2 * Copyright 2010 INRIA Saclay
4 * Use of this software is governed by the MIT 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_mat_private.h>
24 #include <isl_range.h>
25 #include <isl_local_space_private.h>
26 #include <isl_aff_private.h>
27 #include <isl_val_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 /* Multiply the constant polynomial "up" by "v".
807 static __isl_give
struct isl_upoly
*isl_upoly_cst_scale_val(
808 __isl_take
struct isl_upoly
*up
, __isl_keep isl_val
*v
)
810 struct isl_upoly_cst
*cst
;
812 if (isl_upoly_is_zero(up
))
815 up
= isl_upoly_cow(up
);
819 cst
= isl_upoly_as_cst(up
);
821 isl_int_mul(cst
->n
, cst
->n
, v
->n
);
822 isl_int_mul(cst
->d
, cst
->d
, v
->d
);
823 isl_upoly_cst_reduce(cst
);
828 /* Multiply the polynomial "up" by "v".
830 static __isl_give
struct isl_upoly
*isl_upoly_scale_val(
831 __isl_take
struct isl_upoly
*up
, __isl_keep isl_val
*v
)
834 struct isl_upoly_rec
*rec
;
839 if (isl_upoly_is_cst(up
))
840 return isl_upoly_cst_scale_val(up
, v
);
842 up
= isl_upoly_cow(up
);
843 rec
= isl_upoly_as_rec(up
);
847 for (i
= 0; i
< rec
->n
; ++i
) {
848 rec
->p
[i
] = isl_upoly_scale_val(rec
->p
[i
], v
);
859 __isl_give
struct isl_upoly
*isl_upoly_mul_cst(__isl_take
struct isl_upoly
*up1
,
860 __isl_take
struct isl_upoly
*up2
)
862 struct isl_upoly_cst
*cst1
;
863 struct isl_upoly_cst
*cst2
;
865 up1
= isl_upoly_cow(up1
);
869 cst1
= isl_upoly_as_cst(up1
);
870 cst2
= isl_upoly_as_cst(up2
);
872 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->n
);
873 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
875 isl_upoly_cst_reduce(cst1
);
885 __isl_give
struct isl_upoly
*isl_upoly_mul_rec(__isl_take
struct isl_upoly
*up1
,
886 __isl_take
struct isl_upoly
*up2
)
888 struct isl_upoly_rec
*rec1
;
889 struct isl_upoly_rec
*rec2
;
890 struct isl_upoly_rec
*res
= NULL
;
894 rec1
= isl_upoly_as_rec(up1
);
895 rec2
= isl_upoly_as_rec(up2
);
898 size
= rec1
->n
+ rec2
->n
- 1;
899 res
= isl_upoly_alloc_rec(up1
->ctx
, up1
->var
, size
);
903 for (i
= 0; i
< rec1
->n
; ++i
) {
904 res
->p
[i
] = isl_upoly_mul(isl_upoly_copy(rec2
->p
[0]),
905 isl_upoly_copy(rec1
->p
[i
]));
910 for (; i
< size
; ++i
) {
911 res
->p
[i
] = isl_upoly_zero(up1
->ctx
);
916 for (i
= 0; i
< rec1
->n
; ++i
) {
917 for (j
= 1; j
< rec2
->n
; ++j
) {
918 struct isl_upoly
*up
;
919 up
= isl_upoly_mul(isl_upoly_copy(rec2
->p
[j
]),
920 isl_upoly_copy(rec1
->p
[i
]));
921 res
->p
[i
+ j
] = isl_upoly_sum(res
->p
[i
+ j
], up
);
934 isl_upoly_free(&res
->up
);
938 __isl_give
struct isl_upoly
*isl_upoly_mul(__isl_take
struct isl_upoly
*up1
,
939 __isl_take
struct isl_upoly
*up2
)
944 if (isl_upoly_is_nan(up1
)) {
949 if (isl_upoly_is_nan(up2
)) {
954 if (isl_upoly_is_zero(up1
)) {
959 if (isl_upoly_is_zero(up2
)) {
964 if (isl_upoly_is_one(up1
)) {
969 if (isl_upoly_is_one(up2
)) {
974 if (up1
->var
< up2
->var
)
975 return isl_upoly_mul(up2
, up1
);
977 if (up2
->var
< up1
->var
) {
979 struct isl_upoly_rec
*rec
;
980 if (isl_upoly_is_infty(up2
) || isl_upoly_is_neginfty(up2
)) {
981 isl_ctx
*ctx
= up1
->ctx
;
984 return isl_upoly_nan(ctx
);
986 up1
= isl_upoly_cow(up1
);
987 rec
= isl_upoly_as_rec(up1
);
991 for (i
= 0; i
< rec
->n
; ++i
) {
992 rec
->p
[i
] = isl_upoly_mul(rec
->p
[i
],
993 isl_upoly_copy(up2
));
1001 if (isl_upoly_is_cst(up1
))
1002 return isl_upoly_mul_cst(up1
, up2
);
1004 return isl_upoly_mul_rec(up1
, up2
);
1006 isl_upoly_free(up1
);
1007 isl_upoly_free(up2
);
1011 __isl_give
struct isl_upoly
*isl_upoly_pow(__isl_take
struct isl_upoly
*up
,
1014 struct isl_upoly
*res
;
1022 res
= isl_upoly_copy(up
);
1024 res
= isl_upoly_one(up
->ctx
);
1026 while (power
>>= 1) {
1027 up
= isl_upoly_mul(up
, isl_upoly_copy(up
));
1029 res
= isl_upoly_mul(res
, isl_upoly_copy(up
));
1036 __isl_give isl_qpolynomial
*isl_qpolynomial_alloc(__isl_take isl_space
*dim
,
1037 unsigned n_div
, __isl_take
struct isl_upoly
*up
)
1039 struct isl_qpolynomial
*qp
= NULL
;
1045 if (!isl_space_is_set(dim
))
1046 isl_die(isl_space_get_ctx(dim
), isl_error_invalid
,
1047 "domain of polynomial should be a set", goto error
);
1049 total
= isl_space_dim(dim
, isl_dim_all
);
1051 qp
= isl_calloc_type(dim
->ctx
, struct isl_qpolynomial
);
1056 qp
->div
= isl_mat_alloc(dim
->ctx
, n_div
, 1 + 1 + total
+ n_div
);
1065 isl_space_free(dim
);
1067 isl_qpolynomial_free(qp
);
1071 __isl_give isl_qpolynomial
*isl_qpolynomial_copy(__isl_keep isl_qpolynomial
*qp
)
1080 __isl_give isl_qpolynomial
*isl_qpolynomial_dup(__isl_keep isl_qpolynomial
*qp
)
1082 struct isl_qpolynomial
*dup
;
1087 dup
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
), qp
->div
->n_row
,
1088 isl_upoly_copy(qp
->upoly
));
1091 isl_mat_free(dup
->div
);
1092 dup
->div
= isl_mat_copy(qp
->div
);
1098 isl_qpolynomial_free(dup
);
1102 __isl_give isl_qpolynomial
*isl_qpolynomial_cow(__isl_take isl_qpolynomial
*qp
)
1110 return isl_qpolynomial_dup(qp
);
1113 void *isl_qpolynomial_free(__isl_take isl_qpolynomial
*qp
)
1121 isl_space_free(qp
->dim
);
1122 isl_mat_free(qp
->div
);
1123 isl_upoly_free(qp
->upoly
);
1129 __isl_give
struct isl_upoly
*isl_upoly_var_pow(isl_ctx
*ctx
, int pos
, int power
)
1132 struct isl_upoly_rec
*rec
;
1133 struct isl_upoly_cst
*cst
;
1135 rec
= isl_upoly_alloc_rec(ctx
, pos
, 1 + power
);
1138 for (i
= 0; i
< 1 + power
; ++i
) {
1139 rec
->p
[i
] = isl_upoly_zero(ctx
);
1144 cst
= isl_upoly_as_cst(rec
->p
[power
]);
1145 isl_int_set_si(cst
->n
, 1);
1149 isl_upoly_free(&rec
->up
);
1153 /* r array maps original positions to new positions.
1155 static __isl_give
struct isl_upoly
*reorder(__isl_take
struct isl_upoly
*up
,
1159 struct isl_upoly_rec
*rec
;
1160 struct isl_upoly
*base
;
1161 struct isl_upoly
*res
;
1163 if (isl_upoly_is_cst(up
))
1166 rec
= isl_upoly_as_rec(up
);
1170 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
1172 base
= isl_upoly_var_pow(up
->ctx
, r
[up
->var
], 1);
1173 res
= reorder(isl_upoly_copy(rec
->p
[rec
->n
- 1]), r
);
1175 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1176 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
1177 res
= isl_upoly_sum(res
, reorder(isl_upoly_copy(rec
->p
[i
]), r
));
1180 isl_upoly_free(base
);
1189 static int compatible_divs(__isl_keep isl_mat
*div1
, __isl_keep isl_mat
*div2
)
1194 isl_assert(div1
->ctx
, div1
->n_row
>= div2
->n_row
&&
1195 div1
->n_col
>= div2
->n_col
, return -1);
1197 if (div1
->n_row
== div2
->n_row
)
1198 return isl_mat_is_equal(div1
, div2
);
1200 n_row
= div1
->n_row
;
1201 n_col
= div1
->n_col
;
1202 div1
->n_row
= div2
->n_row
;
1203 div1
->n_col
= div2
->n_col
;
1205 equal
= isl_mat_is_equal(div1
, div2
);
1207 div1
->n_row
= n_row
;
1208 div1
->n_col
= n_col
;
1213 static int cmp_row(__isl_keep isl_mat
*div
, int i
, int j
)
1217 li
= isl_seq_last_non_zero(div
->row
[i
], div
->n_col
);
1218 lj
= isl_seq_last_non_zero(div
->row
[j
], div
->n_col
);
1223 return isl_seq_cmp(div
->row
[i
], div
->row
[j
], div
->n_col
);
1226 struct isl_div_sort_info
{
1231 static int div_sort_cmp(const void *p1
, const void *p2
)
1233 const struct isl_div_sort_info
*i1
, *i2
;
1234 i1
= (const struct isl_div_sort_info
*) p1
;
1235 i2
= (const struct isl_div_sort_info
*) p2
;
1237 return cmp_row(i1
->div
, i1
->row
, i2
->row
);
1240 /* Sort divs and remove duplicates.
1242 static __isl_give isl_qpolynomial
*sort_divs(__isl_take isl_qpolynomial
*qp
)
1247 struct isl_div_sort_info
*array
= NULL
;
1248 int *pos
= NULL
, *at
= NULL
;
1249 int *reordering
= NULL
;
1254 if (qp
->div
->n_row
<= 1)
1257 div_pos
= isl_space_dim(qp
->dim
, isl_dim_all
);
1259 array
= isl_alloc_array(qp
->div
->ctx
, struct isl_div_sort_info
,
1261 pos
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1262 at
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1263 len
= qp
->div
->n_col
- 2;
1264 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
1265 if (!array
|| !pos
|| !at
|| !reordering
)
1268 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1269 array
[i
].div
= qp
->div
;
1275 qsort(array
, qp
->div
->n_row
, sizeof(struct isl_div_sort_info
),
1278 for (i
= 0; i
< div_pos
; ++i
)
1281 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1282 if (pos
[array
[i
].row
] == i
)
1284 qp
->div
= isl_mat_swap_rows(qp
->div
, i
, pos
[array
[i
].row
]);
1285 pos
[at
[i
]] = pos
[array
[i
].row
];
1286 at
[pos
[array
[i
].row
]] = at
[i
];
1287 at
[i
] = array
[i
].row
;
1288 pos
[array
[i
].row
] = i
;
1292 for (i
= 0; i
< len
- div_pos
; ++i
) {
1294 isl_seq_eq(qp
->div
->row
[i
- skip
- 1],
1295 qp
->div
->row
[i
- skip
], qp
->div
->n_col
)) {
1296 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
1297 isl_mat_col_add(qp
->div
, 2 + div_pos
+ i
- skip
- 1,
1298 2 + div_pos
+ i
- skip
);
1299 qp
->div
= isl_mat_drop_cols(qp
->div
,
1300 2 + div_pos
+ i
- skip
, 1);
1303 reordering
[div_pos
+ array
[i
].row
] = div_pos
+ i
- skip
;
1306 qp
->upoly
= reorder(qp
->upoly
, reordering
);
1308 if (!qp
->upoly
|| !qp
->div
)
1322 isl_qpolynomial_free(qp
);
1326 static __isl_give
struct isl_upoly
*expand(__isl_take
struct isl_upoly
*up
,
1327 int *exp
, int first
)
1330 struct isl_upoly_rec
*rec
;
1332 if (isl_upoly_is_cst(up
))
1335 if (up
->var
< first
)
1338 if (exp
[up
->var
- first
] == up
->var
- first
)
1341 up
= isl_upoly_cow(up
);
1345 up
->var
= exp
[up
->var
- first
] + first
;
1347 rec
= isl_upoly_as_rec(up
);
1351 for (i
= 0; i
< rec
->n
; ++i
) {
1352 rec
->p
[i
] = expand(rec
->p
[i
], exp
, first
);
1363 static __isl_give isl_qpolynomial
*with_merged_divs(
1364 __isl_give isl_qpolynomial
*(*fn
)(__isl_take isl_qpolynomial
*qp1
,
1365 __isl_take isl_qpolynomial
*qp2
),
1366 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
1370 isl_mat
*div
= NULL
;
1372 qp1
= isl_qpolynomial_cow(qp1
);
1373 qp2
= isl_qpolynomial_cow(qp2
);
1378 isl_assert(qp1
->div
->ctx
, qp1
->div
->n_row
>= qp2
->div
->n_row
&&
1379 qp1
->div
->n_col
>= qp2
->div
->n_col
, goto error
);
1381 exp1
= isl_alloc_array(qp1
->div
->ctx
, int, qp1
->div
->n_row
);
1382 exp2
= isl_alloc_array(qp2
->div
->ctx
, int, qp2
->div
->n_row
);
1386 div
= isl_merge_divs(qp1
->div
, qp2
->div
, exp1
, exp2
);
1390 isl_mat_free(qp1
->div
);
1391 qp1
->div
= isl_mat_copy(div
);
1392 isl_mat_free(qp2
->div
);
1393 qp2
->div
= isl_mat_copy(div
);
1395 qp1
->upoly
= expand(qp1
->upoly
, exp1
, div
->n_col
- div
->n_row
- 2);
1396 qp2
->upoly
= expand(qp2
->upoly
, exp2
, div
->n_col
- div
->n_row
- 2);
1398 if (!qp1
->upoly
|| !qp2
->upoly
)
1405 return fn(qp1
, qp2
);
1410 isl_qpolynomial_free(qp1
);
1411 isl_qpolynomial_free(qp2
);
1415 __isl_give isl_qpolynomial
*isl_qpolynomial_add(__isl_take isl_qpolynomial
*qp1
,
1416 __isl_take isl_qpolynomial
*qp2
)
1418 qp1
= isl_qpolynomial_cow(qp1
);
1423 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1424 return isl_qpolynomial_add(qp2
, qp1
);
1426 isl_assert(qp1
->dim
->ctx
, isl_space_is_equal(qp1
->dim
, qp2
->dim
), goto error
);
1427 if (!compatible_divs(qp1
->div
, qp2
->div
))
1428 return with_merged_divs(isl_qpolynomial_add
, qp1
, qp2
);
1430 qp1
->upoly
= isl_upoly_sum(qp1
->upoly
, isl_upoly_copy(qp2
->upoly
));
1434 isl_qpolynomial_free(qp2
);
1438 isl_qpolynomial_free(qp1
);
1439 isl_qpolynomial_free(qp2
);
1443 __isl_give isl_qpolynomial
*isl_qpolynomial_add_on_domain(
1444 __isl_keep isl_set
*dom
,
1445 __isl_take isl_qpolynomial
*qp1
,
1446 __isl_take isl_qpolynomial
*qp2
)
1448 qp1
= isl_qpolynomial_add(qp1
, qp2
);
1449 qp1
= isl_qpolynomial_gist(qp1
, isl_set_copy(dom
));
1453 __isl_give isl_qpolynomial
*isl_qpolynomial_sub(__isl_take isl_qpolynomial
*qp1
,
1454 __isl_take isl_qpolynomial
*qp2
)
1456 return isl_qpolynomial_add(qp1
, isl_qpolynomial_neg(qp2
));
1459 __isl_give isl_qpolynomial
*isl_qpolynomial_add_isl_int(
1460 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1462 if (isl_int_is_zero(v
))
1465 qp
= isl_qpolynomial_cow(qp
);
1469 qp
->upoly
= isl_upoly_add_isl_int(qp
->upoly
, v
);
1475 isl_qpolynomial_free(qp
);
1480 __isl_give isl_qpolynomial
*isl_qpolynomial_neg(__isl_take isl_qpolynomial
*qp
)
1485 return isl_qpolynomial_mul_isl_int(qp
, qp
->dim
->ctx
->negone
);
1488 __isl_give isl_qpolynomial
*isl_qpolynomial_mul_isl_int(
1489 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1491 if (isl_int_is_one(v
))
1494 if (qp
&& isl_int_is_zero(v
)) {
1495 isl_qpolynomial
*zero
;
1496 zero
= isl_qpolynomial_zero_on_domain(isl_space_copy(qp
->dim
));
1497 isl_qpolynomial_free(qp
);
1501 qp
= isl_qpolynomial_cow(qp
);
1505 qp
->upoly
= isl_upoly_mul_isl_int(qp
->upoly
, v
);
1511 isl_qpolynomial_free(qp
);
1515 __isl_give isl_qpolynomial
*isl_qpolynomial_scale(
1516 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1518 return isl_qpolynomial_mul_isl_int(qp
, v
);
1521 /* Multiply "qp" by "v".
1523 __isl_give isl_qpolynomial
*isl_qpolynomial_scale_val(
1524 __isl_take isl_qpolynomial
*qp
, __isl_take isl_val
*v
)
1529 if (!isl_val_is_rat(v
))
1530 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
1531 "expecting rational factor", goto error
);
1533 if (isl_val_is_one(v
)) {
1538 if (isl_val_is_zero(v
)) {
1541 space
= isl_qpolynomial_get_domain_space(qp
);
1542 isl_qpolynomial_free(qp
);
1544 return isl_qpolynomial_zero_on_domain(space
);
1547 qp
= isl_qpolynomial_cow(qp
);
1551 qp
->upoly
= isl_upoly_scale_val(qp
->upoly
, v
);
1553 qp
= isl_qpolynomial_free(qp
);
1559 isl_qpolynomial_free(qp
);
1563 __isl_give isl_qpolynomial
*isl_qpolynomial_mul(__isl_take isl_qpolynomial
*qp1
,
1564 __isl_take isl_qpolynomial
*qp2
)
1566 qp1
= isl_qpolynomial_cow(qp1
);
1571 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1572 return isl_qpolynomial_mul(qp2
, qp1
);
1574 isl_assert(qp1
->dim
->ctx
, isl_space_is_equal(qp1
->dim
, qp2
->dim
), goto error
);
1575 if (!compatible_divs(qp1
->div
, qp2
->div
))
1576 return with_merged_divs(isl_qpolynomial_mul
, qp1
, qp2
);
1578 qp1
->upoly
= isl_upoly_mul(qp1
->upoly
, isl_upoly_copy(qp2
->upoly
));
1582 isl_qpolynomial_free(qp2
);
1586 isl_qpolynomial_free(qp1
);
1587 isl_qpolynomial_free(qp2
);
1591 __isl_give isl_qpolynomial
*isl_qpolynomial_pow(__isl_take isl_qpolynomial
*qp
,
1594 qp
= isl_qpolynomial_cow(qp
);
1599 qp
->upoly
= isl_upoly_pow(qp
->upoly
, power
);
1605 isl_qpolynomial_free(qp
);
1609 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_pow(
1610 __isl_take isl_pw_qpolynomial
*pwqp
, unsigned power
)
1617 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
1621 for (i
= 0; i
< pwqp
->n
; ++i
) {
1622 pwqp
->p
[i
].qp
= isl_qpolynomial_pow(pwqp
->p
[i
].qp
, power
);
1624 return isl_pw_qpolynomial_free(pwqp
);
1630 __isl_give isl_qpolynomial
*isl_qpolynomial_zero_on_domain(
1631 __isl_take isl_space
*dim
)
1635 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
1638 __isl_give isl_qpolynomial
*isl_qpolynomial_one_on_domain(
1639 __isl_take isl_space
*dim
)
1643 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_one(dim
->ctx
));
1646 __isl_give isl_qpolynomial
*isl_qpolynomial_infty_on_domain(
1647 __isl_take isl_space
*dim
)
1651 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_infty(dim
->ctx
));
1654 __isl_give isl_qpolynomial
*isl_qpolynomial_neginfty_on_domain(
1655 __isl_take isl_space
*dim
)
1659 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_neginfty(dim
->ctx
));
1662 __isl_give isl_qpolynomial
*isl_qpolynomial_nan_on_domain(
1663 __isl_take isl_space
*dim
)
1667 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_nan(dim
->ctx
));
1670 __isl_give isl_qpolynomial
*isl_qpolynomial_cst_on_domain(
1671 __isl_take isl_space
*dim
,
1674 struct isl_qpolynomial
*qp
;
1675 struct isl_upoly_cst
*cst
;
1680 qp
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
1684 cst
= isl_upoly_as_cst(qp
->upoly
);
1685 isl_int_set(cst
->n
, v
);
1690 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial
*qp
,
1691 isl_int
*n
, isl_int
*d
)
1693 struct isl_upoly_cst
*cst
;
1698 if (!isl_upoly_is_cst(qp
->upoly
))
1701 cst
= isl_upoly_as_cst(qp
->upoly
);
1706 isl_int_set(*n
, cst
->n
);
1708 isl_int_set(*d
, cst
->d
);
1713 /* Return the constant term of "up".
1715 static __isl_give isl_val
*isl_upoly_get_constant_val(
1716 __isl_keep
struct isl_upoly
*up
)
1718 struct isl_upoly_cst
*cst
;
1723 while (!isl_upoly_is_cst(up
)) {
1724 struct isl_upoly_rec
*rec
;
1726 rec
= isl_upoly_as_rec(up
);
1732 cst
= isl_upoly_as_cst(up
);
1735 return isl_val_rat_from_isl_int(cst
->up
.ctx
, cst
->n
, cst
->d
);
1738 /* Return the constant term of "qp".
1740 __isl_give isl_val
*isl_qpolynomial_get_constant_val(
1741 __isl_keep isl_qpolynomial
*qp
)
1746 return isl_upoly_get_constant_val(qp
->upoly
);
1749 int isl_upoly_is_affine(__isl_keep
struct isl_upoly
*up
)
1752 struct isl_upoly_rec
*rec
;
1760 rec
= isl_upoly_as_rec(up
);
1767 isl_assert(up
->ctx
, rec
->n
> 1, return -1);
1769 is_cst
= isl_upoly_is_cst(rec
->p
[1]);
1775 return isl_upoly_is_affine(rec
->p
[0]);
1778 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial
*qp
)
1783 if (qp
->div
->n_row
> 0)
1786 return isl_upoly_is_affine(qp
->upoly
);
1789 static void update_coeff(__isl_keep isl_vec
*aff
,
1790 __isl_keep
struct isl_upoly_cst
*cst
, int pos
)
1795 if (isl_int_is_zero(cst
->n
))
1800 isl_int_gcd(gcd
, cst
->d
, aff
->el
[0]);
1801 isl_int_divexact(f
, cst
->d
, gcd
);
1802 isl_int_divexact(gcd
, aff
->el
[0], gcd
);
1803 isl_seq_scale(aff
->el
, aff
->el
, f
, aff
->size
);
1804 isl_int_mul(aff
->el
[1 + pos
], gcd
, cst
->n
);
1809 int isl_upoly_update_affine(__isl_keep
struct isl_upoly
*up
,
1810 __isl_keep isl_vec
*aff
)
1812 struct isl_upoly_cst
*cst
;
1813 struct isl_upoly_rec
*rec
;
1819 struct isl_upoly_cst
*cst
;
1821 cst
= isl_upoly_as_cst(up
);
1824 update_coeff(aff
, cst
, 0);
1828 rec
= isl_upoly_as_rec(up
);
1831 isl_assert(up
->ctx
, rec
->n
== 2, return -1);
1833 cst
= isl_upoly_as_cst(rec
->p
[1]);
1836 update_coeff(aff
, cst
, 1 + up
->var
);
1838 return isl_upoly_update_affine(rec
->p
[0], aff
);
1841 __isl_give isl_vec
*isl_qpolynomial_extract_affine(
1842 __isl_keep isl_qpolynomial
*qp
)
1850 d
= isl_space_dim(qp
->dim
, isl_dim_all
);
1851 aff
= isl_vec_alloc(qp
->div
->ctx
, 2 + d
+ qp
->div
->n_row
);
1855 isl_seq_clr(aff
->el
+ 1, 1 + d
+ qp
->div
->n_row
);
1856 isl_int_set_si(aff
->el
[0], 1);
1858 if (isl_upoly_update_affine(qp
->upoly
, aff
) < 0)
1867 int isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial
*qp1
,
1868 __isl_keep isl_qpolynomial
*qp2
)
1875 equal
= isl_space_is_equal(qp1
->dim
, qp2
->dim
);
1876 if (equal
< 0 || !equal
)
1879 equal
= isl_mat_is_equal(qp1
->div
, qp2
->div
);
1880 if (equal
< 0 || !equal
)
1883 return isl_upoly_is_equal(qp1
->upoly
, qp2
->upoly
);
1886 static void upoly_update_den(__isl_keep
struct isl_upoly
*up
, isl_int
*d
)
1889 struct isl_upoly_rec
*rec
;
1891 if (isl_upoly_is_cst(up
)) {
1892 struct isl_upoly_cst
*cst
;
1893 cst
= isl_upoly_as_cst(up
);
1896 isl_int_lcm(*d
, *d
, cst
->d
);
1900 rec
= isl_upoly_as_rec(up
);
1904 for (i
= 0; i
< rec
->n
; ++i
)
1905 upoly_update_den(rec
->p
[i
], d
);
1908 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial
*qp
, isl_int
*d
)
1910 isl_int_set_si(*d
, 1);
1913 upoly_update_den(qp
->upoly
, d
);
1916 __isl_give isl_qpolynomial
*isl_qpolynomial_var_pow_on_domain(
1917 __isl_take isl_space
*dim
, int pos
, int power
)
1919 struct isl_ctx
*ctx
;
1926 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_var_pow(ctx
, pos
, power
));
1929 __isl_give isl_qpolynomial
*isl_qpolynomial_var_on_domain(__isl_take isl_space
*dim
,
1930 enum isl_dim_type type
, unsigned pos
)
1935 isl_assert(dim
->ctx
, isl_space_dim(dim
, isl_dim_in
) == 0, goto error
);
1936 isl_assert(dim
->ctx
, pos
< isl_space_dim(dim
, type
), goto error
);
1938 if (type
== isl_dim_set
)
1939 pos
+= isl_space_dim(dim
, isl_dim_param
);
1941 return isl_qpolynomial_var_pow_on_domain(dim
, pos
, 1);
1943 isl_space_free(dim
);
1947 __isl_give
struct isl_upoly
*isl_upoly_subs(__isl_take
struct isl_upoly
*up
,
1948 unsigned first
, unsigned n
, __isl_keep
struct isl_upoly
**subs
)
1951 struct isl_upoly_rec
*rec
;
1952 struct isl_upoly
*base
, *res
;
1957 if (isl_upoly_is_cst(up
))
1960 if (up
->var
< first
)
1963 rec
= isl_upoly_as_rec(up
);
1967 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
1969 if (up
->var
>= first
+ n
)
1970 base
= isl_upoly_var_pow(up
->ctx
, up
->var
, 1);
1972 base
= isl_upoly_copy(subs
[up
->var
- first
]);
1974 res
= isl_upoly_subs(isl_upoly_copy(rec
->p
[rec
->n
- 1]), first
, n
, subs
);
1975 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1976 struct isl_upoly
*t
;
1977 t
= isl_upoly_subs(isl_upoly_copy(rec
->p
[i
]), first
, n
, subs
);
1978 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
1979 res
= isl_upoly_sum(res
, t
);
1982 isl_upoly_free(base
);
1991 __isl_give
struct isl_upoly
*isl_upoly_from_affine(isl_ctx
*ctx
, isl_int
*f
,
1992 isl_int denom
, unsigned len
)
1995 struct isl_upoly
*up
;
1997 isl_assert(ctx
, len
>= 1, return NULL
);
1999 up
= isl_upoly_rat_cst(ctx
, f
[0], denom
);
2000 for (i
= 0; i
< len
- 1; ++i
) {
2001 struct isl_upoly
*t
;
2002 struct isl_upoly
*c
;
2004 if (isl_int_is_zero(f
[1 + i
]))
2007 c
= isl_upoly_rat_cst(ctx
, f
[1 + i
], denom
);
2008 t
= isl_upoly_var_pow(ctx
, i
, 1);
2009 t
= isl_upoly_mul(c
, t
);
2010 up
= isl_upoly_sum(up
, t
);
2016 /* Remove common factor of non-constant terms and denominator.
2018 static void normalize_div(__isl_keep isl_qpolynomial
*qp
, int div
)
2020 isl_ctx
*ctx
= qp
->div
->ctx
;
2021 unsigned total
= qp
->div
->n_col
- 2;
2023 isl_seq_gcd(qp
->div
->row
[div
] + 2, total
, &ctx
->normalize_gcd
);
2024 isl_int_gcd(ctx
->normalize_gcd
,
2025 ctx
->normalize_gcd
, qp
->div
->row
[div
][0]);
2026 if (isl_int_is_one(ctx
->normalize_gcd
))
2029 isl_seq_scale_down(qp
->div
->row
[div
] + 2, qp
->div
->row
[div
] + 2,
2030 ctx
->normalize_gcd
, total
);
2031 isl_int_divexact(qp
->div
->row
[div
][0], qp
->div
->row
[div
][0],
2032 ctx
->normalize_gcd
);
2033 isl_int_fdiv_q(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1],
2034 ctx
->normalize_gcd
);
2037 /* Replace the integer division identified by "div" by the polynomial "s".
2038 * The integer division is assumed not to appear in the definition
2039 * of any other integer divisions.
2041 static __isl_give isl_qpolynomial
*substitute_div(
2042 __isl_take isl_qpolynomial
*qp
,
2043 int div
, __isl_take
struct isl_upoly
*s
)
2052 qp
= isl_qpolynomial_cow(qp
);
2056 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
2057 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ div
, 1, &s
);
2061 reordering
= isl_alloc_array(qp
->dim
->ctx
, int, total
+ qp
->div
->n_row
);
2064 for (i
= 0; i
< total
+ div
; ++i
)
2066 for (i
= total
+ div
+ 1; i
< total
+ qp
->div
->n_row
; ++i
)
2067 reordering
[i
] = i
- 1;
2068 qp
->div
= isl_mat_drop_rows(qp
->div
, div
, 1);
2069 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + total
+ div
, 1);
2070 qp
->upoly
= reorder(qp
->upoly
, reordering
);
2073 if (!qp
->upoly
|| !qp
->div
)
2079 isl_qpolynomial_free(qp
);
2084 /* Replace all integer divisions [e/d] that turn out to not actually be integer
2085 * divisions because d is equal to 1 by their definition, i.e., e.
2087 static __isl_give isl_qpolynomial
*substitute_non_divs(
2088 __isl_take isl_qpolynomial
*qp
)
2092 struct isl_upoly
*s
;
2097 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
2098 for (i
= 0; qp
&& i
< qp
->div
->n_row
; ++i
) {
2099 if (!isl_int_is_one(qp
->div
->row
[i
][0]))
2101 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
2102 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
2104 isl_seq_combine(qp
->div
->row
[j
] + 1,
2105 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
2106 qp
->div
->row
[j
][2 + total
+ i
],
2107 qp
->div
->row
[i
] + 1, 1 + total
+ i
);
2108 isl_int_set_si(qp
->div
->row
[j
][2 + total
+ i
], 0);
2109 normalize_div(qp
, j
);
2111 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
2112 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
2113 qp
= substitute_div(qp
, i
, s
);
2120 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
2121 * with d the denominator. When replacing the coefficient e of x by
2122 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
2123 * inside the division, so we need to add floor(e/d) * x outside.
2124 * That is, we replace q by q' + floor(e/d) * x and we therefore need
2125 * to adjust the coefficient of x in each later div that depends on the
2126 * current div "div" and also in the affine expression "aff"
2127 * (if it too depends on "div").
2129 static void reduce_div(__isl_keep isl_qpolynomial
*qp
, int div
,
2130 __isl_keep isl_vec
*aff
)
2134 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
2137 for (i
= 0; i
< 1 + total
+ div
; ++i
) {
2138 if (isl_int_is_nonneg(qp
->div
->row
[div
][1 + i
]) &&
2139 isl_int_lt(qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]))
2141 isl_int_fdiv_q(v
, qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
2142 isl_int_fdiv_r(qp
->div
->row
[div
][1 + i
],
2143 qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
2144 if (!isl_int_is_zero(aff
->el
[1 + total
+ div
]))
2145 isl_int_addmul(aff
->el
[i
], v
, aff
->el
[1 + total
+ div
]);
2146 for (j
= div
+ 1; j
< qp
->div
->n_row
; ++j
) {
2147 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ div
]))
2149 isl_int_addmul(qp
->div
->row
[j
][1 + i
],
2150 v
, qp
->div
->row
[j
][2 + total
+ div
]);
2156 /* Check if the last non-zero coefficient is bigger that half of the
2157 * denominator. If so, we will invert the div to further reduce the number
2158 * of distinct divs that may appear.
2159 * If the last non-zero coefficient is exactly half the denominator,
2160 * then we continue looking for earlier coefficients that are bigger
2161 * than half the denominator.
2163 static int needs_invert(__isl_keep isl_mat
*div
, int row
)
2168 for (i
= div
->n_col
- 1; i
>= 1; --i
) {
2169 if (isl_int_is_zero(div
->row
[row
][i
]))
2171 isl_int_mul_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
2172 cmp
= isl_int_cmp(div
->row
[row
][i
], div
->row
[row
][0]);
2173 isl_int_divexact_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
2183 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
2184 * We only invert the coefficients of e (and the coefficient of q in
2185 * later divs and in "aff"). After calling this function, the
2186 * coefficients of e should be reduced again.
2188 static void invert_div(__isl_keep isl_qpolynomial
*qp
, int div
,
2189 __isl_keep isl_vec
*aff
)
2191 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
2193 isl_seq_neg(qp
->div
->row
[div
] + 1,
2194 qp
->div
->row
[div
] + 1, qp
->div
->n_col
- 1);
2195 isl_int_sub_ui(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1], 1);
2196 isl_int_add(qp
->div
->row
[div
][1],
2197 qp
->div
->row
[div
][1], qp
->div
->row
[div
][0]);
2198 if (!isl_int_is_zero(aff
->el
[1 + total
+ div
]))
2199 isl_int_neg(aff
->el
[1 + total
+ div
], aff
->el
[1 + total
+ div
]);
2200 isl_mat_col_mul(qp
->div
, 2 + total
+ div
,
2201 qp
->div
->ctx
->negone
, 2 + total
+ div
);
2204 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2205 * in the interval [0, d-1], with d the denominator and such that the
2206 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2208 * After the reduction, some divs may have become redundant or identical,
2209 * so we call substitute_non_divs and sort_divs. If these functions
2210 * eliminate divs or merge two or more divs into one, the coefficients
2211 * of the enclosing divs may have to be reduced again, so we call
2212 * ourselves recursively if the number of divs decreases.
2214 static __isl_give isl_qpolynomial
*reduce_divs(__isl_take isl_qpolynomial
*qp
)
2217 isl_vec
*aff
= NULL
;
2218 struct isl_upoly
*s
;
2224 aff
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
2225 aff
= isl_vec_clr(aff
);
2229 isl_int_set_si(aff
->el
[1 + qp
->upoly
->var
], 1);
2231 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2232 normalize_div(qp
, i
);
2233 reduce_div(qp
, i
, aff
);
2234 if (needs_invert(qp
->div
, i
)) {
2235 invert_div(qp
, i
, aff
);
2236 reduce_div(qp
, i
, aff
);
2240 s
= isl_upoly_from_affine(qp
->div
->ctx
, aff
->el
,
2241 qp
->div
->ctx
->one
, aff
->size
);
2242 qp
->upoly
= isl_upoly_subs(qp
->upoly
, qp
->upoly
->var
, 1, &s
);
2249 n_div
= qp
->div
->n_row
;
2250 qp
= substitute_non_divs(qp
);
2252 if (qp
&& qp
->div
->n_row
< n_div
)
2253 return reduce_divs(qp
);
2257 isl_qpolynomial_free(qp
);
2262 __isl_give isl_qpolynomial
*isl_qpolynomial_rat_cst_on_domain(
2263 __isl_take isl_space
*dim
, const isl_int n
, const isl_int d
)
2265 struct isl_qpolynomial
*qp
;
2266 struct isl_upoly_cst
*cst
;
2271 qp
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
2275 cst
= isl_upoly_as_cst(qp
->upoly
);
2276 isl_int_set(cst
->n
, n
);
2277 isl_int_set(cst
->d
, d
);
2282 /* Return an isl_qpolynomial that is equal to "val" on domain space "domain".
2284 __isl_give isl_qpolynomial
*isl_qpolynomial_val_on_domain(
2285 __isl_take isl_space
*domain
, __isl_take isl_val
*val
)
2287 isl_qpolynomial
*qp
;
2288 struct isl_upoly_cst
*cst
;
2290 if (!domain
|| !val
)
2293 qp
= isl_qpolynomial_alloc(domain
, 0, isl_upoly_zero(domain
->ctx
));
2297 cst
= isl_upoly_as_cst(qp
->upoly
);
2298 isl_int_set(cst
->n
, val
->n
);
2299 isl_int_set(cst
->d
, val
->d
);
2304 isl_space_free(domain
);
2309 static int up_set_active(__isl_keep
struct isl_upoly
*up
, int *active
, int d
)
2311 struct isl_upoly_rec
*rec
;
2317 if (isl_upoly_is_cst(up
))
2321 active
[up
->var
] = 1;
2323 rec
= isl_upoly_as_rec(up
);
2324 for (i
= 0; i
< rec
->n
; ++i
)
2325 if (up_set_active(rec
->p
[i
], active
, d
) < 0)
2331 static int set_active(__isl_keep isl_qpolynomial
*qp
, int *active
)
2334 int d
= isl_space_dim(qp
->dim
, isl_dim_all
);
2339 for (i
= 0; i
< d
; ++i
)
2340 for (j
= 0; j
< qp
->div
->n_row
; ++j
) {
2341 if (isl_int_is_zero(qp
->div
->row
[j
][2 + i
]))
2347 return up_set_active(qp
->upoly
, active
, d
);
2350 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial
*qp
,
2351 enum isl_dim_type type
, unsigned first
, unsigned n
)
2362 isl_assert(qp
->dim
->ctx
,
2363 first
+ n
<= isl_qpolynomial_dim(qp
, type
), return -1);
2364 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2365 type
== isl_dim_in
, return -1);
2367 active
= isl_calloc_array(qp
->dim
->ctx
, int,
2368 isl_space_dim(qp
->dim
, isl_dim_all
));
2369 if (set_active(qp
, active
) < 0)
2372 if (type
== isl_dim_in
)
2373 first
+= isl_space_dim(qp
->dim
, isl_dim_param
);
2374 for (i
= 0; i
< n
; ++i
)
2375 if (active
[first
+ i
]) {
2388 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2389 * of the divs that do appear in the quasi-polynomial.
2391 static __isl_give isl_qpolynomial
*remove_redundant_divs(
2392 __isl_take isl_qpolynomial
*qp
)
2399 int *reordering
= NULL
;
2406 if (qp
->div
->n_row
== 0)
2409 d
= isl_space_dim(qp
->dim
, isl_dim_all
);
2410 len
= qp
->div
->n_col
- 2;
2411 ctx
= isl_qpolynomial_get_ctx(qp
);
2412 active
= isl_calloc_array(ctx
, int, len
);
2416 if (up_set_active(qp
->upoly
, active
, len
) < 0)
2419 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
2420 if (!active
[d
+ i
]) {
2424 for (j
= 0; j
< i
; ++j
) {
2425 if (isl_int_is_zero(qp
->div
->row
[i
][2 + d
+ j
]))
2437 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
2441 for (i
= 0; i
< d
; ++i
)
2445 n_div
= qp
->div
->n_row
;
2446 for (i
= 0; i
< n_div
; ++i
) {
2447 if (!active
[d
+ i
]) {
2448 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
2449 qp
->div
= isl_mat_drop_cols(qp
->div
,
2450 2 + d
+ i
- skip
, 1);
2453 reordering
[d
+ i
] = d
+ i
- skip
;
2456 qp
->upoly
= reorder(qp
->upoly
, reordering
);
2458 if (!qp
->upoly
|| !qp
->div
)
2468 isl_qpolynomial_free(qp
);
2472 __isl_give
struct isl_upoly
*isl_upoly_drop(__isl_take
struct isl_upoly
*up
,
2473 unsigned first
, unsigned n
)
2476 struct isl_upoly_rec
*rec
;
2480 if (n
== 0 || up
->var
< 0 || up
->var
< first
)
2482 if (up
->var
< first
+ n
) {
2483 up
= replace_by_constant_term(up
);
2484 return isl_upoly_drop(up
, first
, n
);
2486 up
= isl_upoly_cow(up
);
2490 rec
= isl_upoly_as_rec(up
);
2494 for (i
= 0; i
< rec
->n
; ++i
) {
2495 rec
->p
[i
] = isl_upoly_drop(rec
->p
[i
], first
, n
);
2506 __isl_give isl_qpolynomial
*isl_qpolynomial_set_dim_name(
2507 __isl_take isl_qpolynomial
*qp
,
2508 enum isl_dim_type type
, unsigned pos
, const char *s
)
2510 qp
= isl_qpolynomial_cow(qp
);
2513 qp
->dim
= isl_space_set_dim_name(qp
->dim
, type
, pos
, s
);
2518 isl_qpolynomial_free(qp
);
2522 __isl_give isl_qpolynomial
*isl_qpolynomial_drop_dims(
2523 __isl_take isl_qpolynomial
*qp
,
2524 enum isl_dim_type type
, unsigned first
, unsigned n
)
2528 if (type
== isl_dim_out
)
2529 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
2530 "cannot drop output/set dimension",
2532 if (type
== isl_dim_in
)
2534 if (n
== 0 && !isl_space_is_named_or_nested(qp
->dim
, type
))
2537 qp
= isl_qpolynomial_cow(qp
);
2541 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_space_dim(qp
->dim
, type
),
2543 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2544 type
== isl_dim_set
, goto error
);
2546 qp
->dim
= isl_space_drop_dims(qp
->dim
, type
, first
, n
);
2550 if (type
== isl_dim_set
)
2551 first
+= isl_space_dim(qp
->dim
, isl_dim_param
);
2553 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + first
, n
);
2557 qp
->upoly
= isl_upoly_drop(qp
->upoly
, first
, n
);
2563 isl_qpolynomial_free(qp
);
2567 /* Project the domain of the quasi-polynomial onto its parameter space.
2568 * The quasi-polynomial may not involve any of the domain dimensions.
2570 __isl_give isl_qpolynomial
*isl_qpolynomial_project_domain_on_params(
2571 __isl_take isl_qpolynomial
*qp
)
2577 n
= isl_qpolynomial_dim(qp
, isl_dim_in
);
2578 involves
= isl_qpolynomial_involves_dims(qp
, isl_dim_in
, 0, n
);
2580 return isl_qpolynomial_free(qp
);
2582 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
2583 "polynomial involves some of the domain dimensions",
2584 return isl_qpolynomial_free(qp
));
2585 qp
= isl_qpolynomial_drop_dims(qp
, isl_dim_in
, 0, n
);
2586 space
= isl_qpolynomial_get_domain_space(qp
);
2587 space
= isl_space_params(space
);
2588 qp
= isl_qpolynomial_reset_domain_space(qp
, space
);
2592 static __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities_lifted(
2593 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2599 struct isl_upoly
*up
;
2603 if (eq
->n_eq
== 0) {
2604 isl_basic_set_free(eq
);
2608 qp
= isl_qpolynomial_cow(qp
);
2611 qp
->div
= isl_mat_cow(qp
->div
);
2615 total
= 1 + isl_space_dim(eq
->dim
, isl_dim_all
);
2617 isl_int_init(denom
);
2618 for (i
= 0; i
< eq
->n_eq
; ++i
) {
2619 j
= isl_seq_last_non_zero(eq
->eq
[i
], total
+ n_div
);
2620 if (j
< 0 || j
== 0 || j
>= total
)
2623 for (k
= 0; k
< qp
->div
->n_row
; ++k
) {
2624 if (isl_int_is_zero(qp
->div
->row
[k
][1 + j
]))
2626 isl_seq_elim(qp
->div
->row
[k
] + 1, eq
->eq
[i
], j
, total
,
2627 &qp
->div
->row
[k
][0]);
2628 normalize_div(qp
, k
);
2631 if (isl_int_is_pos(eq
->eq
[i
][j
]))
2632 isl_seq_neg(eq
->eq
[i
], eq
->eq
[i
], total
);
2633 isl_int_abs(denom
, eq
->eq
[i
][j
]);
2634 isl_int_set_si(eq
->eq
[i
][j
], 0);
2636 up
= isl_upoly_from_affine(qp
->dim
->ctx
,
2637 eq
->eq
[i
], denom
, total
);
2638 qp
->upoly
= isl_upoly_subs(qp
->upoly
, j
- 1, 1, &up
);
2641 isl_int_clear(denom
);
2646 isl_basic_set_free(eq
);
2648 qp
= substitute_non_divs(qp
);
2653 isl_basic_set_free(eq
);
2654 isl_qpolynomial_free(qp
);
2658 /* Exploit the equalities in "eq" to simplify the quasi-polynomial.
2660 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities(
2661 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2665 if (qp
->div
->n_row
> 0)
2666 eq
= isl_basic_set_add_dims(eq
, isl_dim_set
, qp
->div
->n_row
);
2667 return isl_qpolynomial_substitute_equalities_lifted(qp
, eq
);
2669 isl_basic_set_free(eq
);
2670 isl_qpolynomial_free(qp
);
2674 static __isl_give isl_basic_set
*add_div_constraints(
2675 __isl_take isl_basic_set
*bset
, __isl_take isl_mat
*div
)
2683 bset
= isl_basic_set_extend_constraints(bset
, 0, 2 * div
->n_row
);
2686 total
= isl_basic_set_total_dim(bset
);
2687 for (i
= 0; i
< div
->n_row
; ++i
)
2688 if (isl_basic_set_add_div_constraints_var(bset
,
2689 total
- div
->n_row
+ i
, div
->row
[i
]) < 0)
2696 isl_basic_set_free(bset
);
2700 /* Look for equalities among the variables shared by context and qp
2701 * and the integer divisions of qp, if any.
2702 * The equalities are then used to eliminate variables and/or integer
2703 * divisions from qp.
2705 __isl_give isl_qpolynomial
*isl_qpolynomial_gist(
2706 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
2712 if (qp
->div
->n_row
> 0) {
2713 isl_basic_set
*bset
;
2714 context
= isl_set_add_dims(context
, isl_dim_set
,
2716 bset
= isl_basic_set_universe(isl_set_get_space(context
));
2717 bset
= add_div_constraints(bset
, isl_mat_copy(qp
->div
));
2718 context
= isl_set_intersect(context
,
2719 isl_set_from_basic_set(bset
));
2722 aff
= isl_set_affine_hull(context
);
2723 return isl_qpolynomial_substitute_equalities_lifted(qp
, aff
);
2725 isl_qpolynomial_free(qp
);
2726 isl_set_free(context
);
2730 __isl_give isl_qpolynomial
*isl_qpolynomial_gist_params(
2731 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
2733 isl_space
*space
= isl_qpolynomial_get_domain_space(qp
);
2734 isl_set
*dom_context
= isl_set_universe(space
);
2735 dom_context
= isl_set_intersect_params(dom_context
, context
);
2736 return isl_qpolynomial_gist(qp
, dom_context
);
2739 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_from_qpolynomial(
2740 __isl_take isl_qpolynomial
*qp
)
2746 if (isl_qpolynomial_is_zero(qp
)) {
2747 isl_space
*dim
= isl_qpolynomial_get_space(qp
);
2748 isl_qpolynomial_free(qp
);
2749 return isl_pw_qpolynomial_zero(dim
);
2752 dom
= isl_set_universe(isl_qpolynomial_get_domain_space(qp
));
2753 return isl_pw_qpolynomial_alloc(dom
, qp
);
2757 #define PW isl_pw_qpolynomial
2759 #define EL isl_qpolynomial
2761 #define EL_IS_ZERO is_zero
2765 #define IS_ZERO is_zero
2768 #undef DEFAULT_IS_ZERO
2769 #define DEFAULT_IS_ZERO 1
2773 #include <isl_pw_templ.c>
2776 #define UNION isl_union_pw_qpolynomial
2778 #define PART isl_pw_qpolynomial
2780 #define PARTS pw_qpolynomial
2781 #define ALIGN_DOMAIN
2783 #include <isl_union_templ.c>
2785 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial
*pwqp
)
2793 if (!isl_set_plain_is_universe(pwqp
->p
[0].set
))
2796 return isl_qpolynomial_is_one(pwqp
->p
[0].qp
);
2799 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add(
2800 __isl_take isl_pw_qpolynomial
*pwqp1
,
2801 __isl_take isl_pw_qpolynomial
*pwqp2
)
2803 return isl_pw_qpolynomial_union_add_(pwqp1
, pwqp2
);
2806 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_mul(
2807 __isl_take isl_pw_qpolynomial
*pwqp1
,
2808 __isl_take isl_pw_qpolynomial
*pwqp2
)
2811 struct isl_pw_qpolynomial
*res
;
2813 if (!pwqp1
|| !pwqp2
)
2816 isl_assert(pwqp1
->dim
->ctx
, isl_space_is_equal(pwqp1
->dim
, pwqp2
->dim
),
2819 if (isl_pw_qpolynomial_is_zero(pwqp1
)) {
2820 isl_pw_qpolynomial_free(pwqp2
);
2824 if (isl_pw_qpolynomial_is_zero(pwqp2
)) {
2825 isl_pw_qpolynomial_free(pwqp1
);
2829 if (isl_pw_qpolynomial_is_one(pwqp1
)) {
2830 isl_pw_qpolynomial_free(pwqp1
);
2834 if (isl_pw_qpolynomial_is_one(pwqp2
)) {
2835 isl_pw_qpolynomial_free(pwqp2
);
2839 n
= pwqp1
->n
* pwqp2
->n
;
2840 res
= isl_pw_qpolynomial_alloc_size(isl_space_copy(pwqp1
->dim
), n
);
2842 for (i
= 0; i
< pwqp1
->n
; ++i
) {
2843 for (j
= 0; j
< pwqp2
->n
; ++j
) {
2844 struct isl_set
*common
;
2845 struct isl_qpolynomial
*prod
;
2846 common
= isl_set_intersect(isl_set_copy(pwqp1
->p
[i
].set
),
2847 isl_set_copy(pwqp2
->p
[j
].set
));
2848 if (isl_set_plain_is_empty(common
)) {
2849 isl_set_free(common
);
2853 prod
= isl_qpolynomial_mul(
2854 isl_qpolynomial_copy(pwqp1
->p
[i
].qp
),
2855 isl_qpolynomial_copy(pwqp2
->p
[j
].qp
));
2857 res
= isl_pw_qpolynomial_add_piece(res
, common
, prod
);
2861 isl_pw_qpolynomial_free(pwqp1
);
2862 isl_pw_qpolynomial_free(pwqp2
);
2866 isl_pw_qpolynomial_free(pwqp1
);
2867 isl_pw_qpolynomial_free(pwqp2
);
2871 __isl_give
struct isl_upoly
*isl_upoly_eval(
2872 __isl_take
struct isl_upoly
*up
, __isl_take isl_vec
*vec
)
2875 struct isl_upoly_rec
*rec
;
2876 struct isl_upoly
*res
;
2877 struct isl_upoly
*base
;
2879 if (isl_upoly_is_cst(up
)) {
2884 rec
= isl_upoly_as_rec(up
);
2888 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
2890 base
= isl_upoly_rat_cst(up
->ctx
, vec
->el
[1 + up
->var
], vec
->el
[0]);
2892 res
= isl_upoly_eval(isl_upoly_copy(rec
->p
[rec
->n
- 1]),
2895 for (i
= rec
->n
- 2; i
>= 0; --i
) {
2896 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
2897 res
= isl_upoly_sum(res
,
2898 isl_upoly_eval(isl_upoly_copy(rec
->p
[i
]),
2899 isl_vec_copy(vec
)));
2902 isl_upoly_free(base
);
2912 __isl_give isl_qpolynomial
*isl_qpolynomial_eval(
2913 __isl_take isl_qpolynomial
*qp
, __isl_take isl_point
*pnt
)
2916 struct isl_upoly
*up
;
2921 isl_assert(pnt
->dim
->ctx
, isl_space_is_equal(pnt
->dim
, qp
->dim
), goto error
);
2923 if (qp
->div
->n_row
== 0)
2924 ext
= isl_vec_copy(pnt
->vec
);
2927 unsigned dim
= isl_space_dim(qp
->dim
, isl_dim_all
);
2928 ext
= isl_vec_alloc(qp
->dim
->ctx
, 1 + dim
+ qp
->div
->n_row
);
2932 isl_seq_cpy(ext
->el
, pnt
->vec
->el
, pnt
->vec
->size
);
2933 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2934 isl_seq_inner_product(qp
->div
->row
[i
] + 1, ext
->el
,
2935 1 + dim
+ i
, &ext
->el
[1+dim
+i
]);
2936 isl_int_fdiv_q(ext
->el
[1+dim
+i
], ext
->el
[1+dim
+i
],
2937 qp
->div
->row
[i
][0]);
2941 up
= isl_upoly_eval(isl_upoly_copy(qp
->upoly
), ext
);
2945 dim
= isl_space_copy(qp
->dim
);
2946 isl_qpolynomial_free(qp
);
2947 isl_point_free(pnt
);
2949 return isl_qpolynomial_alloc(dim
, 0, up
);
2951 isl_qpolynomial_free(qp
);
2952 isl_point_free(pnt
);
2956 int isl_upoly_cmp(__isl_keep
struct isl_upoly_cst
*cst1
,
2957 __isl_keep
struct isl_upoly_cst
*cst2
)
2962 isl_int_mul(t
, cst1
->n
, cst2
->d
);
2963 isl_int_submul(t
, cst2
->n
, cst1
->d
);
2964 cmp
= isl_int_sgn(t
);
2969 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial
*qp1
,
2970 __isl_keep isl_qpolynomial
*qp2
)
2972 struct isl_upoly_cst
*cst1
, *cst2
;
2976 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), return -1);
2977 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), return -1);
2978 if (isl_qpolynomial_is_nan(qp1
))
2980 if (isl_qpolynomial_is_nan(qp2
))
2982 cst1
= isl_upoly_as_cst(qp1
->upoly
);
2983 cst2
= isl_upoly_as_cst(qp2
->upoly
);
2985 return isl_upoly_cmp(cst1
, cst2
) <= 0;
2988 __isl_give isl_qpolynomial
*isl_qpolynomial_min_cst(
2989 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
2991 struct isl_upoly_cst
*cst1
, *cst2
;
2996 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), goto error
);
2997 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), goto error
);
2998 cst1
= isl_upoly_as_cst(qp1
->upoly
);
2999 cst2
= isl_upoly_as_cst(qp2
->upoly
);
3000 cmp
= isl_upoly_cmp(cst1
, cst2
);
3003 isl_qpolynomial_free(qp2
);
3005 isl_qpolynomial_free(qp1
);
3010 isl_qpolynomial_free(qp1
);
3011 isl_qpolynomial_free(qp2
);
3015 __isl_give isl_qpolynomial
*isl_qpolynomial_max_cst(
3016 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
3018 struct isl_upoly_cst
*cst1
, *cst2
;
3023 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), goto error
);
3024 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), goto error
);
3025 cst1
= isl_upoly_as_cst(qp1
->upoly
);
3026 cst2
= isl_upoly_as_cst(qp2
->upoly
);
3027 cmp
= isl_upoly_cmp(cst1
, cst2
);
3030 isl_qpolynomial_free(qp2
);
3032 isl_qpolynomial_free(qp1
);
3037 isl_qpolynomial_free(qp1
);
3038 isl_qpolynomial_free(qp2
);
3042 __isl_give isl_qpolynomial
*isl_qpolynomial_insert_dims(
3043 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
,
3044 unsigned first
, unsigned n
)
3052 if (type
== isl_dim_out
)
3053 isl_die(qp
->div
->ctx
, isl_error_invalid
,
3054 "cannot insert output/set dimensions",
3056 if (type
== isl_dim_in
)
3058 if (n
== 0 && !isl_space_is_named_or_nested(qp
->dim
, type
))
3061 qp
= isl_qpolynomial_cow(qp
);
3065 isl_assert(qp
->div
->ctx
, first
<= isl_space_dim(qp
->dim
, type
),
3068 g_pos
= pos(qp
->dim
, type
) + first
;
3070 qp
->div
= isl_mat_insert_zero_cols(qp
->div
, 2 + g_pos
, n
);
3074 total
= qp
->div
->n_col
- 2;
3075 if (total
> g_pos
) {
3077 exp
= isl_alloc_array(qp
->div
->ctx
, int, total
- g_pos
);
3080 for (i
= 0; i
< total
- g_pos
; ++i
)
3082 qp
->upoly
= expand(qp
->upoly
, exp
, g_pos
);
3088 qp
->dim
= isl_space_insert_dims(qp
->dim
, type
, first
, n
);
3094 isl_qpolynomial_free(qp
);
3098 __isl_give isl_qpolynomial
*isl_qpolynomial_add_dims(
3099 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
, unsigned n
)
3103 pos
= isl_qpolynomial_dim(qp
, type
);
3105 return isl_qpolynomial_insert_dims(qp
, type
, pos
, n
);
3108 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add_dims(
3109 __isl_take isl_pw_qpolynomial
*pwqp
,
3110 enum isl_dim_type type
, unsigned n
)
3114 pos
= isl_pw_qpolynomial_dim(pwqp
, type
);
3116 return isl_pw_qpolynomial_insert_dims(pwqp
, type
, pos
, n
);
3119 static int *reordering_move(isl_ctx
*ctx
,
3120 unsigned len
, unsigned dst
, unsigned src
, unsigned n
)
3125 reordering
= isl_alloc_array(ctx
, int, len
);
3130 for (i
= 0; i
< dst
; ++i
)
3132 for (i
= 0; i
< n
; ++i
)
3133 reordering
[src
+ i
] = dst
+ i
;
3134 for (i
= 0; i
< src
- dst
; ++i
)
3135 reordering
[dst
+ i
] = dst
+ n
+ i
;
3136 for (i
= 0; i
< len
- src
- n
; ++i
)
3137 reordering
[src
+ n
+ i
] = src
+ n
+ i
;
3139 for (i
= 0; i
< src
; ++i
)
3141 for (i
= 0; i
< n
; ++i
)
3142 reordering
[src
+ i
] = dst
+ i
;
3143 for (i
= 0; i
< dst
- src
; ++i
)
3144 reordering
[src
+ n
+ i
] = src
+ i
;
3145 for (i
= 0; i
< len
- dst
- n
; ++i
)
3146 reordering
[dst
+ n
+ i
] = dst
+ n
+ i
;
3152 __isl_give isl_qpolynomial
*isl_qpolynomial_move_dims(
3153 __isl_take isl_qpolynomial
*qp
,
3154 enum isl_dim_type dst_type
, unsigned dst_pos
,
3155 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
3161 qp
= isl_qpolynomial_cow(qp
);
3165 if (dst_type
== isl_dim_out
|| src_type
== isl_dim_out
)
3166 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
3167 "cannot move output/set dimension",
3169 if (dst_type
== isl_dim_in
)
3170 dst_type
= isl_dim_set
;
3171 if (src_type
== isl_dim_in
)
3172 src_type
= isl_dim_set
;
3174 isl_assert(qp
->dim
->ctx
, src_pos
+ n
<= isl_space_dim(qp
->dim
, src_type
),
3177 g_dst_pos
= pos(qp
->dim
, dst_type
) + dst_pos
;
3178 g_src_pos
= pos(qp
->dim
, src_type
) + src_pos
;
3179 if (dst_type
> src_type
)
3182 qp
->div
= isl_mat_move_cols(qp
->div
, 2 + g_dst_pos
, 2 + g_src_pos
, n
);
3189 reordering
= reordering_move(qp
->dim
->ctx
,
3190 qp
->div
->n_col
- 2, g_dst_pos
, g_src_pos
, n
);
3194 qp
->upoly
= reorder(qp
->upoly
, reordering
);
3199 qp
->dim
= isl_space_move_dims(qp
->dim
, dst_type
, dst_pos
, src_type
, src_pos
, n
);
3205 isl_qpolynomial_free(qp
);
3209 __isl_give isl_qpolynomial
*isl_qpolynomial_from_affine(__isl_take isl_space
*dim
,
3210 isl_int
*f
, isl_int denom
)
3212 struct isl_upoly
*up
;
3214 dim
= isl_space_domain(dim
);
3218 up
= isl_upoly_from_affine(dim
->ctx
, f
, denom
,
3219 1 + isl_space_dim(dim
, isl_dim_all
));
3221 return isl_qpolynomial_alloc(dim
, 0, up
);
3224 __isl_give isl_qpolynomial
*isl_qpolynomial_from_aff(__isl_take isl_aff
*aff
)
3227 struct isl_upoly
*up
;
3228 isl_qpolynomial
*qp
;
3233 ctx
= isl_aff_get_ctx(aff
);
3234 up
= isl_upoly_from_affine(ctx
, aff
->v
->el
+ 1, aff
->v
->el
[0],
3237 qp
= isl_qpolynomial_alloc(isl_aff_get_domain_space(aff
),
3238 aff
->ls
->div
->n_row
, up
);
3242 isl_mat_free(qp
->div
);
3243 qp
->div
= isl_mat_copy(aff
->ls
->div
);
3244 qp
->div
= isl_mat_cow(qp
->div
);
3249 qp
= reduce_divs(qp
);
3250 qp
= remove_redundant_divs(qp
);
3257 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_from_pw_aff(
3258 __isl_take isl_pw_aff
*pwaff
)
3261 isl_pw_qpolynomial
*pwqp
;
3266 pwqp
= isl_pw_qpolynomial_alloc_size(isl_pw_aff_get_space(pwaff
),
3269 for (i
= 0; i
< pwaff
->n
; ++i
) {
3271 isl_qpolynomial
*qp
;
3273 dom
= isl_set_copy(pwaff
->p
[i
].set
);
3274 qp
= isl_qpolynomial_from_aff(isl_aff_copy(pwaff
->p
[i
].aff
));
3275 pwqp
= isl_pw_qpolynomial_add_piece(pwqp
, dom
, qp
);
3278 isl_pw_aff_free(pwaff
);
3282 __isl_give isl_qpolynomial
*isl_qpolynomial_from_constraint(
3283 __isl_take isl_constraint
*c
, enum isl_dim_type type
, unsigned pos
)
3287 aff
= isl_constraint_get_bound(c
, type
, pos
);
3288 isl_constraint_free(c
);
3289 return isl_qpolynomial_from_aff(aff
);
3292 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3293 * in "qp" by subs[i].
3295 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute(
3296 __isl_take isl_qpolynomial
*qp
,
3297 enum isl_dim_type type
, unsigned first
, unsigned n
,
3298 __isl_keep isl_qpolynomial
**subs
)
3301 struct isl_upoly
**ups
;
3306 qp
= isl_qpolynomial_cow(qp
);
3310 if (type
== isl_dim_out
)
3311 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
3312 "cannot substitute output/set dimension",
3314 if (type
== isl_dim_in
)
3317 for (i
= 0; i
< n
; ++i
)
3321 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_space_dim(qp
->dim
, type
),
3324 for (i
= 0; i
< n
; ++i
)
3325 isl_assert(qp
->dim
->ctx
, isl_space_is_equal(qp
->dim
, subs
[i
]->dim
),
3328 isl_assert(qp
->dim
->ctx
, qp
->div
->n_row
== 0, goto error
);
3329 for (i
= 0; i
< n
; ++i
)
3330 isl_assert(qp
->dim
->ctx
, subs
[i
]->div
->n_row
== 0, goto error
);
3332 first
+= pos(qp
->dim
, type
);
3334 ups
= isl_alloc_array(qp
->dim
->ctx
, struct isl_upoly
*, n
);
3337 for (i
= 0; i
< n
; ++i
)
3338 ups
[i
] = subs
[i
]->upoly
;
3340 qp
->upoly
= isl_upoly_subs(qp
->upoly
, first
, n
, ups
);
3349 isl_qpolynomial_free(qp
);
3353 /* Extend "bset" with extra set dimensions for each integer division
3354 * in "qp" and then call "fn" with the extended bset and the polynomial
3355 * that results from replacing each of the integer divisions by the
3356 * corresponding extra set dimension.
3358 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial
*qp
,
3359 __isl_keep isl_basic_set
*bset
,
3360 int (*fn
)(__isl_take isl_basic_set
*bset
,
3361 __isl_take isl_qpolynomial
*poly
, void *user
), void *user
)
3365 isl_qpolynomial
*poly
;
3369 if (qp
->div
->n_row
== 0)
3370 return fn(isl_basic_set_copy(bset
), isl_qpolynomial_copy(qp
),
3373 div
= isl_mat_copy(qp
->div
);
3374 dim
= isl_space_copy(qp
->dim
);
3375 dim
= isl_space_add_dims(dim
, isl_dim_set
, qp
->div
->n_row
);
3376 poly
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_copy(qp
->upoly
));
3377 bset
= isl_basic_set_copy(bset
);
3378 bset
= isl_basic_set_add_dims(bset
, isl_dim_set
, qp
->div
->n_row
);
3379 bset
= add_div_constraints(bset
, div
);
3381 return fn(bset
, poly
, user
);
3386 /* Return total degree in variables first (inclusive) up to last (exclusive).
3388 int isl_upoly_degree(__isl_keep
struct isl_upoly
*up
, int first
, int last
)
3392 struct isl_upoly_rec
*rec
;
3396 if (isl_upoly_is_zero(up
))
3398 if (isl_upoly_is_cst(up
) || up
->var
< first
)
3401 rec
= isl_upoly_as_rec(up
);
3405 for (i
= 0; i
< rec
->n
; ++i
) {
3408 if (isl_upoly_is_zero(rec
->p
[i
]))
3410 d
= isl_upoly_degree(rec
->p
[i
], first
, last
);
3420 /* Return total degree in set variables.
3422 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial
*poly
)
3430 ovar
= isl_space_offset(poly
->dim
, isl_dim_set
);
3431 nvar
= isl_space_dim(poly
->dim
, isl_dim_set
);
3432 return isl_upoly_degree(poly
->upoly
, ovar
, ovar
+ nvar
);
3435 __isl_give
struct isl_upoly
*isl_upoly_coeff(__isl_keep
struct isl_upoly
*up
,
3436 unsigned pos
, int deg
)
3439 struct isl_upoly_rec
*rec
;
3444 if (isl_upoly_is_cst(up
) || up
->var
< pos
) {
3446 return isl_upoly_copy(up
);
3448 return isl_upoly_zero(up
->ctx
);
3451 rec
= isl_upoly_as_rec(up
);
3455 if (up
->var
== pos
) {
3457 return isl_upoly_copy(rec
->p
[deg
]);
3459 return isl_upoly_zero(up
->ctx
);
3462 up
= isl_upoly_copy(up
);
3463 up
= isl_upoly_cow(up
);
3464 rec
= isl_upoly_as_rec(up
);
3468 for (i
= 0; i
< rec
->n
; ++i
) {
3469 struct isl_upoly
*t
;
3470 t
= isl_upoly_coeff(rec
->p
[i
], pos
, deg
);
3473 isl_upoly_free(rec
->p
[i
]);
3483 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3485 __isl_give isl_qpolynomial
*isl_qpolynomial_coeff(
3486 __isl_keep isl_qpolynomial
*qp
,
3487 enum isl_dim_type type
, unsigned t_pos
, int deg
)
3490 struct isl_upoly
*up
;
3496 if (type
== isl_dim_out
)
3497 isl_die(qp
->div
->ctx
, isl_error_invalid
,
3498 "output/set dimension does not have a coefficient",
3500 if (type
== isl_dim_in
)
3503 isl_assert(qp
->div
->ctx
, t_pos
< isl_space_dim(qp
->dim
, type
),
3506 g_pos
= pos(qp
->dim
, type
) + t_pos
;
3507 up
= isl_upoly_coeff(qp
->upoly
, g_pos
, deg
);
3509 c
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
), qp
->div
->n_row
, up
);
3512 isl_mat_free(c
->div
);
3513 c
->div
= isl_mat_copy(qp
->div
);
3518 isl_qpolynomial_free(c
);
3522 /* Homogenize the polynomial in the variables first (inclusive) up to
3523 * last (exclusive) by inserting powers of variable first.
3524 * Variable first is assumed not to appear in the input.
3526 __isl_give
struct isl_upoly
*isl_upoly_homogenize(
3527 __isl_take
struct isl_upoly
*up
, int deg
, int target
,
3528 int first
, int last
)
3531 struct isl_upoly_rec
*rec
;
3535 if (isl_upoly_is_zero(up
))
3539 if (isl_upoly_is_cst(up
) || up
->var
< first
) {
3540 struct isl_upoly
*hom
;
3542 hom
= isl_upoly_var_pow(up
->ctx
, first
, target
- deg
);
3545 rec
= isl_upoly_as_rec(hom
);
3546 rec
->p
[target
- deg
] = isl_upoly_mul(rec
->p
[target
- deg
], up
);
3551 up
= isl_upoly_cow(up
);
3552 rec
= isl_upoly_as_rec(up
);
3556 for (i
= 0; i
< rec
->n
; ++i
) {
3557 if (isl_upoly_is_zero(rec
->p
[i
]))
3559 rec
->p
[i
] = isl_upoly_homogenize(rec
->p
[i
],
3560 up
->var
< last
? deg
+ i
: i
, target
,
3572 /* Homogenize the polynomial in the set variables by introducing
3573 * powers of an extra set variable at position 0.
3575 __isl_give isl_qpolynomial
*isl_qpolynomial_homogenize(
3576 __isl_take isl_qpolynomial
*poly
)
3580 int deg
= isl_qpolynomial_degree(poly
);
3585 poly
= isl_qpolynomial_insert_dims(poly
, isl_dim_in
, 0, 1);
3586 poly
= isl_qpolynomial_cow(poly
);
3590 ovar
= isl_space_offset(poly
->dim
, isl_dim_set
);
3591 nvar
= isl_space_dim(poly
->dim
, isl_dim_set
);
3592 poly
->upoly
= isl_upoly_homogenize(poly
->upoly
, 0, deg
,
3599 isl_qpolynomial_free(poly
);
3603 __isl_give isl_term
*isl_term_alloc(__isl_take isl_space
*dim
,
3604 __isl_take isl_mat
*div
)
3612 n
= isl_space_dim(dim
, isl_dim_all
) + div
->n_row
;
3614 term
= isl_calloc(dim
->ctx
, struct isl_term
,
3615 sizeof(struct isl_term
) + (n
- 1) * sizeof(int));
3622 isl_int_init(term
->n
);
3623 isl_int_init(term
->d
);
3627 isl_space_free(dim
);
3632 __isl_give isl_term
*isl_term_copy(__isl_keep isl_term
*term
)
3641 __isl_give isl_term
*isl_term_dup(__isl_keep isl_term
*term
)
3650 total
= isl_space_dim(term
->dim
, isl_dim_all
) + term
->div
->n_row
;
3652 dup
= isl_term_alloc(isl_space_copy(term
->dim
), isl_mat_copy(term
->div
));
3656 isl_int_set(dup
->n
, term
->n
);
3657 isl_int_set(dup
->d
, term
->d
);
3659 for (i
= 0; i
< total
; ++i
)
3660 dup
->pow
[i
] = term
->pow
[i
];
3665 __isl_give isl_term
*isl_term_cow(__isl_take isl_term
*term
)
3673 return isl_term_dup(term
);
3676 void isl_term_free(__isl_take isl_term
*term
)
3681 if (--term
->ref
> 0)
3684 isl_space_free(term
->dim
);
3685 isl_mat_free(term
->div
);
3686 isl_int_clear(term
->n
);
3687 isl_int_clear(term
->d
);
3691 unsigned isl_term_dim(__isl_keep isl_term
*term
, enum isl_dim_type type
)
3699 case isl_dim_out
: return isl_space_dim(term
->dim
, type
);
3700 case isl_dim_div
: return term
->div
->n_row
;
3701 case isl_dim_all
: return isl_space_dim(term
->dim
, isl_dim_all
) +
3707 isl_ctx
*isl_term_get_ctx(__isl_keep isl_term
*term
)
3709 return term
? term
->dim
->ctx
: NULL
;
3712 void isl_term_get_num(__isl_keep isl_term
*term
, isl_int
*n
)
3716 isl_int_set(*n
, term
->n
);
3719 void isl_term_get_den(__isl_keep isl_term
*term
, isl_int
*d
)
3723 isl_int_set(*d
, term
->d
);
3726 /* Return the coefficient of the term "term".
3728 __isl_give isl_val
*isl_term_get_coefficient_val(__isl_keep isl_term
*term
)
3733 return isl_val_rat_from_isl_int(isl_term_get_ctx(term
),
3737 int isl_term_get_exp(__isl_keep isl_term
*term
,
3738 enum isl_dim_type type
, unsigned pos
)
3743 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, type
), return -1);
3745 if (type
>= isl_dim_set
)
3746 pos
+= isl_space_dim(term
->dim
, isl_dim_param
);
3747 if (type
>= isl_dim_div
)
3748 pos
+= isl_space_dim(term
->dim
, isl_dim_set
);
3750 return term
->pow
[pos
];
3753 __isl_give isl_aff
*isl_term_get_div(__isl_keep isl_term
*term
, unsigned pos
)
3755 isl_local_space
*ls
;
3761 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, isl_dim_div
),
3764 ls
= isl_local_space_alloc_div(isl_space_copy(term
->dim
),
3765 isl_mat_copy(term
->div
));
3766 aff
= isl_aff_alloc(ls
);
3770 isl_seq_cpy(aff
->v
->el
, term
->div
->row
[pos
], aff
->v
->size
);
3772 aff
= isl_aff_normalize(aff
);
3777 __isl_give isl_term
*isl_upoly_foreach_term(__isl_keep
struct isl_upoly
*up
,
3778 int (*fn
)(__isl_take isl_term
*term
, void *user
),
3779 __isl_take isl_term
*term
, void *user
)
3782 struct isl_upoly_rec
*rec
;
3787 if (isl_upoly_is_zero(up
))
3790 isl_assert(up
->ctx
, !isl_upoly_is_nan(up
), goto error
);
3791 isl_assert(up
->ctx
, !isl_upoly_is_infty(up
), goto error
);
3792 isl_assert(up
->ctx
, !isl_upoly_is_neginfty(up
), goto error
);
3794 if (isl_upoly_is_cst(up
)) {
3795 struct isl_upoly_cst
*cst
;
3796 cst
= isl_upoly_as_cst(up
);
3799 term
= isl_term_cow(term
);
3802 isl_int_set(term
->n
, cst
->n
);
3803 isl_int_set(term
->d
, cst
->d
);
3804 if (fn(isl_term_copy(term
), user
) < 0)
3809 rec
= isl_upoly_as_rec(up
);
3813 for (i
= 0; i
< rec
->n
; ++i
) {
3814 term
= isl_term_cow(term
);
3817 term
->pow
[up
->var
] = i
;
3818 term
= isl_upoly_foreach_term(rec
->p
[i
], fn
, term
, user
);
3822 term
->pow
[up
->var
] = 0;
3826 isl_term_free(term
);
3830 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial
*qp
,
3831 int (*fn
)(__isl_take isl_term
*term
, void *user
), void *user
)
3838 term
= isl_term_alloc(isl_space_copy(qp
->dim
), isl_mat_copy(qp
->div
));
3842 term
= isl_upoly_foreach_term(qp
->upoly
, fn
, term
, user
);
3844 isl_term_free(term
);
3846 return term
? 0 : -1;
3849 __isl_give isl_qpolynomial
*isl_qpolynomial_from_term(__isl_take isl_term
*term
)
3851 struct isl_upoly
*up
;
3852 isl_qpolynomial
*qp
;
3858 n
= isl_space_dim(term
->dim
, isl_dim_all
) + term
->div
->n_row
;
3860 up
= isl_upoly_rat_cst(term
->dim
->ctx
, term
->n
, term
->d
);
3861 for (i
= 0; i
< n
; ++i
) {
3864 up
= isl_upoly_mul(up
,
3865 isl_upoly_var_pow(term
->dim
->ctx
, i
, term
->pow
[i
]));
3868 qp
= isl_qpolynomial_alloc(isl_space_copy(term
->dim
), term
->div
->n_row
, up
);
3871 isl_mat_free(qp
->div
);
3872 qp
->div
= isl_mat_copy(term
->div
);
3876 isl_term_free(term
);
3879 isl_qpolynomial_free(qp
);
3880 isl_term_free(term
);
3884 __isl_give isl_qpolynomial
*isl_qpolynomial_lift(__isl_take isl_qpolynomial
*qp
,
3885 __isl_take isl_space
*dim
)
3894 if (isl_space_is_equal(qp
->dim
, dim
)) {
3895 isl_space_free(dim
);
3899 qp
= isl_qpolynomial_cow(qp
);
3903 extra
= isl_space_dim(dim
, isl_dim_set
) -
3904 isl_space_dim(qp
->dim
, isl_dim_set
);
3905 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
3906 if (qp
->div
->n_row
) {
3909 exp
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
3912 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3914 qp
->upoly
= expand(qp
->upoly
, exp
, total
);
3919 qp
->div
= isl_mat_insert_cols(qp
->div
, 2 + total
, extra
);
3922 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3923 isl_seq_clr(qp
->div
->row
[i
] + 2 + total
, extra
);
3925 isl_space_free(qp
->dim
);
3930 isl_space_free(dim
);
3931 isl_qpolynomial_free(qp
);
3935 /* For each parameter or variable that does not appear in qp,
3936 * first eliminate the variable from all constraints and then set it to zero.
3938 static __isl_give isl_set
*fix_inactive(__isl_take isl_set
*set
,
3939 __isl_keep isl_qpolynomial
*qp
)
3950 d
= isl_space_dim(set
->dim
, isl_dim_all
);
3951 active
= isl_calloc_array(set
->ctx
, int, d
);
3952 if (set_active(qp
, active
) < 0)
3955 for (i
= 0; i
< d
; ++i
)
3964 nparam
= isl_space_dim(set
->dim
, isl_dim_param
);
3965 nvar
= isl_space_dim(set
->dim
, isl_dim_set
);
3966 for (i
= 0; i
< nparam
; ++i
) {
3969 set
= isl_set_eliminate(set
, isl_dim_param
, i
, 1);
3970 set
= isl_set_fix_si(set
, isl_dim_param
, i
, 0);
3972 for (i
= 0; i
< nvar
; ++i
) {
3973 if (active
[nparam
+ i
])
3975 set
= isl_set_eliminate(set
, isl_dim_set
, i
, 1);
3976 set
= isl_set_fix_si(set
, isl_dim_set
, i
, 0);
3988 struct isl_opt_data
{
3989 isl_qpolynomial
*qp
;
3991 isl_qpolynomial
*opt
;
3995 static int opt_fn(__isl_take isl_point
*pnt
, void *user
)
3997 struct isl_opt_data
*data
= (struct isl_opt_data
*)user
;
3998 isl_qpolynomial
*val
;
4000 val
= isl_qpolynomial_eval(isl_qpolynomial_copy(data
->qp
), pnt
);
4004 } else if (data
->max
) {
4005 data
->opt
= isl_qpolynomial_max_cst(data
->opt
, val
);
4007 data
->opt
= isl_qpolynomial_min_cst(data
->opt
, val
);
4013 __isl_give isl_qpolynomial
*isl_qpolynomial_opt_on_domain(
4014 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*set
, int max
)
4016 struct isl_opt_data data
= { NULL
, 1, NULL
, max
};
4021 if (isl_upoly_is_cst(qp
->upoly
)) {
4026 set
= fix_inactive(set
, qp
);
4029 if (isl_set_foreach_point(set
, opt_fn
, &data
) < 0)
4033 isl_space
*space
= isl_qpolynomial_get_domain_space(qp
);
4034 data
.opt
= isl_qpolynomial_zero_on_domain(space
);
4038 isl_qpolynomial_free(qp
);
4042 isl_qpolynomial_free(qp
);
4043 isl_qpolynomial_free(data
.opt
);
4047 __isl_give isl_qpolynomial
*isl_qpolynomial_morph_domain(
4048 __isl_take isl_qpolynomial
*qp
, __isl_take isl_morph
*morph
)
4053 struct isl_upoly
**subs
;
4054 isl_mat
*mat
, *diag
;
4056 qp
= isl_qpolynomial_cow(qp
);
4061 isl_assert(ctx
, isl_space_is_equal(qp
->dim
, morph
->dom
->dim
), goto error
);
4063 n_sub
= morph
->inv
->n_row
- 1;
4064 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
4065 n_sub
+= qp
->div
->n_row
;
4066 subs
= isl_calloc_array(ctx
, struct isl_upoly
*, n_sub
);
4070 for (i
= 0; 1 + i
< morph
->inv
->n_row
; ++i
)
4071 subs
[i
] = isl_upoly_from_affine(ctx
, morph
->inv
->row
[1 + i
],
4072 morph
->inv
->row
[0][0], morph
->inv
->n_col
);
4073 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
4074 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4075 subs
[morph
->inv
->n_row
- 1 + i
] =
4076 isl_upoly_var_pow(ctx
, morph
->inv
->n_col
- 1 + i
, 1);
4078 qp
->upoly
= isl_upoly_subs(qp
->upoly
, 0, n_sub
, subs
);
4080 for (i
= 0; i
< n_sub
; ++i
)
4081 isl_upoly_free(subs
[i
]);
4084 diag
= isl_mat_diag(ctx
, 1, morph
->inv
->row
[0][0]);
4085 mat
= isl_mat_diagonal(diag
, isl_mat_copy(morph
->inv
));
4086 diag
= isl_mat_diag(ctx
, qp
->div
->n_row
, morph
->inv
->row
[0][0]);
4087 mat
= isl_mat_diagonal(mat
, diag
);
4088 qp
->div
= isl_mat_product(qp
->div
, mat
);
4089 isl_space_free(qp
->dim
);
4090 qp
->dim
= isl_space_copy(morph
->ran
->dim
);
4092 if (!qp
->upoly
|| !qp
->div
|| !qp
->dim
)
4095 isl_morph_free(morph
);
4099 isl_qpolynomial_free(qp
);
4100 isl_morph_free(morph
);
4104 static int neg_entry(void **entry
, void *user
)
4106 isl_pw_qpolynomial
**pwqp
= (isl_pw_qpolynomial
**)entry
;
4108 *pwqp
= isl_pw_qpolynomial_neg(*pwqp
);
4110 return *pwqp
? 0 : -1;
4113 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_neg(
4114 __isl_take isl_union_pw_qpolynomial
*upwqp
)
4116 upwqp
= isl_union_pw_qpolynomial_cow(upwqp
);
4120 if (isl_hash_table_foreach(upwqp
->dim
->ctx
, &upwqp
->table
,
4121 &neg_entry
, NULL
) < 0)
4126 isl_union_pw_qpolynomial_free(upwqp
);
4130 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_mul(
4131 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
4132 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
4134 return match_bin_op(upwqp1
, upwqp2
, &isl_pw_qpolynomial_mul
);
4137 /* Reorder the columns of the given div definitions according to the
4140 static __isl_give isl_mat
*reorder_divs(__isl_take isl_mat
*div
,
4141 __isl_take isl_reordering
*r
)
4150 extra
= isl_space_dim(r
->dim
, isl_dim_all
) + div
->n_row
- r
->len
;
4151 mat
= isl_mat_alloc(div
->ctx
, div
->n_row
, div
->n_col
+ extra
);
4155 for (i
= 0; i
< div
->n_row
; ++i
) {
4156 isl_seq_cpy(mat
->row
[i
], div
->row
[i
], 2);
4157 isl_seq_clr(mat
->row
[i
] + 2, mat
->n_col
- 2);
4158 for (j
= 0; j
< r
->len
; ++j
)
4159 isl_int_set(mat
->row
[i
][2 + r
->pos
[j
]],
4160 div
->row
[i
][2 + j
]);
4163 isl_reordering_free(r
);
4167 isl_reordering_free(r
);
4172 /* Reorder the dimension of "qp" according to the given reordering.
4174 __isl_give isl_qpolynomial
*isl_qpolynomial_realign_domain(
4175 __isl_take isl_qpolynomial
*qp
, __isl_take isl_reordering
*r
)
4177 qp
= isl_qpolynomial_cow(qp
);
4181 r
= isl_reordering_extend(r
, qp
->div
->n_row
);
4185 qp
->div
= reorder_divs(qp
->div
, isl_reordering_copy(r
));
4189 qp
->upoly
= reorder(qp
->upoly
, r
->pos
);
4193 qp
= isl_qpolynomial_reset_domain_space(qp
, isl_space_copy(r
->dim
));
4195 isl_reordering_free(r
);
4198 isl_qpolynomial_free(qp
);
4199 isl_reordering_free(r
);
4203 __isl_give isl_qpolynomial
*isl_qpolynomial_align_params(
4204 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*model
)
4209 if (!isl_space_match(qp
->dim
, isl_dim_param
, model
, isl_dim_param
)) {
4210 isl_reordering
*exp
;
4212 model
= isl_space_drop_dims(model
, isl_dim_in
,
4213 0, isl_space_dim(model
, isl_dim_in
));
4214 model
= isl_space_drop_dims(model
, isl_dim_out
,
4215 0, isl_space_dim(model
, isl_dim_out
));
4216 exp
= isl_parameter_alignment_reordering(qp
->dim
, model
);
4217 exp
= isl_reordering_extend_space(exp
,
4218 isl_qpolynomial_get_domain_space(qp
));
4219 qp
= isl_qpolynomial_realign_domain(qp
, exp
);
4222 isl_space_free(model
);
4225 isl_space_free(model
);
4226 isl_qpolynomial_free(qp
);
4230 struct isl_split_periods_data
{
4232 isl_pw_qpolynomial
*res
;
4235 /* Create a slice where the integer division "div" has the fixed value "v".
4236 * In particular, if "div" refers to floor(f/m), then create a slice
4238 * m v <= f <= m v + (m - 1)
4243 * -f + m v + (m - 1) >= 0
4245 static __isl_give isl_set
*set_div_slice(__isl_take isl_space
*dim
,
4246 __isl_keep isl_qpolynomial
*qp
, int div
, isl_int v
)
4249 isl_basic_set
*bset
= NULL
;
4255 total
= isl_space_dim(dim
, isl_dim_all
);
4256 bset
= isl_basic_set_alloc_space(isl_space_copy(dim
), 0, 0, 2);
4258 k
= isl_basic_set_alloc_inequality(bset
);
4261 isl_seq_cpy(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4262 isl_int_submul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4264 k
= isl_basic_set_alloc_inequality(bset
);
4267 isl_seq_neg(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4268 isl_int_addmul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4269 isl_int_add(bset
->ineq
[k
][0], bset
->ineq
[k
][0], qp
->div
->row
[div
][0]);
4270 isl_int_sub_ui(bset
->ineq
[k
][0], bset
->ineq
[k
][0], 1);
4272 isl_space_free(dim
);
4273 return isl_set_from_basic_set(bset
);
4275 isl_basic_set_free(bset
);
4276 isl_space_free(dim
);
4280 static int split_periods(__isl_take isl_set
*set
,
4281 __isl_take isl_qpolynomial
*qp
, void *user
);
4283 /* Create a slice of the domain "set" such that integer division "div"
4284 * has the fixed value "v" and add the results to data->res,
4285 * replacing the integer division by "v" in "qp".
4287 static int set_div(__isl_take isl_set
*set
,
4288 __isl_take isl_qpolynomial
*qp
, int div
, isl_int v
,
4289 struct isl_split_periods_data
*data
)
4294 struct isl_upoly
*cst
;
4296 slice
= set_div_slice(isl_set_get_space(set
), qp
, div
, v
);
4297 set
= isl_set_intersect(set
, slice
);
4302 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4304 for (i
= div
+ 1; i
< qp
->div
->n_row
; ++i
) {
4305 if (isl_int_is_zero(qp
->div
->row
[i
][2 + total
+ div
]))
4307 isl_int_addmul(qp
->div
->row
[i
][1],
4308 qp
->div
->row
[i
][2 + total
+ div
], v
);
4309 isl_int_set_si(qp
->div
->row
[i
][2 + total
+ div
], 0);
4312 cst
= isl_upoly_rat_cst(qp
->dim
->ctx
, v
, qp
->dim
->ctx
->one
);
4313 qp
= substitute_div(qp
, div
, cst
);
4315 return split_periods(set
, qp
, data
);
4318 isl_qpolynomial_free(qp
);
4322 /* Split the domain "set" such that integer division "div"
4323 * has a fixed value (ranging from "min" to "max") on each slice
4324 * and add the results to data->res.
4326 static int split_div(__isl_take isl_set
*set
,
4327 __isl_take isl_qpolynomial
*qp
, int div
, isl_int min
, isl_int max
,
4328 struct isl_split_periods_data
*data
)
4330 for (; isl_int_le(min
, max
); isl_int_add_ui(min
, min
, 1)) {
4331 isl_set
*set_i
= isl_set_copy(set
);
4332 isl_qpolynomial
*qp_i
= isl_qpolynomial_copy(qp
);
4334 if (set_div(set_i
, qp_i
, div
, min
, data
) < 0)
4338 isl_qpolynomial_free(qp
);
4342 isl_qpolynomial_free(qp
);
4346 /* If "qp" refers to any integer division
4347 * that can only attain "max_periods" distinct values on "set"
4348 * then split the domain along those distinct values.
4349 * Add the results (or the original if no splitting occurs)
4352 static int split_periods(__isl_take isl_set
*set
,
4353 __isl_take isl_qpolynomial
*qp
, void *user
)
4356 isl_pw_qpolynomial
*pwqp
;
4357 struct isl_split_periods_data
*data
;
4362 data
= (struct isl_split_periods_data
*)user
;
4367 if (qp
->div
->n_row
== 0) {
4368 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4369 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4375 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4376 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4377 enum isl_lp_result lp_res
;
4379 if (isl_seq_first_non_zero(qp
->div
->row
[i
] + 2 + total
,
4380 qp
->div
->n_row
) != -1)
4383 lp_res
= isl_set_solve_lp(set
, 0, qp
->div
->row
[i
] + 1,
4384 set
->ctx
->one
, &min
, NULL
, NULL
);
4385 if (lp_res
== isl_lp_error
)
4387 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4389 isl_int_fdiv_q(min
, min
, qp
->div
->row
[i
][0]);
4391 lp_res
= isl_set_solve_lp(set
, 1, qp
->div
->row
[i
] + 1,
4392 set
->ctx
->one
, &max
, NULL
, NULL
);
4393 if (lp_res
== isl_lp_error
)
4395 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4397 isl_int_fdiv_q(max
, max
, qp
->div
->row
[i
][0]);
4399 isl_int_sub(max
, max
, min
);
4400 if (isl_int_cmp_si(max
, data
->max_periods
) < 0) {
4401 isl_int_add(max
, max
, min
);
4406 if (i
< qp
->div
->n_row
) {
4407 r
= split_div(set
, qp
, i
, min
, max
, data
);
4409 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4410 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4422 isl_qpolynomial_free(qp
);
4426 /* If any quasi-polynomial in pwqp refers to any integer division
4427 * that can only attain "max_periods" distinct values on its domain
4428 * then split the domain along those distinct values.
4430 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_split_periods(
4431 __isl_take isl_pw_qpolynomial
*pwqp
, int max_periods
)
4433 struct isl_split_periods_data data
;
4435 data
.max_periods
= max_periods
;
4436 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp
));
4438 if (isl_pw_qpolynomial_foreach_piece(pwqp
, &split_periods
, &data
) < 0)
4441 isl_pw_qpolynomial_free(pwqp
);
4445 isl_pw_qpolynomial_free(data
.res
);
4446 isl_pw_qpolynomial_free(pwqp
);
4450 /* Construct a piecewise quasipolynomial that is constant on the given
4451 * domain. In particular, it is
4454 * infinity if cst == -1
4456 static __isl_give isl_pw_qpolynomial
*constant_on_domain(
4457 __isl_take isl_basic_set
*bset
, int cst
)
4460 isl_qpolynomial
*qp
;
4465 bset
= isl_basic_set_params(bset
);
4466 dim
= isl_basic_set_get_space(bset
);
4468 qp
= isl_qpolynomial_infty_on_domain(dim
);
4470 qp
= isl_qpolynomial_zero_on_domain(dim
);
4472 qp
= isl_qpolynomial_one_on_domain(dim
);
4473 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset
), qp
);
4476 /* Factor bset, call fn on each of the factors and return the product.
4478 * If no factors can be found, simply call fn on the input.
4479 * Otherwise, construct the factors based on the factorizer,
4480 * call fn on each factor and compute the product.
4482 static __isl_give isl_pw_qpolynomial
*compressed_multiplicative_call(
4483 __isl_take isl_basic_set
*bset
,
4484 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4490 isl_qpolynomial
*qp
;
4491 isl_pw_qpolynomial
*pwqp
;
4495 f
= isl_basic_set_factorizer(bset
);
4498 if (f
->n_group
== 0) {
4499 isl_factorizer_free(f
);
4503 nparam
= isl_basic_set_dim(bset
, isl_dim_param
);
4504 nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
4506 dim
= isl_basic_set_get_space(bset
);
4507 dim
= isl_space_domain(dim
);
4508 set
= isl_set_universe(isl_space_copy(dim
));
4509 qp
= isl_qpolynomial_one_on_domain(dim
);
4510 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4512 bset
= isl_morph_basic_set(isl_morph_copy(f
->morph
), bset
);
4514 for (i
= 0, n
= 0; i
< f
->n_group
; ++i
) {
4515 isl_basic_set
*bset_i
;
4516 isl_pw_qpolynomial
*pwqp_i
;
4518 bset_i
= isl_basic_set_copy(bset
);
4519 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4520 nparam
+ n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4521 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4523 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
,
4524 n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4525 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
, 0, n
);
4527 pwqp_i
= fn(bset_i
);
4528 pwqp
= isl_pw_qpolynomial_mul(pwqp
, pwqp_i
);
4533 isl_basic_set_free(bset
);
4534 isl_factorizer_free(f
);
4538 isl_basic_set_free(bset
);
4542 /* Factor bset, call fn on each of the factors and return the product.
4543 * The function is assumed to evaluate to zero on empty domains,
4544 * to one on zero-dimensional domains and to infinity on unbounded domains
4545 * and will not be called explicitly on zero-dimensional or unbounded domains.
4547 * We first check for some special cases and remove all equalities.
4548 * Then we hand over control to compressed_multiplicative_call.
4550 __isl_give isl_pw_qpolynomial
*isl_basic_set_multiplicative_call(
4551 __isl_take isl_basic_set
*bset
,
4552 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4556 isl_pw_qpolynomial
*pwqp
;
4561 if (isl_basic_set_plain_is_empty(bset
))
4562 return constant_on_domain(bset
, 0);
4564 if (isl_basic_set_dim(bset
, isl_dim_set
) == 0)
4565 return constant_on_domain(bset
, 1);
4567 bounded
= isl_basic_set_is_bounded(bset
);
4571 return constant_on_domain(bset
, -1);
4573 if (bset
->n_eq
== 0)
4574 return compressed_multiplicative_call(bset
, fn
);
4576 morph
= isl_basic_set_full_compression(bset
);
4577 bset
= isl_morph_basic_set(isl_morph_copy(morph
), bset
);
4579 pwqp
= compressed_multiplicative_call(bset
, fn
);
4581 morph
= isl_morph_dom_params(morph
);
4582 morph
= isl_morph_ran_params(morph
);
4583 morph
= isl_morph_inverse(morph
);
4585 pwqp
= isl_pw_qpolynomial_morph_domain(pwqp
, morph
);
4589 isl_basic_set_free(bset
);
4593 /* Drop all floors in "qp", turning each integer division [a/m] into
4594 * a rational division a/m. If "down" is set, then the integer division
4595 * is replaces by (a-(m-1))/m instead.
4597 static __isl_give isl_qpolynomial
*qp_drop_floors(
4598 __isl_take isl_qpolynomial
*qp
, int down
)
4601 struct isl_upoly
*s
;
4605 if (qp
->div
->n_row
== 0)
4608 qp
= isl_qpolynomial_cow(qp
);
4612 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
4614 isl_int_sub(qp
->div
->row
[i
][1],
4615 qp
->div
->row
[i
][1], qp
->div
->row
[i
][0]);
4616 isl_int_add_ui(qp
->div
->row
[i
][1],
4617 qp
->div
->row
[i
][1], 1);
4619 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
4620 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
4621 qp
= substitute_div(qp
, i
, s
);
4629 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4630 * a rational division a/m.
4632 static __isl_give isl_pw_qpolynomial
*pwqp_drop_floors(
4633 __isl_take isl_pw_qpolynomial
*pwqp
)
4640 if (isl_pw_qpolynomial_is_zero(pwqp
))
4643 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
4647 for (i
= 0; i
< pwqp
->n
; ++i
) {
4648 pwqp
->p
[i
].qp
= qp_drop_floors(pwqp
->p
[i
].qp
, 0);
4655 isl_pw_qpolynomial_free(pwqp
);
4659 /* Adjust all the integer divisions in "qp" such that they are at least
4660 * one over the given orthant (identified by "signs"). This ensures
4661 * that they will still be non-negative even after subtracting (m-1)/m.
4663 * In particular, f is replaced by f' + v, changing f = [a/m]
4664 * to f' = [(a - m v)/m].
4665 * If the constant term k in a is smaller than m,
4666 * the constant term of v is set to floor(k/m) - 1.
4667 * For any other term, if the coefficient c and the variable x have
4668 * the same sign, then no changes are needed.
4669 * Otherwise, if the variable is positive (and c is negative),
4670 * then the coefficient of x in v is set to floor(c/m).
4671 * If the variable is negative (and c is positive),
4672 * then the coefficient of x in v is set to ceil(c/m).
4674 static __isl_give isl_qpolynomial
*make_divs_pos(__isl_take isl_qpolynomial
*qp
,
4680 struct isl_upoly
*s
;
4682 qp
= isl_qpolynomial_cow(qp
);
4685 qp
->div
= isl_mat_cow(qp
->div
);
4689 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4690 v
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
4692 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4693 isl_int
*row
= qp
->div
->row
[i
];
4697 if (isl_int_lt(row
[1], row
[0])) {
4698 isl_int_fdiv_q(v
->el
[0], row
[1], row
[0]);
4699 isl_int_sub_ui(v
->el
[0], v
->el
[0], 1);
4700 isl_int_submul(row
[1], row
[0], v
->el
[0]);
4702 for (j
= 0; j
< total
; ++j
) {
4703 if (isl_int_sgn(row
[2 + j
]) * signs
[j
] >= 0)
4706 isl_int_cdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4708 isl_int_fdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4709 isl_int_submul(row
[2 + j
], row
[0], v
->el
[1 + j
]);
4711 for (j
= 0; j
< i
; ++j
) {
4712 if (isl_int_sgn(row
[2 + total
+ j
]) >= 0)
4714 isl_int_fdiv_q(v
->el
[1 + total
+ j
],
4715 row
[2 + total
+ j
], row
[0]);
4716 isl_int_submul(row
[2 + total
+ j
],
4717 row
[0], v
->el
[1 + total
+ j
]);
4719 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
4720 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
4722 isl_seq_combine(qp
->div
->row
[j
] + 1,
4723 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
4724 qp
->div
->row
[j
][2 + total
+ i
], v
->el
, v
->size
);
4726 isl_int_set_si(v
->el
[1 + total
+ i
], 1);
4727 s
= isl_upoly_from_affine(qp
->dim
->ctx
, v
->el
,
4728 qp
->div
->ctx
->one
, v
->size
);
4729 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ i
, 1, &s
);
4739 isl_qpolynomial_free(qp
);
4743 struct isl_to_poly_data
{
4745 isl_pw_qpolynomial
*res
;
4746 isl_qpolynomial
*qp
;
4749 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4750 * We first make all integer divisions positive and then split the
4751 * quasipolynomials into terms with sign data->sign (the direction
4752 * of the requested approximation) and terms with the opposite sign.
4753 * In the first set of terms, each integer division [a/m] is
4754 * overapproximated by a/m, while in the second it is underapproximated
4757 static int to_polynomial_on_orthant(__isl_take isl_set
*orthant
, int *signs
,
4760 struct isl_to_poly_data
*data
= user
;
4761 isl_pw_qpolynomial
*t
;
4762 isl_qpolynomial
*qp
, *up
, *down
;
4764 qp
= isl_qpolynomial_copy(data
->qp
);
4765 qp
= make_divs_pos(qp
, signs
);
4767 up
= isl_qpolynomial_terms_of_sign(qp
, signs
, data
->sign
);
4768 up
= qp_drop_floors(up
, 0);
4769 down
= isl_qpolynomial_terms_of_sign(qp
, signs
, -data
->sign
);
4770 down
= qp_drop_floors(down
, 1);
4772 isl_qpolynomial_free(qp
);
4773 qp
= isl_qpolynomial_add(up
, down
);
4775 t
= isl_pw_qpolynomial_alloc(orthant
, qp
);
4776 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, t
);
4781 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4782 * the polynomial will be an overapproximation. If "sign" is negative,
4783 * it will be an underapproximation. If "sign" is zero, the approximation
4784 * will lie somewhere in between.
4786 * In particular, is sign == 0, we simply drop the floors, turning
4787 * the integer divisions into rational divisions.
4788 * Otherwise, we split the domains into orthants, make all integer divisions
4789 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4790 * depending on the requested sign and the sign of the term in which
4791 * the integer division appears.
4793 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_to_polynomial(
4794 __isl_take isl_pw_qpolynomial
*pwqp
, int sign
)
4797 struct isl_to_poly_data data
;
4800 return pwqp_drop_floors(pwqp
);
4806 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp
));
4808 for (i
= 0; i
< pwqp
->n
; ++i
) {
4809 if (pwqp
->p
[i
].qp
->div
->n_row
== 0) {
4810 isl_pw_qpolynomial
*t
;
4811 t
= isl_pw_qpolynomial_alloc(
4812 isl_set_copy(pwqp
->p
[i
].set
),
4813 isl_qpolynomial_copy(pwqp
->p
[i
].qp
));
4814 data
.res
= isl_pw_qpolynomial_add_disjoint(data
.res
, t
);
4817 data
.qp
= pwqp
->p
[i
].qp
;
4818 if (isl_set_foreach_orthant(pwqp
->p
[i
].set
,
4819 &to_polynomial_on_orthant
, &data
) < 0)
4823 isl_pw_qpolynomial_free(pwqp
);
4827 isl_pw_qpolynomial_free(pwqp
);
4828 isl_pw_qpolynomial_free(data
.res
);
4832 static int poly_entry(void **entry
, void *user
)
4835 isl_pw_qpolynomial
**pwqp
= (isl_pw_qpolynomial
**)entry
;
4837 *pwqp
= isl_pw_qpolynomial_to_polynomial(*pwqp
, *sign
);
4839 return *pwqp
? 0 : -1;
4842 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_to_polynomial(
4843 __isl_take isl_union_pw_qpolynomial
*upwqp
, int sign
)
4845 upwqp
= isl_union_pw_qpolynomial_cow(upwqp
);
4849 if (isl_hash_table_foreach(upwqp
->dim
->ctx
, &upwqp
->table
,
4850 &poly_entry
, &sign
) < 0)
4855 isl_union_pw_qpolynomial_free(upwqp
);
4859 __isl_give isl_basic_map
*isl_basic_map_from_qpolynomial(
4860 __isl_take isl_qpolynomial
*qp
)
4864 isl_vec
*aff
= NULL
;
4865 isl_basic_map
*bmap
= NULL
;
4871 if (!isl_upoly_is_affine(qp
->upoly
))
4872 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
4873 "input quasi-polynomial not affine", goto error
);
4874 aff
= isl_qpolynomial_extract_affine(qp
);
4877 dim
= isl_qpolynomial_get_space(qp
);
4878 pos
= 1 + isl_space_offset(dim
, isl_dim_out
);
4879 n_div
= qp
->div
->n_row
;
4880 bmap
= isl_basic_map_alloc_space(dim
, n_div
, 1, 2 * n_div
);
4882 for (i
= 0; i
< n_div
; ++i
) {
4883 k
= isl_basic_map_alloc_div(bmap
);
4886 isl_seq_cpy(bmap
->div
[k
], qp
->div
->row
[i
], qp
->div
->n_col
);
4887 isl_int_set_si(bmap
->div
[k
][qp
->div
->n_col
], 0);
4888 if (isl_basic_map_add_div_constraints(bmap
, k
) < 0)
4891 k
= isl_basic_map_alloc_equality(bmap
);
4894 isl_int_neg(bmap
->eq
[k
][pos
], aff
->el
[0]);
4895 isl_seq_cpy(bmap
->eq
[k
], aff
->el
+ 1, pos
);
4896 isl_seq_cpy(bmap
->eq
[k
] + pos
+ 1, aff
->el
+ 1 + pos
, n_div
);
4899 isl_qpolynomial_free(qp
);
4900 bmap
= isl_basic_map_finalize(bmap
);
4904 isl_qpolynomial_free(qp
);
4905 isl_basic_map_free(bmap
);