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>
16 #include <isl_lp_private.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_vec_private.h>
25 #include <isl_range.h>
26 #include <isl_local.h>
27 #include <isl_local_space_private.h>
28 #include <isl_aff_private.h>
29 #include <isl_val_private.h>
30 #include <isl_config.h>
31 #include <isl/deprecated/polynomial_int.h>
33 static unsigned pos(__isl_keep isl_space
*dim
, enum isl_dim_type type
)
36 case isl_dim_param
: return 0;
37 case isl_dim_in
: return dim
->nparam
;
38 case isl_dim_out
: return dim
->nparam
+ dim
->n_in
;
43 int isl_upoly_is_cst(__isl_keep
struct isl_upoly
*up
)
51 __isl_keep
struct isl_upoly_cst
*isl_upoly_as_cst(__isl_keep
struct isl_upoly
*up
)
56 isl_assert(up
->ctx
, up
->var
< 0, return NULL
);
58 return (struct isl_upoly_cst
*)up
;
61 __isl_keep
struct isl_upoly_rec
*isl_upoly_as_rec(__isl_keep
struct isl_upoly
*up
)
66 isl_assert(up
->ctx
, up
->var
>= 0, return NULL
);
68 return (struct isl_upoly_rec
*)up
;
71 /* Compare two polynomials.
73 * Return -1 if "up1" is "smaller" than "up2", 1 if "up1" is "greater"
74 * than "up2" and 0 if they are equal.
76 static int isl_upoly_plain_cmp(__isl_keep
struct isl_upoly
*up1
,
77 __isl_keep
struct isl_upoly
*up2
)
80 struct isl_upoly_rec
*rec1
, *rec2
;
88 if (up1
->var
!= up2
->var
)
89 return up1
->var
- up2
->var
;
91 if (isl_upoly_is_cst(up1
)) {
92 struct isl_upoly_cst
*cst1
, *cst2
;
95 cst1
= isl_upoly_as_cst(up1
);
96 cst2
= isl_upoly_as_cst(up2
);
99 cmp
= isl_int_cmp(cst1
->n
, cst2
->n
);
102 return isl_int_cmp(cst1
->d
, cst2
->d
);
105 rec1
= isl_upoly_as_rec(up1
);
106 rec2
= isl_upoly_as_rec(up2
);
110 if (rec1
->n
!= rec2
->n
)
111 return rec1
->n
- rec2
->n
;
113 for (i
= 0; i
< rec1
->n
; ++i
) {
114 int cmp
= isl_upoly_plain_cmp(rec1
->p
[i
], rec2
->p
[i
]);
122 isl_bool
isl_upoly_is_equal(__isl_keep
struct isl_upoly
*up1
,
123 __isl_keep
struct isl_upoly
*up2
)
126 struct isl_upoly_rec
*rec1
, *rec2
;
129 return isl_bool_error
;
131 return isl_bool_true
;
132 if (up1
->var
!= up2
->var
)
133 return isl_bool_false
;
134 if (isl_upoly_is_cst(up1
)) {
135 struct isl_upoly_cst
*cst1
, *cst2
;
136 cst1
= isl_upoly_as_cst(up1
);
137 cst2
= isl_upoly_as_cst(up2
);
139 return isl_bool_error
;
140 return isl_int_eq(cst1
->n
, cst2
->n
) &&
141 isl_int_eq(cst1
->d
, cst2
->d
);
144 rec1
= isl_upoly_as_rec(up1
);
145 rec2
= isl_upoly_as_rec(up2
);
147 return isl_bool_error
;
149 if (rec1
->n
!= rec2
->n
)
150 return isl_bool_false
;
152 for (i
= 0; i
< rec1
->n
; ++i
) {
153 isl_bool eq
= isl_upoly_is_equal(rec1
->p
[i
], rec2
->p
[i
]);
158 return isl_bool_true
;
161 int isl_upoly_is_zero(__isl_keep
struct isl_upoly
*up
)
163 struct isl_upoly_cst
*cst
;
167 if (!isl_upoly_is_cst(up
))
170 cst
= isl_upoly_as_cst(up
);
174 return isl_int_is_zero(cst
->n
) && isl_int_is_pos(cst
->d
);
177 int isl_upoly_sgn(__isl_keep
struct isl_upoly
*up
)
179 struct isl_upoly_cst
*cst
;
183 if (!isl_upoly_is_cst(up
))
186 cst
= isl_upoly_as_cst(up
);
190 return isl_int_sgn(cst
->n
);
193 int isl_upoly_is_nan(__isl_keep
struct isl_upoly
*up
)
195 struct isl_upoly_cst
*cst
;
199 if (!isl_upoly_is_cst(up
))
202 cst
= isl_upoly_as_cst(up
);
206 return isl_int_is_zero(cst
->n
) && isl_int_is_zero(cst
->d
);
209 int isl_upoly_is_infty(__isl_keep
struct isl_upoly
*up
)
211 struct isl_upoly_cst
*cst
;
215 if (!isl_upoly_is_cst(up
))
218 cst
= isl_upoly_as_cst(up
);
222 return isl_int_is_pos(cst
->n
) && isl_int_is_zero(cst
->d
);
225 int isl_upoly_is_neginfty(__isl_keep
struct isl_upoly
*up
)
227 struct isl_upoly_cst
*cst
;
231 if (!isl_upoly_is_cst(up
))
234 cst
= isl_upoly_as_cst(up
);
238 return isl_int_is_neg(cst
->n
) && isl_int_is_zero(cst
->d
);
241 int isl_upoly_is_one(__isl_keep
struct isl_upoly
*up
)
243 struct isl_upoly_cst
*cst
;
247 if (!isl_upoly_is_cst(up
))
250 cst
= isl_upoly_as_cst(up
);
254 return isl_int_eq(cst
->n
, cst
->d
) && isl_int_is_pos(cst
->d
);
257 int isl_upoly_is_negone(__isl_keep
struct isl_upoly
*up
)
259 struct isl_upoly_cst
*cst
;
263 if (!isl_upoly_is_cst(up
))
266 cst
= isl_upoly_as_cst(up
);
270 return isl_int_is_negone(cst
->n
) && isl_int_is_one(cst
->d
);
273 __isl_give
struct isl_upoly_cst
*isl_upoly_cst_alloc(struct isl_ctx
*ctx
)
275 struct isl_upoly_cst
*cst
;
277 cst
= isl_alloc_type(ctx
, struct isl_upoly_cst
);
286 isl_int_init(cst
->n
);
287 isl_int_init(cst
->d
);
292 __isl_give
struct isl_upoly
*isl_upoly_zero(struct isl_ctx
*ctx
)
294 struct isl_upoly_cst
*cst
;
296 cst
= isl_upoly_cst_alloc(ctx
);
300 isl_int_set_si(cst
->n
, 0);
301 isl_int_set_si(cst
->d
, 1);
306 __isl_give
struct isl_upoly
*isl_upoly_one(struct isl_ctx
*ctx
)
308 struct isl_upoly_cst
*cst
;
310 cst
= isl_upoly_cst_alloc(ctx
);
314 isl_int_set_si(cst
->n
, 1);
315 isl_int_set_si(cst
->d
, 1);
320 __isl_give
struct isl_upoly
*isl_upoly_infty(struct isl_ctx
*ctx
)
322 struct isl_upoly_cst
*cst
;
324 cst
= isl_upoly_cst_alloc(ctx
);
328 isl_int_set_si(cst
->n
, 1);
329 isl_int_set_si(cst
->d
, 0);
334 __isl_give
struct isl_upoly
*isl_upoly_neginfty(struct isl_ctx
*ctx
)
336 struct isl_upoly_cst
*cst
;
338 cst
= isl_upoly_cst_alloc(ctx
);
342 isl_int_set_si(cst
->n
, -1);
343 isl_int_set_si(cst
->d
, 0);
348 __isl_give
struct isl_upoly
*isl_upoly_nan(struct isl_ctx
*ctx
)
350 struct isl_upoly_cst
*cst
;
352 cst
= isl_upoly_cst_alloc(ctx
);
356 isl_int_set_si(cst
->n
, 0);
357 isl_int_set_si(cst
->d
, 0);
362 __isl_give
struct isl_upoly
*isl_upoly_rat_cst(struct isl_ctx
*ctx
,
363 isl_int n
, isl_int d
)
365 struct isl_upoly_cst
*cst
;
367 cst
= isl_upoly_cst_alloc(ctx
);
371 isl_int_set(cst
->n
, n
);
372 isl_int_set(cst
->d
, d
);
377 __isl_give
struct isl_upoly_rec
*isl_upoly_alloc_rec(struct isl_ctx
*ctx
,
380 struct isl_upoly_rec
*rec
;
382 isl_assert(ctx
, var
>= 0, return NULL
);
383 isl_assert(ctx
, size
>= 0, return NULL
);
384 rec
= isl_calloc(ctx
, struct isl_upoly_rec
,
385 sizeof(struct isl_upoly_rec
) +
386 size
* sizeof(struct isl_upoly
*));
401 __isl_give isl_qpolynomial
*isl_qpolynomial_reset_domain_space(
402 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*dim
)
404 qp
= isl_qpolynomial_cow(qp
);
408 isl_space_free(qp
->dim
);
413 isl_qpolynomial_free(qp
);
418 /* Reset the space of "qp". This function is called from isl_pw_templ.c
419 * and doesn't know if the space of an element object is represented
420 * directly or through its domain. It therefore passes along both.
422 __isl_give isl_qpolynomial
*isl_qpolynomial_reset_space_and_domain(
423 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*space
,
424 __isl_take isl_space
*domain
)
426 isl_space_free(space
);
427 return isl_qpolynomial_reset_domain_space(qp
, domain
);
430 isl_ctx
*isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial
*qp
)
432 return qp
? qp
->dim
->ctx
: NULL
;
435 __isl_give isl_space
*isl_qpolynomial_get_domain_space(
436 __isl_keep isl_qpolynomial
*qp
)
438 return qp
? isl_space_copy(qp
->dim
) : NULL
;
441 __isl_give isl_space
*isl_qpolynomial_get_space(__isl_keep isl_qpolynomial
*qp
)
446 space
= isl_space_copy(qp
->dim
);
447 space
= isl_space_from_domain(space
);
448 space
= isl_space_add_dims(space
, isl_dim_out
, 1);
452 /* Externally, an isl_qpolynomial has a map space, but internally, the
453 * ls field corresponds to the domain of that space.
455 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial
*qp
,
456 enum isl_dim_type type
)
460 if (type
== isl_dim_out
)
462 if (type
== isl_dim_in
)
464 return isl_space_dim(qp
->dim
, type
);
467 /* Return the offset of the first coefficient of type "type" in
468 * the domain of "qp".
470 unsigned isl_qpolynomial_domain_offset(__isl_keep isl_qpolynomial
*qp
,
471 enum isl_dim_type type
)
480 return 1 + isl_space_offset(qp
->dim
, type
);
482 return 1 + isl_space_dim(qp
->dim
, isl_dim_all
);
488 isl_bool
isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial
*qp
)
490 return qp
? isl_upoly_is_zero(qp
->upoly
) : isl_bool_error
;
493 isl_bool
isl_qpolynomial_is_one(__isl_keep isl_qpolynomial
*qp
)
495 return qp
? isl_upoly_is_one(qp
->upoly
) : isl_bool_error
;
498 isl_bool
isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial
*qp
)
500 return qp
? isl_upoly_is_nan(qp
->upoly
) : isl_bool_error
;
503 isl_bool
isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial
*qp
)
505 return qp
? isl_upoly_is_infty(qp
->upoly
) : isl_bool_error
;
508 isl_bool
isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial
*qp
)
510 return qp
? isl_upoly_is_neginfty(qp
->upoly
) : isl_bool_error
;
513 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial
*qp
)
515 return qp
? isl_upoly_sgn(qp
->upoly
) : 0;
518 static void upoly_free_cst(__isl_take
struct isl_upoly_cst
*cst
)
520 isl_int_clear(cst
->n
);
521 isl_int_clear(cst
->d
);
524 static void upoly_free_rec(__isl_take
struct isl_upoly_rec
*rec
)
528 for (i
= 0; i
< rec
->n
; ++i
)
529 isl_upoly_free(rec
->p
[i
]);
532 __isl_give
struct isl_upoly
*isl_upoly_copy(__isl_keep
struct isl_upoly
*up
)
541 __isl_give
struct isl_upoly
*isl_upoly_dup_cst(__isl_keep
struct isl_upoly
*up
)
543 struct isl_upoly_cst
*cst
;
544 struct isl_upoly_cst
*dup
;
546 cst
= isl_upoly_as_cst(up
);
550 dup
= isl_upoly_as_cst(isl_upoly_zero(up
->ctx
));
553 isl_int_set(dup
->n
, cst
->n
);
554 isl_int_set(dup
->d
, cst
->d
);
559 __isl_give
struct isl_upoly
*isl_upoly_dup_rec(__isl_keep
struct isl_upoly
*up
)
562 struct isl_upoly_rec
*rec
;
563 struct isl_upoly_rec
*dup
;
565 rec
= isl_upoly_as_rec(up
);
569 dup
= isl_upoly_alloc_rec(up
->ctx
, up
->var
, rec
->n
);
573 for (i
= 0; i
< rec
->n
; ++i
) {
574 dup
->p
[i
] = isl_upoly_copy(rec
->p
[i
]);
582 isl_upoly_free(&dup
->up
);
586 __isl_give
struct isl_upoly
*isl_upoly_dup(__isl_keep
struct isl_upoly
*up
)
591 if (isl_upoly_is_cst(up
))
592 return isl_upoly_dup_cst(up
);
594 return isl_upoly_dup_rec(up
);
597 __isl_give
struct isl_upoly
*isl_upoly_cow(__isl_take
struct isl_upoly
*up
)
605 return isl_upoly_dup(up
);
608 void isl_upoly_free(__isl_take
struct isl_upoly
*up
)
617 upoly_free_cst((struct isl_upoly_cst
*)up
);
619 upoly_free_rec((struct isl_upoly_rec
*)up
);
621 isl_ctx_deref(up
->ctx
);
625 static void isl_upoly_cst_reduce(__isl_keep
struct isl_upoly_cst
*cst
)
630 isl_int_gcd(gcd
, cst
->n
, cst
->d
);
631 if (!isl_int_is_zero(gcd
) && !isl_int_is_one(gcd
)) {
632 isl_int_divexact(cst
->n
, cst
->n
, gcd
);
633 isl_int_divexact(cst
->d
, cst
->d
, gcd
);
638 __isl_give
struct isl_upoly
*isl_upoly_sum_cst(__isl_take
struct isl_upoly
*up1
,
639 __isl_take
struct isl_upoly
*up2
)
641 struct isl_upoly_cst
*cst1
;
642 struct isl_upoly_cst
*cst2
;
644 up1
= isl_upoly_cow(up1
);
648 cst1
= isl_upoly_as_cst(up1
);
649 cst2
= isl_upoly_as_cst(up2
);
651 if (isl_int_eq(cst1
->d
, cst2
->d
))
652 isl_int_add(cst1
->n
, cst1
->n
, cst2
->n
);
654 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->d
);
655 isl_int_addmul(cst1
->n
, cst2
->n
, cst1
->d
);
656 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
659 isl_upoly_cst_reduce(cst1
);
669 static __isl_give
struct isl_upoly
*replace_by_zero(
670 __isl_take
struct isl_upoly
*up
)
678 return isl_upoly_zero(ctx
);
681 static __isl_give
struct isl_upoly
*replace_by_constant_term(
682 __isl_take
struct isl_upoly
*up
)
684 struct isl_upoly_rec
*rec
;
685 struct isl_upoly
*cst
;
690 rec
= isl_upoly_as_rec(up
);
693 cst
= isl_upoly_copy(rec
->p
[0]);
701 __isl_give
struct isl_upoly
*isl_upoly_sum(__isl_take
struct isl_upoly
*up1
,
702 __isl_take
struct isl_upoly
*up2
)
705 struct isl_upoly_rec
*rec1
, *rec2
;
710 if (isl_upoly_is_nan(up1
)) {
715 if (isl_upoly_is_nan(up2
)) {
720 if (isl_upoly_is_zero(up1
)) {
725 if (isl_upoly_is_zero(up2
)) {
730 if (up1
->var
< up2
->var
)
731 return isl_upoly_sum(up2
, up1
);
733 if (up2
->var
< up1
->var
) {
734 struct isl_upoly_rec
*rec
;
735 if (isl_upoly_is_infty(up2
) || isl_upoly_is_neginfty(up2
)) {
739 up1
= isl_upoly_cow(up1
);
740 rec
= isl_upoly_as_rec(up1
);
743 rec
->p
[0] = isl_upoly_sum(rec
->p
[0], up2
);
745 up1
= replace_by_constant_term(up1
);
749 if (isl_upoly_is_cst(up1
))
750 return isl_upoly_sum_cst(up1
, up2
);
752 rec1
= isl_upoly_as_rec(up1
);
753 rec2
= isl_upoly_as_rec(up2
);
757 if (rec1
->n
< rec2
->n
)
758 return isl_upoly_sum(up2
, up1
);
760 up1
= isl_upoly_cow(up1
);
761 rec1
= isl_upoly_as_rec(up1
);
765 for (i
= rec2
->n
- 1; i
>= 0; --i
) {
766 rec1
->p
[i
] = isl_upoly_sum(rec1
->p
[i
],
767 isl_upoly_copy(rec2
->p
[i
]));
770 if (i
== rec1
->n
- 1 && isl_upoly_is_zero(rec1
->p
[i
])) {
771 isl_upoly_free(rec1
->p
[i
]);
777 up1
= replace_by_zero(up1
);
778 else if (rec1
->n
== 1)
779 up1
= replace_by_constant_term(up1
);
790 __isl_give
struct isl_upoly
*isl_upoly_cst_add_isl_int(
791 __isl_take
struct isl_upoly
*up
, isl_int v
)
793 struct isl_upoly_cst
*cst
;
795 up
= isl_upoly_cow(up
);
799 cst
= isl_upoly_as_cst(up
);
801 isl_int_addmul(cst
->n
, cst
->d
, v
);
806 __isl_give
struct isl_upoly
*isl_upoly_add_isl_int(
807 __isl_take
struct isl_upoly
*up
, isl_int v
)
809 struct isl_upoly_rec
*rec
;
814 if (isl_upoly_is_cst(up
))
815 return isl_upoly_cst_add_isl_int(up
, v
);
817 up
= isl_upoly_cow(up
);
818 rec
= isl_upoly_as_rec(up
);
822 rec
->p
[0] = isl_upoly_add_isl_int(rec
->p
[0], v
);
832 __isl_give
struct isl_upoly
*isl_upoly_cst_mul_isl_int(
833 __isl_take
struct isl_upoly
*up
, isl_int v
)
835 struct isl_upoly_cst
*cst
;
837 if (isl_upoly_is_zero(up
))
840 up
= isl_upoly_cow(up
);
844 cst
= isl_upoly_as_cst(up
);
846 isl_int_mul(cst
->n
, cst
->n
, v
);
851 __isl_give
struct isl_upoly
*isl_upoly_mul_isl_int(
852 __isl_take
struct isl_upoly
*up
, isl_int v
)
855 struct isl_upoly_rec
*rec
;
860 if (isl_upoly_is_cst(up
))
861 return isl_upoly_cst_mul_isl_int(up
, v
);
863 up
= isl_upoly_cow(up
);
864 rec
= isl_upoly_as_rec(up
);
868 for (i
= 0; i
< rec
->n
; ++i
) {
869 rec
->p
[i
] = isl_upoly_mul_isl_int(rec
->p
[i
], v
);
880 /* Multiply the constant polynomial "up" by "v".
882 static __isl_give
struct isl_upoly
*isl_upoly_cst_scale_val(
883 __isl_take
struct isl_upoly
*up
, __isl_keep isl_val
*v
)
885 struct isl_upoly_cst
*cst
;
887 if (isl_upoly_is_zero(up
))
890 up
= isl_upoly_cow(up
);
894 cst
= isl_upoly_as_cst(up
);
896 isl_int_mul(cst
->n
, cst
->n
, v
->n
);
897 isl_int_mul(cst
->d
, cst
->d
, v
->d
);
898 isl_upoly_cst_reduce(cst
);
903 /* Multiply the polynomial "up" by "v".
905 static __isl_give
struct isl_upoly
*isl_upoly_scale_val(
906 __isl_take
struct isl_upoly
*up
, __isl_keep isl_val
*v
)
909 struct isl_upoly_rec
*rec
;
914 if (isl_upoly_is_cst(up
))
915 return isl_upoly_cst_scale_val(up
, v
);
917 up
= isl_upoly_cow(up
);
918 rec
= isl_upoly_as_rec(up
);
922 for (i
= 0; i
< rec
->n
; ++i
) {
923 rec
->p
[i
] = isl_upoly_scale_val(rec
->p
[i
], v
);
934 __isl_give
struct isl_upoly
*isl_upoly_mul_cst(__isl_take
struct isl_upoly
*up1
,
935 __isl_take
struct isl_upoly
*up2
)
937 struct isl_upoly_cst
*cst1
;
938 struct isl_upoly_cst
*cst2
;
940 up1
= isl_upoly_cow(up1
);
944 cst1
= isl_upoly_as_cst(up1
);
945 cst2
= isl_upoly_as_cst(up2
);
947 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->n
);
948 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
950 isl_upoly_cst_reduce(cst1
);
960 __isl_give
struct isl_upoly
*isl_upoly_mul_rec(__isl_take
struct isl_upoly
*up1
,
961 __isl_take
struct isl_upoly
*up2
)
963 struct isl_upoly_rec
*rec1
;
964 struct isl_upoly_rec
*rec2
;
965 struct isl_upoly_rec
*res
= NULL
;
969 rec1
= isl_upoly_as_rec(up1
);
970 rec2
= isl_upoly_as_rec(up2
);
973 size
= rec1
->n
+ rec2
->n
- 1;
974 res
= isl_upoly_alloc_rec(up1
->ctx
, up1
->var
, size
);
978 for (i
= 0; i
< rec1
->n
; ++i
) {
979 res
->p
[i
] = isl_upoly_mul(isl_upoly_copy(rec2
->p
[0]),
980 isl_upoly_copy(rec1
->p
[i
]));
985 for (; i
< size
; ++i
) {
986 res
->p
[i
] = isl_upoly_zero(up1
->ctx
);
991 for (i
= 0; i
< rec1
->n
; ++i
) {
992 for (j
= 1; j
< rec2
->n
; ++j
) {
993 struct isl_upoly
*up
;
994 up
= isl_upoly_mul(isl_upoly_copy(rec2
->p
[j
]),
995 isl_upoly_copy(rec1
->p
[i
]));
996 res
->p
[i
+ j
] = isl_upoly_sum(res
->p
[i
+ j
], up
);
1002 isl_upoly_free(up1
);
1003 isl_upoly_free(up2
);
1007 isl_upoly_free(up1
);
1008 isl_upoly_free(up2
);
1009 isl_upoly_free(&res
->up
);
1013 __isl_give
struct isl_upoly
*isl_upoly_mul(__isl_take
struct isl_upoly
*up1
,
1014 __isl_take
struct isl_upoly
*up2
)
1019 if (isl_upoly_is_nan(up1
)) {
1020 isl_upoly_free(up2
);
1024 if (isl_upoly_is_nan(up2
)) {
1025 isl_upoly_free(up1
);
1029 if (isl_upoly_is_zero(up1
)) {
1030 isl_upoly_free(up2
);
1034 if (isl_upoly_is_zero(up2
)) {
1035 isl_upoly_free(up1
);
1039 if (isl_upoly_is_one(up1
)) {
1040 isl_upoly_free(up1
);
1044 if (isl_upoly_is_one(up2
)) {
1045 isl_upoly_free(up2
);
1049 if (up1
->var
< up2
->var
)
1050 return isl_upoly_mul(up2
, up1
);
1052 if (up2
->var
< up1
->var
) {
1054 struct isl_upoly_rec
*rec
;
1055 if (isl_upoly_is_infty(up2
) || isl_upoly_is_neginfty(up2
)) {
1056 isl_ctx
*ctx
= up1
->ctx
;
1057 isl_upoly_free(up1
);
1058 isl_upoly_free(up2
);
1059 return isl_upoly_nan(ctx
);
1061 up1
= isl_upoly_cow(up1
);
1062 rec
= isl_upoly_as_rec(up1
);
1066 for (i
= 0; i
< rec
->n
; ++i
) {
1067 rec
->p
[i
] = isl_upoly_mul(rec
->p
[i
],
1068 isl_upoly_copy(up2
));
1072 isl_upoly_free(up2
);
1076 if (isl_upoly_is_cst(up1
))
1077 return isl_upoly_mul_cst(up1
, up2
);
1079 return isl_upoly_mul_rec(up1
, up2
);
1081 isl_upoly_free(up1
);
1082 isl_upoly_free(up2
);
1086 __isl_give
struct isl_upoly
*isl_upoly_pow(__isl_take
struct isl_upoly
*up
,
1089 struct isl_upoly
*res
;
1097 res
= isl_upoly_copy(up
);
1099 res
= isl_upoly_one(up
->ctx
);
1101 while (power
>>= 1) {
1102 up
= isl_upoly_mul(up
, isl_upoly_copy(up
));
1104 res
= isl_upoly_mul(res
, isl_upoly_copy(up
));
1111 __isl_give isl_qpolynomial
*isl_qpolynomial_alloc(__isl_take isl_space
*dim
,
1112 unsigned n_div
, __isl_take
struct isl_upoly
*up
)
1114 struct isl_qpolynomial
*qp
= NULL
;
1120 if (!isl_space_is_set(dim
))
1121 isl_die(isl_space_get_ctx(dim
), isl_error_invalid
,
1122 "domain of polynomial should be a set", goto error
);
1124 total
= isl_space_dim(dim
, isl_dim_all
);
1126 qp
= isl_calloc_type(dim
->ctx
, struct isl_qpolynomial
);
1131 qp
->div
= isl_mat_alloc(dim
->ctx
, n_div
, 1 + 1 + total
+ n_div
);
1140 isl_space_free(dim
);
1142 isl_qpolynomial_free(qp
);
1146 __isl_give isl_qpolynomial
*isl_qpolynomial_copy(__isl_keep isl_qpolynomial
*qp
)
1155 __isl_give isl_qpolynomial
*isl_qpolynomial_dup(__isl_keep isl_qpolynomial
*qp
)
1157 struct isl_qpolynomial
*dup
;
1162 dup
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
), qp
->div
->n_row
,
1163 isl_upoly_copy(qp
->upoly
));
1166 isl_mat_free(dup
->div
);
1167 dup
->div
= isl_mat_copy(qp
->div
);
1173 isl_qpolynomial_free(dup
);
1177 __isl_give isl_qpolynomial
*isl_qpolynomial_cow(__isl_take isl_qpolynomial
*qp
)
1185 return isl_qpolynomial_dup(qp
);
1188 __isl_null isl_qpolynomial
*isl_qpolynomial_free(
1189 __isl_take isl_qpolynomial
*qp
)
1197 isl_space_free(qp
->dim
);
1198 isl_mat_free(qp
->div
);
1199 isl_upoly_free(qp
->upoly
);
1205 __isl_give
struct isl_upoly
*isl_upoly_var_pow(isl_ctx
*ctx
, int pos
, int power
)
1208 struct isl_upoly_rec
*rec
;
1209 struct isl_upoly_cst
*cst
;
1211 rec
= isl_upoly_alloc_rec(ctx
, pos
, 1 + power
);
1214 for (i
= 0; i
< 1 + power
; ++i
) {
1215 rec
->p
[i
] = isl_upoly_zero(ctx
);
1220 cst
= isl_upoly_as_cst(rec
->p
[power
]);
1221 isl_int_set_si(cst
->n
, 1);
1225 isl_upoly_free(&rec
->up
);
1229 /* r array maps original positions to new positions.
1231 static __isl_give
struct isl_upoly
*reorder(__isl_take
struct isl_upoly
*up
,
1235 struct isl_upoly_rec
*rec
;
1236 struct isl_upoly
*base
;
1237 struct isl_upoly
*res
;
1239 if (isl_upoly_is_cst(up
))
1242 rec
= isl_upoly_as_rec(up
);
1246 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
1248 base
= isl_upoly_var_pow(up
->ctx
, r
[up
->var
], 1);
1249 res
= reorder(isl_upoly_copy(rec
->p
[rec
->n
- 1]), r
);
1251 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1252 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
1253 res
= isl_upoly_sum(res
, reorder(isl_upoly_copy(rec
->p
[i
]), r
));
1256 isl_upoly_free(base
);
1265 static int compatible_divs(__isl_keep isl_mat
*div1
, __isl_keep isl_mat
*div2
)
1270 isl_assert(div1
->ctx
, div1
->n_row
>= div2
->n_row
&&
1271 div1
->n_col
>= div2
->n_col
, return -1);
1273 if (div1
->n_row
== div2
->n_row
)
1274 return isl_mat_is_equal(div1
, div2
);
1276 n_row
= div1
->n_row
;
1277 n_col
= div1
->n_col
;
1278 div1
->n_row
= div2
->n_row
;
1279 div1
->n_col
= div2
->n_col
;
1281 equal
= isl_mat_is_equal(div1
, div2
);
1283 div1
->n_row
= n_row
;
1284 div1
->n_col
= n_col
;
1289 static int cmp_row(__isl_keep isl_mat
*div
, int i
, int j
)
1293 li
= isl_seq_last_non_zero(div
->row
[i
], div
->n_col
);
1294 lj
= isl_seq_last_non_zero(div
->row
[j
], div
->n_col
);
1299 return isl_seq_cmp(div
->row
[i
], div
->row
[j
], div
->n_col
);
1302 struct isl_div_sort_info
{
1307 static int div_sort_cmp(const void *p1
, const void *p2
)
1309 const struct isl_div_sort_info
*i1
, *i2
;
1310 i1
= (const struct isl_div_sort_info
*) p1
;
1311 i2
= (const struct isl_div_sort_info
*) p2
;
1313 return cmp_row(i1
->div
, i1
->row
, i2
->row
);
1316 /* Sort divs and remove duplicates.
1318 static __isl_give isl_qpolynomial
*sort_divs(__isl_take isl_qpolynomial
*qp
)
1323 struct isl_div_sort_info
*array
= NULL
;
1324 int *pos
= NULL
, *at
= NULL
;
1325 int *reordering
= NULL
;
1330 if (qp
->div
->n_row
<= 1)
1333 div_pos
= isl_space_dim(qp
->dim
, isl_dim_all
);
1335 array
= isl_alloc_array(qp
->div
->ctx
, struct isl_div_sort_info
,
1337 pos
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1338 at
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1339 len
= qp
->div
->n_col
- 2;
1340 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
1341 if (!array
|| !pos
|| !at
|| !reordering
)
1344 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1345 array
[i
].div
= qp
->div
;
1351 qsort(array
, qp
->div
->n_row
, sizeof(struct isl_div_sort_info
),
1354 for (i
= 0; i
< div_pos
; ++i
)
1357 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1358 if (pos
[array
[i
].row
] == i
)
1360 qp
->div
= isl_mat_swap_rows(qp
->div
, i
, pos
[array
[i
].row
]);
1361 pos
[at
[i
]] = pos
[array
[i
].row
];
1362 at
[pos
[array
[i
].row
]] = at
[i
];
1363 at
[i
] = array
[i
].row
;
1364 pos
[array
[i
].row
] = i
;
1368 for (i
= 0; i
< len
- div_pos
; ++i
) {
1370 isl_seq_eq(qp
->div
->row
[i
- skip
- 1],
1371 qp
->div
->row
[i
- skip
], qp
->div
->n_col
)) {
1372 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
1373 isl_mat_col_add(qp
->div
, 2 + div_pos
+ i
- skip
- 1,
1374 2 + div_pos
+ i
- skip
);
1375 qp
->div
= isl_mat_drop_cols(qp
->div
,
1376 2 + div_pos
+ i
- skip
, 1);
1379 reordering
[div_pos
+ array
[i
].row
] = div_pos
+ i
- skip
;
1382 qp
->upoly
= reorder(qp
->upoly
, reordering
);
1384 if (!qp
->upoly
|| !qp
->div
)
1398 isl_qpolynomial_free(qp
);
1402 static __isl_give
struct isl_upoly
*expand(__isl_take
struct isl_upoly
*up
,
1403 int *exp
, int first
)
1406 struct isl_upoly_rec
*rec
;
1408 if (isl_upoly_is_cst(up
))
1411 if (up
->var
< first
)
1414 if (exp
[up
->var
- first
] == up
->var
- first
)
1417 up
= isl_upoly_cow(up
);
1421 up
->var
= exp
[up
->var
- first
] + first
;
1423 rec
= isl_upoly_as_rec(up
);
1427 for (i
= 0; i
< rec
->n
; ++i
) {
1428 rec
->p
[i
] = expand(rec
->p
[i
], exp
, first
);
1439 static __isl_give isl_qpolynomial
*with_merged_divs(
1440 __isl_give isl_qpolynomial
*(*fn
)(__isl_take isl_qpolynomial
*qp1
,
1441 __isl_take isl_qpolynomial
*qp2
),
1442 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
1446 isl_mat
*div
= NULL
;
1449 qp1
= isl_qpolynomial_cow(qp1
);
1450 qp2
= isl_qpolynomial_cow(qp2
);
1455 isl_assert(qp1
->div
->ctx
, qp1
->div
->n_row
>= qp2
->div
->n_row
&&
1456 qp1
->div
->n_col
>= qp2
->div
->n_col
, goto error
);
1458 n_div1
= qp1
->div
->n_row
;
1459 n_div2
= qp2
->div
->n_row
;
1460 exp1
= isl_alloc_array(qp1
->div
->ctx
, int, n_div1
);
1461 exp2
= isl_alloc_array(qp2
->div
->ctx
, int, n_div2
);
1462 if ((n_div1
&& !exp1
) || (n_div2
&& !exp2
))
1465 div
= isl_merge_divs(qp1
->div
, qp2
->div
, exp1
, exp2
);
1469 isl_mat_free(qp1
->div
);
1470 qp1
->div
= isl_mat_copy(div
);
1471 isl_mat_free(qp2
->div
);
1472 qp2
->div
= isl_mat_copy(div
);
1474 qp1
->upoly
= expand(qp1
->upoly
, exp1
, div
->n_col
- div
->n_row
- 2);
1475 qp2
->upoly
= expand(qp2
->upoly
, exp2
, div
->n_col
- div
->n_row
- 2);
1477 if (!qp1
->upoly
|| !qp2
->upoly
)
1484 return fn(qp1
, qp2
);
1489 isl_qpolynomial_free(qp1
);
1490 isl_qpolynomial_free(qp2
);
1494 __isl_give isl_qpolynomial
*isl_qpolynomial_add(__isl_take isl_qpolynomial
*qp1
,
1495 __isl_take isl_qpolynomial
*qp2
)
1497 qp1
= isl_qpolynomial_cow(qp1
);
1502 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1503 return isl_qpolynomial_add(qp2
, qp1
);
1505 isl_assert(qp1
->dim
->ctx
, isl_space_is_equal(qp1
->dim
, qp2
->dim
), goto error
);
1506 if (!compatible_divs(qp1
->div
, qp2
->div
))
1507 return with_merged_divs(isl_qpolynomial_add
, qp1
, qp2
);
1509 qp1
->upoly
= isl_upoly_sum(qp1
->upoly
, isl_upoly_copy(qp2
->upoly
));
1513 isl_qpolynomial_free(qp2
);
1517 isl_qpolynomial_free(qp1
);
1518 isl_qpolynomial_free(qp2
);
1522 __isl_give isl_qpolynomial
*isl_qpolynomial_add_on_domain(
1523 __isl_keep isl_set
*dom
,
1524 __isl_take isl_qpolynomial
*qp1
,
1525 __isl_take isl_qpolynomial
*qp2
)
1527 qp1
= isl_qpolynomial_add(qp1
, qp2
);
1528 qp1
= isl_qpolynomial_gist(qp1
, isl_set_copy(dom
));
1532 __isl_give isl_qpolynomial
*isl_qpolynomial_sub(__isl_take isl_qpolynomial
*qp1
,
1533 __isl_take isl_qpolynomial
*qp2
)
1535 return isl_qpolynomial_add(qp1
, isl_qpolynomial_neg(qp2
));
1538 __isl_give isl_qpolynomial
*isl_qpolynomial_add_isl_int(
1539 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1541 if (isl_int_is_zero(v
))
1544 qp
= isl_qpolynomial_cow(qp
);
1548 qp
->upoly
= isl_upoly_add_isl_int(qp
->upoly
, v
);
1554 isl_qpolynomial_free(qp
);
1559 __isl_give isl_qpolynomial
*isl_qpolynomial_neg(__isl_take isl_qpolynomial
*qp
)
1564 return isl_qpolynomial_mul_isl_int(qp
, qp
->dim
->ctx
->negone
);
1567 __isl_give isl_qpolynomial
*isl_qpolynomial_mul_isl_int(
1568 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1570 if (isl_int_is_one(v
))
1573 if (qp
&& isl_int_is_zero(v
)) {
1574 isl_qpolynomial
*zero
;
1575 zero
= isl_qpolynomial_zero_on_domain(isl_space_copy(qp
->dim
));
1576 isl_qpolynomial_free(qp
);
1580 qp
= isl_qpolynomial_cow(qp
);
1584 qp
->upoly
= isl_upoly_mul_isl_int(qp
->upoly
, v
);
1590 isl_qpolynomial_free(qp
);
1594 __isl_give isl_qpolynomial
*isl_qpolynomial_scale(
1595 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1597 return isl_qpolynomial_mul_isl_int(qp
, v
);
1600 /* Multiply "qp" by "v".
1602 __isl_give isl_qpolynomial
*isl_qpolynomial_scale_val(
1603 __isl_take isl_qpolynomial
*qp
, __isl_take isl_val
*v
)
1608 if (!isl_val_is_rat(v
))
1609 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
1610 "expecting rational factor", goto error
);
1612 if (isl_val_is_one(v
)) {
1617 if (isl_val_is_zero(v
)) {
1620 space
= isl_qpolynomial_get_domain_space(qp
);
1621 isl_qpolynomial_free(qp
);
1623 return isl_qpolynomial_zero_on_domain(space
);
1626 qp
= isl_qpolynomial_cow(qp
);
1630 qp
->upoly
= isl_upoly_scale_val(qp
->upoly
, v
);
1632 qp
= isl_qpolynomial_free(qp
);
1638 isl_qpolynomial_free(qp
);
1642 /* Divide "qp" by "v".
1644 __isl_give isl_qpolynomial
*isl_qpolynomial_scale_down_val(
1645 __isl_take isl_qpolynomial
*qp
, __isl_take isl_val
*v
)
1650 if (!isl_val_is_rat(v
))
1651 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
1652 "expecting rational factor", goto error
);
1653 if (isl_val_is_zero(v
))
1654 isl_die(isl_val_get_ctx(v
), isl_error_invalid
,
1655 "cannot scale down by zero", goto error
);
1657 return isl_qpolynomial_scale_val(qp
, isl_val_inv(v
));
1660 isl_qpolynomial_free(qp
);
1664 __isl_give isl_qpolynomial
*isl_qpolynomial_mul(__isl_take isl_qpolynomial
*qp1
,
1665 __isl_take isl_qpolynomial
*qp2
)
1667 qp1
= isl_qpolynomial_cow(qp1
);
1672 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1673 return isl_qpolynomial_mul(qp2
, qp1
);
1675 isl_assert(qp1
->dim
->ctx
, isl_space_is_equal(qp1
->dim
, qp2
->dim
), goto error
);
1676 if (!compatible_divs(qp1
->div
, qp2
->div
))
1677 return with_merged_divs(isl_qpolynomial_mul
, qp1
, qp2
);
1679 qp1
->upoly
= isl_upoly_mul(qp1
->upoly
, isl_upoly_copy(qp2
->upoly
));
1683 isl_qpolynomial_free(qp2
);
1687 isl_qpolynomial_free(qp1
);
1688 isl_qpolynomial_free(qp2
);
1692 __isl_give isl_qpolynomial
*isl_qpolynomial_pow(__isl_take isl_qpolynomial
*qp
,
1695 qp
= isl_qpolynomial_cow(qp
);
1700 qp
->upoly
= isl_upoly_pow(qp
->upoly
, power
);
1706 isl_qpolynomial_free(qp
);
1710 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_pow(
1711 __isl_take isl_pw_qpolynomial
*pwqp
, unsigned power
)
1718 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
1722 for (i
= 0; i
< pwqp
->n
; ++i
) {
1723 pwqp
->p
[i
].qp
= isl_qpolynomial_pow(pwqp
->p
[i
].qp
, power
);
1725 return isl_pw_qpolynomial_free(pwqp
);
1731 __isl_give isl_qpolynomial
*isl_qpolynomial_zero_on_domain(
1732 __isl_take isl_space
*dim
)
1736 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
1739 __isl_give isl_qpolynomial
*isl_qpolynomial_one_on_domain(
1740 __isl_take isl_space
*dim
)
1744 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_one(dim
->ctx
));
1747 __isl_give isl_qpolynomial
*isl_qpolynomial_infty_on_domain(
1748 __isl_take isl_space
*dim
)
1752 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_infty(dim
->ctx
));
1755 __isl_give isl_qpolynomial
*isl_qpolynomial_neginfty_on_domain(
1756 __isl_take isl_space
*dim
)
1760 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_neginfty(dim
->ctx
));
1763 __isl_give isl_qpolynomial
*isl_qpolynomial_nan_on_domain(
1764 __isl_take isl_space
*dim
)
1768 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_nan(dim
->ctx
));
1771 __isl_give isl_qpolynomial
*isl_qpolynomial_cst_on_domain(
1772 __isl_take isl_space
*dim
,
1775 struct isl_qpolynomial
*qp
;
1776 struct isl_upoly_cst
*cst
;
1781 qp
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
1785 cst
= isl_upoly_as_cst(qp
->upoly
);
1786 isl_int_set(cst
->n
, v
);
1791 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial
*qp
,
1792 isl_int
*n
, isl_int
*d
)
1794 struct isl_upoly_cst
*cst
;
1799 if (!isl_upoly_is_cst(qp
->upoly
))
1802 cst
= isl_upoly_as_cst(qp
->upoly
);
1807 isl_int_set(*n
, cst
->n
);
1809 isl_int_set(*d
, cst
->d
);
1814 /* Return the constant term of "up".
1816 static __isl_give isl_val
*isl_upoly_get_constant_val(
1817 __isl_keep
struct isl_upoly
*up
)
1819 struct isl_upoly_cst
*cst
;
1824 while (!isl_upoly_is_cst(up
)) {
1825 struct isl_upoly_rec
*rec
;
1827 rec
= isl_upoly_as_rec(up
);
1833 cst
= isl_upoly_as_cst(up
);
1836 return isl_val_rat_from_isl_int(cst
->up
.ctx
, cst
->n
, cst
->d
);
1839 /* Return the constant term of "qp".
1841 __isl_give isl_val
*isl_qpolynomial_get_constant_val(
1842 __isl_keep isl_qpolynomial
*qp
)
1847 return isl_upoly_get_constant_val(qp
->upoly
);
1850 int isl_upoly_is_affine(__isl_keep
struct isl_upoly
*up
)
1853 struct isl_upoly_rec
*rec
;
1861 rec
= isl_upoly_as_rec(up
);
1868 isl_assert(up
->ctx
, rec
->n
> 1, return -1);
1870 is_cst
= isl_upoly_is_cst(rec
->p
[1]);
1876 return isl_upoly_is_affine(rec
->p
[0]);
1879 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial
*qp
)
1884 if (qp
->div
->n_row
> 0)
1887 return isl_upoly_is_affine(qp
->upoly
);
1890 static void update_coeff(__isl_keep isl_vec
*aff
,
1891 __isl_keep
struct isl_upoly_cst
*cst
, int pos
)
1896 if (isl_int_is_zero(cst
->n
))
1901 isl_int_gcd(gcd
, cst
->d
, aff
->el
[0]);
1902 isl_int_divexact(f
, cst
->d
, gcd
);
1903 isl_int_divexact(gcd
, aff
->el
[0], gcd
);
1904 isl_seq_scale(aff
->el
, aff
->el
, f
, aff
->size
);
1905 isl_int_mul(aff
->el
[1 + pos
], gcd
, cst
->n
);
1910 int isl_upoly_update_affine(__isl_keep
struct isl_upoly
*up
,
1911 __isl_keep isl_vec
*aff
)
1913 struct isl_upoly_cst
*cst
;
1914 struct isl_upoly_rec
*rec
;
1920 struct isl_upoly_cst
*cst
;
1922 cst
= isl_upoly_as_cst(up
);
1925 update_coeff(aff
, cst
, 0);
1929 rec
= isl_upoly_as_rec(up
);
1932 isl_assert(up
->ctx
, rec
->n
== 2, return -1);
1934 cst
= isl_upoly_as_cst(rec
->p
[1]);
1937 update_coeff(aff
, cst
, 1 + up
->var
);
1939 return isl_upoly_update_affine(rec
->p
[0], aff
);
1942 __isl_give isl_vec
*isl_qpolynomial_extract_affine(
1943 __isl_keep isl_qpolynomial
*qp
)
1951 d
= isl_space_dim(qp
->dim
, isl_dim_all
);
1952 aff
= isl_vec_alloc(qp
->div
->ctx
, 2 + d
+ qp
->div
->n_row
);
1956 isl_seq_clr(aff
->el
+ 1, 1 + d
+ qp
->div
->n_row
);
1957 isl_int_set_si(aff
->el
[0], 1);
1959 if (isl_upoly_update_affine(qp
->upoly
, aff
) < 0)
1968 /* Compare two quasi-polynomials.
1970 * Return -1 if "qp1" is "smaller" than "qp2", 1 if "qp1" is "greater"
1971 * than "qp2" and 0 if they are equal.
1973 int isl_qpolynomial_plain_cmp(__isl_keep isl_qpolynomial
*qp1
,
1974 __isl_keep isl_qpolynomial
*qp2
)
1985 cmp
= isl_space_cmp(qp1
->dim
, qp2
->dim
);
1989 cmp
= isl_local_cmp(qp1
->div
, qp2
->div
);
1993 return isl_upoly_plain_cmp(qp1
->upoly
, qp2
->upoly
);
1996 /* Is "qp1" obviously equal to "qp2"?
1998 * NaN is not equal to anything, not even to another NaN.
2000 isl_bool
isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial
*qp1
,
2001 __isl_keep isl_qpolynomial
*qp2
)
2006 return isl_bool_error
;
2008 if (isl_qpolynomial_is_nan(qp1
) || isl_qpolynomial_is_nan(qp2
))
2009 return isl_bool_false
;
2011 equal
= isl_space_is_equal(qp1
->dim
, qp2
->dim
);
2012 if (equal
< 0 || !equal
)
2015 equal
= isl_mat_is_equal(qp1
->div
, qp2
->div
);
2016 if (equal
< 0 || !equal
)
2019 return isl_upoly_is_equal(qp1
->upoly
, qp2
->upoly
);
2022 static void upoly_update_den(__isl_keep
struct isl_upoly
*up
, isl_int
*d
)
2025 struct isl_upoly_rec
*rec
;
2027 if (isl_upoly_is_cst(up
)) {
2028 struct isl_upoly_cst
*cst
;
2029 cst
= isl_upoly_as_cst(up
);
2032 isl_int_lcm(*d
, *d
, cst
->d
);
2036 rec
= isl_upoly_as_rec(up
);
2040 for (i
= 0; i
< rec
->n
; ++i
)
2041 upoly_update_den(rec
->p
[i
], d
);
2044 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial
*qp
, isl_int
*d
)
2046 isl_int_set_si(*d
, 1);
2049 upoly_update_den(qp
->upoly
, d
);
2052 __isl_give isl_qpolynomial
*isl_qpolynomial_var_pow_on_domain(
2053 __isl_take isl_space
*dim
, int pos
, int power
)
2055 struct isl_ctx
*ctx
;
2062 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_var_pow(ctx
, pos
, power
));
2065 __isl_give isl_qpolynomial
*isl_qpolynomial_var_on_domain(__isl_take isl_space
*dim
,
2066 enum isl_dim_type type
, unsigned pos
)
2071 isl_assert(dim
->ctx
, isl_space_dim(dim
, isl_dim_in
) == 0, goto error
);
2072 isl_assert(dim
->ctx
, pos
< isl_space_dim(dim
, type
), goto error
);
2074 if (type
== isl_dim_set
)
2075 pos
+= isl_space_dim(dim
, isl_dim_param
);
2077 return isl_qpolynomial_var_pow_on_domain(dim
, pos
, 1);
2079 isl_space_free(dim
);
2083 __isl_give
struct isl_upoly
*isl_upoly_subs(__isl_take
struct isl_upoly
*up
,
2084 unsigned first
, unsigned n
, __isl_keep
struct isl_upoly
**subs
)
2087 struct isl_upoly_rec
*rec
;
2088 struct isl_upoly
*base
, *res
;
2093 if (isl_upoly_is_cst(up
))
2096 if (up
->var
< first
)
2099 rec
= isl_upoly_as_rec(up
);
2103 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
2105 if (up
->var
>= first
+ n
)
2106 base
= isl_upoly_var_pow(up
->ctx
, up
->var
, 1);
2108 base
= isl_upoly_copy(subs
[up
->var
- first
]);
2110 res
= isl_upoly_subs(isl_upoly_copy(rec
->p
[rec
->n
- 1]), first
, n
, subs
);
2111 for (i
= rec
->n
- 2; i
>= 0; --i
) {
2112 struct isl_upoly
*t
;
2113 t
= isl_upoly_subs(isl_upoly_copy(rec
->p
[i
]), first
, n
, subs
);
2114 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
2115 res
= isl_upoly_sum(res
, t
);
2118 isl_upoly_free(base
);
2127 __isl_give
struct isl_upoly
*isl_upoly_from_affine(isl_ctx
*ctx
, isl_int
*f
,
2128 isl_int denom
, unsigned len
)
2131 struct isl_upoly
*up
;
2133 isl_assert(ctx
, len
>= 1, return NULL
);
2135 up
= isl_upoly_rat_cst(ctx
, f
[0], denom
);
2136 for (i
= 0; i
< len
- 1; ++i
) {
2137 struct isl_upoly
*t
;
2138 struct isl_upoly
*c
;
2140 if (isl_int_is_zero(f
[1 + i
]))
2143 c
= isl_upoly_rat_cst(ctx
, f
[1 + i
], denom
);
2144 t
= isl_upoly_var_pow(ctx
, i
, 1);
2145 t
= isl_upoly_mul(c
, t
);
2146 up
= isl_upoly_sum(up
, t
);
2152 /* Remove common factor of non-constant terms and denominator.
2154 static void normalize_div(__isl_keep isl_qpolynomial
*qp
, int div
)
2156 isl_ctx
*ctx
= qp
->div
->ctx
;
2157 unsigned total
= qp
->div
->n_col
- 2;
2159 isl_seq_gcd(qp
->div
->row
[div
] + 2, total
, &ctx
->normalize_gcd
);
2160 isl_int_gcd(ctx
->normalize_gcd
,
2161 ctx
->normalize_gcd
, qp
->div
->row
[div
][0]);
2162 if (isl_int_is_one(ctx
->normalize_gcd
))
2165 isl_seq_scale_down(qp
->div
->row
[div
] + 2, qp
->div
->row
[div
] + 2,
2166 ctx
->normalize_gcd
, total
);
2167 isl_int_divexact(qp
->div
->row
[div
][0], qp
->div
->row
[div
][0],
2168 ctx
->normalize_gcd
);
2169 isl_int_fdiv_q(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1],
2170 ctx
->normalize_gcd
);
2173 /* Replace the integer division identified by "div" by the polynomial "s".
2174 * The integer division is assumed not to appear in the definition
2175 * of any other integer divisions.
2177 static __isl_give isl_qpolynomial
*substitute_div(
2178 __isl_take isl_qpolynomial
*qp
,
2179 int div
, __isl_take
struct isl_upoly
*s
)
2188 qp
= isl_qpolynomial_cow(qp
);
2192 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
2193 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ div
, 1, &s
);
2197 reordering
= isl_alloc_array(qp
->dim
->ctx
, int, total
+ qp
->div
->n_row
);
2200 for (i
= 0; i
< total
+ div
; ++i
)
2202 for (i
= total
+ div
+ 1; i
< total
+ qp
->div
->n_row
; ++i
)
2203 reordering
[i
] = i
- 1;
2204 qp
->div
= isl_mat_drop_rows(qp
->div
, div
, 1);
2205 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + total
+ div
, 1);
2206 qp
->upoly
= reorder(qp
->upoly
, reordering
);
2209 if (!qp
->upoly
|| !qp
->div
)
2215 isl_qpolynomial_free(qp
);
2220 /* Replace all integer divisions [e/d] that turn out to not actually be integer
2221 * divisions because d is equal to 1 by their definition, i.e., e.
2223 static __isl_give isl_qpolynomial
*substitute_non_divs(
2224 __isl_take isl_qpolynomial
*qp
)
2228 struct isl_upoly
*s
;
2233 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
2234 for (i
= 0; qp
&& i
< qp
->div
->n_row
; ++i
) {
2235 if (!isl_int_is_one(qp
->div
->row
[i
][0]))
2237 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
2238 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
2240 isl_seq_combine(qp
->div
->row
[j
] + 1,
2241 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
2242 qp
->div
->row
[j
][2 + total
+ i
],
2243 qp
->div
->row
[i
] + 1, 1 + total
+ i
);
2244 isl_int_set_si(qp
->div
->row
[j
][2 + total
+ i
], 0);
2245 normalize_div(qp
, j
);
2247 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
2248 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
2249 qp
= substitute_div(qp
, i
, s
);
2256 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
2257 * with d the denominator. When replacing the coefficient e of x by
2258 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
2259 * inside the division, so we need to add floor(e/d) * x outside.
2260 * That is, we replace q by q' + floor(e/d) * x and we therefore need
2261 * to adjust the coefficient of x in each later div that depends on the
2262 * current div "div" and also in the affine expression "aff"
2263 * (if it too depends on "div").
2265 static void reduce_div(__isl_keep isl_qpolynomial
*qp
, int div
,
2266 __isl_keep isl_vec
*aff
)
2270 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
2273 for (i
= 0; i
< 1 + total
+ div
; ++i
) {
2274 if (isl_int_is_nonneg(qp
->div
->row
[div
][1 + i
]) &&
2275 isl_int_lt(qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]))
2277 isl_int_fdiv_q(v
, qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
2278 isl_int_fdiv_r(qp
->div
->row
[div
][1 + i
],
2279 qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
2280 if (!isl_int_is_zero(aff
->el
[1 + total
+ div
]))
2281 isl_int_addmul(aff
->el
[i
], v
, aff
->el
[1 + total
+ div
]);
2282 for (j
= div
+ 1; j
< qp
->div
->n_row
; ++j
) {
2283 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ div
]))
2285 isl_int_addmul(qp
->div
->row
[j
][1 + i
],
2286 v
, qp
->div
->row
[j
][2 + total
+ div
]);
2292 /* Check if the last non-zero coefficient is bigger that half of the
2293 * denominator. If so, we will invert the div to further reduce the number
2294 * of distinct divs that may appear.
2295 * If the last non-zero coefficient is exactly half the denominator,
2296 * then we continue looking for earlier coefficients that are bigger
2297 * than half the denominator.
2299 static int needs_invert(__isl_keep isl_mat
*div
, int row
)
2304 for (i
= div
->n_col
- 1; i
>= 1; --i
) {
2305 if (isl_int_is_zero(div
->row
[row
][i
]))
2307 isl_int_mul_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
2308 cmp
= isl_int_cmp(div
->row
[row
][i
], div
->row
[row
][0]);
2309 isl_int_divexact_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
2319 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
2320 * We only invert the coefficients of e (and the coefficient of q in
2321 * later divs and in "aff"). After calling this function, the
2322 * coefficients of e should be reduced again.
2324 static void invert_div(__isl_keep isl_qpolynomial
*qp
, int div
,
2325 __isl_keep isl_vec
*aff
)
2327 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
2329 isl_seq_neg(qp
->div
->row
[div
] + 1,
2330 qp
->div
->row
[div
] + 1, qp
->div
->n_col
- 1);
2331 isl_int_sub_ui(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1], 1);
2332 isl_int_add(qp
->div
->row
[div
][1],
2333 qp
->div
->row
[div
][1], qp
->div
->row
[div
][0]);
2334 if (!isl_int_is_zero(aff
->el
[1 + total
+ div
]))
2335 isl_int_neg(aff
->el
[1 + total
+ div
], aff
->el
[1 + total
+ div
]);
2336 isl_mat_col_mul(qp
->div
, 2 + total
+ div
,
2337 qp
->div
->ctx
->negone
, 2 + total
+ div
);
2340 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2341 * in the interval [0, d-1], with d the denominator and such that the
2342 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2344 * After the reduction, some divs may have become redundant or identical,
2345 * so we call substitute_non_divs and sort_divs. If these functions
2346 * eliminate divs or merge two or more divs into one, the coefficients
2347 * of the enclosing divs may have to be reduced again, so we call
2348 * ourselves recursively if the number of divs decreases.
2350 static __isl_give isl_qpolynomial
*reduce_divs(__isl_take isl_qpolynomial
*qp
)
2353 isl_vec
*aff
= NULL
;
2354 struct isl_upoly
*s
;
2360 aff
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
2361 aff
= isl_vec_clr(aff
);
2365 isl_int_set_si(aff
->el
[1 + qp
->upoly
->var
], 1);
2367 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2368 normalize_div(qp
, i
);
2369 reduce_div(qp
, i
, aff
);
2370 if (needs_invert(qp
->div
, i
)) {
2371 invert_div(qp
, i
, aff
);
2372 reduce_div(qp
, i
, aff
);
2376 s
= isl_upoly_from_affine(qp
->div
->ctx
, aff
->el
,
2377 qp
->div
->ctx
->one
, aff
->size
);
2378 qp
->upoly
= isl_upoly_subs(qp
->upoly
, qp
->upoly
->var
, 1, &s
);
2385 n_div
= qp
->div
->n_row
;
2386 qp
= substitute_non_divs(qp
);
2388 if (qp
&& qp
->div
->n_row
< n_div
)
2389 return reduce_divs(qp
);
2393 isl_qpolynomial_free(qp
);
2398 __isl_give isl_qpolynomial
*isl_qpolynomial_rat_cst_on_domain(
2399 __isl_take isl_space
*dim
, const isl_int n
, const isl_int d
)
2401 struct isl_qpolynomial
*qp
;
2402 struct isl_upoly_cst
*cst
;
2407 qp
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
2411 cst
= isl_upoly_as_cst(qp
->upoly
);
2412 isl_int_set(cst
->n
, n
);
2413 isl_int_set(cst
->d
, d
);
2418 /* Return an isl_qpolynomial that is equal to "val" on domain space "domain".
2420 __isl_give isl_qpolynomial
*isl_qpolynomial_val_on_domain(
2421 __isl_take isl_space
*domain
, __isl_take isl_val
*val
)
2423 isl_qpolynomial
*qp
;
2424 struct isl_upoly_cst
*cst
;
2426 if (!domain
|| !val
)
2429 qp
= isl_qpolynomial_alloc(isl_space_copy(domain
), 0,
2430 isl_upoly_zero(domain
->ctx
));
2434 cst
= isl_upoly_as_cst(qp
->upoly
);
2435 isl_int_set(cst
->n
, val
->n
);
2436 isl_int_set(cst
->d
, val
->d
);
2438 isl_space_free(domain
);
2442 isl_space_free(domain
);
2447 static int up_set_active(__isl_keep
struct isl_upoly
*up
, int *active
, int d
)
2449 struct isl_upoly_rec
*rec
;
2455 if (isl_upoly_is_cst(up
))
2459 active
[up
->var
] = 1;
2461 rec
= isl_upoly_as_rec(up
);
2462 for (i
= 0; i
< rec
->n
; ++i
)
2463 if (up_set_active(rec
->p
[i
], active
, d
) < 0)
2469 static int set_active(__isl_keep isl_qpolynomial
*qp
, int *active
)
2472 int d
= isl_space_dim(qp
->dim
, isl_dim_all
);
2477 for (i
= 0; i
< d
; ++i
)
2478 for (j
= 0; j
< qp
->div
->n_row
; ++j
) {
2479 if (isl_int_is_zero(qp
->div
->row
[j
][2 + i
]))
2485 return up_set_active(qp
->upoly
, active
, d
);
2488 isl_bool
isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial
*qp
,
2489 enum isl_dim_type type
, unsigned first
, unsigned n
)
2493 isl_bool involves
= isl_bool_false
;
2496 return isl_bool_error
;
2498 return isl_bool_false
;
2500 isl_assert(qp
->dim
->ctx
,
2501 first
+ n
<= isl_qpolynomial_dim(qp
, type
),
2502 return isl_bool_error
);
2503 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2504 type
== isl_dim_in
, return isl_bool_error
);
2506 active
= isl_calloc_array(qp
->dim
->ctx
, int,
2507 isl_space_dim(qp
->dim
, isl_dim_all
));
2508 if (set_active(qp
, active
) < 0)
2511 if (type
== isl_dim_in
)
2512 first
+= isl_space_dim(qp
->dim
, isl_dim_param
);
2513 for (i
= 0; i
< n
; ++i
)
2514 if (active
[first
+ i
]) {
2515 involves
= isl_bool_true
;
2524 return isl_bool_error
;
2527 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2528 * of the divs that do appear in the quasi-polynomial.
2530 static __isl_give isl_qpolynomial
*remove_redundant_divs(
2531 __isl_take isl_qpolynomial
*qp
)
2538 int *reordering
= NULL
;
2545 if (qp
->div
->n_row
== 0)
2548 d
= isl_space_dim(qp
->dim
, isl_dim_all
);
2549 len
= qp
->div
->n_col
- 2;
2550 ctx
= isl_qpolynomial_get_ctx(qp
);
2551 active
= isl_calloc_array(ctx
, int, len
);
2555 if (up_set_active(qp
->upoly
, active
, len
) < 0)
2558 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
2559 if (!active
[d
+ i
]) {
2563 for (j
= 0; j
< i
; ++j
) {
2564 if (isl_int_is_zero(qp
->div
->row
[i
][2 + d
+ j
]))
2576 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
2580 for (i
= 0; i
< d
; ++i
)
2584 n_div
= qp
->div
->n_row
;
2585 for (i
= 0; i
< n_div
; ++i
) {
2586 if (!active
[d
+ i
]) {
2587 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
2588 qp
->div
= isl_mat_drop_cols(qp
->div
,
2589 2 + d
+ i
- skip
, 1);
2592 reordering
[d
+ i
] = d
+ i
- skip
;
2595 qp
->upoly
= reorder(qp
->upoly
, reordering
);
2597 if (!qp
->upoly
|| !qp
->div
)
2607 isl_qpolynomial_free(qp
);
2611 __isl_give
struct isl_upoly
*isl_upoly_drop(__isl_take
struct isl_upoly
*up
,
2612 unsigned first
, unsigned n
)
2615 struct isl_upoly_rec
*rec
;
2619 if (n
== 0 || up
->var
< 0 || up
->var
< first
)
2621 if (up
->var
< first
+ n
) {
2622 up
= replace_by_constant_term(up
);
2623 return isl_upoly_drop(up
, first
, n
);
2625 up
= isl_upoly_cow(up
);
2629 rec
= isl_upoly_as_rec(up
);
2633 for (i
= 0; i
< rec
->n
; ++i
) {
2634 rec
->p
[i
] = isl_upoly_drop(rec
->p
[i
], first
, n
);
2645 __isl_give isl_qpolynomial
*isl_qpolynomial_set_dim_name(
2646 __isl_take isl_qpolynomial
*qp
,
2647 enum isl_dim_type type
, unsigned pos
, const char *s
)
2649 qp
= isl_qpolynomial_cow(qp
);
2652 qp
->dim
= isl_space_set_dim_name(qp
->dim
, type
, pos
, s
);
2657 isl_qpolynomial_free(qp
);
2661 __isl_give isl_qpolynomial
*isl_qpolynomial_drop_dims(
2662 __isl_take isl_qpolynomial
*qp
,
2663 enum isl_dim_type type
, unsigned first
, unsigned n
)
2667 if (type
== isl_dim_out
)
2668 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
2669 "cannot drop output/set dimension",
2671 if (type
== isl_dim_in
)
2673 if (n
== 0 && !isl_space_is_named_or_nested(qp
->dim
, type
))
2676 qp
= isl_qpolynomial_cow(qp
);
2680 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_space_dim(qp
->dim
, type
),
2682 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2683 type
== isl_dim_set
, goto error
);
2685 qp
->dim
= isl_space_drop_dims(qp
->dim
, type
, first
, n
);
2689 if (type
== isl_dim_set
)
2690 first
+= isl_space_dim(qp
->dim
, isl_dim_param
);
2692 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + first
, n
);
2696 qp
->upoly
= isl_upoly_drop(qp
->upoly
, first
, n
);
2702 isl_qpolynomial_free(qp
);
2706 /* Project the domain of the quasi-polynomial onto its parameter space.
2707 * The quasi-polynomial may not involve any of the domain dimensions.
2709 __isl_give isl_qpolynomial
*isl_qpolynomial_project_domain_on_params(
2710 __isl_take isl_qpolynomial
*qp
)
2716 n
= isl_qpolynomial_dim(qp
, isl_dim_in
);
2717 involves
= isl_qpolynomial_involves_dims(qp
, isl_dim_in
, 0, n
);
2719 return isl_qpolynomial_free(qp
);
2721 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
2722 "polynomial involves some of the domain dimensions",
2723 return isl_qpolynomial_free(qp
));
2724 qp
= isl_qpolynomial_drop_dims(qp
, isl_dim_in
, 0, n
);
2725 space
= isl_qpolynomial_get_domain_space(qp
);
2726 space
= isl_space_params(space
);
2727 qp
= isl_qpolynomial_reset_domain_space(qp
, space
);
2731 static __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities_lifted(
2732 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2738 struct isl_upoly
*up
;
2742 if (eq
->n_eq
== 0) {
2743 isl_basic_set_free(eq
);
2747 qp
= isl_qpolynomial_cow(qp
);
2750 qp
->div
= isl_mat_cow(qp
->div
);
2754 total
= 1 + isl_space_dim(eq
->dim
, isl_dim_all
);
2756 isl_int_init(denom
);
2757 for (i
= 0; i
< eq
->n_eq
; ++i
) {
2758 j
= isl_seq_last_non_zero(eq
->eq
[i
], total
+ n_div
);
2759 if (j
< 0 || j
== 0 || j
>= total
)
2762 for (k
= 0; k
< qp
->div
->n_row
; ++k
) {
2763 if (isl_int_is_zero(qp
->div
->row
[k
][1 + j
]))
2765 isl_seq_elim(qp
->div
->row
[k
] + 1, eq
->eq
[i
], j
, total
,
2766 &qp
->div
->row
[k
][0]);
2767 normalize_div(qp
, k
);
2770 if (isl_int_is_pos(eq
->eq
[i
][j
]))
2771 isl_seq_neg(eq
->eq
[i
], eq
->eq
[i
], total
);
2772 isl_int_abs(denom
, eq
->eq
[i
][j
]);
2773 isl_int_set_si(eq
->eq
[i
][j
], 0);
2775 up
= isl_upoly_from_affine(qp
->dim
->ctx
,
2776 eq
->eq
[i
], denom
, total
);
2777 qp
->upoly
= isl_upoly_subs(qp
->upoly
, j
- 1, 1, &up
);
2780 isl_int_clear(denom
);
2785 isl_basic_set_free(eq
);
2787 qp
= substitute_non_divs(qp
);
2792 isl_basic_set_free(eq
);
2793 isl_qpolynomial_free(qp
);
2797 /* Exploit the equalities in "eq" to simplify the quasi-polynomial.
2799 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities(
2800 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2804 if (qp
->div
->n_row
> 0)
2805 eq
= isl_basic_set_add_dims(eq
, isl_dim_set
, qp
->div
->n_row
);
2806 return isl_qpolynomial_substitute_equalities_lifted(qp
, eq
);
2808 isl_basic_set_free(eq
);
2809 isl_qpolynomial_free(qp
);
2813 static __isl_give isl_basic_set
*add_div_constraints(
2814 __isl_take isl_basic_set
*bset
, __isl_take isl_mat
*div
)
2822 bset
= isl_basic_set_extend_constraints(bset
, 0, 2 * div
->n_row
);
2825 total
= isl_basic_set_total_dim(bset
);
2826 for (i
= 0; i
< div
->n_row
; ++i
)
2827 if (isl_basic_set_add_div_constraints_var(bset
,
2828 total
- div
->n_row
+ i
, div
->row
[i
]) < 0)
2835 isl_basic_set_free(bset
);
2839 /* Look for equalities among the variables shared by context and qp
2840 * and the integer divisions of qp, if any.
2841 * The equalities are then used to eliminate variables and/or integer
2842 * divisions from qp.
2844 __isl_give isl_qpolynomial
*isl_qpolynomial_gist(
2845 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
2851 if (qp
->div
->n_row
> 0) {
2852 isl_basic_set
*bset
;
2853 context
= isl_set_add_dims(context
, isl_dim_set
,
2855 bset
= isl_basic_set_universe(isl_set_get_space(context
));
2856 bset
= add_div_constraints(bset
, isl_mat_copy(qp
->div
));
2857 context
= isl_set_intersect(context
,
2858 isl_set_from_basic_set(bset
));
2861 aff
= isl_set_affine_hull(context
);
2862 return isl_qpolynomial_substitute_equalities_lifted(qp
, aff
);
2864 isl_qpolynomial_free(qp
);
2865 isl_set_free(context
);
2869 __isl_give isl_qpolynomial
*isl_qpolynomial_gist_params(
2870 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
2872 isl_space
*space
= isl_qpolynomial_get_domain_space(qp
);
2873 isl_set
*dom_context
= isl_set_universe(space
);
2874 dom_context
= isl_set_intersect_params(dom_context
, context
);
2875 return isl_qpolynomial_gist(qp
, dom_context
);
2878 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_from_qpolynomial(
2879 __isl_take isl_qpolynomial
*qp
)
2885 if (isl_qpolynomial_is_zero(qp
)) {
2886 isl_space
*dim
= isl_qpolynomial_get_space(qp
);
2887 isl_qpolynomial_free(qp
);
2888 return isl_pw_qpolynomial_zero(dim
);
2891 dom
= isl_set_universe(isl_qpolynomial_get_domain_space(qp
));
2892 return isl_pw_qpolynomial_alloc(dom
, qp
);
2896 #define PW isl_pw_qpolynomial
2898 #define EL isl_qpolynomial
2900 #define EL_IS_ZERO is_zero
2904 #define IS_ZERO is_zero
2907 #undef DEFAULT_IS_ZERO
2908 #define DEFAULT_IS_ZERO 1
2912 #include <isl_pw_templ.c>
2915 #define UNION isl_union_pw_qpolynomial
2917 #define PART isl_pw_qpolynomial
2919 #define PARTS pw_qpolynomial
2921 #include <isl_union_single.c>
2922 #include <isl_union_eval.c>
2923 #include <isl_union_neg.c>
2925 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial
*pwqp
)
2933 if (!isl_set_plain_is_universe(pwqp
->p
[0].set
))
2936 return isl_qpolynomial_is_one(pwqp
->p
[0].qp
);
2939 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add(
2940 __isl_take isl_pw_qpolynomial
*pwqp1
,
2941 __isl_take isl_pw_qpolynomial
*pwqp2
)
2943 return isl_pw_qpolynomial_union_add_(pwqp1
, pwqp2
);
2946 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_mul(
2947 __isl_take isl_pw_qpolynomial
*pwqp1
,
2948 __isl_take isl_pw_qpolynomial
*pwqp2
)
2951 struct isl_pw_qpolynomial
*res
;
2953 if (!pwqp1
|| !pwqp2
)
2956 isl_assert(pwqp1
->dim
->ctx
, isl_space_is_equal(pwqp1
->dim
, pwqp2
->dim
),
2959 if (isl_pw_qpolynomial_is_zero(pwqp1
)) {
2960 isl_pw_qpolynomial_free(pwqp2
);
2964 if (isl_pw_qpolynomial_is_zero(pwqp2
)) {
2965 isl_pw_qpolynomial_free(pwqp1
);
2969 if (isl_pw_qpolynomial_is_one(pwqp1
)) {
2970 isl_pw_qpolynomial_free(pwqp1
);
2974 if (isl_pw_qpolynomial_is_one(pwqp2
)) {
2975 isl_pw_qpolynomial_free(pwqp2
);
2979 n
= pwqp1
->n
* pwqp2
->n
;
2980 res
= isl_pw_qpolynomial_alloc_size(isl_space_copy(pwqp1
->dim
), n
);
2982 for (i
= 0; i
< pwqp1
->n
; ++i
) {
2983 for (j
= 0; j
< pwqp2
->n
; ++j
) {
2984 struct isl_set
*common
;
2985 struct isl_qpolynomial
*prod
;
2986 common
= isl_set_intersect(isl_set_copy(pwqp1
->p
[i
].set
),
2987 isl_set_copy(pwqp2
->p
[j
].set
));
2988 if (isl_set_plain_is_empty(common
)) {
2989 isl_set_free(common
);
2993 prod
= isl_qpolynomial_mul(
2994 isl_qpolynomial_copy(pwqp1
->p
[i
].qp
),
2995 isl_qpolynomial_copy(pwqp2
->p
[j
].qp
));
2997 res
= isl_pw_qpolynomial_add_piece(res
, common
, prod
);
3001 isl_pw_qpolynomial_free(pwqp1
);
3002 isl_pw_qpolynomial_free(pwqp2
);
3006 isl_pw_qpolynomial_free(pwqp1
);
3007 isl_pw_qpolynomial_free(pwqp2
);
3011 __isl_give isl_val
*isl_upoly_eval(__isl_take
struct isl_upoly
*up
,
3012 __isl_take isl_vec
*vec
)
3015 struct isl_upoly_rec
*rec
;
3019 if (isl_upoly_is_cst(up
)) {
3021 res
= isl_upoly_get_constant_val(up
);
3026 rec
= isl_upoly_as_rec(up
);
3030 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
3032 base
= isl_val_rat_from_isl_int(up
->ctx
,
3033 vec
->el
[1 + up
->var
], vec
->el
[0]);
3035 res
= isl_upoly_eval(isl_upoly_copy(rec
->p
[rec
->n
- 1]),
3038 for (i
= rec
->n
- 2; i
>= 0; --i
) {
3039 res
= isl_val_mul(res
, isl_val_copy(base
));
3040 res
= isl_val_add(res
,
3041 isl_upoly_eval(isl_upoly_copy(rec
->p
[i
]),
3042 isl_vec_copy(vec
)));
3055 __isl_give isl_val
*isl_qpolynomial_eval(__isl_take isl_qpolynomial
*qp
,
3056 __isl_take isl_point
*pnt
)
3063 isl_assert(pnt
->dim
->ctx
, isl_space_is_equal(pnt
->dim
, qp
->dim
), goto error
);
3065 if (qp
->div
->n_row
== 0)
3066 ext
= isl_vec_copy(pnt
->vec
);
3069 unsigned dim
= isl_space_dim(qp
->dim
, isl_dim_all
);
3070 ext
= isl_vec_alloc(qp
->dim
->ctx
, 1 + dim
+ qp
->div
->n_row
);
3074 isl_seq_cpy(ext
->el
, pnt
->vec
->el
, pnt
->vec
->size
);
3075 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
3076 isl_seq_inner_product(qp
->div
->row
[i
] + 1, ext
->el
,
3077 1 + dim
+ i
, &ext
->el
[1+dim
+i
]);
3078 isl_int_fdiv_q(ext
->el
[1+dim
+i
], ext
->el
[1+dim
+i
],
3079 qp
->div
->row
[i
][0]);
3083 v
= isl_upoly_eval(isl_upoly_copy(qp
->upoly
), ext
);
3085 isl_qpolynomial_free(qp
);
3086 isl_point_free(pnt
);
3090 isl_qpolynomial_free(qp
);
3091 isl_point_free(pnt
);
3095 int isl_upoly_cmp(__isl_keep
struct isl_upoly_cst
*cst1
,
3096 __isl_keep
struct isl_upoly_cst
*cst2
)
3101 isl_int_mul(t
, cst1
->n
, cst2
->d
);
3102 isl_int_submul(t
, cst2
->n
, cst1
->d
);
3103 cmp
= isl_int_sgn(t
);
3108 __isl_give isl_qpolynomial
*isl_qpolynomial_insert_dims(
3109 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
,
3110 unsigned first
, unsigned n
)
3118 if (type
== isl_dim_out
)
3119 isl_die(qp
->div
->ctx
, isl_error_invalid
,
3120 "cannot insert output/set dimensions",
3122 if (type
== isl_dim_in
)
3124 if (n
== 0 && !isl_space_is_named_or_nested(qp
->dim
, type
))
3127 qp
= isl_qpolynomial_cow(qp
);
3131 isl_assert(qp
->div
->ctx
, first
<= isl_space_dim(qp
->dim
, type
),
3134 g_pos
= pos(qp
->dim
, type
) + first
;
3136 qp
->div
= isl_mat_insert_zero_cols(qp
->div
, 2 + g_pos
, n
);
3140 total
= qp
->div
->n_col
- 2;
3141 if (total
> g_pos
) {
3143 exp
= isl_alloc_array(qp
->div
->ctx
, int, total
- g_pos
);
3146 for (i
= 0; i
< total
- g_pos
; ++i
)
3148 qp
->upoly
= expand(qp
->upoly
, exp
, g_pos
);
3154 qp
->dim
= isl_space_insert_dims(qp
->dim
, type
, first
, n
);
3160 isl_qpolynomial_free(qp
);
3164 __isl_give isl_qpolynomial
*isl_qpolynomial_add_dims(
3165 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
, unsigned n
)
3169 pos
= isl_qpolynomial_dim(qp
, type
);
3171 return isl_qpolynomial_insert_dims(qp
, type
, pos
, n
);
3174 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add_dims(
3175 __isl_take isl_pw_qpolynomial
*pwqp
,
3176 enum isl_dim_type type
, unsigned n
)
3180 pos
= isl_pw_qpolynomial_dim(pwqp
, type
);
3182 return isl_pw_qpolynomial_insert_dims(pwqp
, type
, pos
, n
);
3185 static int *reordering_move(isl_ctx
*ctx
,
3186 unsigned len
, unsigned dst
, unsigned src
, unsigned n
)
3191 reordering
= isl_alloc_array(ctx
, int, len
);
3196 for (i
= 0; i
< dst
; ++i
)
3198 for (i
= 0; i
< n
; ++i
)
3199 reordering
[src
+ i
] = dst
+ i
;
3200 for (i
= 0; i
< src
- dst
; ++i
)
3201 reordering
[dst
+ i
] = dst
+ n
+ i
;
3202 for (i
= 0; i
< len
- src
- n
; ++i
)
3203 reordering
[src
+ n
+ i
] = src
+ n
+ i
;
3205 for (i
= 0; i
< src
; ++i
)
3207 for (i
= 0; i
< n
; ++i
)
3208 reordering
[src
+ i
] = dst
+ i
;
3209 for (i
= 0; i
< dst
- src
; ++i
)
3210 reordering
[src
+ n
+ i
] = src
+ i
;
3211 for (i
= 0; i
< len
- dst
- n
; ++i
)
3212 reordering
[dst
+ n
+ i
] = dst
+ n
+ i
;
3218 __isl_give isl_qpolynomial
*isl_qpolynomial_move_dims(
3219 __isl_take isl_qpolynomial
*qp
,
3220 enum isl_dim_type dst_type
, unsigned dst_pos
,
3221 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
3230 qp
= isl_qpolynomial_cow(qp
);
3234 if (dst_type
== isl_dim_out
|| src_type
== isl_dim_out
)
3235 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
3236 "cannot move output/set dimension",
3238 if (dst_type
== isl_dim_in
)
3239 dst_type
= isl_dim_set
;
3240 if (src_type
== isl_dim_in
)
3241 src_type
= isl_dim_set
;
3243 isl_assert(qp
->dim
->ctx
, src_pos
+ n
<= isl_space_dim(qp
->dim
, src_type
),
3246 g_dst_pos
= pos(qp
->dim
, dst_type
) + dst_pos
;
3247 g_src_pos
= pos(qp
->dim
, src_type
) + src_pos
;
3248 if (dst_type
> src_type
)
3251 qp
->div
= isl_mat_move_cols(qp
->div
, 2 + g_dst_pos
, 2 + g_src_pos
, n
);
3258 reordering
= reordering_move(qp
->dim
->ctx
,
3259 qp
->div
->n_col
- 2, g_dst_pos
, g_src_pos
, n
);
3263 qp
->upoly
= reorder(qp
->upoly
, reordering
);
3268 qp
->dim
= isl_space_move_dims(qp
->dim
, dst_type
, dst_pos
, src_type
, src_pos
, n
);
3274 isl_qpolynomial_free(qp
);
3278 __isl_give isl_qpolynomial
*isl_qpolynomial_from_affine(__isl_take isl_space
*dim
,
3279 isl_int
*f
, isl_int denom
)
3281 struct isl_upoly
*up
;
3283 dim
= isl_space_domain(dim
);
3287 up
= isl_upoly_from_affine(dim
->ctx
, f
, denom
,
3288 1 + isl_space_dim(dim
, isl_dim_all
));
3290 return isl_qpolynomial_alloc(dim
, 0, up
);
3293 __isl_give isl_qpolynomial
*isl_qpolynomial_from_aff(__isl_take isl_aff
*aff
)
3296 struct isl_upoly
*up
;
3297 isl_qpolynomial
*qp
;
3302 ctx
= isl_aff_get_ctx(aff
);
3303 up
= isl_upoly_from_affine(ctx
, aff
->v
->el
+ 1, aff
->v
->el
[0],
3306 qp
= isl_qpolynomial_alloc(isl_aff_get_domain_space(aff
),
3307 aff
->ls
->div
->n_row
, up
);
3311 isl_mat_free(qp
->div
);
3312 qp
->div
= isl_mat_copy(aff
->ls
->div
);
3313 qp
->div
= isl_mat_cow(qp
->div
);
3318 qp
= reduce_divs(qp
);
3319 qp
= remove_redundant_divs(qp
);
3323 return isl_qpolynomial_free(qp
);
3326 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_from_pw_aff(
3327 __isl_take isl_pw_aff
*pwaff
)
3330 isl_pw_qpolynomial
*pwqp
;
3335 pwqp
= isl_pw_qpolynomial_alloc_size(isl_pw_aff_get_space(pwaff
),
3338 for (i
= 0; i
< pwaff
->n
; ++i
) {
3340 isl_qpolynomial
*qp
;
3342 dom
= isl_set_copy(pwaff
->p
[i
].set
);
3343 qp
= isl_qpolynomial_from_aff(isl_aff_copy(pwaff
->p
[i
].aff
));
3344 pwqp
= isl_pw_qpolynomial_add_piece(pwqp
, dom
, qp
);
3347 isl_pw_aff_free(pwaff
);
3351 __isl_give isl_qpolynomial
*isl_qpolynomial_from_constraint(
3352 __isl_take isl_constraint
*c
, enum isl_dim_type type
, unsigned pos
)
3356 aff
= isl_constraint_get_bound(c
, type
, pos
);
3357 isl_constraint_free(c
);
3358 return isl_qpolynomial_from_aff(aff
);
3361 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3362 * in "qp" by subs[i].
3364 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute(
3365 __isl_take isl_qpolynomial
*qp
,
3366 enum isl_dim_type type
, unsigned first
, unsigned n
,
3367 __isl_keep isl_qpolynomial
**subs
)
3370 struct isl_upoly
**ups
;
3375 qp
= isl_qpolynomial_cow(qp
);
3379 if (type
== isl_dim_out
)
3380 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
3381 "cannot substitute output/set dimension",
3383 if (type
== isl_dim_in
)
3386 for (i
= 0; i
< n
; ++i
)
3390 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_space_dim(qp
->dim
, type
),
3393 for (i
= 0; i
< n
; ++i
)
3394 isl_assert(qp
->dim
->ctx
, isl_space_is_equal(qp
->dim
, subs
[i
]->dim
),
3397 isl_assert(qp
->dim
->ctx
, qp
->div
->n_row
== 0, goto error
);
3398 for (i
= 0; i
< n
; ++i
)
3399 isl_assert(qp
->dim
->ctx
, subs
[i
]->div
->n_row
== 0, goto error
);
3401 first
+= pos(qp
->dim
, type
);
3403 ups
= isl_alloc_array(qp
->dim
->ctx
, struct isl_upoly
*, n
);
3406 for (i
= 0; i
< n
; ++i
)
3407 ups
[i
] = subs
[i
]->upoly
;
3409 qp
->upoly
= isl_upoly_subs(qp
->upoly
, first
, n
, ups
);
3418 isl_qpolynomial_free(qp
);
3422 /* Extend "bset" with extra set dimensions for each integer division
3423 * in "qp" and then call "fn" with the extended bset and the polynomial
3424 * that results from replacing each of the integer divisions by the
3425 * corresponding extra set dimension.
3427 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial
*qp
,
3428 __isl_keep isl_basic_set
*bset
,
3429 int (*fn
)(__isl_take isl_basic_set
*bset
,
3430 __isl_take isl_qpolynomial
*poly
, void *user
), void *user
)
3434 isl_qpolynomial
*poly
;
3438 if (qp
->div
->n_row
== 0)
3439 return fn(isl_basic_set_copy(bset
), isl_qpolynomial_copy(qp
),
3442 div
= isl_mat_copy(qp
->div
);
3443 dim
= isl_space_copy(qp
->dim
);
3444 dim
= isl_space_add_dims(dim
, isl_dim_set
, qp
->div
->n_row
);
3445 poly
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_copy(qp
->upoly
));
3446 bset
= isl_basic_set_copy(bset
);
3447 bset
= isl_basic_set_add_dims(bset
, isl_dim_set
, qp
->div
->n_row
);
3448 bset
= add_div_constraints(bset
, div
);
3450 return fn(bset
, poly
, user
);
3455 /* Return total degree in variables first (inclusive) up to last (exclusive).
3457 int isl_upoly_degree(__isl_keep
struct isl_upoly
*up
, int first
, int last
)
3461 struct isl_upoly_rec
*rec
;
3465 if (isl_upoly_is_zero(up
))
3467 if (isl_upoly_is_cst(up
) || up
->var
< first
)
3470 rec
= isl_upoly_as_rec(up
);
3474 for (i
= 0; i
< rec
->n
; ++i
) {
3477 if (isl_upoly_is_zero(rec
->p
[i
]))
3479 d
= isl_upoly_degree(rec
->p
[i
], first
, last
);
3489 /* Return total degree in set variables.
3491 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial
*poly
)
3499 ovar
= isl_space_offset(poly
->dim
, isl_dim_set
);
3500 nvar
= isl_space_dim(poly
->dim
, isl_dim_set
);
3501 return isl_upoly_degree(poly
->upoly
, ovar
, ovar
+ nvar
);
3504 __isl_give
struct isl_upoly
*isl_upoly_coeff(__isl_keep
struct isl_upoly
*up
,
3505 unsigned pos
, int deg
)
3508 struct isl_upoly_rec
*rec
;
3513 if (isl_upoly_is_cst(up
) || up
->var
< pos
) {
3515 return isl_upoly_copy(up
);
3517 return isl_upoly_zero(up
->ctx
);
3520 rec
= isl_upoly_as_rec(up
);
3524 if (up
->var
== pos
) {
3526 return isl_upoly_copy(rec
->p
[deg
]);
3528 return isl_upoly_zero(up
->ctx
);
3531 up
= isl_upoly_copy(up
);
3532 up
= isl_upoly_cow(up
);
3533 rec
= isl_upoly_as_rec(up
);
3537 for (i
= 0; i
< rec
->n
; ++i
) {
3538 struct isl_upoly
*t
;
3539 t
= isl_upoly_coeff(rec
->p
[i
], pos
, deg
);
3542 isl_upoly_free(rec
->p
[i
]);
3552 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3554 __isl_give isl_qpolynomial
*isl_qpolynomial_coeff(
3555 __isl_keep isl_qpolynomial
*qp
,
3556 enum isl_dim_type type
, unsigned t_pos
, int deg
)
3559 struct isl_upoly
*up
;
3565 if (type
== isl_dim_out
)
3566 isl_die(qp
->div
->ctx
, isl_error_invalid
,
3567 "output/set dimension does not have a coefficient",
3569 if (type
== isl_dim_in
)
3572 isl_assert(qp
->div
->ctx
, t_pos
< isl_space_dim(qp
->dim
, type
),
3575 g_pos
= pos(qp
->dim
, type
) + t_pos
;
3576 up
= isl_upoly_coeff(qp
->upoly
, g_pos
, deg
);
3578 c
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
), qp
->div
->n_row
, up
);
3581 isl_mat_free(c
->div
);
3582 c
->div
= isl_mat_copy(qp
->div
);
3587 isl_qpolynomial_free(c
);
3591 /* Homogenize the polynomial in the variables first (inclusive) up to
3592 * last (exclusive) by inserting powers of variable first.
3593 * Variable first is assumed not to appear in the input.
3595 __isl_give
struct isl_upoly
*isl_upoly_homogenize(
3596 __isl_take
struct isl_upoly
*up
, int deg
, int target
,
3597 int first
, int last
)
3600 struct isl_upoly_rec
*rec
;
3604 if (isl_upoly_is_zero(up
))
3608 if (isl_upoly_is_cst(up
) || up
->var
< first
) {
3609 struct isl_upoly
*hom
;
3611 hom
= isl_upoly_var_pow(up
->ctx
, first
, target
- deg
);
3614 rec
= isl_upoly_as_rec(hom
);
3615 rec
->p
[target
- deg
] = isl_upoly_mul(rec
->p
[target
- deg
], up
);
3620 up
= isl_upoly_cow(up
);
3621 rec
= isl_upoly_as_rec(up
);
3625 for (i
= 0; i
< rec
->n
; ++i
) {
3626 if (isl_upoly_is_zero(rec
->p
[i
]))
3628 rec
->p
[i
] = isl_upoly_homogenize(rec
->p
[i
],
3629 up
->var
< last
? deg
+ i
: i
, target
,
3641 /* Homogenize the polynomial in the set variables by introducing
3642 * powers of an extra set variable at position 0.
3644 __isl_give isl_qpolynomial
*isl_qpolynomial_homogenize(
3645 __isl_take isl_qpolynomial
*poly
)
3649 int deg
= isl_qpolynomial_degree(poly
);
3654 poly
= isl_qpolynomial_insert_dims(poly
, isl_dim_in
, 0, 1);
3655 poly
= isl_qpolynomial_cow(poly
);
3659 ovar
= isl_space_offset(poly
->dim
, isl_dim_set
);
3660 nvar
= isl_space_dim(poly
->dim
, isl_dim_set
);
3661 poly
->upoly
= isl_upoly_homogenize(poly
->upoly
, 0, deg
,
3668 isl_qpolynomial_free(poly
);
3672 __isl_give isl_term
*isl_term_alloc(__isl_take isl_space
*dim
,
3673 __isl_take isl_mat
*div
)
3681 n
= isl_space_dim(dim
, isl_dim_all
) + div
->n_row
;
3683 term
= isl_calloc(dim
->ctx
, struct isl_term
,
3684 sizeof(struct isl_term
) + (n
- 1) * sizeof(int));
3691 isl_int_init(term
->n
);
3692 isl_int_init(term
->d
);
3696 isl_space_free(dim
);
3701 __isl_give isl_term
*isl_term_copy(__isl_keep isl_term
*term
)
3710 __isl_give isl_term
*isl_term_dup(__isl_keep isl_term
*term
)
3719 total
= isl_space_dim(term
->dim
, isl_dim_all
) + term
->div
->n_row
;
3721 dup
= isl_term_alloc(isl_space_copy(term
->dim
), isl_mat_copy(term
->div
));
3725 isl_int_set(dup
->n
, term
->n
);
3726 isl_int_set(dup
->d
, term
->d
);
3728 for (i
= 0; i
< total
; ++i
)
3729 dup
->pow
[i
] = term
->pow
[i
];
3734 __isl_give isl_term
*isl_term_cow(__isl_take isl_term
*term
)
3742 return isl_term_dup(term
);
3745 void isl_term_free(__isl_take isl_term
*term
)
3750 if (--term
->ref
> 0)
3753 isl_space_free(term
->dim
);
3754 isl_mat_free(term
->div
);
3755 isl_int_clear(term
->n
);
3756 isl_int_clear(term
->d
);
3760 unsigned isl_term_dim(__isl_keep isl_term
*term
, enum isl_dim_type type
)
3768 case isl_dim_out
: return isl_space_dim(term
->dim
, type
);
3769 case isl_dim_div
: return term
->div
->n_row
;
3770 case isl_dim_all
: return isl_space_dim(term
->dim
, isl_dim_all
) +
3776 isl_ctx
*isl_term_get_ctx(__isl_keep isl_term
*term
)
3778 return term
? term
->dim
->ctx
: NULL
;
3781 void isl_term_get_num(__isl_keep isl_term
*term
, isl_int
*n
)
3785 isl_int_set(*n
, term
->n
);
3788 void isl_term_get_den(__isl_keep isl_term
*term
, isl_int
*d
)
3792 isl_int_set(*d
, term
->d
);
3795 /* Return the coefficient of the term "term".
3797 __isl_give isl_val
*isl_term_get_coefficient_val(__isl_keep isl_term
*term
)
3802 return isl_val_rat_from_isl_int(isl_term_get_ctx(term
),
3806 int isl_term_get_exp(__isl_keep isl_term
*term
,
3807 enum isl_dim_type type
, unsigned pos
)
3812 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, type
), return -1);
3814 if (type
>= isl_dim_set
)
3815 pos
+= isl_space_dim(term
->dim
, isl_dim_param
);
3816 if (type
>= isl_dim_div
)
3817 pos
+= isl_space_dim(term
->dim
, isl_dim_set
);
3819 return term
->pow
[pos
];
3822 __isl_give isl_aff
*isl_term_get_div(__isl_keep isl_term
*term
, unsigned pos
)
3824 isl_local_space
*ls
;
3830 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, isl_dim_div
),
3833 ls
= isl_local_space_alloc_div(isl_space_copy(term
->dim
),
3834 isl_mat_copy(term
->div
));
3835 aff
= isl_aff_alloc(ls
);
3839 isl_seq_cpy(aff
->v
->el
, term
->div
->row
[pos
], aff
->v
->size
);
3841 aff
= isl_aff_normalize(aff
);
3846 __isl_give isl_term
*isl_upoly_foreach_term(__isl_keep
struct isl_upoly
*up
,
3847 isl_stat (*fn
)(__isl_take isl_term
*term
, void *user
),
3848 __isl_take isl_term
*term
, void *user
)
3851 struct isl_upoly_rec
*rec
;
3856 if (isl_upoly_is_zero(up
))
3859 isl_assert(up
->ctx
, !isl_upoly_is_nan(up
), goto error
);
3860 isl_assert(up
->ctx
, !isl_upoly_is_infty(up
), goto error
);
3861 isl_assert(up
->ctx
, !isl_upoly_is_neginfty(up
), goto error
);
3863 if (isl_upoly_is_cst(up
)) {
3864 struct isl_upoly_cst
*cst
;
3865 cst
= isl_upoly_as_cst(up
);
3868 term
= isl_term_cow(term
);
3871 isl_int_set(term
->n
, cst
->n
);
3872 isl_int_set(term
->d
, cst
->d
);
3873 if (fn(isl_term_copy(term
), user
) < 0)
3878 rec
= isl_upoly_as_rec(up
);
3882 for (i
= 0; i
< rec
->n
; ++i
) {
3883 term
= isl_term_cow(term
);
3886 term
->pow
[up
->var
] = i
;
3887 term
= isl_upoly_foreach_term(rec
->p
[i
], fn
, term
, user
);
3891 term
->pow
[up
->var
] = 0;
3895 isl_term_free(term
);
3899 isl_stat
isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial
*qp
,
3900 isl_stat (*fn
)(__isl_take isl_term
*term
, void *user
), void *user
)
3905 return isl_stat_error
;
3907 term
= isl_term_alloc(isl_space_copy(qp
->dim
), isl_mat_copy(qp
->div
));
3909 return isl_stat_error
;
3911 term
= isl_upoly_foreach_term(qp
->upoly
, fn
, term
, user
);
3913 isl_term_free(term
);
3915 return term
? isl_stat_ok
: isl_stat_error
;
3918 __isl_give isl_qpolynomial
*isl_qpolynomial_from_term(__isl_take isl_term
*term
)
3920 struct isl_upoly
*up
;
3921 isl_qpolynomial
*qp
;
3927 n
= isl_space_dim(term
->dim
, isl_dim_all
) + term
->div
->n_row
;
3929 up
= isl_upoly_rat_cst(term
->dim
->ctx
, term
->n
, term
->d
);
3930 for (i
= 0; i
< n
; ++i
) {
3933 up
= isl_upoly_mul(up
,
3934 isl_upoly_var_pow(term
->dim
->ctx
, i
, term
->pow
[i
]));
3937 qp
= isl_qpolynomial_alloc(isl_space_copy(term
->dim
), term
->div
->n_row
, up
);
3940 isl_mat_free(qp
->div
);
3941 qp
->div
= isl_mat_copy(term
->div
);
3945 isl_term_free(term
);
3948 isl_qpolynomial_free(qp
);
3949 isl_term_free(term
);
3953 __isl_give isl_qpolynomial
*isl_qpolynomial_lift(__isl_take isl_qpolynomial
*qp
,
3954 __isl_take isl_space
*dim
)
3963 if (isl_space_is_equal(qp
->dim
, dim
)) {
3964 isl_space_free(dim
);
3968 qp
= isl_qpolynomial_cow(qp
);
3972 extra
= isl_space_dim(dim
, isl_dim_set
) -
3973 isl_space_dim(qp
->dim
, isl_dim_set
);
3974 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
3975 if (qp
->div
->n_row
) {
3978 exp
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
3981 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3983 qp
->upoly
= expand(qp
->upoly
, exp
, total
);
3988 qp
->div
= isl_mat_insert_cols(qp
->div
, 2 + total
, extra
);
3991 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3992 isl_seq_clr(qp
->div
->row
[i
] + 2 + total
, extra
);
3994 isl_space_free(qp
->dim
);
3999 isl_space_free(dim
);
4000 isl_qpolynomial_free(qp
);
4004 /* For each parameter or variable that does not appear in qp,
4005 * first eliminate the variable from all constraints and then set it to zero.
4007 static __isl_give isl_set
*fix_inactive(__isl_take isl_set
*set
,
4008 __isl_keep isl_qpolynomial
*qp
)
4019 d
= isl_space_dim(set
->dim
, isl_dim_all
);
4020 active
= isl_calloc_array(set
->ctx
, int, d
);
4021 if (set_active(qp
, active
) < 0)
4024 for (i
= 0; i
< d
; ++i
)
4033 nparam
= isl_space_dim(set
->dim
, isl_dim_param
);
4034 nvar
= isl_space_dim(set
->dim
, isl_dim_set
);
4035 for (i
= 0; i
< nparam
; ++i
) {
4038 set
= isl_set_eliminate(set
, isl_dim_param
, i
, 1);
4039 set
= isl_set_fix_si(set
, isl_dim_param
, i
, 0);
4041 for (i
= 0; i
< nvar
; ++i
) {
4042 if (active
[nparam
+ i
])
4044 set
= isl_set_eliminate(set
, isl_dim_set
, i
, 1);
4045 set
= isl_set_fix_si(set
, isl_dim_set
, i
, 0);
4057 struct isl_opt_data
{
4058 isl_qpolynomial
*qp
;
4064 static isl_stat
opt_fn(__isl_take isl_point
*pnt
, void *user
)
4066 struct isl_opt_data
*data
= (struct isl_opt_data
*)user
;
4069 val
= isl_qpolynomial_eval(isl_qpolynomial_copy(data
->qp
), pnt
);
4073 } else if (data
->max
) {
4074 data
->opt
= isl_val_max(data
->opt
, val
);
4076 data
->opt
= isl_val_min(data
->opt
, val
);
4082 __isl_give isl_val
*isl_qpolynomial_opt_on_domain(
4083 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*set
, int max
)
4085 struct isl_opt_data data
= { NULL
, 1, NULL
, max
};
4090 if (isl_upoly_is_cst(qp
->upoly
)) {
4092 data
.opt
= isl_qpolynomial_get_constant_val(qp
);
4093 isl_qpolynomial_free(qp
);
4097 set
= fix_inactive(set
, qp
);
4100 if (isl_set_foreach_point(set
, opt_fn
, &data
) < 0)
4104 data
.opt
= isl_val_zero(isl_set_get_ctx(set
));
4107 isl_qpolynomial_free(qp
);
4111 isl_qpolynomial_free(qp
);
4112 isl_val_free(data
.opt
);
4116 __isl_give isl_qpolynomial
*isl_qpolynomial_morph_domain(
4117 __isl_take isl_qpolynomial
*qp
, __isl_take isl_morph
*morph
)
4122 struct isl_upoly
**subs
;
4123 isl_mat
*mat
, *diag
;
4125 qp
= isl_qpolynomial_cow(qp
);
4130 isl_assert(ctx
, isl_space_is_equal(qp
->dim
, morph
->dom
->dim
), goto error
);
4132 n_sub
= morph
->inv
->n_row
- 1;
4133 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
4134 n_sub
+= qp
->div
->n_row
;
4135 subs
= isl_calloc_array(ctx
, struct isl_upoly
*, n_sub
);
4139 for (i
= 0; 1 + i
< morph
->inv
->n_row
; ++i
)
4140 subs
[i
] = isl_upoly_from_affine(ctx
, morph
->inv
->row
[1 + i
],
4141 morph
->inv
->row
[0][0], morph
->inv
->n_col
);
4142 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
4143 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4144 subs
[morph
->inv
->n_row
- 1 + i
] =
4145 isl_upoly_var_pow(ctx
, morph
->inv
->n_col
- 1 + i
, 1);
4147 qp
->upoly
= isl_upoly_subs(qp
->upoly
, 0, n_sub
, subs
);
4149 for (i
= 0; i
< n_sub
; ++i
)
4150 isl_upoly_free(subs
[i
]);
4153 diag
= isl_mat_diag(ctx
, 1, morph
->inv
->row
[0][0]);
4154 mat
= isl_mat_diagonal(diag
, isl_mat_copy(morph
->inv
));
4155 diag
= isl_mat_diag(ctx
, qp
->div
->n_row
, morph
->inv
->row
[0][0]);
4156 mat
= isl_mat_diagonal(mat
, diag
);
4157 qp
->div
= isl_mat_product(qp
->div
, mat
);
4158 isl_space_free(qp
->dim
);
4159 qp
->dim
= isl_space_copy(morph
->ran
->dim
);
4161 if (!qp
->upoly
|| !qp
->div
|| !qp
->dim
)
4164 isl_morph_free(morph
);
4168 isl_qpolynomial_free(qp
);
4169 isl_morph_free(morph
);
4173 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_mul(
4174 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
4175 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
4177 return isl_union_pw_qpolynomial_match_bin_op(upwqp1
, upwqp2
,
4178 &isl_pw_qpolynomial_mul
);
4181 /* Reorder the columns of the given div definitions according to the
4184 static __isl_give isl_mat
*reorder_divs(__isl_take isl_mat
*div
,
4185 __isl_take isl_reordering
*r
)
4194 extra
= isl_space_dim(r
->dim
, isl_dim_all
) + div
->n_row
- r
->len
;
4195 mat
= isl_mat_alloc(div
->ctx
, div
->n_row
, div
->n_col
+ extra
);
4199 for (i
= 0; i
< div
->n_row
; ++i
) {
4200 isl_seq_cpy(mat
->row
[i
], div
->row
[i
], 2);
4201 isl_seq_clr(mat
->row
[i
] + 2, mat
->n_col
- 2);
4202 for (j
= 0; j
< r
->len
; ++j
)
4203 isl_int_set(mat
->row
[i
][2 + r
->pos
[j
]],
4204 div
->row
[i
][2 + j
]);
4207 isl_reordering_free(r
);
4211 isl_reordering_free(r
);
4216 /* Reorder the dimension of "qp" according to the given reordering.
4218 __isl_give isl_qpolynomial
*isl_qpolynomial_realign_domain(
4219 __isl_take isl_qpolynomial
*qp
, __isl_take isl_reordering
*r
)
4221 qp
= isl_qpolynomial_cow(qp
);
4225 r
= isl_reordering_extend(r
, qp
->div
->n_row
);
4229 qp
->div
= reorder_divs(qp
->div
, isl_reordering_copy(r
));
4233 qp
->upoly
= reorder(qp
->upoly
, r
->pos
);
4237 qp
= isl_qpolynomial_reset_domain_space(qp
, isl_space_copy(r
->dim
));
4239 isl_reordering_free(r
);
4242 isl_qpolynomial_free(qp
);
4243 isl_reordering_free(r
);
4247 __isl_give isl_qpolynomial
*isl_qpolynomial_align_params(
4248 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*model
)
4253 if (!isl_space_match(qp
->dim
, isl_dim_param
, model
, isl_dim_param
)) {
4254 isl_reordering
*exp
;
4256 model
= isl_space_drop_dims(model
, isl_dim_in
,
4257 0, isl_space_dim(model
, isl_dim_in
));
4258 model
= isl_space_drop_dims(model
, isl_dim_out
,
4259 0, isl_space_dim(model
, isl_dim_out
));
4260 exp
= isl_parameter_alignment_reordering(qp
->dim
, model
);
4261 exp
= isl_reordering_extend_space(exp
,
4262 isl_qpolynomial_get_domain_space(qp
));
4263 qp
= isl_qpolynomial_realign_domain(qp
, exp
);
4266 isl_space_free(model
);
4269 isl_space_free(model
);
4270 isl_qpolynomial_free(qp
);
4274 struct isl_split_periods_data
{
4276 isl_pw_qpolynomial
*res
;
4279 /* Create a slice where the integer division "div" has the fixed value "v".
4280 * In particular, if "div" refers to floor(f/m), then create a slice
4282 * m v <= f <= m v + (m - 1)
4287 * -f + m v + (m - 1) >= 0
4289 static __isl_give isl_set
*set_div_slice(__isl_take isl_space
*dim
,
4290 __isl_keep isl_qpolynomial
*qp
, int div
, isl_int v
)
4293 isl_basic_set
*bset
= NULL
;
4299 total
= isl_space_dim(dim
, isl_dim_all
);
4300 bset
= isl_basic_set_alloc_space(isl_space_copy(dim
), 0, 0, 2);
4302 k
= isl_basic_set_alloc_inequality(bset
);
4305 isl_seq_cpy(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4306 isl_int_submul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4308 k
= isl_basic_set_alloc_inequality(bset
);
4311 isl_seq_neg(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4312 isl_int_addmul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4313 isl_int_add(bset
->ineq
[k
][0], bset
->ineq
[k
][0], qp
->div
->row
[div
][0]);
4314 isl_int_sub_ui(bset
->ineq
[k
][0], bset
->ineq
[k
][0], 1);
4316 isl_space_free(dim
);
4317 return isl_set_from_basic_set(bset
);
4319 isl_basic_set_free(bset
);
4320 isl_space_free(dim
);
4324 static isl_stat
split_periods(__isl_take isl_set
*set
,
4325 __isl_take isl_qpolynomial
*qp
, void *user
);
4327 /* Create a slice of the domain "set" such that integer division "div"
4328 * has the fixed value "v" and add the results to data->res,
4329 * replacing the integer division by "v" in "qp".
4331 static isl_stat
set_div(__isl_take isl_set
*set
,
4332 __isl_take isl_qpolynomial
*qp
, int div
, isl_int v
,
4333 struct isl_split_periods_data
*data
)
4338 struct isl_upoly
*cst
;
4340 slice
= set_div_slice(isl_set_get_space(set
), qp
, div
, v
);
4341 set
= isl_set_intersect(set
, slice
);
4346 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4348 for (i
= div
+ 1; i
< qp
->div
->n_row
; ++i
) {
4349 if (isl_int_is_zero(qp
->div
->row
[i
][2 + total
+ div
]))
4351 isl_int_addmul(qp
->div
->row
[i
][1],
4352 qp
->div
->row
[i
][2 + total
+ div
], v
);
4353 isl_int_set_si(qp
->div
->row
[i
][2 + total
+ div
], 0);
4356 cst
= isl_upoly_rat_cst(qp
->dim
->ctx
, v
, qp
->dim
->ctx
->one
);
4357 qp
= substitute_div(qp
, div
, cst
);
4359 return split_periods(set
, qp
, data
);
4362 isl_qpolynomial_free(qp
);
4366 /* Split the domain "set" such that integer division "div"
4367 * has a fixed value (ranging from "min" to "max") on each slice
4368 * and add the results to data->res.
4370 static isl_stat
split_div(__isl_take isl_set
*set
,
4371 __isl_take isl_qpolynomial
*qp
, int div
, isl_int min
, isl_int max
,
4372 struct isl_split_periods_data
*data
)
4374 for (; isl_int_le(min
, max
); isl_int_add_ui(min
, min
, 1)) {
4375 isl_set
*set_i
= isl_set_copy(set
);
4376 isl_qpolynomial
*qp_i
= isl_qpolynomial_copy(qp
);
4378 if (set_div(set_i
, qp_i
, div
, min
, data
) < 0)
4382 isl_qpolynomial_free(qp
);
4386 isl_qpolynomial_free(qp
);
4387 return isl_stat_error
;
4390 /* If "qp" refers to any integer division
4391 * that can only attain "max_periods" distinct values on "set"
4392 * then split the domain along those distinct values.
4393 * Add the results (or the original if no splitting occurs)
4396 static isl_stat
split_periods(__isl_take isl_set
*set
,
4397 __isl_take isl_qpolynomial
*qp
, void *user
)
4400 isl_pw_qpolynomial
*pwqp
;
4401 struct isl_split_periods_data
*data
;
4404 isl_stat r
= isl_stat_ok
;
4406 data
= (struct isl_split_periods_data
*)user
;
4411 if (qp
->div
->n_row
== 0) {
4412 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4413 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4419 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4420 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4421 enum isl_lp_result lp_res
;
4423 if (isl_seq_first_non_zero(qp
->div
->row
[i
] + 2 + total
,
4424 qp
->div
->n_row
) != -1)
4427 lp_res
= isl_set_solve_lp(set
, 0, qp
->div
->row
[i
] + 1,
4428 set
->ctx
->one
, &min
, NULL
, NULL
);
4429 if (lp_res
== isl_lp_error
)
4431 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4433 isl_int_fdiv_q(min
, min
, qp
->div
->row
[i
][0]);
4435 lp_res
= isl_set_solve_lp(set
, 1, qp
->div
->row
[i
] + 1,
4436 set
->ctx
->one
, &max
, NULL
, NULL
);
4437 if (lp_res
== isl_lp_error
)
4439 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4441 isl_int_fdiv_q(max
, max
, qp
->div
->row
[i
][0]);
4443 isl_int_sub(max
, max
, min
);
4444 if (isl_int_cmp_si(max
, data
->max_periods
) < 0) {
4445 isl_int_add(max
, max
, min
);
4450 if (i
< qp
->div
->n_row
) {
4451 r
= split_div(set
, qp
, i
, min
, max
, data
);
4453 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4454 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4466 isl_qpolynomial_free(qp
);
4467 return isl_stat_error
;
4470 /* If any quasi-polynomial in pwqp refers to any integer division
4471 * that can only attain "max_periods" distinct values on its domain
4472 * then split the domain along those distinct values.
4474 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_split_periods(
4475 __isl_take isl_pw_qpolynomial
*pwqp
, int max_periods
)
4477 struct isl_split_periods_data data
;
4479 data
.max_periods
= max_periods
;
4480 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp
));
4482 if (isl_pw_qpolynomial_foreach_piece(pwqp
, &split_periods
, &data
) < 0)
4485 isl_pw_qpolynomial_free(pwqp
);
4489 isl_pw_qpolynomial_free(data
.res
);
4490 isl_pw_qpolynomial_free(pwqp
);
4494 /* Construct a piecewise quasipolynomial that is constant on the given
4495 * domain. In particular, it is
4498 * infinity if cst == -1
4500 static __isl_give isl_pw_qpolynomial
*constant_on_domain(
4501 __isl_take isl_basic_set
*bset
, int cst
)
4504 isl_qpolynomial
*qp
;
4509 bset
= isl_basic_set_params(bset
);
4510 dim
= isl_basic_set_get_space(bset
);
4512 qp
= isl_qpolynomial_infty_on_domain(dim
);
4514 qp
= isl_qpolynomial_zero_on_domain(dim
);
4516 qp
= isl_qpolynomial_one_on_domain(dim
);
4517 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset
), qp
);
4520 /* Factor bset, call fn on each of the factors and return the product.
4522 * If no factors can be found, simply call fn on the input.
4523 * Otherwise, construct the factors based on the factorizer,
4524 * call fn on each factor and compute the product.
4526 static __isl_give isl_pw_qpolynomial
*compressed_multiplicative_call(
4527 __isl_take isl_basic_set
*bset
,
4528 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4534 isl_qpolynomial
*qp
;
4535 isl_pw_qpolynomial
*pwqp
;
4539 f
= isl_basic_set_factorizer(bset
);
4542 if (f
->n_group
== 0) {
4543 isl_factorizer_free(f
);
4547 nparam
= isl_basic_set_dim(bset
, isl_dim_param
);
4548 nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
4550 dim
= isl_basic_set_get_space(bset
);
4551 dim
= isl_space_domain(dim
);
4552 set
= isl_set_universe(isl_space_copy(dim
));
4553 qp
= isl_qpolynomial_one_on_domain(dim
);
4554 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4556 bset
= isl_morph_basic_set(isl_morph_copy(f
->morph
), bset
);
4558 for (i
= 0, n
= 0; i
< f
->n_group
; ++i
) {
4559 isl_basic_set
*bset_i
;
4560 isl_pw_qpolynomial
*pwqp_i
;
4562 bset_i
= isl_basic_set_copy(bset
);
4563 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4564 nparam
+ n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4565 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4567 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
,
4568 n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4569 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
, 0, n
);
4571 pwqp_i
= fn(bset_i
);
4572 pwqp
= isl_pw_qpolynomial_mul(pwqp
, pwqp_i
);
4577 isl_basic_set_free(bset
);
4578 isl_factorizer_free(f
);
4582 isl_basic_set_free(bset
);
4586 /* Factor bset, call fn on each of the factors and return the product.
4587 * The function is assumed to evaluate to zero on empty domains,
4588 * to one on zero-dimensional domains and to infinity on unbounded domains
4589 * and will not be called explicitly on zero-dimensional or unbounded domains.
4591 * We first check for some special cases and remove all equalities.
4592 * Then we hand over control to compressed_multiplicative_call.
4594 __isl_give isl_pw_qpolynomial
*isl_basic_set_multiplicative_call(
4595 __isl_take isl_basic_set
*bset
,
4596 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4600 isl_pw_qpolynomial
*pwqp
;
4605 if (isl_basic_set_plain_is_empty(bset
))
4606 return constant_on_domain(bset
, 0);
4608 if (isl_basic_set_dim(bset
, isl_dim_set
) == 0)
4609 return constant_on_domain(bset
, 1);
4611 bounded
= isl_basic_set_is_bounded(bset
);
4615 return constant_on_domain(bset
, -1);
4617 if (bset
->n_eq
== 0)
4618 return compressed_multiplicative_call(bset
, fn
);
4620 morph
= isl_basic_set_full_compression(bset
);
4621 bset
= isl_morph_basic_set(isl_morph_copy(morph
), bset
);
4623 pwqp
= compressed_multiplicative_call(bset
, fn
);
4625 morph
= isl_morph_dom_params(morph
);
4626 morph
= isl_morph_ran_params(morph
);
4627 morph
= isl_morph_inverse(morph
);
4629 pwqp
= isl_pw_qpolynomial_morph_domain(pwqp
, morph
);
4633 isl_basic_set_free(bset
);
4637 /* Drop all floors in "qp", turning each integer division [a/m] into
4638 * a rational division a/m. If "down" is set, then the integer division
4639 * is replaced by (a-(m-1))/m instead.
4641 static __isl_give isl_qpolynomial
*qp_drop_floors(
4642 __isl_take isl_qpolynomial
*qp
, int down
)
4645 struct isl_upoly
*s
;
4649 if (qp
->div
->n_row
== 0)
4652 qp
= isl_qpolynomial_cow(qp
);
4656 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
4658 isl_int_sub(qp
->div
->row
[i
][1],
4659 qp
->div
->row
[i
][1], qp
->div
->row
[i
][0]);
4660 isl_int_add_ui(qp
->div
->row
[i
][1],
4661 qp
->div
->row
[i
][1], 1);
4663 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
4664 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
4665 qp
= substitute_div(qp
, i
, s
);
4673 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4674 * a rational division a/m.
4676 static __isl_give isl_pw_qpolynomial
*pwqp_drop_floors(
4677 __isl_take isl_pw_qpolynomial
*pwqp
)
4684 if (isl_pw_qpolynomial_is_zero(pwqp
))
4687 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
4691 for (i
= 0; i
< pwqp
->n
; ++i
) {
4692 pwqp
->p
[i
].qp
= qp_drop_floors(pwqp
->p
[i
].qp
, 0);
4699 isl_pw_qpolynomial_free(pwqp
);
4703 /* Adjust all the integer divisions in "qp" such that they are at least
4704 * one over the given orthant (identified by "signs"). This ensures
4705 * that they will still be non-negative even after subtracting (m-1)/m.
4707 * In particular, f is replaced by f' + v, changing f = [a/m]
4708 * to f' = [(a - m v)/m].
4709 * If the constant term k in a is smaller than m,
4710 * the constant term of v is set to floor(k/m) - 1.
4711 * For any other term, if the coefficient c and the variable x have
4712 * the same sign, then no changes are needed.
4713 * Otherwise, if the variable is positive (and c is negative),
4714 * then the coefficient of x in v is set to floor(c/m).
4715 * If the variable is negative (and c is positive),
4716 * then the coefficient of x in v is set to ceil(c/m).
4718 static __isl_give isl_qpolynomial
*make_divs_pos(__isl_take isl_qpolynomial
*qp
,
4724 struct isl_upoly
*s
;
4726 qp
= isl_qpolynomial_cow(qp
);
4729 qp
->div
= isl_mat_cow(qp
->div
);
4733 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4734 v
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
4736 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4737 isl_int
*row
= qp
->div
->row
[i
];
4741 if (isl_int_lt(row
[1], row
[0])) {
4742 isl_int_fdiv_q(v
->el
[0], row
[1], row
[0]);
4743 isl_int_sub_ui(v
->el
[0], v
->el
[0], 1);
4744 isl_int_submul(row
[1], row
[0], v
->el
[0]);
4746 for (j
= 0; j
< total
; ++j
) {
4747 if (isl_int_sgn(row
[2 + j
]) * signs
[j
] >= 0)
4750 isl_int_cdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4752 isl_int_fdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4753 isl_int_submul(row
[2 + j
], row
[0], v
->el
[1 + j
]);
4755 for (j
= 0; j
< i
; ++j
) {
4756 if (isl_int_sgn(row
[2 + total
+ j
]) >= 0)
4758 isl_int_fdiv_q(v
->el
[1 + total
+ j
],
4759 row
[2 + total
+ j
], row
[0]);
4760 isl_int_submul(row
[2 + total
+ j
],
4761 row
[0], v
->el
[1 + total
+ j
]);
4763 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
4764 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
4766 isl_seq_combine(qp
->div
->row
[j
] + 1,
4767 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
4768 qp
->div
->row
[j
][2 + total
+ i
], v
->el
, v
->size
);
4770 isl_int_set_si(v
->el
[1 + total
+ i
], 1);
4771 s
= isl_upoly_from_affine(qp
->dim
->ctx
, v
->el
,
4772 qp
->div
->ctx
->one
, v
->size
);
4773 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ i
, 1, &s
);
4783 isl_qpolynomial_free(qp
);
4787 struct isl_to_poly_data
{
4789 isl_pw_qpolynomial
*res
;
4790 isl_qpolynomial
*qp
;
4793 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4794 * We first make all integer divisions positive and then split the
4795 * quasipolynomials into terms with sign data->sign (the direction
4796 * of the requested approximation) and terms with the opposite sign.
4797 * In the first set of terms, each integer division [a/m] is
4798 * overapproximated by a/m, while in the second it is underapproximated
4801 static int to_polynomial_on_orthant(__isl_take isl_set
*orthant
, int *signs
,
4804 struct isl_to_poly_data
*data
= user
;
4805 isl_pw_qpolynomial
*t
;
4806 isl_qpolynomial
*qp
, *up
, *down
;
4808 qp
= isl_qpolynomial_copy(data
->qp
);
4809 qp
= make_divs_pos(qp
, signs
);
4811 up
= isl_qpolynomial_terms_of_sign(qp
, signs
, data
->sign
);
4812 up
= qp_drop_floors(up
, 0);
4813 down
= isl_qpolynomial_terms_of_sign(qp
, signs
, -data
->sign
);
4814 down
= qp_drop_floors(down
, 1);
4816 isl_qpolynomial_free(qp
);
4817 qp
= isl_qpolynomial_add(up
, down
);
4819 t
= isl_pw_qpolynomial_alloc(orthant
, qp
);
4820 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, t
);
4825 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4826 * the polynomial will be an overapproximation. If "sign" is negative,
4827 * it will be an underapproximation. If "sign" is zero, the approximation
4828 * will lie somewhere in between.
4830 * In particular, is sign == 0, we simply drop the floors, turning
4831 * the integer divisions into rational divisions.
4832 * Otherwise, we split the domains into orthants, make all integer divisions
4833 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4834 * depending on the requested sign and the sign of the term in which
4835 * the integer division appears.
4837 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_to_polynomial(
4838 __isl_take isl_pw_qpolynomial
*pwqp
, int sign
)
4841 struct isl_to_poly_data data
;
4844 return pwqp_drop_floors(pwqp
);
4850 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp
));
4852 for (i
= 0; i
< pwqp
->n
; ++i
) {
4853 if (pwqp
->p
[i
].qp
->div
->n_row
== 0) {
4854 isl_pw_qpolynomial
*t
;
4855 t
= isl_pw_qpolynomial_alloc(
4856 isl_set_copy(pwqp
->p
[i
].set
),
4857 isl_qpolynomial_copy(pwqp
->p
[i
].qp
));
4858 data
.res
= isl_pw_qpolynomial_add_disjoint(data
.res
, t
);
4861 data
.qp
= pwqp
->p
[i
].qp
;
4862 if (isl_set_foreach_orthant(pwqp
->p
[i
].set
,
4863 &to_polynomial_on_orthant
, &data
) < 0)
4867 isl_pw_qpolynomial_free(pwqp
);
4871 isl_pw_qpolynomial_free(pwqp
);
4872 isl_pw_qpolynomial_free(data
.res
);
4876 static __isl_give isl_pw_qpolynomial
*poly_entry(
4877 __isl_take isl_pw_qpolynomial
*pwqp
, void *user
)
4881 return isl_pw_qpolynomial_to_polynomial(pwqp
, *sign
);
4884 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_to_polynomial(
4885 __isl_take isl_union_pw_qpolynomial
*upwqp
, int sign
)
4887 return isl_union_pw_qpolynomial_transform_inplace(upwqp
,
4888 &poly_entry
, &sign
);
4891 __isl_give isl_basic_map
*isl_basic_map_from_qpolynomial(
4892 __isl_take isl_qpolynomial
*qp
)
4896 isl_vec
*aff
= NULL
;
4897 isl_basic_map
*bmap
= NULL
;
4903 if (!isl_upoly_is_affine(qp
->upoly
))
4904 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
4905 "input quasi-polynomial not affine", goto error
);
4906 aff
= isl_qpolynomial_extract_affine(qp
);
4909 dim
= isl_qpolynomial_get_space(qp
);
4910 pos
= 1 + isl_space_offset(dim
, isl_dim_out
);
4911 n_div
= qp
->div
->n_row
;
4912 bmap
= isl_basic_map_alloc_space(dim
, n_div
, 1, 2 * n_div
);
4914 for (i
= 0; i
< n_div
; ++i
) {
4915 k
= isl_basic_map_alloc_div(bmap
);
4918 isl_seq_cpy(bmap
->div
[k
], qp
->div
->row
[i
], qp
->div
->n_col
);
4919 isl_int_set_si(bmap
->div
[k
][qp
->div
->n_col
], 0);
4920 if (isl_basic_map_add_div_constraints(bmap
, k
) < 0)
4923 k
= isl_basic_map_alloc_equality(bmap
);
4926 isl_int_neg(bmap
->eq
[k
][pos
], aff
->el
[0]);
4927 isl_seq_cpy(bmap
->eq
[k
], aff
->el
+ 1, pos
);
4928 isl_seq_cpy(bmap
->eq
[k
] + pos
+ 1, aff
->el
+ 1 + pos
, n_div
);
4931 isl_qpolynomial_free(qp
);
4932 bmap
= isl_basic_map_finalize(bmap
);
4936 isl_qpolynomial_free(qp
);
4937 isl_basic_map_free(bmap
);