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 /* Return the number of variables of the given type in the domain of "qp".
454 unsigned isl_qpolynomial_domain_dim(__isl_keep isl_qpolynomial
*qp
,
455 enum isl_dim_type type
)
459 if (type
== isl_dim_div
)
460 return qp
->div
->n_row
;
461 if (type
== isl_dim_all
)
462 return isl_space_dim(qp
->dim
, isl_dim_all
) +
463 isl_qpolynomial_domain_dim(qp
, isl_dim_div
);
464 return isl_space_dim(qp
->dim
, type
);
467 /* Externally, an isl_qpolynomial has a map space, but internally, the
468 * ls field corresponds to the domain of that space.
470 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial
*qp
,
471 enum isl_dim_type type
)
475 if (type
== isl_dim_out
)
477 if (type
== isl_dim_in
)
479 return isl_qpolynomial_domain_dim(qp
, type
);
482 /* Return the offset of the first coefficient of type "type" in
483 * the domain of "qp".
485 unsigned isl_qpolynomial_domain_offset(__isl_keep isl_qpolynomial
*qp
,
486 enum isl_dim_type type
)
495 return 1 + isl_space_offset(qp
->dim
, type
);
497 return 1 + isl_space_dim(qp
->dim
, isl_dim_all
);
503 isl_bool
isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial
*qp
)
505 return qp
? isl_upoly_is_zero(qp
->upoly
) : isl_bool_error
;
508 isl_bool
isl_qpolynomial_is_one(__isl_keep isl_qpolynomial
*qp
)
510 return qp
? isl_upoly_is_one(qp
->upoly
) : isl_bool_error
;
513 isl_bool
isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial
*qp
)
515 return qp
? isl_upoly_is_nan(qp
->upoly
) : isl_bool_error
;
518 isl_bool
isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial
*qp
)
520 return qp
? isl_upoly_is_infty(qp
->upoly
) : isl_bool_error
;
523 isl_bool
isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial
*qp
)
525 return qp
? isl_upoly_is_neginfty(qp
->upoly
) : isl_bool_error
;
528 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial
*qp
)
530 return qp
? isl_upoly_sgn(qp
->upoly
) : 0;
533 static void upoly_free_cst(__isl_take
struct isl_upoly_cst
*cst
)
535 isl_int_clear(cst
->n
);
536 isl_int_clear(cst
->d
);
539 static void upoly_free_rec(__isl_take
struct isl_upoly_rec
*rec
)
543 for (i
= 0; i
< rec
->n
; ++i
)
544 isl_upoly_free(rec
->p
[i
]);
547 __isl_give
struct isl_upoly
*isl_upoly_copy(__isl_keep
struct isl_upoly
*up
)
556 __isl_give
struct isl_upoly
*isl_upoly_dup_cst(__isl_keep
struct isl_upoly
*up
)
558 struct isl_upoly_cst
*cst
;
559 struct isl_upoly_cst
*dup
;
561 cst
= isl_upoly_as_cst(up
);
565 dup
= isl_upoly_as_cst(isl_upoly_zero(up
->ctx
));
568 isl_int_set(dup
->n
, cst
->n
);
569 isl_int_set(dup
->d
, cst
->d
);
574 __isl_give
struct isl_upoly
*isl_upoly_dup_rec(__isl_keep
struct isl_upoly
*up
)
577 struct isl_upoly_rec
*rec
;
578 struct isl_upoly_rec
*dup
;
580 rec
= isl_upoly_as_rec(up
);
584 dup
= isl_upoly_alloc_rec(up
->ctx
, up
->var
, rec
->n
);
588 for (i
= 0; i
< rec
->n
; ++i
) {
589 dup
->p
[i
] = isl_upoly_copy(rec
->p
[i
]);
597 isl_upoly_free(&dup
->up
);
601 __isl_give
struct isl_upoly
*isl_upoly_dup(__isl_keep
struct isl_upoly
*up
)
606 if (isl_upoly_is_cst(up
))
607 return isl_upoly_dup_cst(up
);
609 return isl_upoly_dup_rec(up
);
612 __isl_give
struct isl_upoly
*isl_upoly_cow(__isl_take
struct isl_upoly
*up
)
620 return isl_upoly_dup(up
);
623 void isl_upoly_free(__isl_take
struct isl_upoly
*up
)
632 upoly_free_cst((struct isl_upoly_cst
*)up
);
634 upoly_free_rec((struct isl_upoly_rec
*)up
);
636 isl_ctx_deref(up
->ctx
);
640 static void isl_upoly_cst_reduce(__isl_keep
struct isl_upoly_cst
*cst
)
645 isl_int_gcd(gcd
, cst
->n
, cst
->d
);
646 if (!isl_int_is_zero(gcd
) && !isl_int_is_one(gcd
)) {
647 isl_int_divexact(cst
->n
, cst
->n
, gcd
);
648 isl_int_divexact(cst
->d
, cst
->d
, gcd
);
653 __isl_give
struct isl_upoly
*isl_upoly_sum_cst(__isl_take
struct isl_upoly
*up1
,
654 __isl_take
struct isl_upoly
*up2
)
656 struct isl_upoly_cst
*cst1
;
657 struct isl_upoly_cst
*cst2
;
659 up1
= isl_upoly_cow(up1
);
663 cst1
= isl_upoly_as_cst(up1
);
664 cst2
= isl_upoly_as_cst(up2
);
666 if (isl_int_eq(cst1
->d
, cst2
->d
))
667 isl_int_add(cst1
->n
, cst1
->n
, cst2
->n
);
669 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->d
);
670 isl_int_addmul(cst1
->n
, cst2
->n
, cst1
->d
);
671 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
674 isl_upoly_cst_reduce(cst1
);
684 static __isl_give
struct isl_upoly
*replace_by_zero(
685 __isl_take
struct isl_upoly
*up
)
693 return isl_upoly_zero(ctx
);
696 static __isl_give
struct isl_upoly
*replace_by_constant_term(
697 __isl_take
struct isl_upoly
*up
)
699 struct isl_upoly_rec
*rec
;
700 struct isl_upoly
*cst
;
705 rec
= isl_upoly_as_rec(up
);
708 cst
= isl_upoly_copy(rec
->p
[0]);
716 __isl_give
struct isl_upoly
*isl_upoly_sum(__isl_take
struct isl_upoly
*up1
,
717 __isl_take
struct isl_upoly
*up2
)
720 struct isl_upoly_rec
*rec1
, *rec2
;
725 if (isl_upoly_is_nan(up1
)) {
730 if (isl_upoly_is_nan(up2
)) {
735 if (isl_upoly_is_zero(up1
)) {
740 if (isl_upoly_is_zero(up2
)) {
745 if (up1
->var
< up2
->var
)
746 return isl_upoly_sum(up2
, up1
);
748 if (up2
->var
< up1
->var
) {
749 struct isl_upoly_rec
*rec
;
750 if (isl_upoly_is_infty(up2
) || isl_upoly_is_neginfty(up2
)) {
754 up1
= isl_upoly_cow(up1
);
755 rec
= isl_upoly_as_rec(up1
);
758 rec
->p
[0] = isl_upoly_sum(rec
->p
[0], up2
);
760 up1
= replace_by_constant_term(up1
);
764 if (isl_upoly_is_cst(up1
))
765 return isl_upoly_sum_cst(up1
, up2
);
767 rec1
= isl_upoly_as_rec(up1
);
768 rec2
= isl_upoly_as_rec(up2
);
772 if (rec1
->n
< rec2
->n
)
773 return isl_upoly_sum(up2
, up1
);
775 up1
= isl_upoly_cow(up1
);
776 rec1
= isl_upoly_as_rec(up1
);
780 for (i
= rec2
->n
- 1; i
>= 0; --i
) {
781 rec1
->p
[i
] = isl_upoly_sum(rec1
->p
[i
],
782 isl_upoly_copy(rec2
->p
[i
]));
785 if (i
== rec1
->n
- 1 && isl_upoly_is_zero(rec1
->p
[i
])) {
786 isl_upoly_free(rec1
->p
[i
]);
792 up1
= replace_by_zero(up1
);
793 else if (rec1
->n
== 1)
794 up1
= replace_by_constant_term(up1
);
805 __isl_give
struct isl_upoly
*isl_upoly_cst_add_isl_int(
806 __isl_take
struct isl_upoly
*up
, isl_int v
)
808 struct isl_upoly_cst
*cst
;
810 up
= isl_upoly_cow(up
);
814 cst
= isl_upoly_as_cst(up
);
816 isl_int_addmul(cst
->n
, cst
->d
, v
);
821 __isl_give
struct isl_upoly
*isl_upoly_add_isl_int(
822 __isl_take
struct isl_upoly
*up
, isl_int v
)
824 struct isl_upoly_rec
*rec
;
829 if (isl_upoly_is_cst(up
))
830 return isl_upoly_cst_add_isl_int(up
, v
);
832 up
= isl_upoly_cow(up
);
833 rec
= isl_upoly_as_rec(up
);
837 rec
->p
[0] = isl_upoly_add_isl_int(rec
->p
[0], v
);
847 __isl_give
struct isl_upoly
*isl_upoly_cst_mul_isl_int(
848 __isl_take
struct isl_upoly
*up
, isl_int v
)
850 struct isl_upoly_cst
*cst
;
852 if (isl_upoly_is_zero(up
))
855 up
= isl_upoly_cow(up
);
859 cst
= isl_upoly_as_cst(up
);
861 isl_int_mul(cst
->n
, cst
->n
, v
);
866 __isl_give
struct isl_upoly
*isl_upoly_mul_isl_int(
867 __isl_take
struct isl_upoly
*up
, isl_int v
)
870 struct isl_upoly_rec
*rec
;
875 if (isl_upoly_is_cst(up
))
876 return isl_upoly_cst_mul_isl_int(up
, v
);
878 up
= isl_upoly_cow(up
);
879 rec
= isl_upoly_as_rec(up
);
883 for (i
= 0; i
< rec
->n
; ++i
) {
884 rec
->p
[i
] = isl_upoly_mul_isl_int(rec
->p
[i
], v
);
895 /* Multiply the constant polynomial "up" by "v".
897 static __isl_give
struct isl_upoly
*isl_upoly_cst_scale_val(
898 __isl_take
struct isl_upoly
*up
, __isl_keep isl_val
*v
)
900 struct isl_upoly_cst
*cst
;
902 if (isl_upoly_is_zero(up
))
905 up
= isl_upoly_cow(up
);
909 cst
= isl_upoly_as_cst(up
);
911 isl_int_mul(cst
->n
, cst
->n
, v
->n
);
912 isl_int_mul(cst
->d
, cst
->d
, v
->d
);
913 isl_upoly_cst_reduce(cst
);
918 /* Multiply the polynomial "up" by "v".
920 static __isl_give
struct isl_upoly
*isl_upoly_scale_val(
921 __isl_take
struct isl_upoly
*up
, __isl_keep isl_val
*v
)
924 struct isl_upoly_rec
*rec
;
929 if (isl_upoly_is_cst(up
))
930 return isl_upoly_cst_scale_val(up
, v
);
932 up
= isl_upoly_cow(up
);
933 rec
= isl_upoly_as_rec(up
);
937 for (i
= 0; i
< rec
->n
; ++i
) {
938 rec
->p
[i
] = isl_upoly_scale_val(rec
->p
[i
], v
);
949 __isl_give
struct isl_upoly
*isl_upoly_mul_cst(__isl_take
struct isl_upoly
*up1
,
950 __isl_take
struct isl_upoly
*up2
)
952 struct isl_upoly_cst
*cst1
;
953 struct isl_upoly_cst
*cst2
;
955 up1
= isl_upoly_cow(up1
);
959 cst1
= isl_upoly_as_cst(up1
);
960 cst2
= isl_upoly_as_cst(up2
);
962 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->n
);
963 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
965 isl_upoly_cst_reduce(cst1
);
975 __isl_give
struct isl_upoly
*isl_upoly_mul_rec(__isl_take
struct isl_upoly
*up1
,
976 __isl_take
struct isl_upoly
*up2
)
978 struct isl_upoly_rec
*rec1
;
979 struct isl_upoly_rec
*rec2
;
980 struct isl_upoly_rec
*res
= NULL
;
984 rec1
= isl_upoly_as_rec(up1
);
985 rec2
= isl_upoly_as_rec(up2
);
988 size
= rec1
->n
+ rec2
->n
- 1;
989 res
= isl_upoly_alloc_rec(up1
->ctx
, up1
->var
, size
);
993 for (i
= 0; i
< rec1
->n
; ++i
) {
994 res
->p
[i
] = isl_upoly_mul(isl_upoly_copy(rec2
->p
[0]),
995 isl_upoly_copy(rec1
->p
[i
]));
1000 for (; i
< size
; ++i
) {
1001 res
->p
[i
] = isl_upoly_zero(up1
->ctx
);
1006 for (i
= 0; i
< rec1
->n
; ++i
) {
1007 for (j
= 1; j
< rec2
->n
; ++j
) {
1008 struct isl_upoly
*up
;
1009 up
= isl_upoly_mul(isl_upoly_copy(rec2
->p
[j
]),
1010 isl_upoly_copy(rec1
->p
[i
]));
1011 res
->p
[i
+ j
] = isl_upoly_sum(res
->p
[i
+ j
], up
);
1017 isl_upoly_free(up1
);
1018 isl_upoly_free(up2
);
1022 isl_upoly_free(up1
);
1023 isl_upoly_free(up2
);
1024 isl_upoly_free(&res
->up
);
1028 __isl_give
struct isl_upoly
*isl_upoly_mul(__isl_take
struct isl_upoly
*up1
,
1029 __isl_take
struct isl_upoly
*up2
)
1034 if (isl_upoly_is_nan(up1
)) {
1035 isl_upoly_free(up2
);
1039 if (isl_upoly_is_nan(up2
)) {
1040 isl_upoly_free(up1
);
1044 if (isl_upoly_is_zero(up1
)) {
1045 isl_upoly_free(up2
);
1049 if (isl_upoly_is_zero(up2
)) {
1050 isl_upoly_free(up1
);
1054 if (isl_upoly_is_one(up1
)) {
1055 isl_upoly_free(up1
);
1059 if (isl_upoly_is_one(up2
)) {
1060 isl_upoly_free(up2
);
1064 if (up1
->var
< up2
->var
)
1065 return isl_upoly_mul(up2
, up1
);
1067 if (up2
->var
< up1
->var
) {
1069 struct isl_upoly_rec
*rec
;
1070 if (isl_upoly_is_infty(up2
) || isl_upoly_is_neginfty(up2
)) {
1071 isl_ctx
*ctx
= up1
->ctx
;
1072 isl_upoly_free(up1
);
1073 isl_upoly_free(up2
);
1074 return isl_upoly_nan(ctx
);
1076 up1
= isl_upoly_cow(up1
);
1077 rec
= isl_upoly_as_rec(up1
);
1081 for (i
= 0; i
< rec
->n
; ++i
) {
1082 rec
->p
[i
] = isl_upoly_mul(rec
->p
[i
],
1083 isl_upoly_copy(up2
));
1087 isl_upoly_free(up2
);
1091 if (isl_upoly_is_cst(up1
))
1092 return isl_upoly_mul_cst(up1
, up2
);
1094 return isl_upoly_mul_rec(up1
, up2
);
1096 isl_upoly_free(up1
);
1097 isl_upoly_free(up2
);
1101 __isl_give
struct isl_upoly
*isl_upoly_pow(__isl_take
struct isl_upoly
*up
,
1104 struct isl_upoly
*res
;
1112 res
= isl_upoly_copy(up
);
1114 res
= isl_upoly_one(up
->ctx
);
1116 while (power
>>= 1) {
1117 up
= isl_upoly_mul(up
, isl_upoly_copy(up
));
1119 res
= isl_upoly_mul(res
, isl_upoly_copy(up
));
1126 __isl_give isl_qpolynomial
*isl_qpolynomial_alloc(__isl_take isl_space
*dim
,
1127 unsigned n_div
, __isl_take
struct isl_upoly
*up
)
1129 struct isl_qpolynomial
*qp
= NULL
;
1135 if (!isl_space_is_set(dim
))
1136 isl_die(isl_space_get_ctx(dim
), isl_error_invalid
,
1137 "domain of polynomial should be a set", goto error
);
1139 total
= isl_space_dim(dim
, isl_dim_all
);
1141 qp
= isl_calloc_type(dim
->ctx
, struct isl_qpolynomial
);
1146 qp
->div
= isl_mat_alloc(dim
->ctx
, n_div
, 1 + 1 + total
+ n_div
);
1155 isl_space_free(dim
);
1157 isl_qpolynomial_free(qp
);
1161 __isl_give isl_qpolynomial
*isl_qpolynomial_copy(__isl_keep isl_qpolynomial
*qp
)
1170 __isl_give isl_qpolynomial
*isl_qpolynomial_dup(__isl_keep isl_qpolynomial
*qp
)
1172 struct isl_qpolynomial
*dup
;
1177 dup
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
), qp
->div
->n_row
,
1178 isl_upoly_copy(qp
->upoly
));
1181 isl_mat_free(dup
->div
);
1182 dup
->div
= isl_mat_copy(qp
->div
);
1188 isl_qpolynomial_free(dup
);
1192 __isl_give isl_qpolynomial
*isl_qpolynomial_cow(__isl_take isl_qpolynomial
*qp
)
1200 return isl_qpolynomial_dup(qp
);
1203 __isl_null isl_qpolynomial
*isl_qpolynomial_free(
1204 __isl_take isl_qpolynomial
*qp
)
1212 isl_space_free(qp
->dim
);
1213 isl_mat_free(qp
->div
);
1214 isl_upoly_free(qp
->upoly
);
1220 __isl_give
struct isl_upoly
*isl_upoly_var_pow(isl_ctx
*ctx
, int pos
, int power
)
1223 struct isl_upoly_rec
*rec
;
1224 struct isl_upoly_cst
*cst
;
1226 rec
= isl_upoly_alloc_rec(ctx
, pos
, 1 + power
);
1229 for (i
= 0; i
< 1 + power
; ++i
) {
1230 rec
->p
[i
] = isl_upoly_zero(ctx
);
1235 cst
= isl_upoly_as_cst(rec
->p
[power
]);
1236 isl_int_set_si(cst
->n
, 1);
1240 isl_upoly_free(&rec
->up
);
1244 /* r array maps original positions to new positions.
1246 static __isl_give
struct isl_upoly
*reorder(__isl_take
struct isl_upoly
*up
,
1250 struct isl_upoly_rec
*rec
;
1251 struct isl_upoly
*base
;
1252 struct isl_upoly
*res
;
1254 if (isl_upoly_is_cst(up
))
1257 rec
= isl_upoly_as_rec(up
);
1261 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
1263 base
= isl_upoly_var_pow(up
->ctx
, r
[up
->var
], 1);
1264 res
= reorder(isl_upoly_copy(rec
->p
[rec
->n
- 1]), r
);
1266 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1267 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
1268 res
= isl_upoly_sum(res
, reorder(isl_upoly_copy(rec
->p
[i
]), r
));
1271 isl_upoly_free(base
);
1280 static int compatible_divs(__isl_keep isl_mat
*div1
, __isl_keep isl_mat
*div2
)
1285 isl_assert(div1
->ctx
, div1
->n_row
>= div2
->n_row
&&
1286 div1
->n_col
>= div2
->n_col
, return -1);
1288 if (div1
->n_row
== div2
->n_row
)
1289 return isl_mat_is_equal(div1
, div2
);
1291 n_row
= div1
->n_row
;
1292 n_col
= div1
->n_col
;
1293 div1
->n_row
= div2
->n_row
;
1294 div1
->n_col
= div2
->n_col
;
1296 equal
= isl_mat_is_equal(div1
, div2
);
1298 div1
->n_row
= n_row
;
1299 div1
->n_col
= n_col
;
1304 static int cmp_row(__isl_keep isl_mat
*div
, int i
, int j
)
1308 li
= isl_seq_last_non_zero(div
->row
[i
], div
->n_col
);
1309 lj
= isl_seq_last_non_zero(div
->row
[j
], div
->n_col
);
1314 return isl_seq_cmp(div
->row
[i
], div
->row
[j
], div
->n_col
);
1317 struct isl_div_sort_info
{
1322 static int div_sort_cmp(const void *p1
, const void *p2
)
1324 const struct isl_div_sort_info
*i1
, *i2
;
1325 i1
= (const struct isl_div_sort_info
*) p1
;
1326 i2
= (const struct isl_div_sort_info
*) p2
;
1328 return cmp_row(i1
->div
, i1
->row
, i2
->row
);
1331 /* Sort divs and remove duplicates.
1333 static __isl_give isl_qpolynomial
*sort_divs(__isl_take isl_qpolynomial
*qp
)
1338 struct isl_div_sort_info
*array
= NULL
;
1339 int *pos
= NULL
, *at
= NULL
;
1340 int *reordering
= NULL
;
1345 if (qp
->div
->n_row
<= 1)
1348 div_pos
= isl_space_dim(qp
->dim
, isl_dim_all
);
1350 array
= isl_alloc_array(qp
->div
->ctx
, struct isl_div_sort_info
,
1352 pos
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1353 at
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1354 len
= qp
->div
->n_col
- 2;
1355 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
1356 if (!array
|| !pos
|| !at
|| !reordering
)
1359 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1360 array
[i
].div
= qp
->div
;
1366 qsort(array
, qp
->div
->n_row
, sizeof(struct isl_div_sort_info
),
1369 for (i
= 0; i
< div_pos
; ++i
)
1372 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1373 if (pos
[array
[i
].row
] == i
)
1375 qp
->div
= isl_mat_swap_rows(qp
->div
, i
, pos
[array
[i
].row
]);
1376 pos
[at
[i
]] = pos
[array
[i
].row
];
1377 at
[pos
[array
[i
].row
]] = at
[i
];
1378 at
[i
] = array
[i
].row
;
1379 pos
[array
[i
].row
] = i
;
1383 for (i
= 0; i
< len
- div_pos
; ++i
) {
1385 isl_seq_eq(qp
->div
->row
[i
- skip
- 1],
1386 qp
->div
->row
[i
- skip
], qp
->div
->n_col
)) {
1387 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
1388 isl_mat_col_add(qp
->div
, 2 + div_pos
+ i
- skip
- 1,
1389 2 + div_pos
+ i
- skip
);
1390 qp
->div
= isl_mat_drop_cols(qp
->div
,
1391 2 + div_pos
+ i
- skip
, 1);
1394 reordering
[div_pos
+ array
[i
].row
] = div_pos
+ i
- skip
;
1397 qp
->upoly
= reorder(qp
->upoly
, reordering
);
1399 if (!qp
->upoly
|| !qp
->div
)
1413 isl_qpolynomial_free(qp
);
1417 static __isl_give
struct isl_upoly
*expand(__isl_take
struct isl_upoly
*up
,
1418 int *exp
, int first
)
1421 struct isl_upoly_rec
*rec
;
1423 if (isl_upoly_is_cst(up
))
1426 if (up
->var
< first
)
1429 if (exp
[up
->var
- first
] == up
->var
- first
)
1432 up
= isl_upoly_cow(up
);
1436 up
->var
= exp
[up
->var
- first
] + first
;
1438 rec
= isl_upoly_as_rec(up
);
1442 for (i
= 0; i
< rec
->n
; ++i
) {
1443 rec
->p
[i
] = expand(rec
->p
[i
], exp
, first
);
1454 static __isl_give isl_qpolynomial
*with_merged_divs(
1455 __isl_give isl_qpolynomial
*(*fn
)(__isl_take isl_qpolynomial
*qp1
,
1456 __isl_take isl_qpolynomial
*qp2
),
1457 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
1461 isl_mat
*div
= NULL
;
1464 qp1
= isl_qpolynomial_cow(qp1
);
1465 qp2
= isl_qpolynomial_cow(qp2
);
1470 isl_assert(qp1
->div
->ctx
, qp1
->div
->n_row
>= qp2
->div
->n_row
&&
1471 qp1
->div
->n_col
>= qp2
->div
->n_col
, goto error
);
1473 n_div1
= qp1
->div
->n_row
;
1474 n_div2
= qp2
->div
->n_row
;
1475 exp1
= isl_alloc_array(qp1
->div
->ctx
, int, n_div1
);
1476 exp2
= isl_alloc_array(qp2
->div
->ctx
, int, n_div2
);
1477 if ((n_div1
&& !exp1
) || (n_div2
&& !exp2
))
1480 div
= isl_merge_divs(qp1
->div
, qp2
->div
, exp1
, exp2
);
1484 isl_mat_free(qp1
->div
);
1485 qp1
->div
= isl_mat_copy(div
);
1486 isl_mat_free(qp2
->div
);
1487 qp2
->div
= isl_mat_copy(div
);
1489 qp1
->upoly
= expand(qp1
->upoly
, exp1
, div
->n_col
- div
->n_row
- 2);
1490 qp2
->upoly
= expand(qp2
->upoly
, exp2
, div
->n_col
- div
->n_row
- 2);
1492 if (!qp1
->upoly
|| !qp2
->upoly
)
1499 return fn(qp1
, qp2
);
1504 isl_qpolynomial_free(qp1
);
1505 isl_qpolynomial_free(qp2
);
1509 __isl_give isl_qpolynomial
*isl_qpolynomial_add(__isl_take isl_qpolynomial
*qp1
,
1510 __isl_take isl_qpolynomial
*qp2
)
1512 qp1
= isl_qpolynomial_cow(qp1
);
1517 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1518 return isl_qpolynomial_add(qp2
, qp1
);
1520 isl_assert(qp1
->dim
->ctx
, isl_space_is_equal(qp1
->dim
, qp2
->dim
), goto error
);
1521 if (!compatible_divs(qp1
->div
, qp2
->div
))
1522 return with_merged_divs(isl_qpolynomial_add
, qp1
, qp2
);
1524 qp1
->upoly
= isl_upoly_sum(qp1
->upoly
, isl_upoly_copy(qp2
->upoly
));
1528 isl_qpolynomial_free(qp2
);
1532 isl_qpolynomial_free(qp1
);
1533 isl_qpolynomial_free(qp2
);
1537 __isl_give isl_qpolynomial
*isl_qpolynomial_add_on_domain(
1538 __isl_keep isl_set
*dom
,
1539 __isl_take isl_qpolynomial
*qp1
,
1540 __isl_take isl_qpolynomial
*qp2
)
1542 qp1
= isl_qpolynomial_add(qp1
, qp2
);
1543 qp1
= isl_qpolynomial_gist(qp1
, isl_set_copy(dom
));
1547 __isl_give isl_qpolynomial
*isl_qpolynomial_sub(__isl_take isl_qpolynomial
*qp1
,
1548 __isl_take isl_qpolynomial
*qp2
)
1550 return isl_qpolynomial_add(qp1
, isl_qpolynomial_neg(qp2
));
1553 __isl_give isl_qpolynomial
*isl_qpolynomial_add_isl_int(
1554 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1556 if (isl_int_is_zero(v
))
1559 qp
= isl_qpolynomial_cow(qp
);
1563 qp
->upoly
= isl_upoly_add_isl_int(qp
->upoly
, v
);
1569 isl_qpolynomial_free(qp
);
1574 __isl_give isl_qpolynomial
*isl_qpolynomial_neg(__isl_take isl_qpolynomial
*qp
)
1579 return isl_qpolynomial_mul_isl_int(qp
, qp
->dim
->ctx
->negone
);
1582 __isl_give isl_qpolynomial
*isl_qpolynomial_mul_isl_int(
1583 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1585 if (isl_int_is_one(v
))
1588 if (qp
&& isl_int_is_zero(v
)) {
1589 isl_qpolynomial
*zero
;
1590 zero
= isl_qpolynomial_zero_on_domain(isl_space_copy(qp
->dim
));
1591 isl_qpolynomial_free(qp
);
1595 qp
= isl_qpolynomial_cow(qp
);
1599 qp
->upoly
= isl_upoly_mul_isl_int(qp
->upoly
, v
);
1605 isl_qpolynomial_free(qp
);
1609 __isl_give isl_qpolynomial
*isl_qpolynomial_scale(
1610 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1612 return isl_qpolynomial_mul_isl_int(qp
, v
);
1615 /* Multiply "qp" by "v".
1617 __isl_give isl_qpolynomial
*isl_qpolynomial_scale_val(
1618 __isl_take isl_qpolynomial
*qp
, __isl_take isl_val
*v
)
1623 if (!isl_val_is_rat(v
))
1624 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
1625 "expecting rational factor", goto error
);
1627 if (isl_val_is_one(v
)) {
1632 if (isl_val_is_zero(v
)) {
1635 space
= isl_qpolynomial_get_domain_space(qp
);
1636 isl_qpolynomial_free(qp
);
1638 return isl_qpolynomial_zero_on_domain(space
);
1641 qp
= isl_qpolynomial_cow(qp
);
1645 qp
->upoly
= isl_upoly_scale_val(qp
->upoly
, v
);
1647 qp
= isl_qpolynomial_free(qp
);
1653 isl_qpolynomial_free(qp
);
1657 /* Divide "qp" by "v".
1659 __isl_give isl_qpolynomial
*isl_qpolynomial_scale_down_val(
1660 __isl_take isl_qpolynomial
*qp
, __isl_take isl_val
*v
)
1665 if (!isl_val_is_rat(v
))
1666 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
1667 "expecting rational factor", goto error
);
1668 if (isl_val_is_zero(v
))
1669 isl_die(isl_val_get_ctx(v
), isl_error_invalid
,
1670 "cannot scale down by zero", goto error
);
1672 return isl_qpolynomial_scale_val(qp
, isl_val_inv(v
));
1675 isl_qpolynomial_free(qp
);
1679 __isl_give isl_qpolynomial
*isl_qpolynomial_mul(__isl_take isl_qpolynomial
*qp1
,
1680 __isl_take isl_qpolynomial
*qp2
)
1682 qp1
= isl_qpolynomial_cow(qp1
);
1687 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1688 return isl_qpolynomial_mul(qp2
, qp1
);
1690 isl_assert(qp1
->dim
->ctx
, isl_space_is_equal(qp1
->dim
, qp2
->dim
), goto error
);
1691 if (!compatible_divs(qp1
->div
, qp2
->div
))
1692 return with_merged_divs(isl_qpolynomial_mul
, qp1
, qp2
);
1694 qp1
->upoly
= isl_upoly_mul(qp1
->upoly
, isl_upoly_copy(qp2
->upoly
));
1698 isl_qpolynomial_free(qp2
);
1702 isl_qpolynomial_free(qp1
);
1703 isl_qpolynomial_free(qp2
);
1707 __isl_give isl_qpolynomial
*isl_qpolynomial_pow(__isl_take isl_qpolynomial
*qp
,
1710 qp
= isl_qpolynomial_cow(qp
);
1715 qp
->upoly
= isl_upoly_pow(qp
->upoly
, power
);
1721 isl_qpolynomial_free(qp
);
1725 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_pow(
1726 __isl_take isl_pw_qpolynomial
*pwqp
, unsigned power
)
1733 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
1737 for (i
= 0; i
< pwqp
->n
; ++i
) {
1738 pwqp
->p
[i
].qp
= isl_qpolynomial_pow(pwqp
->p
[i
].qp
, power
);
1740 return isl_pw_qpolynomial_free(pwqp
);
1746 __isl_give isl_qpolynomial
*isl_qpolynomial_zero_on_domain(
1747 __isl_take isl_space
*dim
)
1751 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
1754 __isl_give isl_qpolynomial
*isl_qpolynomial_one_on_domain(
1755 __isl_take isl_space
*dim
)
1759 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_one(dim
->ctx
));
1762 __isl_give isl_qpolynomial
*isl_qpolynomial_infty_on_domain(
1763 __isl_take isl_space
*dim
)
1767 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_infty(dim
->ctx
));
1770 __isl_give isl_qpolynomial
*isl_qpolynomial_neginfty_on_domain(
1771 __isl_take isl_space
*dim
)
1775 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_neginfty(dim
->ctx
));
1778 __isl_give isl_qpolynomial
*isl_qpolynomial_nan_on_domain(
1779 __isl_take isl_space
*dim
)
1783 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_nan(dim
->ctx
));
1786 __isl_give isl_qpolynomial
*isl_qpolynomial_cst_on_domain(
1787 __isl_take isl_space
*dim
,
1790 struct isl_qpolynomial
*qp
;
1791 struct isl_upoly_cst
*cst
;
1796 qp
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
1800 cst
= isl_upoly_as_cst(qp
->upoly
);
1801 isl_int_set(cst
->n
, v
);
1806 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial
*qp
,
1807 isl_int
*n
, isl_int
*d
)
1809 struct isl_upoly_cst
*cst
;
1814 if (!isl_upoly_is_cst(qp
->upoly
))
1817 cst
= isl_upoly_as_cst(qp
->upoly
);
1822 isl_int_set(*n
, cst
->n
);
1824 isl_int_set(*d
, cst
->d
);
1829 /* Return the constant term of "up".
1831 static __isl_give isl_val
*isl_upoly_get_constant_val(
1832 __isl_keep
struct isl_upoly
*up
)
1834 struct isl_upoly_cst
*cst
;
1839 while (!isl_upoly_is_cst(up
)) {
1840 struct isl_upoly_rec
*rec
;
1842 rec
= isl_upoly_as_rec(up
);
1848 cst
= isl_upoly_as_cst(up
);
1851 return isl_val_rat_from_isl_int(cst
->up
.ctx
, cst
->n
, cst
->d
);
1854 /* Return the constant term of "qp".
1856 __isl_give isl_val
*isl_qpolynomial_get_constant_val(
1857 __isl_keep isl_qpolynomial
*qp
)
1862 return isl_upoly_get_constant_val(qp
->upoly
);
1865 int isl_upoly_is_affine(__isl_keep
struct isl_upoly
*up
)
1868 struct isl_upoly_rec
*rec
;
1876 rec
= isl_upoly_as_rec(up
);
1883 isl_assert(up
->ctx
, rec
->n
> 1, return -1);
1885 is_cst
= isl_upoly_is_cst(rec
->p
[1]);
1891 return isl_upoly_is_affine(rec
->p
[0]);
1894 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial
*qp
)
1899 if (qp
->div
->n_row
> 0)
1902 return isl_upoly_is_affine(qp
->upoly
);
1905 static void update_coeff(__isl_keep isl_vec
*aff
,
1906 __isl_keep
struct isl_upoly_cst
*cst
, int pos
)
1911 if (isl_int_is_zero(cst
->n
))
1916 isl_int_gcd(gcd
, cst
->d
, aff
->el
[0]);
1917 isl_int_divexact(f
, cst
->d
, gcd
);
1918 isl_int_divexact(gcd
, aff
->el
[0], gcd
);
1919 isl_seq_scale(aff
->el
, aff
->el
, f
, aff
->size
);
1920 isl_int_mul(aff
->el
[1 + pos
], gcd
, cst
->n
);
1925 int isl_upoly_update_affine(__isl_keep
struct isl_upoly
*up
,
1926 __isl_keep isl_vec
*aff
)
1928 struct isl_upoly_cst
*cst
;
1929 struct isl_upoly_rec
*rec
;
1935 struct isl_upoly_cst
*cst
;
1937 cst
= isl_upoly_as_cst(up
);
1940 update_coeff(aff
, cst
, 0);
1944 rec
= isl_upoly_as_rec(up
);
1947 isl_assert(up
->ctx
, rec
->n
== 2, return -1);
1949 cst
= isl_upoly_as_cst(rec
->p
[1]);
1952 update_coeff(aff
, cst
, 1 + up
->var
);
1954 return isl_upoly_update_affine(rec
->p
[0], aff
);
1957 __isl_give isl_vec
*isl_qpolynomial_extract_affine(
1958 __isl_keep isl_qpolynomial
*qp
)
1966 d
= isl_space_dim(qp
->dim
, isl_dim_all
);
1967 aff
= isl_vec_alloc(qp
->div
->ctx
, 2 + d
+ qp
->div
->n_row
);
1971 isl_seq_clr(aff
->el
+ 1, 1 + d
+ qp
->div
->n_row
);
1972 isl_int_set_si(aff
->el
[0], 1);
1974 if (isl_upoly_update_affine(qp
->upoly
, aff
) < 0)
1983 /* Compare two quasi-polynomials.
1985 * Return -1 if "qp1" is "smaller" than "qp2", 1 if "qp1" is "greater"
1986 * than "qp2" and 0 if they are equal.
1988 int isl_qpolynomial_plain_cmp(__isl_keep isl_qpolynomial
*qp1
,
1989 __isl_keep isl_qpolynomial
*qp2
)
2000 cmp
= isl_space_cmp(qp1
->dim
, qp2
->dim
);
2004 cmp
= isl_local_cmp(qp1
->div
, qp2
->div
);
2008 return isl_upoly_plain_cmp(qp1
->upoly
, qp2
->upoly
);
2011 /* Is "qp1" obviously equal to "qp2"?
2013 * NaN is not equal to anything, not even to another NaN.
2015 isl_bool
isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial
*qp1
,
2016 __isl_keep isl_qpolynomial
*qp2
)
2021 return isl_bool_error
;
2023 if (isl_qpolynomial_is_nan(qp1
) || isl_qpolynomial_is_nan(qp2
))
2024 return isl_bool_false
;
2026 equal
= isl_space_is_equal(qp1
->dim
, qp2
->dim
);
2027 if (equal
< 0 || !equal
)
2030 equal
= isl_mat_is_equal(qp1
->div
, qp2
->div
);
2031 if (equal
< 0 || !equal
)
2034 return isl_upoly_is_equal(qp1
->upoly
, qp2
->upoly
);
2037 static void upoly_update_den(__isl_keep
struct isl_upoly
*up
, isl_int
*d
)
2040 struct isl_upoly_rec
*rec
;
2042 if (isl_upoly_is_cst(up
)) {
2043 struct isl_upoly_cst
*cst
;
2044 cst
= isl_upoly_as_cst(up
);
2047 isl_int_lcm(*d
, *d
, cst
->d
);
2051 rec
= isl_upoly_as_rec(up
);
2055 for (i
= 0; i
< rec
->n
; ++i
)
2056 upoly_update_den(rec
->p
[i
], d
);
2059 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial
*qp
, isl_int
*d
)
2061 isl_int_set_si(*d
, 1);
2064 upoly_update_den(qp
->upoly
, d
);
2067 __isl_give isl_qpolynomial
*isl_qpolynomial_var_pow_on_domain(
2068 __isl_take isl_space
*dim
, int pos
, int power
)
2070 struct isl_ctx
*ctx
;
2077 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_var_pow(ctx
, pos
, power
));
2080 __isl_give isl_qpolynomial
*isl_qpolynomial_var_on_domain(__isl_take isl_space
*dim
,
2081 enum isl_dim_type type
, unsigned pos
)
2086 isl_assert(dim
->ctx
, isl_space_dim(dim
, isl_dim_in
) == 0, goto error
);
2087 isl_assert(dim
->ctx
, pos
< isl_space_dim(dim
, type
), goto error
);
2089 if (type
== isl_dim_set
)
2090 pos
+= isl_space_dim(dim
, isl_dim_param
);
2092 return isl_qpolynomial_var_pow_on_domain(dim
, pos
, 1);
2094 isl_space_free(dim
);
2098 __isl_give
struct isl_upoly
*isl_upoly_subs(__isl_take
struct isl_upoly
*up
,
2099 unsigned first
, unsigned n
, __isl_keep
struct isl_upoly
**subs
)
2102 struct isl_upoly_rec
*rec
;
2103 struct isl_upoly
*base
, *res
;
2108 if (isl_upoly_is_cst(up
))
2111 if (up
->var
< first
)
2114 rec
= isl_upoly_as_rec(up
);
2118 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
2120 if (up
->var
>= first
+ n
)
2121 base
= isl_upoly_var_pow(up
->ctx
, up
->var
, 1);
2123 base
= isl_upoly_copy(subs
[up
->var
- first
]);
2125 res
= isl_upoly_subs(isl_upoly_copy(rec
->p
[rec
->n
- 1]), first
, n
, subs
);
2126 for (i
= rec
->n
- 2; i
>= 0; --i
) {
2127 struct isl_upoly
*t
;
2128 t
= isl_upoly_subs(isl_upoly_copy(rec
->p
[i
]), first
, n
, subs
);
2129 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
2130 res
= isl_upoly_sum(res
, t
);
2133 isl_upoly_free(base
);
2142 __isl_give
struct isl_upoly
*isl_upoly_from_affine(isl_ctx
*ctx
, isl_int
*f
,
2143 isl_int denom
, unsigned len
)
2146 struct isl_upoly
*up
;
2148 isl_assert(ctx
, len
>= 1, return NULL
);
2150 up
= isl_upoly_rat_cst(ctx
, f
[0], denom
);
2151 for (i
= 0; i
< len
- 1; ++i
) {
2152 struct isl_upoly
*t
;
2153 struct isl_upoly
*c
;
2155 if (isl_int_is_zero(f
[1 + i
]))
2158 c
= isl_upoly_rat_cst(ctx
, f
[1 + i
], denom
);
2159 t
= isl_upoly_var_pow(ctx
, i
, 1);
2160 t
= isl_upoly_mul(c
, t
);
2161 up
= isl_upoly_sum(up
, t
);
2167 /* Remove common factor of non-constant terms and denominator.
2169 static void normalize_div(__isl_keep isl_qpolynomial
*qp
, int div
)
2171 isl_ctx
*ctx
= qp
->div
->ctx
;
2172 unsigned total
= qp
->div
->n_col
- 2;
2174 isl_seq_gcd(qp
->div
->row
[div
] + 2, total
, &ctx
->normalize_gcd
);
2175 isl_int_gcd(ctx
->normalize_gcd
,
2176 ctx
->normalize_gcd
, qp
->div
->row
[div
][0]);
2177 if (isl_int_is_one(ctx
->normalize_gcd
))
2180 isl_seq_scale_down(qp
->div
->row
[div
] + 2, qp
->div
->row
[div
] + 2,
2181 ctx
->normalize_gcd
, total
);
2182 isl_int_divexact(qp
->div
->row
[div
][0], qp
->div
->row
[div
][0],
2183 ctx
->normalize_gcd
);
2184 isl_int_fdiv_q(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1],
2185 ctx
->normalize_gcd
);
2188 /* Replace the integer division identified by "div" by the polynomial "s".
2189 * The integer division is assumed not to appear in the definition
2190 * of any other integer divisions.
2192 static __isl_give isl_qpolynomial
*substitute_div(
2193 __isl_take isl_qpolynomial
*qp
,
2194 int div
, __isl_take
struct isl_upoly
*s
)
2203 qp
= isl_qpolynomial_cow(qp
);
2207 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
2208 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ div
, 1, &s
);
2212 reordering
= isl_alloc_array(qp
->dim
->ctx
, int, total
+ qp
->div
->n_row
);
2215 for (i
= 0; i
< total
+ div
; ++i
)
2217 for (i
= total
+ div
+ 1; i
< total
+ qp
->div
->n_row
; ++i
)
2218 reordering
[i
] = i
- 1;
2219 qp
->div
= isl_mat_drop_rows(qp
->div
, div
, 1);
2220 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + total
+ div
, 1);
2221 qp
->upoly
= reorder(qp
->upoly
, reordering
);
2224 if (!qp
->upoly
|| !qp
->div
)
2230 isl_qpolynomial_free(qp
);
2235 /* Replace all integer divisions [e/d] that turn out to not actually be integer
2236 * divisions because d is equal to 1 by their definition, i.e., e.
2238 static __isl_give isl_qpolynomial
*substitute_non_divs(
2239 __isl_take isl_qpolynomial
*qp
)
2243 struct isl_upoly
*s
;
2248 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
2249 for (i
= 0; qp
&& i
< qp
->div
->n_row
; ++i
) {
2250 if (!isl_int_is_one(qp
->div
->row
[i
][0]))
2252 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
2253 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
2255 isl_seq_combine(qp
->div
->row
[j
] + 1,
2256 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
2257 qp
->div
->row
[j
][2 + total
+ i
],
2258 qp
->div
->row
[i
] + 1, 1 + total
+ i
);
2259 isl_int_set_si(qp
->div
->row
[j
][2 + total
+ i
], 0);
2260 normalize_div(qp
, j
);
2262 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
2263 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
2264 qp
= substitute_div(qp
, i
, s
);
2271 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
2272 * with d the denominator. When replacing the coefficient e of x by
2273 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
2274 * inside the division, so we need to add floor(e/d) * x outside.
2275 * That is, we replace q by q' + floor(e/d) * x and we therefore need
2276 * to adjust the coefficient of x in each later div that depends on the
2277 * current div "div" and also in the affine expressions in the rows of "mat"
2278 * (if they too depend on "div").
2280 static void reduce_div(__isl_keep isl_qpolynomial
*qp
, int div
,
2281 __isl_keep isl_mat
**mat
)
2285 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
2288 for (i
= 0; i
< 1 + total
+ div
; ++i
) {
2289 if (isl_int_is_nonneg(qp
->div
->row
[div
][1 + i
]) &&
2290 isl_int_lt(qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]))
2292 isl_int_fdiv_q(v
, qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
2293 isl_int_fdiv_r(qp
->div
->row
[div
][1 + i
],
2294 qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
2295 *mat
= isl_mat_col_addmul(*mat
, i
, v
, 1 + total
+ div
);
2296 for (j
= div
+ 1; j
< qp
->div
->n_row
; ++j
) {
2297 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ div
]))
2299 isl_int_addmul(qp
->div
->row
[j
][1 + i
],
2300 v
, qp
->div
->row
[j
][2 + total
+ div
]);
2306 /* Check if the last non-zero coefficient is bigger that half of the
2307 * denominator. If so, we will invert the div to further reduce the number
2308 * of distinct divs that may appear.
2309 * If the last non-zero coefficient is exactly half the denominator,
2310 * then we continue looking for earlier coefficients that are bigger
2311 * than half the denominator.
2313 static int needs_invert(__isl_keep isl_mat
*div
, int row
)
2318 for (i
= div
->n_col
- 1; i
>= 1; --i
) {
2319 if (isl_int_is_zero(div
->row
[row
][i
]))
2321 isl_int_mul_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
2322 cmp
= isl_int_cmp(div
->row
[row
][i
], div
->row
[row
][0]);
2323 isl_int_divexact_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
2333 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
2334 * We only invert the coefficients of e (and the coefficient of q in
2335 * later divs and in the rows of "mat"). After calling this function, the
2336 * coefficients of e should be reduced again.
2338 static void invert_div(__isl_keep isl_qpolynomial
*qp
, int div
,
2339 __isl_keep isl_mat
**mat
)
2341 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
2343 isl_seq_neg(qp
->div
->row
[div
] + 1,
2344 qp
->div
->row
[div
] + 1, qp
->div
->n_col
- 1);
2345 isl_int_sub_ui(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1], 1);
2346 isl_int_add(qp
->div
->row
[div
][1],
2347 qp
->div
->row
[div
][1], qp
->div
->row
[div
][0]);
2348 *mat
= isl_mat_col_neg(*mat
, 1 + total
+ div
);
2349 isl_mat_col_mul(qp
->div
, 2 + total
+ div
,
2350 qp
->div
->ctx
->negone
, 2 + total
+ div
);
2353 /* Reduce all divs of "qp" to have coefficients
2354 * in the interval [0, d-1], with d the denominator and such that the
2355 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2356 * The modifications to the integer divisions need to be reflected
2357 * in the factors of the polynomial that refer to the original
2358 * integer divisions. To this end, the modifications are collected
2359 * as a set of affine expressions and then plugged into the polynomial.
2361 * After the reduction, some divs may have become redundant or identical,
2362 * so we call substitute_non_divs and sort_divs. If these functions
2363 * eliminate divs or merge two or more divs into one, the coefficients
2364 * of the enclosing divs may have to be reduced again, so we call
2365 * ourselves recursively if the number of divs decreases.
2367 static __isl_give isl_qpolynomial
*reduce_divs(__isl_take isl_qpolynomial
*qp
)
2372 struct isl_upoly
**s
;
2373 unsigned o_div
, n_div
, total
;
2378 total
= isl_qpolynomial_domain_dim(qp
, isl_dim_all
);
2379 n_div
= isl_qpolynomial_domain_dim(qp
, isl_dim_div
);
2380 o_div
= isl_qpolynomial_domain_offset(qp
, isl_dim_div
);
2381 ctx
= isl_qpolynomial_get_ctx(qp
);
2382 mat
= isl_mat_zero(ctx
, n_div
, 1 + total
);
2384 for (i
= 0; i
< n_div
; ++i
)
2385 mat
= isl_mat_set_element_si(mat
, i
, o_div
+ i
, 1);
2387 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2388 normalize_div(qp
, i
);
2389 reduce_div(qp
, i
, &mat
);
2390 if (needs_invert(qp
->div
, i
)) {
2391 invert_div(qp
, i
, &mat
);
2392 reduce_div(qp
, i
, &mat
);
2398 s
= isl_alloc_array(ctx
, struct isl_upoly
*, n_div
);
2401 for (i
= 0; i
< n_div
; ++i
)
2402 s
[i
] = isl_upoly_from_affine(ctx
, mat
->row
[i
], ctx
->one
,
2404 qp
->upoly
= isl_upoly_subs(qp
->upoly
, o_div
- 1, n_div
, s
);
2405 for (i
= 0; i
< n_div
; ++i
)
2406 isl_upoly_free(s
[i
]);
2413 qp
= substitute_non_divs(qp
);
2415 if (qp
&& isl_qpolynomial_domain_dim(qp
, isl_dim_div
) < n_div
)
2416 return reduce_divs(qp
);
2420 isl_qpolynomial_free(qp
);
2425 __isl_give isl_qpolynomial
*isl_qpolynomial_rat_cst_on_domain(
2426 __isl_take isl_space
*dim
, const isl_int n
, const isl_int d
)
2428 struct isl_qpolynomial
*qp
;
2429 struct isl_upoly_cst
*cst
;
2434 qp
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
2438 cst
= isl_upoly_as_cst(qp
->upoly
);
2439 isl_int_set(cst
->n
, n
);
2440 isl_int_set(cst
->d
, d
);
2445 /* Return an isl_qpolynomial that is equal to "val" on domain space "domain".
2447 __isl_give isl_qpolynomial
*isl_qpolynomial_val_on_domain(
2448 __isl_take isl_space
*domain
, __isl_take isl_val
*val
)
2450 isl_qpolynomial
*qp
;
2451 struct isl_upoly_cst
*cst
;
2453 if (!domain
|| !val
)
2456 qp
= isl_qpolynomial_alloc(isl_space_copy(domain
), 0,
2457 isl_upoly_zero(domain
->ctx
));
2461 cst
= isl_upoly_as_cst(qp
->upoly
);
2462 isl_int_set(cst
->n
, val
->n
);
2463 isl_int_set(cst
->d
, val
->d
);
2465 isl_space_free(domain
);
2469 isl_space_free(domain
);
2474 static int up_set_active(__isl_keep
struct isl_upoly
*up
, int *active
, int d
)
2476 struct isl_upoly_rec
*rec
;
2482 if (isl_upoly_is_cst(up
))
2486 active
[up
->var
] = 1;
2488 rec
= isl_upoly_as_rec(up
);
2489 for (i
= 0; i
< rec
->n
; ++i
)
2490 if (up_set_active(rec
->p
[i
], active
, d
) < 0)
2496 static int set_active(__isl_keep isl_qpolynomial
*qp
, int *active
)
2499 int d
= isl_space_dim(qp
->dim
, isl_dim_all
);
2504 for (i
= 0; i
< d
; ++i
)
2505 for (j
= 0; j
< qp
->div
->n_row
; ++j
) {
2506 if (isl_int_is_zero(qp
->div
->row
[j
][2 + i
]))
2512 return up_set_active(qp
->upoly
, active
, d
);
2515 isl_bool
isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial
*qp
,
2516 enum isl_dim_type type
, unsigned first
, unsigned n
)
2520 isl_bool involves
= isl_bool_false
;
2523 return isl_bool_error
;
2525 return isl_bool_false
;
2527 isl_assert(qp
->dim
->ctx
,
2528 first
+ n
<= isl_qpolynomial_dim(qp
, type
),
2529 return isl_bool_error
);
2530 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2531 type
== isl_dim_in
, return isl_bool_error
);
2533 active
= isl_calloc_array(qp
->dim
->ctx
, int,
2534 isl_space_dim(qp
->dim
, isl_dim_all
));
2535 if (set_active(qp
, active
) < 0)
2538 if (type
== isl_dim_in
)
2539 first
+= isl_space_dim(qp
->dim
, isl_dim_param
);
2540 for (i
= 0; i
< n
; ++i
)
2541 if (active
[first
+ i
]) {
2542 involves
= isl_bool_true
;
2551 return isl_bool_error
;
2554 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2555 * of the divs that do appear in the quasi-polynomial.
2557 static __isl_give isl_qpolynomial
*remove_redundant_divs(
2558 __isl_take isl_qpolynomial
*qp
)
2565 int *reordering
= NULL
;
2572 if (qp
->div
->n_row
== 0)
2575 d
= isl_space_dim(qp
->dim
, isl_dim_all
);
2576 len
= qp
->div
->n_col
- 2;
2577 ctx
= isl_qpolynomial_get_ctx(qp
);
2578 active
= isl_calloc_array(ctx
, int, len
);
2582 if (up_set_active(qp
->upoly
, active
, len
) < 0)
2585 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
2586 if (!active
[d
+ i
]) {
2590 for (j
= 0; j
< i
; ++j
) {
2591 if (isl_int_is_zero(qp
->div
->row
[i
][2 + d
+ j
]))
2603 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
2607 for (i
= 0; i
< d
; ++i
)
2611 n_div
= qp
->div
->n_row
;
2612 for (i
= 0; i
< n_div
; ++i
) {
2613 if (!active
[d
+ i
]) {
2614 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
2615 qp
->div
= isl_mat_drop_cols(qp
->div
,
2616 2 + d
+ i
- skip
, 1);
2619 reordering
[d
+ i
] = d
+ i
- skip
;
2622 qp
->upoly
= reorder(qp
->upoly
, reordering
);
2624 if (!qp
->upoly
|| !qp
->div
)
2634 isl_qpolynomial_free(qp
);
2638 __isl_give
struct isl_upoly
*isl_upoly_drop(__isl_take
struct isl_upoly
*up
,
2639 unsigned first
, unsigned n
)
2642 struct isl_upoly_rec
*rec
;
2646 if (n
== 0 || up
->var
< 0 || up
->var
< first
)
2648 if (up
->var
< first
+ n
) {
2649 up
= replace_by_constant_term(up
);
2650 return isl_upoly_drop(up
, first
, n
);
2652 up
= isl_upoly_cow(up
);
2656 rec
= isl_upoly_as_rec(up
);
2660 for (i
= 0; i
< rec
->n
; ++i
) {
2661 rec
->p
[i
] = isl_upoly_drop(rec
->p
[i
], first
, n
);
2672 __isl_give isl_qpolynomial
*isl_qpolynomial_set_dim_name(
2673 __isl_take isl_qpolynomial
*qp
,
2674 enum isl_dim_type type
, unsigned pos
, const char *s
)
2676 qp
= isl_qpolynomial_cow(qp
);
2679 qp
->dim
= isl_space_set_dim_name(qp
->dim
, type
, pos
, s
);
2684 isl_qpolynomial_free(qp
);
2688 __isl_give isl_qpolynomial
*isl_qpolynomial_drop_dims(
2689 __isl_take isl_qpolynomial
*qp
,
2690 enum isl_dim_type type
, unsigned first
, unsigned n
)
2694 if (type
== isl_dim_out
)
2695 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
2696 "cannot drop output/set dimension",
2698 if (type
== isl_dim_in
)
2700 if (n
== 0 && !isl_space_is_named_or_nested(qp
->dim
, type
))
2703 qp
= isl_qpolynomial_cow(qp
);
2707 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_space_dim(qp
->dim
, type
),
2709 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2710 type
== isl_dim_set
, goto error
);
2712 qp
->dim
= isl_space_drop_dims(qp
->dim
, type
, first
, n
);
2716 if (type
== isl_dim_set
)
2717 first
+= isl_space_dim(qp
->dim
, isl_dim_param
);
2719 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + first
, n
);
2723 qp
->upoly
= isl_upoly_drop(qp
->upoly
, first
, n
);
2729 isl_qpolynomial_free(qp
);
2733 /* Project the domain of the quasi-polynomial onto its parameter space.
2734 * The quasi-polynomial may not involve any of the domain dimensions.
2736 __isl_give isl_qpolynomial
*isl_qpolynomial_project_domain_on_params(
2737 __isl_take isl_qpolynomial
*qp
)
2743 n
= isl_qpolynomial_dim(qp
, isl_dim_in
);
2744 involves
= isl_qpolynomial_involves_dims(qp
, isl_dim_in
, 0, n
);
2746 return isl_qpolynomial_free(qp
);
2748 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
2749 "polynomial involves some of the domain dimensions",
2750 return isl_qpolynomial_free(qp
));
2751 qp
= isl_qpolynomial_drop_dims(qp
, isl_dim_in
, 0, n
);
2752 space
= isl_qpolynomial_get_domain_space(qp
);
2753 space
= isl_space_params(space
);
2754 qp
= isl_qpolynomial_reset_domain_space(qp
, space
);
2758 static __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities_lifted(
2759 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2765 struct isl_upoly
*up
;
2769 if (eq
->n_eq
== 0) {
2770 isl_basic_set_free(eq
);
2774 qp
= isl_qpolynomial_cow(qp
);
2777 qp
->div
= isl_mat_cow(qp
->div
);
2781 total
= 1 + isl_space_dim(eq
->dim
, isl_dim_all
);
2783 isl_int_init(denom
);
2784 for (i
= 0; i
< eq
->n_eq
; ++i
) {
2785 j
= isl_seq_last_non_zero(eq
->eq
[i
], total
+ n_div
);
2786 if (j
< 0 || j
== 0 || j
>= total
)
2789 for (k
= 0; k
< qp
->div
->n_row
; ++k
) {
2790 if (isl_int_is_zero(qp
->div
->row
[k
][1 + j
]))
2792 isl_seq_elim(qp
->div
->row
[k
] + 1, eq
->eq
[i
], j
, total
,
2793 &qp
->div
->row
[k
][0]);
2794 normalize_div(qp
, k
);
2797 if (isl_int_is_pos(eq
->eq
[i
][j
]))
2798 isl_seq_neg(eq
->eq
[i
], eq
->eq
[i
], total
);
2799 isl_int_abs(denom
, eq
->eq
[i
][j
]);
2800 isl_int_set_si(eq
->eq
[i
][j
], 0);
2802 up
= isl_upoly_from_affine(qp
->dim
->ctx
,
2803 eq
->eq
[i
], denom
, total
);
2804 qp
->upoly
= isl_upoly_subs(qp
->upoly
, j
- 1, 1, &up
);
2807 isl_int_clear(denom
);
2812 isl_basic_set_free(eq
);
2814 qp
= substitute_non_divs(qp
);
2819 isl_basic_set_free(eq
);
2820 isl_qpolynomial_free(qp
);
2824 /* Exploit the equalities in "eq" to simplify the quasi-polynomial.
2826 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities(
2827 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2831 if (qp
->div
->n_row
> 0)
2832 eq
= isl_basic_set_add_dims(eq
, isl_dim_set
, qp
->div
->n_row
);
2833 return isl_qpolynomial_substitute_equalities_lifted(qp
, eq
);
2835 isl_basic_set_free(eq
);
2836 isl_qpolynomial_free(qp
);
2840 static __isl_give isl_basic_set
*add_div_constraints(
2841 __isl_take isl_basic_set
*bset
, __isl_take isl_mat
*div
)
2849 bset
= isl_basic_set_extend_constraints(bset
, 0, 2 * div
->n_row
);
2852 total
= isl_basic_set_total_dim(bset
);
2853 for (i
= 0; i
< div
->n_row
; ++i
)
2854 if (isl_basic_set_add_div_constraints_var(bset
,
2855 total
- div
->n_row
+ i
, div
->row
[i
]) < 0)
2862 isl_basic_set_free(bset
);
2866 /* Look for equalities among the variables shared by context and qp
2867 * and the integer divisions of qp, if any.
2868 * The equalities are then used to eliminate variables and/or integer
2869 * divisions from qp.
2871 __isl_give isl_qpolynomial
*isl_qpolynomial_gist(
2872 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
2878 if (qp
->div
->n_row
> 0) {
2879 isl_basic_set
*bset
;
2880 context
= isl_set_add_dims(context
, isl_dim_set
,
2882 bset
= isl_basic_set_universe(isl_set_get_space(context
));
2883 bset
= add_div_constraints(bset
, isl_mat_copy(qp
->div
));
2884 context
= isl_set_intersect(context
,
2885 isl_set_from_basic_set(bset
));
2888 aff
= isl_set_affine_hull(context
);
2889 return isl_qpolynomial_substitute_equalities_lifted(qp
, aff
);
2891 isl_qpolynomial_free(qp
);
2892 isl_set_free(context
);
2896 __isl_give isl_qpolynomial
*isl_qpolynomial_gist_params(
2897 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
2899 isl_space
*space
= isl_qpolynomial_get_domain_space(qp
);
2900 isl_set
*dom_context
= isl_set_universe(space
);
2901 dom_context
= isl_set_intersect_params(dom_context
, context
);
2902 return isl_qpolynomial_gist(qp
, dom_context
);
2905 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_from_qpolynomial(
2906 __isl_take isl_qpolynomial
*qp
)
2912 if (isl_qpolynomial_is_zero(qp
)) {
2913 isl_space
*dim
= isl_qpolynomial_get_space(qp
);
2914 isl_qpolynomial_free(qp
);
2915 return isl_pw_qpolynomial_zero(dim
);
2918 dom
= isl_set_universe(isl_qpolynomial_get_domain_space(qp
));
2919 return isl_pw_qpolynomial_alloc(dom
, qp
);
2923 #define PW isl_pw_qpolynomial
2925 #define EL isl_qpolynomial
2927 #define EL_IS_ZERO is_zero
2931 #define IS_ZERO is_zero
2934 #undef DEFAULT_IS_ZERO
2935 #define DEFAULT_IS_ZERO 1
2939 #include <isl_pw_templ.c>
2942 #define UNION isl_union_pw_qpolynomial
2944 #define PART isl_pw_qpolynomial
2946 #define PARTS pw_qpolynomial
2948 #include <isl_union_single.c>
2949 #include <isl_union_eval.c>
2950 #include <isl_union_neg.c>
2952 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial
*pwqp
)
2960 if (!isl_set_plain_is_universe(pwqp
->p
[0].set
))
2963 return isl_qpolynomial_is_one(pwqp
->p
[0].qp
);
2966 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add(
2967 __isl_take isl_pw_qpolynomial
*pwqp1
,
2968 __isl_take isl_pw_qpolynomial
*pwqp2
)
2970 return isl_pw_qpolynomial_union_add_(pwqp1
, pwqp2
);
2973 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_mul(
2974 __isl_take isl_pw_qpolynomial
*pwqp1
,
2975 __isl_take isl_pw_qpolynomial
*pwqp2
)
2978 struct isl_pw_qpolynomial
*res
;
2980 if (!pwqp1
|| !pwqp2
)
2983 isl_assert(pwqp1
->dim
->ctx
, isl_space_is_equal(pwqp1
->dim
, pwqp2
->dim
),
2986 if (isl_pw_qpolynomial_is_zero(pwqp1
)) {
2987 isl_pw_qpolynomial_free(pwqp2
);
2991 if (isl_pw_qpolynomial_is_zero(pwqp2
)) {
2992 isl_pw_qpolynomial_free(pwqp1
);
2996 if (isl_pw_qpolynomial_is_one(pwqp1
)) {
2997 isl_pw_qpolynomial_free(pwqp1
);
3001 if (isl_pw_qpolynomial_is_one(pwqp2
)) {
3002 isl_pw_qpolynomial_free(pwqp2
);
3006 n
= pwqp1
->n
* pwqp2
->n
;
3007 res
= isl_pw_qpolynomial_alloc_size(isl_space_copy(pwqp1
->dim
), n
);
3009 for (i
= 0; i
< pwqp1
->n
; ++i
) {
3010 for (j
= 0; j
< pwqp2
->n
; ++j
) {
3011 struct isl_set
*common
;
3012 struct isl_qpolynomial
*prod
;
3013 common
= isl_set_intersect(isl_set_copy(pwqp1
->p
[i
].set
),
3014 isl_set_copy(pwqp2
->p
[j
].set
));
3015 if (isl_set_plain_is_empty(common
)) {
3016 isl_set_free(common
);
3020 prod
= isl_qpolynomial_mul(
3021 isl_qpolynomial_copy(pwqp1
->p
[i
].qp
),
3022 isl_qpolynomial_copy(pwqp2
->p
[j
].qp
));
3024 res
= isl_pw_qpolynomial_add_piece(res
, common
, prod
);
3028 isl_pw_qpolynomial_free(pwqp1
);
3029 isl_pw_qpolynomial_free(pwqp2
);
3033 isl_pw_qpolynomial_free(pwqp1
);
3034 isl_pw_qpolynomial_free(pwqp2
);
3038 __isl_give isl_val
*isl_upoly_eval(__isl_take
struct isl_upoly
*up
,
3039 __isl_take isl_vec
*vec
)
3042 struct isl_upoly_rec
*rec
;
3046 if (isl_upoly_is_cst(up
)) {
3048 res
= isl_upoly_get_constant_val(up
);
3053 rec
= isl_upoly_as_rec(up
);
3057 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
3059 base
= isl_val_rat_from_isl_int(up
->ctx
,
3060 vec
->el
[1 + up
->var
], vec
->el
[0]);
3062 res
= isl_upoly_eval(isl_upoly_copy(rec
->p
[rec
->n
- 1]),
3065 for (i
= rec
->n
- 2; i
>= 0; --i
) {
3066 res
= isl_val_mul(res
, isl_val_copy(base
));
3067 res
= isl_val_add(res
,
3068 isl_upoly_eval(isl_upoly_copy(rec
->p
[i
]),
3069 isl_vec_copy(vec
)));
3082 __isl_give isl_val
*isl_qpolynomial_eval(__isl_take isl_qpolynomial
*qp
,
3083 __isl_take isl_point
*pnt
)
3090 isl_assert(pnt
->dim
->ctx
, isl_space_is_equal(pnt
->dim
, qp
->dim
), goto error
);
3092 if (qp
->div
->n_row
== 0)
3093 ext
= isl_vec_copy(pnt
->vec
);
3096 unsigned dim
= isl_space_dim(qp
->dim
, isl_dim_all
);
3097 ext
= isl_vec_alloc(qp
->dim
->ctx
, 1 + dim
+ qp
->div
->n_row
);
3101 isl_seq_cpy(ext
->el
, pnt
->vec
->el
, pnt
->vec
->size
);
3102 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
3103 isl_seq_inner_product(qp
->div
->row
[i
] + 1, ext
->el
,
3104 1 + dim
+ i
, &ext
->el
[1+dim
+i
]);
3105 isl_int_fdiv_q(ext
->el
[1+dim
+i
], ext
->el
[1+dim
+i
],
3106 qp
->div
->row
[i
][0]);
3110 v
= isl_upoly_eval(isl_upoly_copy(qp
->upoly
), ext
);
3112 isl_qpolynomial_free(qp
);
3113 isl_point_free(pnt
);
3117 isl_qpolynomial_free(qp
);
3118 isl_point_free(pnt
);
3122 int isl_upoly_cmp(__isl_keep
struct isl_upoly_cst
*cst1
,
3123 __isl_keep
struct isl_upoly_cst
*cst2
)
3128 isl_int_mul(t
, cst1
->n
, cst2
->d
);
3129 isl_int_submul(t
, cst2
->n
, cst1
->d
);
3130 cmp
= isl_int_sgn(t
);
3135 __isl_give isl_qpolynomial
*isl_qpolynomial_insert_dims(
3136 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
,
3137 unsigned first
, unsigned n
)
3145 if (type
== isl_dim_out
)
3146 isl_die(qp
->div
->ctx
, isl_error_invalid
,
3147 "cannot insert output/set dimensions",
3149 if (type
== isl_dim_in
)
3151 if (n
== 0 && !isl_space_is_named_or_nested(qp
->dim
, type
))
3154 qp
= isl_qpolynomial_cow(qp
);
3158 isl_assert(qp
->div
->ctx
, first
<= isl_space_dim(qp
->dim
, type
),
3161 g_pos
= pos(qp
->dim
, type
) + first
;
3163 qp
->div
= isl_mat_insert_zero_cols(qp
->div
, 2 + g_pos
, n
);
3167 total
= qp
->div
->n_col
- 2;
3168 if (total
> g_pos
) {
3170 exp
= isl_alloc_array(qp
->div
->ctx
, int, total
- g_pos
);
3173 for (i
= 0; i
< total
- g_pos
; ++i
)
3175 qp
->upoly
= expand(qp
->upoly
, exp
, g_pos
);
3181 qp
->dim
= isl_space_insert_dims(qp
->dim
, type
, first
, n
);
3187 isl_qpolynomial_free(qp
);
3191 __isl_give isl_qpolynomial
*isl_qpolynomial_add_dims(
3192 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
, unsigned n
)
3196 pos
= isl_qpolynomial_dim(qp
, type
);
3198 return isl_qpolynomial_insert_dims(qp
, type
, pos
, n
);
3201 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add_dims(
3202 __isl_take isl_pw_qpolynomial
*pwqp
,
3203 enum isl_dim_type type
, unsigned n
)
3207 pos
= isl_pw_qpolynomial_dim(pwqp
, type
);
3209 return isl_pw_qpolynomial_insert_dims(pwqp
, type
, pos
, n
);
3212 static int *reordering_move(isl_ctx
*ctx
,
3213 unsigned len
, unsigned dst
, unsigned src
, unsigned n
)
3218 reordering
= isl_alloc_array(ctx
, int, len
);
3223 for (i
= 0; i
< dst
; ++i
)
3225 for (i
= 0; i
< n
; ++i
)
3226 reordering
[src
+ i
] = dst
+ i
;
3227 for (i
= 0; i
< src
- dst
; ++i
)
3228 reordering
[dst
+ i
] = dst
+ n
+ i
;
3229 for (i
= 0; i
< len
- src
- n
; ++i
)
3230 reordering
[src
+ n
+ i
] = src
+ n
+ i
;
3232 for (i
= 0; i
< src
; ++i
)
3234 for (i
= 0; i
< n
; ++i
)
3235 reordering
[src
+ i
] = dst
+ i
;
3236 for (i
= 0; i
< dst
- src
; ++i
)
3237 reordering
[src
+ n
+ i
] = src
+ i
;
3238 for (i
= 0; i
< len
- dst
- n
; ++i
)
3239 reordering
[dst
+ n
+ i
] = dst
+ n
+ i
;
3245 __isl_give isl_qpolynomial
*isl_qpolynomial_move_dims(
3246 __isl_take isl_qpolynomial
*qp
,
3247 enum isl_dim_type dst_type
, unsigned dst_pos
,
3248 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
3257 qp
= isl_qpolynomial_cow(qp
);
3261 if (dst_type
== isl_dim_out
|| src_type
== isl_dim_out
)
3262 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
3263 "cannot move output/set dimension",
3265 if (dst_type
== isl_dim_in
)
3266 dst_type
= isl_dim_set
;
3267 if (src_type
== isl_dim_in
)
3268 src_type
= isl_dim_set
;
3270 isl_assert(qp
->dim
->ctx
, src_pos
+ n
<= isl_space_dim(qp
->dim
, src_type
),
3273 g_dst_pos
= pos(qp
->dim
, dst_type
) + dst_pos
;
3274 g_src_pos
= pos(qp
->dim
, src_type
) + src_pos
;
3275 if (dst_type
> src_type
)
3278 qp
->div
= isl_mat_move_cols(qp
->div
, 2 + g_dst_pos
, 2 + g_src_pos
, n
);
3285 reordering
= reordering_move(qp
->dim
->ctx
,
3286 qp
->div
->n_col
- 2, g_dst_pos
, g_src_pos
, n
);
3290 qp
->upoly
= reorder(qp
->upoly
, reordering
);
3295 qp
->dim
= isl_space_move_dims(qp
->dim
, dst_type
, dst_pos
, src_type
, src_pos
, n
);
3301 isl_qpolynomial_free(qp
);
3305 __isl_give isl_qpolynomial
*isl_qpolynomial_from_affine(__isl_take isl_space
*dim
,
3306 isl_int
*f
, isl_int denom
)
3308 struct isl_upoly
*up
;
3310 dim
= isl_space_domain(dim
);
3314 up
= isl_upoly_from_affine(dim
->ctx
, f
, denom
,
3315 1 + isl_space_dim(dim
, isl_dim_all
));
3317 return isl_qpolynomial_alloc(dim
, 0, up
);
3320 __isl_give isl_qpolynomial
*isl_qpolynomial_from_aff(__isl_take isl_aff
*aff
)
3323 struct isl_upoly
*up
;
3324 isl_qpolynomial
*qp
;
3329 ctx
= isl_aff_get_ctx(aff
);
3330 up
= isl_upoly_from_affine(ctx
, aff
->v
->el
+ 1, aff
->v
->el
[0],
3333 qp
= isl_qpolynomial_alloc(isl_aff_get_domain_space(aff
),
3334 aff
->ls
->div
->n_row
, up
);
3338 isl_mat_free(qp
->div
);
3339 qp
->div
= isl_mat_copy(aff
->ls
->div
);
3340 qp
->div
= isl_mat_cow(qp
->div
);
3345 qp
= reduce_divs(qp
);
3346 qp
= remove_redundant_divs(qp
);
3350 return isl_qpolynomial_free(qp
);
3353 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_from_pw_aff(
3354 __isl_take isl_pw_aff
*pwaff
)
3357 isl_pw_qpolynomial
*pwqp
;
3362 pwqp
= isl_pw_qpolynomial_alloc_size(isl_pw_aff_get_space(pwaff
),
3365 for (i
= 0; i
< pwaff
->n
; ++i
) {
3367 isl_qpolynomial
*qp
;
3369 dom
= isl_set_copy(pwaff
->p
[i
].set
);
3370 qp
= isl_qpolynomial_from_aff(isl_aff_copy(pwaff
->p
[i
].aff
));
3371 pwqp
= isl_pw_qpolynomial_add_piece(pwqp
, dom
, qp
);
3374 isl_pw_aff_free(pwaff
);
3378 __isl_give isl_qpolynomial
*isl_qpolynomial_from_constraint(
3379 __isl_take isl_constraint
*c
, enum isl_dim_type type
, unsigned pos
)
3383 aff
= isl_constraint_get_bound(c
, type
, pos
);
3384 isl_constraint_free(c
);
3385 return isl_qpolynomial_from_aff(aff
);
3388 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3389 * in "qp" by subs[i].
3391 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute(
3392 __isl_take isl_qpolynomial
*qp
,
3393 enum isl_dim_type type
, unsigned first
, unsigned n
,
3394 __isl_keep isl_qpolynomial
**subs
)
3397 struct isl_upoly
**ups
;
3402 qp
= isl_qpolynomial_cow(qp
);
3406 if (type
== isl_dim_out
)
3407 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
3408 "cannot substitute output/set dimension",
3410 if (type
== isl_dim_in
)
3413 for (i
= 0; i
< n
; ++i
)
3417 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_space_dim(qp
->dim
, type
),
3420 for (i
= 0; i
< n
; ++i
)
3421 isl_assert(qp
->dim
->ctx
, isl_space_is_equal(qp
->dim
, subs
[i
]->dim
),
3424 isl_assert(qp
->dim
->ctx
, qp
->div
->n_row
== 0, goto error
);
3425 for (i
= 0; i
< n
; ++i
)
3426 isl_assert(qp
->dim
->ctx
, subs
[i
]->div
->n_row
== 0, goto error
);
3428 first
+= pos(qp
->dim
, type
);
3430 ups
= isl_alloc_array(qp
->dim
->ctx
, struct isl_upoly
*, n
);
3433 for (i
= 0; i
< n
; ++i
)
3434 ups
[i
] = subs
[i
]->upoly
;
3436 qp
->upoly
= isl_upoly_subs(qp
->upoly
, first
, n
, ups
);
3445 isl_qpolynomial_free(qp
);
3449 /* Extend "bset" with extra set dimensions for each integer division
3450 * in "qp" and then call "fn" with the extended bset and the polynomial
3451 * that results from replacing each of the integer divisions by the
3452 * corresponding extra set dimension.
3454 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial
*qp
,
3455 __isl_keep isl_basic_set
*bset
,
3456 int (*fn
)(__isl_take isl_basic_set
*bset
,
3457 __isl_take isl_qpolynomial
*poly
, void *user
), void *user
)
3461 isl_qpolynomial
*poly
;
3465 if (qp
->div
->n_row
== 0)
3466 return fn(isl_basic_set_copy(bset
), isl_qpolynomial_copy(qp
),
3469 div
= isl_mat_copy(qp
->div
);
3470 dim
= isl_space_copy(qp
->dim
);
3471 dim
= isl_space_add_dims(dim
, isl_dim_set
, qp
->div
->n_row
);
3472 poly
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_copy(qp
->upoly
));
3473 bset
= isl_basic_set_copy(bset
);
3474 bset
= isl_basic_set_add_dims(bset
, isl_dim_set
, qp
->div
->n_row
);
3475 bset
= add_div_constraints(bset
, div
);
3477 return fn(bset
, poly
, user
);
3482 /* Return total degree in variables first (inclusive) up to last (exclusive).
3484 int isl_upoly_degree(__isl_keep
struct isl_upoly
*up
, int first
, int last
)
3488 struct isl_upoly_rec
*rec
;
3492 if (isl_upoly_is_zero(up
))
3494 if (isl_upoly_is_cst(up
) || up
->var
< first
)
3497 rec
= isl_upoly_as_rec(up
);
3501 for (i
= 0; i
< rec
->n
; ++i
) {
3504 if (isl_upoly_is_zero(rec
->p
[i
]))
3506 d
= isl_upoly_degree(rec
->p
[i
], first
, last
);
3516 /* Return total degree in set variables.
3518 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial
*poly
)
3526 ovar
= isl_space_offset(poly
->dim
, isl_dim_set
);
3527 nvar
= isl_space_dim(poly
->dim
, isl_dim_set
);
3528 return isl_upoly_degree(poly
->upoly
, ovar
, ovar
+ nvar
);
3531 __isl_give
struct isl_upoly
*isl_upoly_coeff(__isl_keep
struct isl_upoly
*up
,
3532 unsigned pos
, int deg
)
3535 struct isl_upoly_rec
*rec
;
3540 if (isl_upoly_is_cst(up
) || up
->var
< pos
) {
3542 return isl_upoly_copy(up
);
3544 return isl_upoly_zero(up
->ctx
);
3547 rec
= isl_upoly_as_rec(up
);
3551 if (up
->var
== pos
) {
3553 return isl_upoly_copy(rec
->p
[deg
]);
3555 return isl_upoly_zero(up
->ctx
);
3558 up
= isl_upoly_copy(up
);
3559 up
= isl_upoly_cow(up
);
3560 rec
= isl_upoly_as_rec(up
);
3564 for (i
= 0; i
< rec
->n
; ++i
) {
3565 struct isl_upoly
*t
;
3566 t
= isl_upoly_coeff(rec
->p
[i
], pos
, deg
);
3569 isl_upoly_free(rec
->p
[i
]);
3579 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3581 __isl_give isl_qpolynomial
*isl_qpolynomial_coeff(
3582 __isl_keep isl_qpolynomial
*qp
,
3583 enum isl_dim_type type
, unsigned t_pos
, int deg
)
3586 struct isl_upoly
*up
;
3592 if (type
== isl_dim_out
)
3593 isl_die(qp
->div
->ctx
, isl_error_invalid
,
3594 "output/set dimension does not have a coefficient",
3596 if (type
== isl_dim_in
)
3599 isl_assert(qp
->div
->ctx
, t_pos
< isl_space_dim(qp
->dim
, type
),
3602 g_pos
= pos(qp
->dim
, type
) + t_pos
;
3603 up
= isl_upoly_coeff(qp
->upoly
, g_pos
, deg
);
3605 c
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
), qp
->div
->n_row
, up
);
3608 isl_mat_free(c
->div
);
3609 c
->div
= isl_mat_copy(qp
->div
);
3614 isl_qpolynomial_free(c
);
3618 /* Homogenize the polynomial in the variables first (inclusive) up to
3619 * last (exclusive) by inserting powers of variable first.
3620 * Variable first is assumed not to appear in the input.
3622 __isl_give
struct isl_upoly
*isl_upoly_homogenize(
3623 __isl_take
struct isl_upoly
*up
, int deg
, int target
,
3624 int first
, int last
)
3627 struct isl_upoly_rec
*rec
;
3631 if (isl_upoly_is_zero(up
))
3635 if (isl_upoly_is_cst(up
) || up
->var
< first
) {
3636 struct isl_upoly
*hom
;
3638 hom
= isl_upoly_var_pow(up
->ctx
, first
, target
- deg
);
3641 rec
= isl_upoly_as_rec(hom
);
3642 rec
->p
[target
- deg
] = isl_upoly_mul(rec
->p
[target
- deg
], up
);
3647 up
= isl_upoly_cow(up
);
3648 rec
= isl_upoly_as_rec(up
);
3652 for (i
= 0; i
< rec
->n
; ++i
) {
3653 if (isl_upoly_is_zero(rec
->p
[i
]))
3655 rec
->p
[i
] = isl_upoly_homogenize(rec
->p
[i
],
3656 up
->var
< last
? deg
+ i
: i
, target
,
3668 /* Homogenize the polynomial in the set variables by introducing
3669 * powers of an extra set variable at position 0.
3671 __isl_give isl_qpolynomial
*isl_qpolynomial_homogenize(
3672 __isl_take isl_qpolynomial
*poly
)
3676 int deg
= isl_qpolynomial_degree(poly
);
3681 poly
= isl_qpolynomial_insert_dims(poly
, isl_dim_in
, 0, 1);
3682 poly
= isl_qpolynomial_cow(poly
);
3686 ovar
= isl_space_offset(poly
->dim
, isl_dim_set
);
3687 nvar
= isl_space_dim(poly
->dim
, isl_dim_set
);
3688 poly
->upoly
= isl_upoly_homogenize(poly
->upoly
, 0, deg
,
3695 isl_qpolynomial_free(poly
);
3699 __isl_give isl_term
*isl_term_alloc(__isl_take isl_space
*dim
,
3700 __isl_take isl_mat
*div
)
3708 n
= isl_space_dim(dim
, isl_dim_all
) + div
->n_row
;
3710 term
= isl_calloc(dim
->ctx
, struct isl_term
,
3711 sizeof(struct isl_term
) + (n
- 1) * sizeof(int));
3718 isl_int_init(term
->n
);
3719 isl_int_init(term
->d
);
3723 isl_space_free(dim
);
3728 __isl_give isl_term
*isl_term_copy(__isl_keep isl_term
*term
)
3737 __isl_give isl_term
*isl_term_dup(__isl_keep isl_term
*term
)
3746 total
= isl_space_dim(term
->dim
, isl_dim_all
) + term
->div
->n_row
;
3748 dup
= isl_term_alloc(isl_space_copy(term
->dim
), isl_mat_copy(term
->div
));
3752 isl_int_set(dup
->n
, term
->n
);
3753 isl_int_set(dup
->d
, term
->d
);
3755 for (i
= 0; i
< total
; ++i
)
3756 dup
->pow
[i
] = term
->pow
[i
];
3761 __isl_give isl_term
*isl_term_cow(__isl_take isl_term
*term
)
3769 return isl_term_dup(term
);
3772 void isl_term_free(__isl_take isl_term
*term
)
3777 if (--term
->ref
> 0)
3780 isl_space_free(term
->dim
);
3781 isl_mat_free(term
->div
);
3782 isl_int_clear(term
->n
);
3783 isl_int_clear(term
->d
);
3787 unsigned isl_term_dim(__isl_keep isl_term
*term
, enum isl_dim_type type
)
3795 case isl_dim_out
: return isl_space_dim(term
->dim
, type
);
3796 case isl_dim_div
: return term
->div
->n_row
;
3797 case isl_dim_all
: return isl_space_dim(term
->dim
, isl_dim_all
) +
3803 isl_ctx
*isl_term_get_ctx(__isl_keep isl_term
*term
)
3805 return term
? term
->dim
->ctx
: NULL
;
3808 void isl_term_get_num(__isl_keep isl_term
*term
, isl_int
*n
)
3812 isl_int_set(*n
, term
->n
);
3815 void isl_term_get_den(__isl_keep isl_term
*term
, isl_int
*d
)
3819 isl_int_set(*d
, term
->d
);
3822 /* Return the coefficient of the term "term".
3824 __isl_give isl_val
*isl_term_get_coefficient_val(__isl_keep isl_term
*term
)
3829 return isl_val_rat_from_isl_int(isl_term_get_ctx(term
),
3833 int isl_term_get_exp(__isl_keep isl_term
*term
,
3834 enum isl_dim_type type
, unsigned pos
)
3839 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, type
), return -1);
3841 if (type
>= isl_dim_set
)
3842 pos
+= isl_space_dim(term
->dim
, isl_dim_param
);
3843 if (type
>= isl_dim_div
)
3844 pos
+= isl_space_dim(term
->dim
, isl_dim_set
);
3846 return term
->pow
[pos
];
3849 __isl_give isl_aff
*isl_term_get_div(__isl_keep isl_term
*term
, unsigned pos
)
3851 isl_local_space
*ls
;
3857 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, isl_dim_div
),
3860 ls
= isl_local_space_alloc_div(isl_space_copy(term
->dim
),
3861 isl_mat_copy(term
->div
));
3862 aff
= isl_aff_alloc(ls
);
3866 isl_seq_cpy(aff
->v
->el
, term
->div
->row
[pos
], aff
->v
->size
);
3868 aff
= isl_aff_normalize(aff
);
3873 __isl_give isl_term
*isl_upoly_foreach_term(__isl_keep
struct isl_upoly
*up
,
3874 isl_stat (*fn
)(__isl_take isl_term
*term
, void *user
),
3875 __isl_take isl_term
*term
, void *user
)
3878 struct isl_upoly_rec
*rec
;
3883 if (isl_upoly_is_zero(up
))
3886 isl_assert(up
->ctx
, !isl_upoly_is_nan(up
), goto error
);
3887 isl_assert(up
->ctx
, !isl_upoly_is_infty(up
), goto error
);
3888 isl_assert(up
->ctx
, !isl_upoly_is_neginfty(up
), goto error
);
3890 if (isl_upoly_is_cst(up
)) {
3891 struct isl_upoly_cst
*cst
;
3892 cst
= isl_upoly_as_cst(up
);
3895 term
= isl_term_cow(term
);
3898 isl_int_set(term
->n
, cst
->n
);
3899 isl_int_set(term
->d
, cst
->d
);
3900 if (fn(isl_term_copy(term
), user
) < 0)
3905 rec
= isl_upoly_as_rec(up
);
3909 for (i
= 0; i
< rec
->n
; ++i
) {
3910 term
= isl_term_cow(term
);
3913 term
->pow
[up
->var
] = i
;
3914 term
= isl_upoly_foreach_term(rec
->p
[i
], fn
, term
, user
);
3918 term
->pow
[up
->var
] = 0;
3922 isl_term_free(term
);
3926 isl_stat
isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial
*qp
,
3927 isl_stat (*fn
)(__isl_take isl_term
*term
, void *user
), void *user
)
3932 return isl_stat_error
;
3934 term
= isl_term_alloc(isl_space_copy(qp
->dim
), isl_mat_copy(qp
->div
));
3936 return isl_stat_error
;
3938 term
= isl_upoly_foreach_term(qp
->upoly
, fn
, term
, user
);
3940 isl_term_free(term
);
3942 return term
? isl_stat_ok
: isl_stat_error
;
3945 __isl_give isl_qpolynomial
*isl_qpolynomial_from_term(__isl_take isl_term
*term
)
3947 struct isl_upoly
*up
;
3948 isl_qpolynomial
*qp
;
3954 n
= isl_space_dim(term
->dim
, isl_dim_all
) + term
->div
->n_row
;
3956 up
= isl_upoly_rat_cst(term
->dim
->ctx
, term
->n
, term
->d
);
3957 for (i
= 0; i
< n
; ++i
) {
3960 up
= isl_upoly_mul(up
,
3961 isl_upoly_var_pow(term
->dim
->ctx
, i
, term
->pow
[i
]));
3964 qp
= isl_qpolynomial_alloc(isl_space_copy(term
->dim
), term
->div
->n_row
, up
);
3967 isl_mat_free(qp
->div
);
3968 qp
->div
= isl_mat_copy(term
->div
);
3972 isl_term_free(term
);
3975 isl_qpolynomial_free(qp
);
3976 isl_term_free(term
);
3980 __isl_give isl_qpolynomial
*isl_qpolynomial_lift(__isl_take isl_qpolynomial
*qp
,
3981 __isl_take isl_space
*dim
)
3990 if (isl_space_is_equal(qp
->dim
, dim
)) {
3991 isl_space_free(dim
);
3995 qp
= isl_qpolynomial_cow(qp
);
3999 extra
= isl_space_dim(dim
, isl_dim_set
) -
4000 isl_space_dim(qp
->dim
, isl_dim_set
);
4001 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4002 if (qp
->div
->n_row
) {
4005 exp
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
4008 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4010 qp
->upoly
= expand(qp
->upoly
, exp
, total
);
4015 qp
->div
= isl_mat_insert_cols(qp
->div
, 2 + total
, extra
);
4018 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4019 isl_seq_clr(qp
->div
->row
[i
] + 2 + total
, extra
);
4021 isl_space_free(qp
->dim
);
4026 isl_space_free(dim
);
4027 isl_qpolynomial_free(qp
);
4031 /* For each parameter or variable that does not appear in qp,
4032 * first eliminate the variable from all constraints and then set it to zero.
4034 static __isl_give isl_set
*fix_inactive(__isl_take isl_set
*set
,
4035 __isl_keep isl_qpolynomial
*qp
)
4046 d
= isl_space_dim(set
->dim
, isl_dim_all
);
4047 active
= isl_calloc_array(set
->ctx
, int, d
);
4048 if (set_active(qp
, active
) < 0)
4051 for (i
= 0; i
< d
; ++i
)
4060 nparam
= isl_space_dim(set
->dim
, isl_dim_param
);
4061 nvar
= isl_space_dim(set
->dim
, isl_dim_set
);
4062 for (i
= 0; i
< nparam
; ++i
) {
4065 set
= isl_set_eliminate(set
, isl_dim_param
, i
, 1);
4066 set
= isl_set_fix_si(set
, isl_dim_param
, i
, 0);
4068 for (i
= 0; i
< nvar
; ++i
) {
4069 if (active
[nparam
+ i
])
4071 set
= isl_set_eliminate(set
, isl_dim_set
, i
, 1);
4072 set
= isl_set_fix_si(set
, isl_dim_set
, i
, 0);
4084 struct isl_opt_data
{
4085 isl_qpolynomial
*qp
;
4091 static isl_stat
opt_fn(__isl_take isl_point
*pnt
, void *user
)
4093 struct isl_opt_data
*data
= (struct isl_opt_data
*)user
;
4096 val
= isl_qpolynomial_eval(isl_qpolynomial_copy(data
->qp
), pnt
);
4100 } else if (data
->max
) {
4101 data
->opt
= isl_val_max(data
->opt
, val
);
4103 data
->opt
= isl_val_min(data
->opt
, val
);
4109 __isl_give isl_val
*isl_qpolynomial_opt_on_domain(
4110 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*set
, int max
)
4112 struct isl_opt_data data
= { NULL
, 1, NULL
, max
};
4117 if (isl_upoly_is_cst(qp
->upoly
)) {
4119 data
.opt
= isl_qpolynomial_get_constant_val(qp
);
4120 isl_qpolynomial_free(qp
);
4124 set
= fix_inactive(set
, qp
);
4127 if (isl_set_foreach_point(set
, opt_fn
, &data
) < 0)
4131 data
.opt
= isl_val_zero(isl_set_get_ctx(set
));
4134 isl_qpolynomial_free(qp
);
4138 isl_qpolynomial_free(qp
);
4139 isl_val_free(data
.opt
);
4143 __isl_give isl_qpolynomial
*isl_qpolynomial_morph_domain(
4144 __isl_take isl_qpolynomial
*qp
, __isl_take isl_morph
*morph
)
4149 struct isl_upoly
**subs
;
4150 isl_mat
*mat
, *diag
;
4152 qp
= isl_qpolynomial_cow(qp
);
4157 isl_assert(ctx
, isl_space_is_equal(qp
->dim
, morph
->dom
->dim
), goto error
);
4159 n_sub
= morph
->inv
->n_row
- 1;
4160 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
4161 n_sub
+= qp
->div
->n_row
;
4162 subs
= isl_calloc_array(ctx
, struct isl_upoly
*, n_sub
);
4166 for (i
= 0; 1 + i
< morph
->inv
->n_row
; ++i
)
4167 subs
[i
] = isl_upoly_from_affine(ctx
, morph
->inv
->row
[1 + i
],
4168 morph
->inv
->row
[0][0], morph
->inv
->n_col
);
4169 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
4170 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4171 subs
[morph
->inv
->n_row
- 1 + i
] =
4172 isl_upoly_var_pow(ctx
, morph
->inv
->n_col
- 1 + i
, 1);
4174 qp
->upoly
= isl_upoly_subs(qp
->upoly
, 0, n_sub
, subs
);
4176 for (i
= 0; i
< n_sub
; ++i
)
4177 isl_upoly_free(subs
[i
]);
4180 diag
= isl_mat_diag(ctx
, 1, morph
->inv
->row
[0][0]);
4181 mat
= isl_mat_diagonal(diag
, isl_mat_copy(morph
->inv
));
4182 diag
= isl_mat_diag(ctx
, qp
->div
->n_row
, morph
->inv
->row
[0][0]);
4183 mat
= isl_mat_diagonal(mat
, diag
);
4184 qp
->div
= isl_mat_product(qp
->div
, mat
);
4185 isl_space_free(qp
->dim
);
4186 qp
->dim
= isl_space_copy(morph
->ran
->dim
);
4188 if (!qp
->upoly
|| !qp
->div
|| !qp
->dim
)
4191 isl_morph_free(morph
);
4195 isl_qpolynomial_free(qp
);
4196 isl_morph_free(morph
);
4200 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_mul(
4201 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
4202 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
4204 return isl_union_pw_qpolynomial_match_bin_op(upwqp1
, upwqp2
,
4205 &isl_pw_qpolynomial_mul
);
4208 /* Reorder the columns of the given div definitions according to the
4211 static __isl_give isl_mat
*reorder_divs(__isl_take isl_mat
*div
,
4212 __isl_take isl_reordering
*r
)
4221 extra
= isl_space_dim(r
->dim
, isl_dim_all
) + div
->n_row
- r
->len
;
4222 mat
= isl_mat_alloc(div
->ctx
, div
->n_row
, div
->n_col
+ extra
);
4226 for (i
= 0; i
< div
->n_row
; ++i
) {
4227 isl_seq_cpy(mat
->row
[i
], div
->row
[i
], 2);
4228 isl_seq_clr(mat
->row
[i
] + 2, mat
->n_col
- 2);
4229 for (j
= 0; j
< r
->len
; ++j
)
4230 isl_int_set(mat
->row
[i
][2 + r
->pos
[j
]],
4231 div
->row
[i
][2 + j
]);
4234 isl_reordering_free(r
);
4238 isl_reordering_free(r
);
4243 /* Reorder the dimension of "qp" according to the given reordering.
4245 __isl_give isl_qpolynomial
*isl_qpolynomial_realign_domain(
4246 __isl_take isl_qpolynomial
*qp
, __isl_take isl_reordering
*r
)
4248 qp
= isl_qpolynomial_cow(qp
);
4252 r
= isl_reordering_extend(r
, qp
->div
->n_row
);
4256 qp
->div
= reorder_divs(qp
->div
, isl_reordering_copy(r
));
4260 qp
->upoly
= reorder(qp
->upoly
, r
->pos
);
4264 qp
= isl_qpolynomial_reset_domain_space(qp
, isl_space_copy(r
->dim
));
4266 isl_reordering_free(r
);
4269 isl_qpolynomial_free(qp
);
4270 isl_reordering_free(r
);
4274 __isl_give isl_qpolynomial
*isl_qpolynomial_align_params(
4275 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*model
)
4280 if (!isl_space_match(qp
->dim
, isl_dim_param
, model
, isl_dim_param
)) {
4281 isl_reordering
*exp
;
4283 model
= isl_space_drop_dims(model
, isl_dim_in
,
4284 0, isl_space_dim(model
, isl_dim_in
));
4285 model
= isl_space_drop_dims(model
, isl_dim_out
,
4286 0, isl_space_dim(model
, isl_dim_out
));
4287 exp
= isl_parameter_alignment_reordering(qp
->dim
, model
);
4288 exp
= isl_reordering_extend_space(exp
,
4289 isl_qpolynomial_get_domain_space(qp
));
4290 qp
= isl_qpolynomial_realign_domain(qp
, exp
);
4293 isl_space_free(model
);
4296 isl_space_free(model
);
4297 isl_qpolynomial_free(qp
);
4301 struct isl_split_periods_data
{
4303 isl_pw_qpolynomial
*res
;
4306 /* Create a slice where the integer division "div" has the fixed value "v".
4307 * In particular, if "div" refers to floor(f/m), then create a slice
4309 * m v <= f <= m v + (m - 1)
4314 * -f + m v + (m - 1) >= 0
4316 static __isl_give isl_set
*set_div_slice(__isl_take isl_space
*dim
,
4317 __isl_keep isl_qpolynomial
*qp
, int div
, isl_int v
)
4320 isl_basic_set
*bset
= NULL
;
4326 total
= isl_space_dim(dim
, isl_dim_all
);
4327 bset
= isl_basic_set_alloc_space(isl_space_copy(dim
), 0, 0, 2);
4329 k
= isl_basic_set_alloc_inequality(bset
);
4332 isl_seq_cpy(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4333 isl_int_submul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4335 k
= isl_basic_set_alloc_inequality(bset
);
4338 isl_seq_neg(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4339 isl_int_addmul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4340 isl_int_add(bset
->ineq
[k
][0], bset
->ineq
[k
][0], qp
->div
->row
[div
][0]);
4341 isl_int_sub_ui(bset
->ineq
[k
][0], bset
->ineq
[k
][0], 1);
4343 isl_space_free(dim
);
4344 return isl_set_from_basic_set(bset
);
4346 isl_basic_set_free(bset
);
4347 isl_space_free(dim
);
4351 static isl_stat
split_periods(__isl_take isl_set
*set
,
4352 __isl_take isl_qpolynomial
*qp
, void *user
);
4354 /* Create a slice of the domain "set" such that integer division "div"
4355 * has the fixed value "v" and add the results to data->res,
4356 * replacing the integer division by "v" in "qp".
4358 static isl_stat
set_div(__isl_take isl_set
*set
,
4359 __isl_take isl_qpolynomial
*qp
, int div
, isl_int v
,
4360 struct isl_split_periods_data
*data
)
4365 struct isl_upoly
*cst
;
4367 slice
= set_div_slice(isl_set_get_space(set
), qp
, div
, v
);
4368 set
= isl_set_intersect(set
, slice
);
4373 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4375 for (i
= div
+ 1; i
< qp
->div
->n_row
; ++i
) {
4376 if (isl_int_is_zero(qp
->div
->row
[i
][2 + total
+ div
]))
4378 isl_int_addmul(qp
->div
->row
[i
][1],
4379 qp
->div
->row
[i
][2 + total
+ div
], v
);
4380 isl_int_set_si(qp
->div
->row
[i
][2 + total
+ div
], 0);
4383 cst
= isl_upoly_rat_cst(qp
->dim
->ctx
, v
, qp
->dim
->ctx
->one
);
4384 qp
= substitute_div(qp
, div
, cst
);
4386 return split_periods(set
, qp
, data
);
4389 isl_qpolynomial_free(qp
);
4393 /* Split the domain "set" such that integer division "div"
4394 * has a fixed value (ranging from "min" to "max") on each slice
4395 * and add the results to data->res.
4397 static isl_stat
split_div(__isl_take isl_set
*set
,
4398 __isl_take isl_qpolynomial
*qp
, int div
, isl_int min
, isl_int max
,
4399 struct isl_split_periods_data
*data
)
4401 for (; isl_int_le(min
, max
); isl_int_add_ui(min
, min
, 1)) {
4402 isl_set
*set_i
= isl_set_copy(set
);
4403 isl_qpolynomial
*qp_i
= isl_qpolynomial_copy(qp
);
4405 if (set_div(set_i
, qp_i
, div
, min
, data
) < 0)
4409 isl_qpolynomial_free(qp
);
4413 isl_qpolynomial_free(qp
);
4414 return isl_stat_error
;
4417 /* If "qp" refers to any integer division
4418 * that can only attain "max_periods" distinct values on "set"
4419 * then split the domain along those distinct values.
4420 * Add the results (or the original if no splitting occurs)
4423 static isl_stat
split_periods(__isl_take isl_set
*set
,
4424 __isl_take isl_qpolynomial
*qp
, void *user
)
4427 isl_pw_qpolynomial
*pwqp
;
4428 struct isl_split_periods_data
*data
;
4431 isl_stat r
= isl_stat_ok
;
4433 data
= (struct isl_split_periods_data
*)user
;
4438 if (qp
->div
->n_row
== 0) {
4439 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4440 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4446 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4447 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4448 enum isl_lp_result lp_res
;
4450 if (isl_seq_first_non_zero(qp
->div
->row
[i
] + 2 + total
,
4451 qp
->div
->n_row
) != -1)
4454 lp_res
= isl_set_solve_lp(set
, 0, qp
->div
->row
[i
] + 1,
4455 set
->ctx
->one
, &min
, NULL
, NULL
);
4456 if (lp_res
== isl_lp_error
)
4458 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4460 isl_int_fdiv_q(min
, min
, qp
->div
->row
[i
][0]);
4462 lp_res
= isl_set_solve_lp(set
, 1, qp
->div
->row
[i
] + 1,
4463 set
->ctx
->one
, &max
, NULL
, NULL
);
4464 if (lp_res
== isl_lp_error
)
4466 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4468 isl_int_fdiv_q(max
, max
, qp
->div
->row
[i
][0]);
4470 isl_int_sub(max
, max
, min
);
4471 if (isl_int_cmp_si(max
, data
->max_periods
) < 0) {
4472 isl_int_add(max
, max
, min
);
4477 if (i
< qp
->div
->n_row
) {
4478 r
= split_div(set
, qp
, i
, min
, max
, data
);
4480 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4481 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4493 isl_qpolynomial_free(qp
);
4494 return isl_stat_error
;
4497 /* If any quasi-polynomial in pwqp refers to any integer division
4498 * that can only attain "max_periods" distinct values on its domain
4499 * then split the domain along those distinct values.
4501 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_split_periods(
4502 __isl_take isl_pw_qpolynomial
*pwqp
, int max_periods
)
4504 struct isl_split_periods_data data
;
4506 data
.max_periods
= max_periods
;
4507 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp
));
4509 if (isl_pw_qpolynomial_foreach_piece(pwqp
, &split_periods
, &data
) < 0)
4512 isl_pw_qpolynomial_free(pwqp
);
4516 isl_pw_qpolynomial_free(data
.res
);
4517 isl_pw_qpolynomial_free(pwqp
);
4521 /* Construct a piecewise quasipolynomial that is constant on the given
4522 * domain. In particular, it is
4525 * infinity if cst == -1
4527 static __isl_give isl_pw_qpolynomial
*constant_on_domain(
4528 __isl_take isl_basic_set
*bset
, int cst
)
4531 isl_qpolynomial
*qp
;
4536 bset
= isl_basic_set_params(bset
);
4537 dim
= isl_basic_set_get_space(bset
);
4539 qp
= isl_qpolynomial_infty_on_domain(dim
);
4541 qp
= isl_qpolynomial_zero_on_domain(dim
);
4543 qp
= isl_qpolynomial_one_on_domain(dim
);
4544 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset
), qp
);
4547 /* Factor bset, call fn on each of the factors and return the product.
4549 * If no factors can be found, simply call fn on the input.
4550 * Otherwise, construct the factors based on the factorizer,
4551 * call fn on each factor and compute the product.
4553 static __isl_give isl_pw_qpolynomial
*compressed_multiplicative_call(
4554 __isl_take isl_basic_set
*bset
,
4555 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4561 isl_qpolynomial
*qp
;
4562 isl_pw_qpolynomial
*pwqp
;
4566 f
= isl_basic_set_factorizer(bset
);
4569 if (f
->n_group
== 0) {
4570 isl_factorizer_free(f
);
4574 nparam
= isl_basic_set_dim(bset
, isl_dim_param
);
4575 nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
4577 dim
= isl_basic_set_get_space(bset
);
4578 dim
= isl_space_domain(dim
);
4579 set
= isl_set_universe(isl_space_copy(dim
));
4580 qp
= isl_qpolynomial_one_on_domain(dim
);
4581 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4583 bset
= isl_morph_basic_set(isl_morph_copy(f
->morph
), bset
);
4585 for (i
= 0, n
= 0; i
< f
->n_group
; ++i
) {
4586 isl_basic_set
*bset_i
;
4587 isl_pw_qpolynomial
*pwqp_i
;
4589 bset_i
= isl_basic_set_copy(bset
);
4590 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4591 nparam
+ n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4592 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4594 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
,
4595 n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4596 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
, 0, n
);
4598 pwqp_i
= fn(bset_i
);
4599 pwqp
= isl_pw_qpolynomial_mul(pwqp
, pwqp_i
);
4604 isl_basic_set_free(bset
);
4605 isl_factorizer_free(f
);
4609 isl_basic_set_free(bset
);
4613 /* Factor bset, call fn on each of the factors and return the product.
4614 * The function is assumed to evaluate to zero on empty domains,
4615 * to one on zero-dimensional domains and to infinity on unbounded domains
4616 * and will not be called explicitly on zero-dimensional or unbounded domains.
4618 * We first check for some special cases and remove all equalities.
4619 * Then we hand over control to compressed_multiplicative_call.
4621 __isl_give isl_pw_qpolynomial
*isl_basic_set_multiplicative_call(
4622 __isl_take isl_basic_set
*bset
,
4623 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4627 isl_pw_qpolynomial
*pwqp
;
4632 if (isl_basic_set_plain_is_empty(bset
))
4633 return constant_on_domain(bset
, 0);
4635 if (isl_basic_set_dim(bset
, isl_dim_set
) == 0)
4636 return constant_on_domain(bset
, 1);
4638 bounded
= isl_basic_set_is_bounded(bset
);
4642 return constant_on_domain(bset
, -1);
4644 if (bset
->n_eq
== 0)
4645 return compressed_multiplicative_call(bset
, fn
);
4647 morph
= isl_basic_set_full_compression(bset
);
4648 bset
= isl_morph_basic_set(isl_morph_copy(morph
), bset
);
4650 pwqp
= compressed_multiplicative_call(bset
, fn
);
4652 morph
= isl_morph_dom_params(morph
);
4653 morph
= isl_morph_ran_params(morph
);
4654 morph
= isl_morph_inverse(morph
);
4656 pwqp
= isl_pw_qpolynomial_morph_domain(pwqp
, morph
);
4660 isl_basic_set_free(bset
);
4664 /* Drop all floors in "qp", turning each integer division [a/m] into
4665 * a rational division a/m. If "down" is set, then the integer division
4666 * is replaced by (a-(m-1))/m instead.
4668 static __isl_give isl_qpolynomial
*qp_drop_floors(
4669 __isl_take isl_qpolynomial
*qp
, int down
)
4672 struct isl_upoly
*s
;
4676 if (qp
->div
->n_row
== 0)
4679 qp
= isl_qpolynomial_cow(qp
);
4683 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
4685 isl_int_sub(qp
->div
->row
[i
][1],
4686 qp
->div
->row
[i
][1], qp
->div
->row
[i
][0]);
4687 isl_int_add_ui(qp
->div
->row
[i
][1],
4688 qp
->div
->row
[i
][1], 1);
4690 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
4691 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
4692 qp
= substitute_div(qp
, i
, s
);
4700 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4701 * a rational division a/m.
4703 static __isl_give isl_pw_qpolynomial
*pwqp_drop_floors(
4704 __isl_take isl_pw_qpolynomial
*pwqp
)
4711 if (isl_pw_qpolynomial_is_zero(pwqp
))
4714 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
4718 for (i
= 0; i
< pwqp
->n
; ++i
) {
4719 pwqp
->p
[i
].qp
= qp_drop_floors(pwqp
->p
[i
].qp
, 0);
4726 isl_pw_qpolynomial_free(pwqp
);
4730 /* Adjust all the integer divisions in "qp" such that they are at least
4731 * one over the given orthant (identified by "signs"). This ensures
4732 * that they will still be non-negative even after subtracting (m-1)/m.
4734 * In particular, f is replaced by f' + v, changing f = [a/m]
4735 * to f' = [(a - m v)/m].
4736 * If the constant term k in a is smaller than m,
4737 * the constant term of v is set to floor(k/m) - 1.
4738 * For any other term, if the coefficient c and the variable x have
4739 * the same sign, then no changes are needed.
4740 * Otherwise, if the variable is positive (and c is negative),
4741 * then the coefficient of x in v is set to floor(c/m).
4742 * If the variable is negative (and c is positive),
4743 * then the coefficient of x in v is set to ceil(c/m).
4745 static __isl_give isl_qpolynomial
*make_divs_pos(__isl_take isl_qpolynomial
*qp
,
4751 struct isl_upoly
*s
;
4753 qp
= isl_qpolynomial_cow(qp
);
4756 qp
->div
= isl_mat_cow(qp
->div
);
4760 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4761 v
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
4763 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4764 isl_int
*row
= qp
->div
->row
[i
];
4768 if (isl_int_lt(row
[1], row
[0])) {
4769 isl_int_fdiv_q(v
->el
[0], row
[1], row
[0]);
4770 isl_int_sub_ui(v
->el
[0], v
->el
[0], 1);
4771 isl_int_submul(row
[1], row
[0], v
->el
[0]);
4773 for (j
= 0; j
< total
; ++j
) {
4774 if (isl_int_sgn(row
[2 + j
]) * signs
[j
] >= 0)
4777 isl_int_cdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4779 isl_int_fdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4780 isl_int_submul(row
[2 + j
], row
[0], v
->el
[1 + j
]);
4782 for (j
= 0; j
< i
; ++j
) {
4783 if (isl_int_sgn(row
[2 + total
+ j
]) >= 0)
4785 isl_int_fdiv_q(v
->el
[1 + total
+ j
],
4786 row
[2 + total
+ j
], row
[0]);
4787 isl_int_submul(row
[2 + total
+ j
],
4788 row
[0], v
->el
[1 + total
+ j
]);
4790 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
4791 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
4793 isl_seq_combine(qp
->div
->row
[j
] + 1,
4794 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
4795 qp
->div
->row
[j
][2 + total
+ i
], v
->el
, v
->size
);
4797 isl_int_set_si(v
->el
[1 + total
+ i
], 1);
4798 s
= isl_upoly_from_affine(qp
->dim
->ctx
, v
->el
,
4799 qp
->div
->ctx
->one
, v
->size
);
4800 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ i
, 1, &s
);
4810 isl_qpolynomial_free(qp
);
4814 struct isl_to_poly_data
{
4816 isl_pw_qpolynomial
*res
;
4817 isl_qpolynomial
*qp
;
4820 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4821 * We first make all integer divisions positive and then split the
4822 * quasipolynomials into terms with sign data->sign (the direction
4823 * of the requested approximation) and terms with the opposite sign.
4824 * In the first set of terms, each integer division [a/m] is
4825 * overapproximated by a/m, while in the second it is underapproximated
4828 static int to_polynomial_on_orthant(__isl_take isl_set
*orthant
, int *signs
,
4831 struct isl_to_poly_data
*data
= user
;
4832 isl_pw_qpolynomial
*t
;
4833 isl_qpolynomial
*qp
, *up
, *down
;
4835 qp
= isl_qpolynomial_copy(data
->qp
);
4836 qp
= make_divs_pos(qp
, signs
);
4838 up
= isl_qpolynomial_terms_of_sign(qp
, signs
, data
->sign
);
4839 up
= qp_drop_floors(up
, 0);
4840 down
= isl_qpolynomial_terms_of_sign(qp
, signs
, -data
->sign
);
4841 down
= qp_drop_floors(down
, 1);
4843 isl_qpolynomial_free(qp
);
4844 qp
= isl_qpolynomial_add(up
, down
);
4846 t
= isl_pw_qpolynomial_alloc(orthant
, qp
);
4847 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, t
);
4852 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4853 * the polynomial will be an overapproximation. If "sign" is negative,
4854 * it will be an underapproximation. If "sign" is zero, the approximation
4855 * will lie somewhere in between.
4857 * In particular, is sign == 0, we simply drop the floors, turning
4858 * the integer divisions into rational divisions.
4859 * Otherwise, we split the domains into orthants, make all integer divisions
4860 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4861 * depending on the requested sign and the sign of the term in which
4862 * the integer division appears.
4864 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_to_polynomial(
4865 __isl_take isl_pw_qpolynomial
*pwqp
, int sign
)
4868 struct isl_to_poly_data data
;
4871 return pwqp_drop_floors(pwqp
);
4877 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp
));
4879 for (i
= 0; i
< pwqp
->n
; ++i
) {
4880 if (pwqp
->p
[i
].qp
->div
->n_row
== 0) {
4881 isl_pw_qpolynomial
*t
;
4882 t
= isl_pw_qpolynomial_alloc(
4883 isl_set_copy(pwqp
->p
[i
].set
),
4884 isl_qpolynomial_copy(pwqp
->p
[i
].qp
));
4885 data
.res
= isl_pw_qpolynomial_add_disjoint(data
.res
, t
);
4888 data
.qp
= pwqp
->p
[i
].qp
;
4889 if (isl_set_foreach_orthant(pwqp
->p
[i
].set
,
4890 &to_polynomial_on_orthant
, &data
) < 0)
4894 isl_pw_qpolynomial_free(pwqp
);
4898 isl_pw_qpolynomial_free(pwqp
);
4899 isl_pw_qpolynomial_free(data
.res
);
4903 static __isl_give isl_pw_qpolynomial
*poly_entry(
4904 __isl_take isl_pw_qpolynomial
*pwqp
, void *user
)
4908 return isl_pw_qpolynomial_to_polynomial(pwqp
, *sign
);
4911 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_to_polynomial(
4912 __isl_take isl_union_pw_qpolynomial
*upwqp
, int sign
)
4914 return isl_union_pw_qpolynomial_transform_inplace(upwqp
,
4915 &poly_entry
, &sign
);
4918 __isl_give isl_basic_map
*isl_basic_map_from_qpolynomial(
4919 __isl_take isl_qpolynomial
*qp
)
4923 isl_vec
*aff
= NULL
;
4924 isl_basic_map
*bmap
= NULL
;
4930 if (!isl_upoly_is_affine(qp
->upoly
))
4931 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
4932 "input quasi-polynomial not affine", goto error
);
4933 aff
= isl_qpolynomial_extract_affine(qp
);
4936 dim
= isl_qpolynomial_get_space(qp
);
4937 pos
= 1 + isl_space_offset(dim
, isl_dim_out
);
4938 n_div
= qp
->div
->n_row
;
4939 bmap
= isl_basic_map_alloc_space(dim
, n_div
, 1, 2 * n_div
);
4941 for (i
= 0; i
< n_div
; ++i
) {
4942 k
= isl_basic_map_alloc_div(bmap
);
4945 isl_seq_cpy(bmap
->div
[k
], qp
->div
->row
[i
], qp
->div
->n_col
);
4946 isl_int_set_si(bmap
->div
[k
][qp
->div
->n_col
], 0);
4947 if (isl_basic_map_add_div_constraints(bmap
, k
) < 0)
4950 k
= isl_basic_map_alloc_equality(bmap
);
4953 isl_int_neg(bmap
->eq
[k
][pos
], aff
->el
[0]);
4954 isl_seq_cpy(bmap
->eq
[k
], aff
->el
+ 1, pos
);
4955 isl_seq_cpy(bmap
->eq
[k
] + pos
+ 1, aff
->el
+ 1 + pos
, n_div
);
4958 isl_qpolynomial_free(qp
);
4959 bmap
= isl_basic_map_finalize(bmap
);
4963 isl_qpolynomial_free(qp
);
4964 isl_basic_map_free(bmap
);