3225 /* Extend "bset" with extra set dimensions for each integer division
3226 * in "qp" and then call "fn" with the extended bset and the polynomial
3227 * that results from replacing each of the integer divisions by the
3228 * corresponding extra set dimension.
3230 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial
*qp
,
3231 __isl_keep isl_basic_set
*bset
,
3232 int (*fn
)(__isl_take isl_basic_set
*bset
,
3233 __isl_take isl_qpolynomial
*poly
, void *user
), void *user
)
3237 isl_qpolynomial
*poly
;
3241 if (qp
->div
->n_row
== 0)
3242 return fn(isl_basic_set_copy(bset
), isl_qpolynomial_copy(qp
),
3245 div
= isl_mat_copy(qp
->div
);
3246 dim
= isl_space_copy(qp
->dim
);
3247 dim
= isl_space_add_dims(dim
, isl_dim_set
, qp
->div
->n_row
);
3248 poly
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_copy(qp
->upoly
));
3249 bset
= isl_basic_set_copy(bset
);
3250 bset
= isl_basic_set_add(bset
, isl_dim_set
, qp
->div
->n_row
);
3251 bset
= add_div_constraints(bset
, div
);
3253 return fn(bset
, poly
, user
);
3258 /* Return total degree in variables first (inclusive) up to last (exclusive).
3260 int isl_upoly_degree(__isl_keep
struct isl_upoly
*up
, int first
, int last
)
3264 struct isl_upoly_rec
*rec
;
3268 if (isl_upoly_is_zero(up
))
3270 if (isl_upoly_is_cst(up
) || up
->var
< first
)
3273 rec
= isl_upoly_as_rec(up
);
3277 for (i
= 0; i
< rec
->n
; ++i
) {
3280 if (isl_upoly_is_zero(rec
->p
[i
]))
3282 d
= isl_upoly_degree(rec
->p
[i
], first
, last
);
3292 /* Return total degree in set variables.
3294 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial
*poly
)
3302 ovar
= isl_space_offset(poly
->dim
, isl_dim_set
);
3303 nvar
= isl_space_dim(poly
->dim
, isl_dim_set
);
3304 return isl_upoly_degree(poly
->upoly
, ovar
, ovar
+ nvar
);
3307 __isl_give
struct isl_upoly
*isl_upoly_coeff(__isl_keep
struct isl_upoly
*up
,
3308 unsigned pos
, int deg
)
3311 struct isl_upoly_rec
*rec
;
3316 if (isl_upoly_is_cst(up
) || up
->var
< pos
) {
3318 return isl_upoly_copy(up
);
3320 return isl_upoly_zero(up
->ctx
);
3323 rec
= isl_upoly_as_rec(up
);
3327 if (up
->var
== pos
) {
3329 return isl_upoly_copy(rec
->p
[deg
]);
3331 return isl_upoly_zero(up
->ctx
);
3334 up
= isl_upoly_copy(up
);
3335 up
= isl_upoly_cow(up
);
3336 rec
= isl_upoly_as_rec(up
);
3340 for (i
= 0; i
< rec
->n
; ++i
) {
3341 struct isl_upoly
*t
;
3342 t
= isl_upoly_coeff(rec
->p
[i
], pos
, deg
);
3345 isl_upoly_free(rec
->p
[i
]);
3355 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3357 __isl_give isl_qpolynomial
*isl_qpolynomial_coeff(
3358 __isl_keep isl_qpolynomial
*qp
,
3359 enum isl_dim_type type
, unsigned t_pos
, int deg
)
3362 struct isl_upoly
*up
;
3368 if (type
== isl_dim_out
)
3369 isl_die(qp
->div
->ctx
, isl_error_invalid
,
3370 "output/set dimension does not have a coefficient",
3372 if (type
== isl_dim_in
)
3375 isl_assert(qp
->div
->ctx
, t_pos
< isl_space_dim(qp
->dim
, type
),
3378 g_pos
= pos(qp
->dim
, type
) + t_pos
;
3379 up
= isl_upoly_coeff(qp
->upoly
, g_pos
, deg
);
3381 c
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
), qp
->div
->n_row
, up
);
3384 isl_mat_free(c
->div
);
3385 c
->div
= isl_mat_copy(qp
->div
);
3390 isl_qpolynomial_free(c
);
3394 /* Homogenize the polynomial in the variables first (inclusive) up to
3395 * last (exclusive) by inserting powers of variable first.
3396 * Variable first is assumed not to appear in the input.
3398 __isl_give
struct isl_upoly
*isl_upoly_homogenize(
3399 __isl_take
struct isl_upoly
*up
, int deg
, int target
,
3400 int first
, int last
)
3403 struct isl_upoly_rec
*rec
;
3407 if (isl_upoly_is_zero(up
))
3411 if (isl_upoly_is_cst(up
) || up
->var
< first
) {
3412 struct isl_upoly
*hom
;
3414 hom
= isl_upoly_var_pow(up
->ctx
, first
, target
- deg
);
3417 rec
= isl_upoly_as_rec(hom
);
3418 rec
->p
[target
- deg
] = isl_upoly_mul(rec
->p
[target
- deg
], up
);
3423 up
= isl_upoly_cow(up
);
3424 rec
= isl_upoly_as_rec(up
);
3428 for (i
= 0; i
< rec
->n
; ++i
) {
3429 if (isl_upoly_is_zero(rec
->p
[i
]))
3431 rec
->p
[i
] = isl_upoly_homogenize(rec
->p
[i
],
3432 up
->var
< last
? deg
+ i
: i
, target
,
3444 /* Homogenize the polynomial in the set variables by introducing
3445 * powers of an extra set variable at position 0.
3447 __isl_give isl_qpolynomial
*isl_qpolynomial_homogenize(
3448 __isl_take isl_qpolynomial
*poly
)
3452 int deg
= isl_qpolynomial_degree(poly
);
3457 poly
= isl_qpolynomial_insert_dims(poly
, isl_dim_in
, 0, 1);
3458 poly
= isl_qpolynomial_cow(poly
);
3462 ovar
= isl_space_offset(poly
->dim
, isl_dim_set
);
3463 nvar
= isl_space_dim(poly
->dim
, isl_dim_set
);
3464 poly
->upoly
= isl_upoly_homogenize(poly
->upoly
, 0, deg
,
3471 isl_qpolynomial_free(poly
);
3475 __isl_give isl_term
*isl_term_alloc(__isl_take isl_space
*dim
,
3476 __isl_take isl_mat
*div
)
3484 n
= isl_space_dim(dim
, isl_dim_all
) + div
->n_row
;
3486 term
= isl_calloc(dim
->ctx
, struct isl_term
,
3487 sizeof(struct isl_term
) + (n
- 1) * sizeof(int));
3494 isl_int_init(term
->n
);
3495 isl_int_init(term
->d
);
3499 isl_space_free(dim
);
3504 __isl_give isl_term
*isl_term_copy(__isl_keep isl_term
*term
)
3513 __isl_give isl_term
*isl_term_dup(__isl_keep isl_term
*term
)
3522 total
= isl_space_dim(term
->dim
, isl_dim_all
) + term
->div
->n_row
;
3524 dup
= isl_term_alloc(isl_space_copy(term
->dim
), isl_mat_copy(term
->div
));
3528 isl_int_set(dup
->n
, term
->n
);
3529 isl_int_set(dup
->d
, term
->d
);
3531 for (i
= 0; i
< total
; ++i
)
3532 dup
->pow
[i
] = term
->pow
[i
];
3537 __isl_give isl_term
*isl_term_cow(__isl_take isl_term
*term
)
3545 return isl_term_dup(term
);
3548 void isl_term_free(__isl_take isl_term
*term
)
3553 if (--term
->ref
> 0)
3556 isl_space_free(term
->dim
);
3557 isl_mat_free(term
->div
);
3558 isl_int_clear(term
->n
);
3559 isl_int_clear(term
->d
);
3563 unsigned isl_term_dim(__isl_keep isl_term
*term
, enum isl_dim_type type
)
3571 case isl_dim_out
: return isl_space_dim(term
->dim
, type
);
3572 case isl_dim_div
: return term
->div
->n_row
;
3573 case isl_dim_all
: return isl_space_dim(term
->dim
, isl_dim_all
) +
3579 isl_ctx
*isl_term_get_ctx(__isl_keep isl_term
*term
)
3581 return term
? term
->dim
->ctx
: NULL
;
3584 void isl_term_get_num(__isl_keep isl_term
*term
, isl_int
*n
)
3588 isl_int_set(*n
, term
->n
);
3591 void isl_term_get_den(__isl_keep isl_term
*term
, isl_int
*d
)
3595 isl_int_set(*d
, term
->d
);
3598 int isl_term_get_exp(__isl_keep isl_term
*term
,
3599 enum isl_dim_type type
, unsigned pos
)
3604 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, type
), return -1);
3606 if (type
>= isl_dim_set
)
3607 pos
+= isl_space_dim(term
->dim
, isl_dim_param
);
3608 if (type
>= isl_dim_div
)
3609 pos
+= isl_space_dim(term
->dim
, isl_dim_set
);
3611 return term
->pow
[pos
];
3614 __isl_give isl_div
*isl_term_get_div(__isl_keep isl_term
*term
, unsigned pos
)
3616 isl_basic_map
*bmap
;
3623 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, isl_dim_div
),
3626 total
= term
->div
->n_col
- term
->div
->n_row
- 2;
3627 /* No nested divs for now */
3628 isl_assert(term
->dim
->ctx
,
3629 isl_seq_first_non_zero(term
->div
->row
[pos
] + 2 + total
,
3630 term
->div
->n_row
) == -1,
3633 bmap
= isl_basic_map_alloc_space(isl_space_copy(term
->dim
), 1, 0, 0);
3634 if ((k
= isl_basic_map_alloc_div(bmap
)) < 0)
3637 isl_seq_cpy(bmap
->div
[k
], term
->div
->row
[pos
], 2 + total
);
3639 return isl_basic_map_div(bmap
, k
);
3641 isl_basic_map_free(bmap
);
3645 __isl_give isl_term
*isl_upoly_foreach_term(__isl_keep
struct isl_upoly
*up
,
3646 int (*fn
)(__isl_take isl_term
*term
, void *user
),
3647 __isl_take isl_term
*term
, void *user
)
3650 struct isl_upoly_rec
*rec
;
3655 if (isl_upoly_is_zero(up
))
3658 isl_assert(up
->ctx
, !isl_upoly_is_nan(up
), goto error
);
3659 isl_assert(up
->ctx
, !isl_upoly_is_infty(up
), goto error
);
3660 isl_assert(up
->ctx
, !isl_upoly_is_neginfty(up
), goto error
);
3662 if (isl_upoly_is_cst(up
)) {
3663 struct isl_upoly_cst
*cst
;
3664 cst
= isl_upoly_as_cst(up
);
3667 term
= isl_term_cow(term
);
3670 isl_int_set(term
->n
, cst
->n
);
3671 isl_int_set(term
->d
, cst
->d
);
3672 if (fn(isl_term_copy(term
), user
) < 0)
3677 rec
= isl_upoly_as_rec(up
);
3681 for (i
= 0; i
< rec
->n
; ++i
) {
3682 term
= isl_term_cow(term
);
3685 term
->pow
[up
->var
] = i
;
3686 term
= isl_upoly_foreach_term(rec
->p
[i
], fn
, term
, user
);
3690 term
->pow
[up
->var
] = 0;
3694 isl_term_free(term
);
3698 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial
*qp
,
3699 int (*fn
)(__isl_take isl_term
*term
, void *user
), void *user
)
3706 term
= isl_term_alloc(isl_space_copy(qp
->dim
), isl_mat_copy(qp
->div
));
3710 term
= isl_upoly_foreach_term(qp
->upoly
, fn
, term
, user
);
3712 isl_term_free(term
);
3714 return term
? 0 : -1;
3717 __isl_give isl_qpolynomial
*isl_qpolynomial_from_term(__isl_take isl_term
*term
)
3719 struct isl_upoly
*up
;
3720 isl_qpolynomial
*qp
;
3726 n
= isl_space_dim(term
->dim
, isl_dim_all
) + term
->div
->n_row
;
3728 up
= isl_upoly_rat_cst(term
->dim
->ctx
, term
->n
, term
->d
);
3729 for (i
= 0; i
< n
; ++i
) {
3732 up
= isl_upoly_mul(up
,
3733 isl_upoly_var_pow(term
->dim
->ctx
, i
, term
->pow
[i
]));
3736 qp
= isl_qpolynomial_alloc(isl_space_copy(term
->dim
), term
->div
->n_row
, up
);
3739 isl_mat_free(qp
->div
);
3740 qp
->div
= isl_mat_copy(term
->div
);
3744 isl_term_free(term
);
3747 isl_qpolynomial_free(qp
);
3748 isl_term_free(term
);
3752 __isl_give isl_qpolynomial
*isl_qpolynomial_lift(__isl_take isl_qpolynomial
*qp
,
3753 __isl_take isl_space
*dim
)
3762 if (isl_space_is_equal(qp
->dim
, dim
)) {
3763 isl_space_free(dim
);
3767 qp
= isl_qpolynomial_cow(qp
);
3771 extra
= isl_space_dim(dim
, isl_dim_set
) -
3772 isl_space_dim(qp
->dim
, isl_dim_set
);
3773 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
3774 if (qp
->div
->n_row
) {
3777 exp
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
3780 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3782 qp
->upoly
= expand(qp
->upoly
, exp
, total
);
3787 qp
->div
= isl_mat_insert_cols(qp
->div
, 2 + total
, extra
);
3790 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3791 isl_seq_clr(qp
->div
->row
[i
] + 2 + total
, extra
);
3793 isl_space_free(qp
->dim
);
3798 isl_space_free(dim
);
3799 isl_qpolynomial_free(qp
);
3803 /* For each parameter or variable that does not appear in qp,
3804 * first eliminate the variable from all constraints and then set it to zero.
3806 static __isl_give isl_set
*fix_inactive(__isl_take isl_set
*set
,
3807 __isl_keep isl_qpolynomial
*qp
)
3818 d
= isl_space_dim(set
->dim
, isl_dim_all
);
3819 active
= isl_calloc_array(set
->ctx
, int, d
);
3820 if (set_active(qp
, active
) < 0)
3823 for (i
= 0; i
< d
; ++i
)
3832 nparam
= isl_space_dim(set
->dim
, isl_dim_param
);
3833 nvar
= isl_space_dim(set
->dim
, isl_dim_set
);
3834 for (i
= 0; i
< nparam
; ++i
) {
3837 set
= isl_set_eliminate(set
, isl_dim_param
, i
, 1);
3838 set
= isl_set_fix_si(set
, isl_dim_param
, i
, 0);
3840 for (i
= 0; i
< nvar
; ++i
) {
3841 if (active
[nparam
+ i
])
3843 set
= isl_set_eliminate(set
, isl_dim_set
, i
, 1);
3844 set
= isl_set_fix_si(set
, isl_dim_set
, i
, 0);
3856 struct isl_opt_data
{
3857 isl_qpolynomial
*qp
;
3859 isl_qpolynomial
*opt
;
3863 static int opt_fn(__isl_take isl_point
*pnt
, void *user
)
3865 struct isl_opt_data
*data
= (struct isl_opt_data
*)user
;
3866 isl_qpolynomial
*val
;
3868 val
= isl_qpolynomial_eval(isl_qpolynomial_copy(data
->qp
), pnt
);
3872 } else if (data
->max
) {
3873 data
->opt
= isl_qpolynomial_max_cst(data
->opt
, val
);
3875 data
->opt
= isl_qpolynomial_min_cst(data
->opt
, val
);
3881 __isl_give isl_qpolynomial
*isl_qpolynomial_opt_on_domain(
3882 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*set
, int max
)
3884 struct isl_opt_data data
= { NULL
, 1, NULL
, max
};
3889 if (isl_upoly_is_cst(qp
->upoly
)) {
3894 set
= fix_inactive(set
, qp
);
3897 if (isl_set_foreach_point(set
, opt_fn
, &data
) < 0)
3901 isl_space
*space
= isl_qpolynomial_get_domain_space(qp
);
3902 data
.opt
= isl_qpolynomial_zero_on_domain(space
);
3906 isl_qpolynomial_free(qp
);
3910 isl_qpolynomial_free(qp
);
3911 isl_qpolynomial_free(data
.opt
);
3915 __isl_give isl_qpolynomial
*isl_qpolynomial_morph_domain(
3916 __isl_take isl_qpolynomial
*qp
, __isl_take isl_morph
*morph
)
3921 struct isl_upoly
**subs
;
3924 qp
= isl_qpolynomial_cow(qp
);
3929 isl_assert(ctx
, isl_space_is_equal(qp
->dim
, morph
->dom
->dim
), goto error
);
3931 n_sub
= morph
->inv
->n_row
- 1;
3932 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
3933 n_sub
+= qp
->div
->n_row
;
3934 subs
= isl_calloc_array(ctx
, struct isl_upoly
*, n_sub
);
3938 for (i
= 0; 1 + i
< morph
->inv
->n_row
; ++i
)
3939 subs
[i
] = isl_upoly_from_affine(ctx
, morph
->inv
->row
[1 + i
],
3940 morph
->inv
->row
[0][0], morph
->inv
->n_col
);
3941 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
3942 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3943 subs
[morph
->inv
->n_row
- 1 + i
] =
3944 isl_upoly_var_pow(ctx
, morph
->inv
->n_col
- 1 + i
, 1);
3946 qp
->upoly
= isl_upoly_subs(qp
->upoly
, 0, n_sub
, subs
);
3948 for (i
= 0; i
< n_sub
; ++i
)
3949 isl_upoly_free(subs
[i
]);
3952 mat
= isl_mat_diagonal(isl_mat_identity(ctx
, 1), isl_mat_copy(morph
->inv
));
3953 mat
= isl_mat_diagonal(mat
, isl_mat_identity(ctx
, qp
->div
->n_row
));
3954 qp
->div
= isl_mat_product(qp
->div
, mat
);
3955 isl_space_free(qp
->dim
);
3956 qp
->dim
= isl_space_copy(morph
->ran
->dim
);
3958 if (!qp
->upoly
|| !qp
->div
|| !qp
->dim
)
3961 isl_morph_free(morph
);
3965 isl_qpolynomial_free(qp
);
3966 isl_morph_free(morph
);
3970 static int neg_entry(void **entry
, void *user
)
3972 isl_pw_qpolynomial
**pwqp
= (isl_pw_qpolynomial
**)entry
;
3974 *pwqp
= isl_pw_qpolynomial_neg(*pwqp
);
3976 return *pwqp
? 0 : -1;
3979 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_neg(
3980 __isl_take isl_union_pw_qpolynomial
*upwqp
)
3982 upwqp
= isl_union_pw_qpolynomial_cow(upwqp
);
3986 if (isl_hash_table_foreach(upwqp
->dim
->ctx
, &upwqp
->table
,
3987 &neg_entry
, NULL
) < 0)
3992 isl_union_pw_qpolynomial_free(upwqp
);
3996 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_sub(
3997 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
3998 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
4000 return isl_union_pw_qpolynomial_add(upwqp1
,
4001 isl_union_pw_qpolynomial_neg(upwqp2
));
4004 static int mul_entry(void **entry
, void *user
)
4006 struct isl_union_pw_qpolynomial_match_bin_data
*data
= user
;
4008 struct isl_hash_table_entry
*entry2
;
4009 isl_pw_qpolynomial
*pwpq
= *entry
;
4012 hash
= isl_space_get_hash(pwpq
->dim
);
4013 entry2
= isl_hash_table_find(data
->u2
->dim
->ctx
, &data
->u2
->table
,
4014 hash
, &has_dim
, pwpq
->dim
, 0);
4018 pwpq
= isl_pw_qpolynomial_copy(pwpq
);
4019 pwpq
= isl_pw_qpolynomial_mul(pwpq
,
4020 isl_pw_qpolynomial_copy(entry2
->data
));
4022 empty
= isl_pw_qpolynomial_is_zero(pwpq
);
4024 isl_pw_qpolynomial_free(pwpq
);
4028 isl_pw_qpolynomial_free(pwpq
);
4032 data
->res
= isl_union_pw_qpolynomial_add_pw_qpolynomial(data
->res
, pwpq
);
4037 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_mul(
4038 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
4039 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
4041 return match_bin_op(upwqp1
, upwqp2
, &mul_entry
);
4044 /* Reorder the columns of the given div definitions according to the
4047 static __isl_give isl_mat
*reorder_divs(__isl_take isl_mat
*div
,
4048 __isl_take isl_reordering
*r
)
4057 extra
= isl_space_dim(r
->dim
, isl_dim_all
) + div
->n_row
- r
->len
;
4058 mat
= isl_mat_alloc(div
->ctx
, div
->n_row
, div
->n_col
+ extra
);
4062 for (i
= 0; i
< div
->n_row
; ++i
) {
4063 isl_seq_cpy(mat
->row
[i
], div
->row
[i
], 2);
4064 isl_seq_clr(mat
->row
[i
] + 2, mat
->n_col
- 2);
4065 for (j
= 0; j
< r
->len
; ++j
)
4066 isl_int_set(mat
->row
[i
][2 + r
->pos
[j
]],
4067 div
->row
[i
][2 + j
]);
4070 isl_reordering_free(r
);
4074 isl_reordering_free(r
);
4079 /* Reorder the dimension of "qp" according to the given reordering.
4081 __isl_give isl_qpolynomial
*isl_qpolynomial_realign_domain(
4082 __isl_take isl_qpolynomial
*qp
, __isl_take isl_reordering
*r
)
4084 qp
= isl_qpolynomial_cow(qp
);
4088 r
= isl_reordering_extend(r
, qp
->div
->n_row
);
4092 qp
->div
= reorder_divs(qp
->div
, isl_reordering_copy(r
));
4096 qp
->upoly
= reorder(qp
->upoly
, r
->pos
);
4100 qp
= isl_qpolynomial_reset_domain_space(qp
, isl_space_copy(r
->dim
));
4102 isl_reordering_free(r
);
4105 isl_qpolynomial_free(qp
);
4106 isl_reordering_free(r
);
4110 __isl_give isl_qpolynomial
*isl_qpolynomial_align_params(
4111 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*model
)
4116 if (!isl_space_match(qp
->dim
, isl_dim_param
, model
, isl_dim_param
)) {
4117 isl_reordering
*exp
;
4119 model
= isl_space_drop_dims(model
, isl_dim_in
,
4120 0, isl_space_dim(model
, isl_dim_in
));
4121 model
= isl_space_drop_dims(model
, isl_dim_out
,
4122 0, isl_space_dim(model
, isl_dim_out
));
4123 exp
= isl_parameter_alignment_reordering(qp
->dim
, model
);
4124 exp
= isl_reordering_extend_space(exp
,
4125 isl_qpolynomial_get_domain_space(qp
));
4126 qp
= isl_qpolynomial_realign_domain(qp
, exp
);
4129 isl_space_free(model
);
4132 isl_space_free(model
);
4133 isl_qpolynomial_free(qp
);
4137 struct isl_split_periods_data
{
4139 isl_pw_qpolynomial
*res
;
4142 /* Create a slice where the integer division "div" has the fixed value "v".
4143 * In particular, if "div" refers to floor(f/m), then create a slice
4145 * m v <= f <= m v + (m - 1)
4150 * -f + m v + (m - 1) >= 0
4152 static __isl_give isl_set
*set_div_slice(__isl_take isl_space
*dim
,
4153 __isl_keep isl_qpolynomial
*qp
, int div
, isl_int v
)
4156 isl_basic_set
*bset
= NULL
;
4162 total
= isl_space_dim(dim
, isl_dim_all
);
4163 bset
= isl_basic_set_alloc_space(isl_space_copy(dim
), 0, 0, 2);
4165 k
= isl_basic_set_alloc_inequality(bset
);
4168 isl_seq_cpy(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4169 isl_int_submul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4171 k
= isl_basic_set_alloc_inequality(bset
);
4174 isl_seq_neg(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4175 isl_int_addmul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4176 isl_int_add(bset
->ineq
[k
][0], bset
->ineq
[k
][0], qp
->div
->row
[div
][0]);
4177 isl_int_sub_ui(bset
->ineq
[k
][0], bset
->ineq
[k
][0], 1);
4179 isl_space_free(dim
);
4180 return isl_set_from_basic_set(bset
);
4182 isl_basic_set_free(bset
);
4183 isl_space_free(dim
);
4187 static int split_periods(__isl_take isl_set
*set
,
4188 __isl_take isl_qpolynomial
*qp
, void *user
);
4190 /* Create a slice of the domain "set" such that integer division "div"
4191 * has the fixed value "v" and add the results to data->res,
4192 * replacing the integer division by "v" in "qp".
4194 static int set_div(__isl_take isl_set
*set
,
4195 __isl_take isl_qpolynomial
*qp
, int div
, isl_int v
,
4196 struct isl_split_periods_data
*data
)
4201 struct isl_upoly
*cst
;
4203 slice
= set_div_slice(isl_set_get_space(set
), qp
, div
, v
);
4204 set
= isl_set_intersect(set
, slice
);
4209 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4211 for (i
= div
+ 1; i
< qp
->div
->n_row
; ++i
) {
4212 if (isl_int_is_zero(qp
->div
->row
[i
][2 + total
+ div
]))
4214 isl_int_addmul(qp
->div
->row
[i
][1],
4215 qp
->div
->row
[i
][2 + total
+ div
], v
);
4216 isl_int_set_si(qp
->div
->row
[i
][2 + total
+ div
], 0);
4219 cst
= isl_upoly_rat_cst(qp
->dim
->ctx
, v
, qp
->dim
->ctx
->one
);
4220 qp
= substitute_div(qp
, div
, cst
);
4222 return split_periods(set
, qp
, data
);
4225 isl_qpolynomial_free(qp
);
4229 /* Split the domain "set" such that integer division "div"
4230 * has a fixed value (ranging from "min" to "max") on each slice
4231 * and add the results to data->res.
4233 static int split_div(__isl_take isl_set
*set
,
4234 __isl_take isl_qpolynomial
*qp
, int div
, isl_int min
, isl_int max
,
4235 struct isl_split_periods_data
*data
)
4237 for (; isl_int_le(min
, max
); isl_int_add_ui(min
, min
, 1)) {
4238 isl_set
*set_i
= isl_set_copy(set
);
4239 isl_qpolynomial
*qp_i
= isl_qpolynomial_copy(qp
);
4241 if (set_div(set_i
, qp_i
, div
, min
, data
) < 0)
4245 isl_qpolynomial_free(qp
);
4249 isl_qpolynomial_free(qp
);
4253 /* If "qp" refers to any integer division
4254 * that can only attain "max_periods" distinct values on "set"
4255 * then split the domain along those distinct values.
4256 * Add the results (or the original if no splitting occurs)
4259 static int split_periods(__isl_take isl_set
*set
,
4260 __isl_take isl_qpolynomial
*qp
, void *user
)
4263 isl_pw_qpolynomial
*pwqp
;
4264 struct isl_split_periods_data
*data
;
4269 data
= (struct isl_split_periods_data
*)user
;
4274 if (qp
->div
->n_row
== 0) {
4275 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4276 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4282 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4283 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4284 enum isl_lp_result lp_res
;
4286 if (isl_seq_first_non_zero(qp
->div
->row
[i
] + 2 + total
,
4287 qp
->div
->n_row
) != -1)
4290 lp_res
= isl_set_solve_lp(set
, 0, qp
->div
->row
[i
] + 1,
4291 set
->ctx
->one
, &min
, NULL
, NULL
);
4292 if (lp_res
== isl_lp_error
)
4294 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4296 isl_int_fdiv_q(min
, min
, qp
->div
->row
[i
][0]);
4298 lp_res
= isl_set_solve_lp(set
, 1, qp
->div
->row
[i
] + 1,
4299 set
->ctx
->one
, &max
, NULL
, NULL
);
4300 if (lp_res
== isl_lp_error
)
4302 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4304 isl_int_fdiv_q(max
, max
, qp
->div
->row
[i
][0]);
4306 isl_int_sub(max
, max
, min
);
4307 if (isl_int_cmp_si(max
, data
->max_periods
) < 0) {
4308 isl_int_add(max
, max
, min
);
4313 if (i
< qp
->div
->n_row
) {
4314 r
= split_div(set
, qp
, i
, min
, max
, data
);
4316 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4317 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4329 isl_qpolynomial_free(qp
);
4333 /* If any quasi-polynomial in pwqp refers to any integer division
4334 * that can only attain "max_periods" distinct values on its domain
4335 * then split the domain along those distinct values.
4337 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_split_periods(
4338 __isl_take isl_pw_qpolynomial
*pwqp
, int max_periods
)
4340 struct isl_split_periods_data data
;
4342 data
.max_periods
= max_periods
;
4343 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp
));
4345 if (isl_pw_qpolynomial_foreach_piece(pwqp
, &split_periods
, &data
) < 0)
4348 isl_pw_qpolynomial_free(pwqp
);
4352 isl_pw_qpolynomial_free(data
.res
);
4353 isl_pw_qpolynomial_free(pwqp
);
4357 /* Construct a piecewise quasipolynomial that is constant on the given
4358 * domain. In particular, it is
4361 * infinity if cst == -1
4363 static __isl_give isl_pw_qpolynomial
*constant_on_domain(
4364 __isl_take isl_basic_set
*bset
, int cst
)
4367 isl_qpolynomial
*qp
;
4372 bset
= isl_basic_set_params(bset
);
4373 dim
= isl_basic_set_get_space(bset
);
4375 qp
= isl_qpolynomial_infty_on_domain(dim
);
4377 qp
= isl_qpolynomial_zero_on_domain(dim
);
4379 qp
= isl_qpolynomial_one_on_domain(dim
);
4380 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset
), qp
);
4383 /* Factor bset, call fn on each of the factors and return the product.
4385 * If no factors can be found, simply call fn on the input.
4386 * Otherwise, construct the factors based on the factorizer,
4387 * call fn on each factor and compute the product.
4389 static __isl_give isl_pw_qpolynomial
*compressed_multiplicative_call(
4390 __isl_take isl_basic_set
*bset
,
4391 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4397 isl_qpolynomial
*qp
;
4398 isl_pw_qpolynomial
*pwqp
;
4402 f
= isl_basic_set_factorizer(bset
);
4405 if (f
->n_group
== 0) {
4406 isl_factorizer_free(f
);
4410 nparam
= isl_basic_set_dim(bset
, isl_dim_param
);
4411 nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
4413 dim
= isl_basic_set_get_space(bset
);
4414 dim
= isl_space_domain(dim
);
4415 set
= isl_set_universe(isl_space_copy(dim
));
4416 qp
= isl_qpolynomial_one_on_domain(dim
);
4417 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4419 bset
= isl_morph_basic_set(isl_morph_copy(f
->morph
), bset
);
4421 for (i
= 0, n
= 0; i
< f
->n_group
; ++i
) {
4422 isl_basic_set
*bset_i
;
4423 isl_pw_qpolynomial
*pwqp_i
;
4425 bset_i
= isl_basic_set_copy(bset
);
4426 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4427 nparam
+ n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4428 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4430 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
,
4431 n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4432 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
, 0, n
);
4434 pwqp_i
= fn(bset_i
);
4435 pwqp
= isl_pw_qpolynomial_mul(pwqp
, pwqp_i
);
4440 isl_basic_set_free(bset
);
4441 isl_factorizer_free(f
);
4445 isl_basic_set_free(bset
);
4449 /* Factor bset, call fn on each of the factors and return the product.
4450 * The function is assumed to evaluate to zero on empty domains,
4451 * to one on zero-dimensional domains and to infinity on unbounded domains
4452 * and will not be called explicitly on zero-dimensional or unbounded domains.
4454 * We first check for some special cases and remove all equalities.
4455 * Then we hand over control to compressed_multiplicative_call.
4457 __isl_give isl_pw_qpolynomial
*isl_basic_set_multiplicative_call(
4458 __isl_take isl_basic_set
*bset
,
4459 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4463 isl_pw_qpolynomial
*pwqp
;
4468 if (isl_basic_set_plain_is_empty(bset
))
4469 return constant_on_domain(bset
, 0);
4471 if (isl_basic_set_dim(bset
, isl_dim_set
) == 0)
4472 return constant_on_domain(bset
, 1);
4474 bounded
= isl_basic_set_is_bounded(bset
);
4478 return constant_on_domain(bset
, -1);
4480 if (bset
->n_eq
== 0)
4481 return compressed_multiplicative_call(bset
, fn
);
4483 morph
= isl_basic_set_full_compression(bset
);
4484 bset
= isl_morph_basic_set(isl_morph_copy(morph
), bset
);
4486 pwqp
= compressed_multiplicative_call(bset
, fn
);
4488 morph
= isl_morph_dom_params(morph
);
4489 morph
= isl_morph_ran_params(morph
);
4490 morph
= isl_morph_inverse(morph
);
4492 pwqp
= isl_pw_qpolynomial_morph_domain(pwqp
, morph
);
4496 isl_basic_set_free(bset
);
4500 /* Drop all floors in "qp", turning each integer division [a/m] into
4501 * a rational division a/m. If "down" is set, then the integer division
4502 * is replaces by (a-(m-1))/m instead.
4504 static __isl_give isl_qpolynomial
*qp_drop_floors(
4505 __isl_take isl_qpolynomial
*qp
, int down
)
4508 struct isl_upoly
*s
;
4512 if (qp
->div
->n_row
== 0)
4515 qp
= isl_qpolynomial_cow(qp
);
4519 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
4521 isl_int_sub(qp
->div
->row
[i
][1],
4522 qp
->div
->row
[i
][1], qp
->div
->row
[i
][0]);
4523 isl_int_add_ui(qp
->div
->row
[i
][1],
4524 qp
->div
->row
[i
][1], 1);
4526 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
4527 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
4528 qp
= substitute_div(qp
, i
, s
);
4536 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4537 * a rational division a/m.
4539 static __isl_give isl_pw_qpolynomial
*pwqp_drop_floors(
4540 __isl_take isl_pw_qpolynomial
*pwqp
)
4547 if (isl_pw_qpolynomial_is_zero(pwqp
))
4550 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
4554 for (i
= 0; i
< pwqp
->n
; ++i
) {
4555 pwqp
->p
[i
].qp
= qp_drop_floors(pwqp
->p
[i
].qp
, 0);
4562 isl_pw_qpolynomial_free(pwqp
);
4566 /* Adjust all the integer divisions in "qp" such that they are at least
4567 * one over the given orthant (identified by "signs"). This ensures
4568 * that they will still be non-negative even after subtracting (m-1)/m.
4570 * In particular, f is replaced by f' + v, changing f = [a/m]
4571 * to f' = [(a - m v)/m].
4572 * If the constant term k in a is smaller than m,
4573 * the constant term of v is set to floor(k/m) - 1.
4574 * For any other term, if the coefficient c and the variable x have
4575 * the same sign, then no changes are needed.
4576 * Otherwise, if the variable is positive (and c is negative),
4577 * then the coefficient of x in v is set to floor(c/m).
4578 * If the variable is negative (and c is positive),
4579 * then the coefficient of x in v is set to ceil(c/m).
4581 static __isl_give isl_qpolynomial
*make_divs_pos(__isl_take isl_qpolynomial
*qp
,
4587 struct isl_upoly
*s
;
4589 qp
= isl_qpolynomial_cow(qp
);
4592 qp
->div
= isl_mat_cow(qp
->div
);
4596 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4597 v
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
4599 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4600 isl_int
*row
= qp
->div
->row
[i
];
4604 if (isl_int_lt(row
[1], row
[0])) {
4605 isl_int_fdiv_q(v
->el
[0], row
[1], row
[0]);
4606 isl_int_sub_ui(v
->el
[0], v
->el
[0], 1);
4607 isl_int_submul(row
[1], row
[0], v
->el
[0]);
4609 for (j
= 0; j
< total
; ++j
) {
4610 if (isl_int_sgn(row
[2 + j
]) * signs
[j
] >= 0)
4613 isl_int_cdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4615 isl_int_fdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4616 isl_int_submul(row
[2 + j
], row
[0], v
->el
[1 + j
]);
4618 for (j
= 0; j
< i
; ++j
) {
4619 if (isl_int_sgn(row
[2 + total
+ j
]) >= 0)
4621 isl_int_fdiv_q(v
->el
[1 + total
+ j
],
4622 row
[2 + total
+ j
], row
[0]);
4623 isl_int_submul(row
[2 + total
+ j
],
4624 row
[0], v
->el
[1 + total
+ j
]);
4626 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
4627 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
4629 isl_seq_combine(qp
->div
->row
[j
] + 1,
4630 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
4631 qp
->div
->row
[j
][2 + total
+ i
], v
->el
, v
->size
);
4633 isl_int_set_si(v
->el
[1 + total
+ i
], 1);
4634 s
= isl_upoly_from_affine(qp
->dim
->ctx
, v
->el
,
4635 qp
->div
->ctx
->one
, v
->size
);
4636 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ i
, 1, &s
);
4646 isl_qpolynomial_free(qp
);
4650 struct isl_to_poly_data
{
4652 isl_pw_qpolynomial
*res
;
4653 isl_qpolynomial
*qp
;
4656 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4657 * We first make all integer divisions positive and then split the
4658 * quasipolynomials into terms with sign data->sign (the direction
4659 * of the requested approximation) and terms with the opposite sign.
4660 * In the first set of terms, each integer division [a/m] is
4661 * overapproximated by a/m, while in the second it is underapproximated
4664 static int to_polynomial_on_orthant(__isl_take isl_set
*orthant
, int *signs
,
4667 struct isl_to_poly_data
*data
= user
;
4668 isl_pw_qpolynomial
*t
;
4669 isl_qpolynomial
*qp
, *up
, *down
;
4671 qp
= isl_qpolynomial_copy(data
->qp
);
4672 qp
= make_divs_pos(qp
, signs
);
4674 up
= isl_qpolynomial_terms_of_sign(qp
, signs
, data
->sign
);
4675 up
= qp_drop_floors(up
, 0);
4676 down
= isl_qpolynomial_terms_of_sign(qp
, signs
, -data
->sign
);
4677 down
= qp_drop_floors(down
, 1);
4679 isl_qpolynomial_free(qp
);
4680 qp
= isl_qpolynomial_add(up
, down
);
4682 t
= isl_pw_qpolynomial_alloc(orthant
, qp
);
4683 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, t
);
4688 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4689 * the polynomial will be an overapproximation. If "sign" is negative,
4690 * it will be an underapproximation. If "sign" is zero, the approximation
4691 * will lie somewhere in between.
4693 * In particular, is sign == 0, we simply drop the floors, turning
4694 * the integer divisions into rational divisions.
4695 * Otherwise, we split the domains into orthants, make all integer divisions
4696 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4697 * depending on the requested sign and the sign of the term in which
4698 * the integer division appears.
4700 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_to_polynomial(
4701 __isl_take isl_pw_qpolynomial
*pwqp
, int sign
)
4704 struct isl_to_poly_data data
;
4707 return pwqp_drop_floors(pwqp
);
4713 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp
));
4715 for (i
= 0; i
< pwqp
->n
; ++i
) {
4716 if (pwqp
->p
[i
].qp
->div
->n_row
== 0) {
4717 isl_pw_qpolynomial
*t
;
4718 t
= isl_pw_qpolynomial_alloc(
4719 isl_set_copy(pwqp
->p
[i
].set
),
4720 isl_qpolynomial_copy(pwqp
->p
[i
].qp
));
4721 data
.res
= isl_pw_qpolynomial_add_disjoint(data
.res
, t
);
4724 data
.qp
= pwqp
->p
[i
].qp
;
4725 if (isl_set_foreach_orthant(pwqp
->p
[i
].set
,
4726 &to_polynomial_on_orthant
, &data
) < 0)
4730 isl_pw_qpolynomial_free(pwqp
);
4734 isl_pw_qpolynomial_free(pwqp
);
4735 isl_pw_qpolynomial_free(data
.res
);
4739 static int poly_entry(void **entry
, void *user
)
4742 isl_pw_qpolynomial
**pwqp
= (isl_pw_qpolynomial
**)entry
;
4744 *pwqp
= isl_pw_qpolynomial_to_polynomial(*pwqp
, *sign
);
4746 return *pwqp
? 0 : -1;
4749 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_to_polynomial(
4750 __isl_take isl_union_pw_qpolynomial
*upwqp
, int sign
)
4752 upwqp
= isl_union_pw_qpolynomial_cow(upwqp
);
4756 if (isl_hash_table_foreach(upwqp
->dim
->ctx
, &upwqp
->table
,
4757 &poly_entry
, &sign
) < 0)
4762 isl_union_pw_qpolynomial_free(upwqp
);
4766 __isl_give isl_basic_map
*isl_basic_map_from_qpolynomial(
4767 __isl_take isl_qpolynomial
*qp
)
4771 isl_vec
*aff
= NULL
;
4772 isl_basic_map
*bmap
= NULL
;
4778 if (!isl_upoly_is_affine(qp
->upoly
))
4779 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
4780 "input quasi-polynomial not affine", goto error
);
4781 aff
= isl_qpolynomial_extract_affine(qp
);
4784 dim
= isl_qpolynomial_get_space(qp
);
4785 pos
= 1 + isl_space_offset(dim
, isl_dim_out
);
4786 n_div
= qp
->div
->n_row
;
4787 bmap
= isl_basic_map_alloc_space(dim
, n_div
, 1, 2 * n_div
);
4789 for (i
= 0; i
< n_div
; ++i
) {
4790 k
= isl_basic_map_alloc_div(bmap
);
4793 isl_seq_cpy(bmap
->div
[k
], qp
->div
->row
[i
], qp
->div
->n_col
);
4794 isl_int_set_si(bmap
->div
[k
][qp
->div
->n_col
], 0);
4795 if (isl_basic_map_add_div_constraints(bmap
, k
) < 0)
4798 k
= isl_basic_map_alloc_equality(bmap
);
4801 isl_int_neg(bmap
->eq
[k
][pos
], aff
->el
[0]);
4802 isl_seq_cpy(bmap
->eq
[k
], aff
->el
+ 1, pos
);
4803 isl_seq_cpy(bmap
->eq
[k
] + pos
+ 1, aff
->el
+ 1 + pos
, n_div
);
4806 isl_qpolynomial_free(qp
);
4807 bmap
= isl_basic_map_finalize(bmap
);
4811 isl_qpolynomial_free(qp
);
4812 isl_basic_map_free(bmap
);