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 if (type
== isl_dim_out
)
2680 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
2681 "cannot set name of output/set dimension",
2682 return isl_qpolynomial_free(qp
));
2683 if (type
== isl_dim_in
)
2685 qp
->dim
= isl_space_set_dim_name(qp
->dim
, type
, pos
, s
);
2690 isl_qpolynomial_free(qp
);
2694 __isl_give isl_qpolynomial
*isl_qpolynomial_drop_dims(
2695 __isl_take isl_qpolynomial
*qp
,
2696 enum isl_dim_type type
, unsigned first
, unsigned n
)
2700 if (type
== isl_dim_out
)
2701 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
2702 "cannot drop output/set dimension",
2704 if (type
== isl_dim_in
)
2706 if (n
== 0 && !isl_space_is_named_or_nested(qp
->dim
, type
))
2709 qp
= isl_qpolynomial_cow(qp
);
2713 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_space_dim(qp
->dim
, type
),
2715 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2716 type
== isl_dim_set
, goto error
);
2718 qp
->dim
= isl_space_drop_dims(qp
->dim
, type
, first
, n
);
2722 if (type
== isl_dim_set
)
2723 first
+= isl_space_dim(qp
->dim
, isl_dim_param
);
2725 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + first
, n
);
2729 qp
->upoly
= isl_upoly_drop(qp
->upoly
, first
, n
);
2735 isl_qpolynomial_free(qp
);
2739 /* Project the domain of the quasi-polynomial onto its parameter space.
2740 * The quasi-polynomial may not involve any of the domain dimensions.
2742 __isl_give isl_qpolynomial
*isl_qpolynomial_project_domain_on_params(
2743 __isl_take isl_qpolynomial
*qp
)
2749 n
= isl_qpolynomial_dim(qp
, isl_dim_in
);
2750 involves
= isl_qpolynomial_involves_dims(qp
, isl_dim_in
, 0, n
);
2752 return isl_qpolynomial_free(qp
);
2754 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
2755 "polynomial involves some of the domain dimensions",
2756 return isl_qpolynomial_free(qp
));
2757 qp
= isl_qpolynomial_drop_dims(qp
, isl_dim_in
, 0, n
);
2758 space
= isl_qpolynomial_get_domain_space(qp
);
2759 space
= isl_space_params(space
);
2760 qp
= isl_qpolynomial_reset_domain_space(qp
, space
);
2764 static __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities_lifted(
2765 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2771 struct isl_upoly
*up
;
2775 if (eq
->n_eq
== 0) {
2776 isl_basic_set_free(eq
);
2780 qp
= isl_qpolynomial_cow(qp
);
2783 qp
->div
= isl_mat_cow(qp
->div
);
2787 total
= 1 + isl_space_dim(eq
->dim
, isl_dim_all
);
2789 isl_int_init(denom
);
2790 for (i
= 0; i
< eq
->n_eq
; ++i
) {
2791 j
= isl_seq_last_non_zero(eq
->eq
[i
], total
+ n_div
);
2792 if (j
< 0 || j
== 0 || j
>= total
)
2795 for (k
= 0; k
< qp
->div
->n_row
; ++k
) {
2796 if (isl_int_is_zero(qp
->div
->row
[k
][1 + j
]))
2798 isl_seq_elim(qp
->div
->row
[k
] + 1, eq
->eq
[i
], j
, total
,
2799 &qp
->div
->row
[k
][0]);
2800 normalize_div(qp
, k
);
2803 if (isl_int_is_pos(eq
->eq
[i
][j
]))
2804 isl_seq_neg(eq
->eq
[i
], eq
->eq
[i
], total
);
2805 isl_int_abs(denom
, eq
->eq
[i
][j
]);
2806 isl_int_set_si(eq
->eq
[i
][j
], 0);
2808 up
= isl_upoly_from_affine(qp
->dim
->ctx
,
2809 eq
->eq
[i
], denom
, total
);
2810 qp
->upoly
= isl_upoly_subs(qp
->upoly
, j
- 1, 1, &up
);
2813 isl_int_clear(denom
);
2818 isl_basic_set_free(eq
);
2820 qp
= substitute_non_divs(qp
);
2825 isl_basic_set_free(eq
);
2826 isl_qpolynomial_free(qp
);
2830 /* Exploit the equalities in "eq" to simplify the quasi-polynomial.
2832 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities(
2833 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2837 if (qp
->div
->n_row
> 0)
2838 eq
= isl_basic_set_add_dims(eq
, isl_dim_set
, qp
->div
->n_row
);
2839 return isl_qpolynomial_substitute_equalities_lifted(qp
, eq
);
2841 isl_basic_set_free(eq
);
2842 isl_qpolynomial_free(qp
);
2846 static __isl_give isl_basic_set
*add_div_constraints(
2847 __isl_take isl_basic_set
*bset
, __isl_take isl_mat
*div
)
2855 bset
= isl_basic_set_extend_constraints(bset
, 0, 2 * div
->n_row
);
2858 total
= isl_basic_set_total_dim(bset
);
2859 for (i
= 0; i
< div
->n_row
; ++i
)
2860 if (isl_basic_set_add_div_constraints_var(bset
,
2861 total
- div
->n_row
+ i
, div
->row
[i
]) < 0)
2868 isl_basic_set_free(bset
);
2872 /* Look for equalities among the variables shared by context and qp
2873 * and the integer divisions of qp, if any.
2874 * The equalities are then used to eliminate variables and/or integer
2875 * divisions from qp.
2877 __isl_give isl_qpolynomial
*isl_qpolynomial_gist(
2878 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
2884 if (qp
->div
->n_row
> 0) {
2885 isl_basic_set
*bset
;
2886 context
= isl_set_add_dims(context
, isl_dim_set
,
2888 bset
= isl_basic_set_universe(isl_set_get_space(context
));
2889 bset
= add_div_constraints(bset
, isl_mat_copy(qp
->div
));
2890 context
= isl_set_intersect(context
,
2891 isl_set_from_basic_set(bset
));
2894 aff
= isl_set_affine_hull(context
);
2895 return isl_qpolynomial_substitute_equalities_lifted(qp
, aff
);
2897 isl_qpolynomial_free(qp
);
2898 isl_set_free(context
);
2902 __isl_give isl_qpolynomial
*isl_qpolynomial_gist_params(
2903 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
2905 isl_space
*space
= isl_qpolynomial_get_domain_space(qp
);
2906 isl_set
*dom_context
= isl_set_universe(space
);
2907 dom_context
= isl_set_intersect_params(dom_context
, context
);
2908 return isl_qpolynomial_gist(qp
, dom_context
);
2911 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_from_qpolynomial(
2912 __isl_take isl_qpolynomial
*qp
)
2918 if (isl_qpolynomial_is_zero(qp
)) {
2919 isl_space
*dim
= isl_qpolynomial_get_space(qp
);
2920 isl_qpolynomial_free(qp
);
2921 return isl_pw_qpolynomial_zero(dim
);
2924 dom
= isl_set_universe(isl_qpolynomial_get_domain_space(qp
));
2925 return isl_pw_qpolynomial_alloc(dom
, qp
);
2929 #define PW isl_pw_qpolynomial
2931 #define EL isl_qpolynomial
2933 #define EL_IS_ZERO is_zero
2937 #define IS_ZERO is_zero
2940 #undef DEFAULT_IS_ZERO
2941 #define DEFAULT_IS_ZERO 1
2945 #include <isl_pw_templ.c>
2948 #define UNION isl_union_pw_qpolynomial
2950 #define PART isl_pw_qpolynomial
2952 #define PARTS pw_qpolynomial
2954 #include <isl_union_single.c>
2955 #include <isl_union_eval.c>
2956 #include <isl_union_neg.c>
2958 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial
*pwqp
)
2966 if (!isl_set_plain_is_universe(pwqp
->p
[0].set
))
2969 return isl_qpolynomial_is_one(pwqp
->p
[0].qp
);
2972 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add(
2973 __isl_take isl_pw_qpolynomial
*pwqp1
,
2974 __isl_take isl_pw_qpolynomial
*pwqp2
)
2976 return isl_pw_qpolynomial_union_add_(pwqp1
, pwqp2
);
2979 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_mul(
2980 __isl_take isl_pw_qpolynomial
*pwqp1
,
2981 __isl_take isl_pw_qpolynomial
*pwqp2
)
2984 struct isl_pw_qpolynomial
*res
;
2986 if (!pwqp1
|| !pwqp2
)
2989 isl_assert(pwqp1
->dim
->ctx
, isl_space_is_equal(pwqp1
->dim
, pwqp2
->dim
),
2992 if (isl_pw_qpolynomial_is_zero(pwqp1
)) {
2993 isl_pw_qpolynomial_free(pwqp2
);
2997 if (isl_pw_qpolynomial_is_zero(pwqp2
)) {
2998 isl_pw_qpolynomial_free(pwqp1
);
3002 if (isl_pw_qpolynomial_is_one(pwqp1
)) {
3003 isl_pw_qpolynomial_free(pwqp1
);
3007 if (isl_pw_qpolynomial_is_one(pwqp2
)) {
3008 isl_pw_qpolynomial_free(pwqp2
);
3012 n
= pwqp1
->n
* pwqp2
->n
;
3013 res
= isl_pw_qpolynomial_alloc_size(isl_space_copy(pwqp1
->dim
), n
);
3015 for (i
= 0; i
< pwqp1
->n
; ++i
) {
3016 for (j
= 0; j
< pwqp2
->n
; ++j
) {
3017 struct isl_set
*common
;
3018 struct isl_qpolynomial
*prod
;
3019 common
= isl_set_intersect(isl_set_copy(pwqp1
->p
[i
].set
),
3020 isl_set_copy(pwqp2
->p
[j
].set
));
3021 if (isl_set_plain_is_empty(common
)) {
3022 isl_set_free(common
);
3026 prod
= isl_qpolynomial_mul(
3027 isl_qpolynomial_copy(pwqp1
->p
[i
].qp
),
3028 isl_qpolynomial_copy(pwqp2
->p
[j
].qp
));
3030 res
= isl_pw_qpolynomial_add_piece(res
, common
, prod
);
3034 isl_pw_qpolynomial_free(pwqp1
);
3035 isl_pw_qpolynomial_free(pwqp2
);
3039 isl_pw_qpolynomial_free(pwqp1
);
3040 isl_pw_qpolynomial_free(pwqp2
);
3044 __isl_give isl_val
*isl_upoly_eval(__isl_take
struct isl_upoly
*up
,
3045 __isl_take isl_vec
*vec
)
3048 struct isl_upoly_rec
*rec
;
3052 if (isl_upoly_is_cst(up
)) {
3054 res
= isl_upoly_get_constant_val(up
);
3059 rec
= isl_upoly_as_rec(up
);
3063 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
3065 base
= isl_val_rat_from_isl_int(up
->ctx
,
3066 vec
->el
[1 + up
->var
], vec
->el
[0]);
3068 res
= isl_upoly_eval(isl_upoly_copy(rec
->p
[rec
->n
- 1]),
3071 for (i
= rec
->n
- 2; i
>= 0; --i
) {
3072 res
= isl_val_mul(res
, isl_val_copy(base
));
3073 res
= isl_val_add(res
,
3074 isl_upoly_eval(isl_upoly_copy(rec
->p
[i
]),
3075 isl_vec_copy(vec
)));
3088 /* Evaluate "qp" in the void point "pnt".
3089 * In particular, return the value NaN.
3091 static __isl_give isl_val
*eval_void(__isl_take isl_qpolynomial
*qp
,
3092 __isl_take isl_point
*pnt
)
3096 ctx
= isl_point_get_ctx(pnt
);
3097 isl_qpolynomial_free(qp
);
3098 isl_point_free(pnt
);
3099 return isl_val_nan(ctx
);
3102 __isl_give isl_val
*isl_qpolynomial_eval(__isl_take isl_qpolynomial
*qp
,
3103 __isl_take isl_point
*pnt
)
3111 isl_assert(pnt
->dim
->ctx
, isl_space_is_equal(pnt
->dim
, qp
->dim
), goto error
);
3112 is_void
= isl_point_is_void(pnt
);
3116 return eval_void(qp
, pnt
);
3118 if (qp
->div
->n_row
== 0)
3119 ext
= isl_vec_copy(pnt
->vec
);
3122 unsigned dim
= isl_space_dim(qp
->dim
, isl_dim_all
);
3123 ext
= isl_vec_alloc(qp
->dim
->ctx
, 1 + dim
+ qp
->div
->n_row
);
3127 isl_seq_cpy(ext
->el
, pnt
->vec
->el
, pnt
->vec
->size
);
3128 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
3129 isl_seq_inner_product(qp
->div
->row
[i
] + 1, ext
->el
,
3130 1 + dim
+ i
, &ext
->el
[1+dim
+i
]);
3131 isl_int_fdiv_q(ext
->el
[1+dim
+i
], ext
->el
[1+dim
+i
],
3132 qp
->div
->row
[i
][0]);
3136 v
= isl_upoly_eval(isl_upoly_copy(qp
->upoly
), ext
);
3138 isl_qpolynomial_free(qp
);
3139 isl_point_free(pnt
);
3143 isl_qpolynomial_free(qp
);
3144 isl_point_free(pnt
);
3148 int isl_upoly_cmp(__isl_keep
struct isl_upoly_cst
*cst1
,
3149 __isl_keep
struct isl_upoly_cst
*cst2
)
3154 isl_int_mul(t
, cst1
->n
, cst2
->d
);
3155 isl_int_submul(t
, cst2
->n
, cst1
->d
);
3156 cmp
= isl_int_sgn(t
);
3161 __isl_give isl_qpolynomial
*isl_qpolynomial_insert_dims(
3162 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
,
3163 unsigned first
, unsigned n
)
3171 if (type
== isl_dim_out
)
3172 isl_die(qp
->div
->ctx
, isl_error_invalid
,
3173 "cannot insert output/set dimensions",
3175 if (type
== isl_dim_in
)
3177 if (n
== 0 && !isl_space_is_named_or_nested(qp
->dim
, type
))
3180 qp
= isl_qpolynomial_cow(qp
);
3184 isl_assert(qp
->div
->ctx
, first
<= isl_space_dim(qp
->dim
, type
),
3187 g_pos
= pos(qp
->dim
, type
) + first
;
3189 qp
->div
= isl_mat_insert_zero_cols(qp
->div
, 2 + g_pos
, n
);
3193 total
= qp
->div
->n_col
- 2;
3194 if (total
> g_pos
) {
3196 exp
= isl_alloc_array(qp
->div
->ctx
, int, total
- g_pos
);
3199 for (i
= 0; i
< total
- g_pos
; ++i
)
3201 qp
->upoly
= expand(qp
->upoly
, exp
, g_pos
);
3207 qp
->dim
= isl_space_insert_dims(qp
->dim
, type
, first
, n
);
3213 isl_qpolynomial_free(qp
);
3217 __isl_give isl_qpolynomial
*isl_qpolynomial_add_dims(
3218 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
, unsigned n
)
3222 pos
= isl_qpolynomial_dim(qp
, type
);
3224 return isl_qpolynomial_insert_dims(qp
, type
, pos
, n
);
3227 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add_dims(
3228 __isl_take isl_pw_qpolynomial
*pwqp
,
3229 enum isl_dim_type type
, unsigned n
)
3233 pos
= isl_pw_qpolynomial_dim(pwqp
, type
);
3235 return isl_pw_qpolynomial_insert_dims(pwqp
, type
, pos
, n
);
3238 static int *reordering_move(isl_ctx
*ctx
,
3239 unsigned len
, unsigned dst
, unsigned src
, unsigned n
)
3244 reordering
= isl_alloc_array(ctx
, int, len
);
3249 for (i
= 0; i
< dst
; ++i
)
3251 for (i
= 0; i
< n
; ++i
)
3252 reordering
[src
+ i
] = dst
+ i
;
3253 for (i
= 0; i
< src
- dst
; ++i
)
3254 reordering
[dst
+ i
] = dst
+ n
+ i
;
3255 for (i
= 0; i
< len
- src
- n
; ++i
)
3256 reordering
[src
+ n
+ i
] = src
+ n
+ i
;
3258 for (i
= 0; i
< src
; ++i
)
3260 for (i
= 0; i
< n
; ++i
)
3261 reordering
[src
+ i
] = dst
+ i
;
3262 for (i
= 0; i
< dst
- src
; ++i
)
3263 reordering
[src
+ n
+ i
] = src
+ i
;
3264 for (i
= 0; i
< len
- dst
- n
; ++i
)
3265 reordering
[dst
+ n
+ i
] = dst
+ n
+ i
;
3271 __isl_give isl_qpolynomial
*isl_qpolynomial_move_dims(
3272 __isl_take isl_qpolynomial
*qp
,
3273 enum isl_dim_type dst_type
, unsigned dst_pos
,
3274 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
3283 qp
= isl_qpolynomial_cow(qp
);
3287 if (dst_type
== isl_dim_out
|| src_type
== isl_dim_out
)
3288 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
3289 "cannot move output/set dimension",
3291 if (dst_type
== isl_dim_in
)
3292 dst_type
= isl_dim_set
;
3293 if (src_type
== isl_dim_in
)
3294 src_type
= isl_dim_set
;
3296 isl_assert(qp
->dim
->ctx
, src_pos
+ n
<= isl_space_dim(qp
->dim
, src_type
),
3299 g_dst_pos
= pos(qp
->dim
, dst_type
) + dst_pos
;
3300 g_src_pos
= pos(qp
->dim
, src_type
) + src_pos
;
3301 if (dst_type
> src_type
)
3304 qp
->div
= isl_mat_move_cols(qp
->div
, 2 + g_dst_pos
, 2 + g_src_pos
, n
);
3311 reordering
= reordering_move(qp
->dim
->ctx
,
3312 qp
->div
->n_col
- 2, g_dst_pos
, g_src_pos
, n
);
3316 qp
->upoly
= reorder(qp
->upoly
, reordering
);
3321 qp
->dim
= isl_space_move_dims(qp
->dim
, dst_type
, dst_pos
, src_type
, src_pos
, n
);
3327 isl_qpolynomial_free(qp
);
3331 __isl_give isl_qpolynomial
*isl_qpolynomial_from_affine(__isl_take isl_space
*dim
,
3332 isl_int
*f
, isl_int denom
)
3334 struct isl_upoly
*up
;
3336 dim
= isl_space_domain(dim
);
3340 up
= isl_upoly_from_affine(dim
->ctx
, f
, denom
,
3341 1 + isl_space_dim(dim
, isl_dim_all
));
3343 return isl_qpolynomial_alloc(dim
, 0, up
);
3346 __isl_give isl_qpolynomial
*isl_qpolynomial_from_aff(__isl_take isl_aff
*aff
)
3349 struct isl_upoly
*up
;
3350 isl_qpolynomial
*qp
;
3355 ctx
= isl_aff_get_ctx(aff
);
3356 up
= isl_upoly_from_affine(ctx
, aff
->v
->el
+ 1, aff
->v
->el
[0],
3359 qp
= isl_qpolynomial_alloc(isl_aff_get_domain_space(aff
),
3360 aff
->ls
->div
->n_row
, up
);
3364 isl_mat_free(qp
->div
);
3365 qp
->div
= isl_mat_copy(aff
->ls
->div
);
3366 qp
->div
= isl_mat_cow(qp
->div
);
3371 qp
= reduce_divs(qp
);
3372 qp
= remove_redundant_divs(qp
);
3376 return isl_qpolynomial_free(qp
);
3379 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_from_pw_aff(
3380 __isl_take isl_pw_aff
*pwaff
)
3383 isl_pw_qpolynomial
*pwqp
;
3388 pwqp
= isl_pw_qpolynomial_alloc_size(isl_pw_aff_get_space(pwaff
),
3391 for (i
= 0; i
< pwaff
->n
; ++i
) {
3393 isl_qpolynomial
*qp
;
3395 dom
= isl_set_copy(pwaff
->p
[i
].set
);
3396 qp
= isl_qpolynomial_from_aff(isl_aff_copy(pwaff
->p
[i
].aff
));
3397 pwqp
= isl_pw_qpolynomial_add_piece(pwqp
, dom
, qp
);
3400 isl_pw_aff_free(pwaff
);
3404 __isl_give isl_qpolynomial
*isl_qpolynomial_from_constraint(
3405 __isl_take isl_constraint
*c
, enum isl_dim_type type
, unsigned pos
)
3409 aff
= isl_constraint_get_bound(c
, type
, pos
);
3410 isl_constraint_free(c
);
3411 return isl_qpolynomial_from_aff(aff
);
3414 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3415 * in "qp" by subs[i].
3417 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute(
3418 __isl_take isl_qpolynomial
*qp
,
3419 enum isl_dim_type type
, unsigned first
, unsigned n
,
3420 __isl_keep isl_qpolynomial
**subs
)
3423 struct isl_upoly
**ups
;
3428 qp
= isl_qpolynomial_cow(qp
);
3432 if (type
== isl_dim_out
)
3433 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
3434 "cannot substitute output/set dimension",
3436 if (type
== isl_dim_in
)
3439 for (i
= 0; i
< n
; ++i
)
3443 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_space_dim(qp
->dim
, type
),
3446 for (i
= 0; i
< n
; ++i
)
3447 isl_assert(qp
->dim
->ctx
, isl_space_is_equal(qp
->dim
, subs
[i
]->dim
),
3450 isl_assert(qp
->dim
->ctx
, qp
->div
->n_row
== 0, goto error
);
3451 for (i
= 0; i
< n
; ++i
)
3452 isl_assert(qp
->dim
->ctx
, subs
[i
]->div
->n_row
== 0, goto error
);
3454 first
+= pos(qp
->dim
, type
);
3456 ups
= isl_alloc_array(qp
->dim
->ctx
, struct isl_upoly
*, n
);
3459 for (i
= 0; i
< n
; ++i
)
3460 ups
[i
] = subs
[i
]->upoly
;
3462 qp
->upoly
= isl_upoly_subs(qp
->upoly
, first
, n
, ups
);
3471 isl_qpolynomial_free(qp
);
3475 /* Extend "bset" with extra set dimensions for each integer division
3476 * in "qp" and then call "fn" with the extended bset and the polynomial
3477 * that results from replacing each of the integer divisions by the
3478 * corresponding extra set dimension.
3480 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial
*qp
,
3481 __isl_keep isl_basic_set
*bset
,
3482 int (*fn
)(__isl_take isl_basic_set
*bset
,
3483 __isl_take isl_qpolynomial
*poly
, void *user
), void *user
)
3487 isl_qpolynomial
*poly
;
3491 if (qp
->div
->n_row
== 0)
3492 return fn(isl_basic_set_copy(bset
), isl_qpolynomial_copy(qp
),
3495 div
= isl_mat_copy(qp
->div
);
3496 dim
= isl_space_copy(qp
->dim
);
3497 dim
= isl_space_add_dims(dim
, isl_dim_set
, qp
->div
->n_row
);
3498 poly
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_copy(qp
->upoly
));
3499 bset
= isl_basic_set_copy(bset
);
3500 bset
= isl_basic_set_add_dims(bset
, isl_dim_set
, qp
->div
->n_row
);
3501 bset
= add_div_constraints(bset
, div
);
3503 return fn(bset
, poly
, user
);
3508 /* Return total degree in variables first (inclusive) up to last (exclusive).
3510 int isl_upoly_degree(__isl_keep
struct isl_upoly
*up
, int first
, int last
)
3514 struct isl_upoly_rec
*rec
;
3518 if (isl_upoly_is_zero(up
))
3520 if (isl_upoly_is_cst(up
) || up
->var
< first
)
3523 rec
= isl_upoly_as_rec(up
);
3527 for (i
= 0; i
< rec
->n
; ++i
) {
3530 if (isl_upoly_is_zero(rec
->p
[i
]))
3532 d
= isl_upoly_degree(rec
->p
[i
], first
, last
);
3542 /* Return total degree in set variables.
3544 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial
*poly
)
3552 ovar
= isl_space_offset(poly
->dim
, isl_dim_set
);
3553 nvar
= isl_space_dim(poly
->dim
, isl_dim_set
);
3554 return isl_upoly_degree(poly
->upoly
, ovar
, ovar
+ nvar
);
3557 __isl_give
struct isl_upoly
*isl_upoly_coeff(__isl_keep
struct isl_upoly
*up
,
3558 unsigned pos
, int deg
)
3561 struct isl_upoly_rec
*rec
;
3566 if (isl_upoly_is_cst(up
) || up
->var
< pos
) {
3568 return isl_upoly_copy(up
);
3570 return isl_upoly_zero(up
->ctx
);
3573 rec
= isl_upoly_as_rec(up
);
3577 if (up
->var
== pos
) {
3579 return isl_upoly_copy(rec
->p
[deg
]);
3581 return isl_upoly_zero(up
->ctx
);
3584 up
= isl_upoly_copy(up
);
3585 up
= isl_upoly_cow(up
);
3586 rec
= isl_upoly_as_rec(up
);
3590 for (i
= 0; i
< rec
->n
; ++i
) {
3591 struct isl_upoly
*t
;
3592 t
= isl_upoly_coeff(rec
->p
[i
], pos
, deg
);
3595 isl_upoly_free(rec
->p
[i
]);
3605 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3607 __isl_give isl_qpolynomial
*isl_qpolynomial_coeff(
3608 __isl_keep isl_qpolynomial
*qp
,
3609 enum isl_dim_type type
, unsigned t_pos
, int deg
)
3612 struct isl_upoly
*up
;
3618 if (type
== isl_dim_out
)
3619 isl_die(qp
->div
->ctx
, isl_error_invalid
,
3620 "output/set dimension does not have a coefficient",
3622 if (type
== isl_dim_in
)
3625 isl_assert(qp
->div
->ctx
, t_pos
< isl_space_dim(qp
->dim
, type
),
3628 g_pos
= pos(qp
->dim
, type
) + t_pos
;
3629 up
= isl_upoly_coeff(qp
->upoly
, g_pos
, deg
);
3631 c
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
), qp
->div
->n_row
, up
);
3634 isl_mat_free(c
->div
);
3635 c
->div
= isl_mat_copy(qp
->div
);
3640 isl_qpolynomial_free(c
);
3644 /* Homogenize the polynomial in the variables first (inclusive) up to
3645 * last (exclusive) by inserting powers of variable first.
3646 * Variable first is assumed not to appear in the input.
3648 __isl_give
struct isl_upoly
*isl_upoly_homogenize(
3649 __isl_take
struct isl_upoly
*up
, int deg
, int target
,
3650 int first
, int last
)
3653 struct isl_upoly_rec
*rec
;
3657 if (isl_upoly_is_zero(up
))
3661 if (isl_upoly_is_cst(up
) || up
->var
< first
) {
3662 struct isl_upoly
*hom
;
3664 hom
= isl_upoly_var_pow(up
->ctx
, first
, target
- deg
);
3667 rec
= isl_upoly_as_rec(hom
);
3668 rec
->p
[target
- deg
] = isl_upoly_mul(rec
->p
[target
- deg
], up
);
3673 up
= isl_upoly_cow(up
);
3674 rec
= isl_upoly_as_rec(up
);
3678 for (i
= 0; i
< rec
->n
; ++i
) {
3679 if (isl_upoly_is_zero(rec
->p
[i
]))
3681 rec
->p
[i
] = isl_upoly_homogenize(rec
->p
[i
],
3682 up
->var
< last
? deg
+ i
: i
, target
,
3694 /* Homogenize the polynomial in the set variables by introducing
3695 * powers of an extra set variable at position 0.
3697 __isl_give isl_qpolynomial
*isl_qpolynomial_homogenize(
3698 __isl_take isl_qpolynomial
*poly
)
3702 int deg
= isl_qpolynomial_degree(poly
);
3707 poly
= isl_qpolynomial_insert_dims(poly
, isl_dim_in
, 0, 1);
3708 poly
= isl_qpolynomial_cow(poly
);
3712 ovar
= isl_space_offset(poly
->dim
, isl_dim_set
);
3713 nvar
= isl_space_dim(poly
->dim
, isl_dim_set
);
3714 poly
->upoly
= isl_upoly_homogenize(poly
->upoly
, 0, deg
,
3721 isl_qpolynomial_free(poly
);
3725 __isl_give isl_term
*isl_term_alloc(__isl_take isl_space
*dim
,
3726 __isl_take isl_mat
*div
)
3734 n
= isl_space_dim(dim
, isl_dim_all
) + div
->n_row
;
3736 term
= isl_calloc(dim
->ctx
, struct isl_term
,
3737 sizeof(struct isl_term
) + (n
- 1) * sizeof(int));
3744 isl_int_init(term
->n
);
3745 isl_int_init(term
->d
);
3749 isl_space_free(dim
);
3754 __isl_give isl_term
*isl_term_copy(__isl_keep isl_term
*term
)
3763 __isl_give isl_term
*isl_term_dup(__isl_keep isl_term
*term
)
3772 total
= isl_space_dim(term
->dim
, isl_dim_all
) + term
->div
->n_row
;
3774 dup
= isl_term_alloc(isl_space_copy(term
->dim
), isl_mat_copy(term
->div
));
3778 isl_int_set(dup
->n
, term
->n
);
3779 isl_int_set(dup
->d
, term
->d
);
3781 for (i
= 0; i
< total
; ++i
)
3782 dup
->pow
[i
] = term
->pow
[i
];
3787 __isl_give isl_term
*isl_term_cow(__isl_take isl_term
*term
)
3795 return isl_term_dup(term
);
3798 void isl_term_free(__isl_take isl_term
*term
)
3803 if (--term
->ref
> 0)
3806 isl_space_free(term
->dim
);
3807 isl_mat_free(term
->div
);
3808 isl_int_clear(term
->n
);
3809 isl_int_clear(term
->d
);
3813 unsigned isl_term_dim(__isl_keep isl_term
*term
, enum isl_dim_type type
)
3821 case isl_dim_out
: return isl_space_dim(term
->dim
, type
);
3822 case isl_dim_div
: return term
->div
->n_row
;
3823 case isl_dim_all
: return isl_space_dim(term
->dim
, isl_dim_all
) +
3829 isl_ctx
*isl_term_get_ctx(__isl_keep isl_term
*term
)
3831 return term
? term
->dim
->ctx
: NULL
;
3834 void isl_term_get_num(__isl_keep isl_term
*term
, isl_int
*n
)
3838 isl_int_set(*n
, term
->n
);
3841 void isl_term_get_den(__isl_keep isl_term
*term
, isl_int
*d
)
3845 isl_int_set(*d
, term
->d
);
3848 /* Return the coefficient of the term "term".
3850 __isl_give isl_val
*isl_term_get_coefficient_val(__isl_keep isl_term
*term
)
3855 return isl_val_rat_from_isl_int(isl_term_get_ctx(term
),
3859 int isl_term_get_exp(__isl_keep isl_term
*term
,
3860 enum isl_dim_type type
, unsigned pos
)
3865 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, type
), return -1);
3867 if (type
>= isl_dim_set
)
3868 pos
+= isl_space_dim(term
->dim
, isl_dim_param
);
3869 if (type
>= isl_dim_div
)
3870 pos
+= isl_space_dim(term
->dim
, isl_dim_set
);
3872 return term
->pow
[pos
];
3875 __isl_give isl_aff
*isl_term_get_div(__isl_keep isl_term
*term
, unsigned pos
)
3877 isl_local_space
*ls
;
3883 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, isl_dim_div
),
3886 ls
= isl_local_space_alloc_div(isl_space_copy(term
->dim
),
3887 isl_mat_copy(term
->div
));
3888 aff
= isl_aff_alloc(ls
);
3892 isl_seq_cpy(aff
->v
->el
, term
->div
->row
[pos
], aff
->v
->size
);
3894 aff
= isl_aff_normalize(aff
);
3899 __isl_give isl_term
*isl_upoly_foreach_term(__isl_keep
struct isl_upoly
*up
,
3900 isl_stat (*fn
)(__isl_take isl_term
*term
, void *user
),
3901 __isl_take isl_term
*term
, void *user
)
3904 struct isl_upoly_rec
*rec
;
3909 if (isl_upoly_is_zero(up
))
3912 isl_assert(up
->ctx
, !isl_upoly_is_nan(up
), goto error
);
3913 isl_assert(up
->ctx
, !isl_upoly_is_infty(up
), goto error
);
3914 isl_assert(up
->ctx
, !isl_upoly_is_neginfty(up
), goto error
);
3916 if (isl_upoly_is_cst(up
)) {
3917 struct isl_upoly_cst
*cst
;
3918 cst
= isl_upoly_as_cst(up
);
3921 term
= isl_term_cow(term
);
3924 isl_int_set(term
->n
, cst
->n
);
3925 isl_int_set(term
->d
, cst
->d
);
3926 if (fn(isl_term_copy(term
), user
) < 0)
3931 rec
= isl_upoly_as_rec(up
);
3935 for (i
= 0; i
< rec
->n
; ++i
) {
3936 term
= isl_term_cow(term
);
3939 term
->pow
[up
->var
] = i
;
3940 term
= isl_upoly_foreach_term(rec
->p
[i
], fn
, term
, user
);
3944 term
->pow
[up
->var
] = 0;
3948 isl_term_free(term
);
3952 isl_stat
isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial
*qp
,
3953 isl_stat (*fn
)(__isl_take isl_term
*term
, void *user
), void *user
)
3958 return isl_stat_error
;
3960 term
= isl_term_alloc(isl_space_copy(qp
->dim
), isl_mat_copy(qp
->div
));
3962 return isl_stat_error
;
3964 term
= isl_upoly_foreach_term(qp
->upoly
, fn
, term
, user
);
3966 isl_term_free(term
);
3968 return term
? isl_stat_ok
: isl_stat_error
;
3971 __isl_give isl_qpolynomial
*isl_qpolynomial_from_term(__isl_take isl_term
*term
)
3973 struct isl_upoly
*up
;
3974 isl_qpolynomial
*qp
;
3980 n
= isl_space_dim(term
->dim
, isl_dim_all
) + term
->div
->n_row
;
3982 up
= isl_upoly_rat_cst(term
->dim
->ctx
, term
->n
, term
->d
);
3983 for (i
= 0; i
< n
; ++i
) {
3986 up
= isl_upoly_mul(up
,
3987 isl_upoly_var_pow(term
->dim
->ctx
, i
, term
->pow
[i
]));
3990 qp
= isl_qpolynomial_alloc(isl_space_copy(term
->dim
), term
->div
->n_row
, up
);
3993 isl_mat_free(qp
->div
);
3994 qp
->div
= isl_mat_copy(term
->div
);
3998 isl_term_free(term
);
4001 isl_qpolynomial_free(qp
);
4002 isl_term_free(term
);
4006 __isl_give isl_qpolynomial
*isl_qpolynomial_lift(__isl_take isl_qpolynomial
*qp
,
4007 __isl_take isl_space
*dim
)
4016 if (isl_space_is_equal(qp
->dim
, dim
)) {
4017 isl_space_free(dim
);
4021 qp
= isl_qpolynomial_cow(qp
);
4025 extra
= isl_space_dim(dim
, isl_dim_set
) -
4026 isl_space_dim(qp
->dim
, isl_dim_set
);
4027 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4028 if (qp
->div
->n_row
) {
4031 exp
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
4034 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4036 qp
->upoly
= expand(qp
->upoly
, exp
, total
);
4041 qp
->div
= isl_mat_insert_cols(qp
->div
, 2 + total
, extra
);
4044 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4045 isl_seq_clr(qp
->div
->row
[i
] + 2 + total
, extra
);
4047 isl_space_free(qp
->dim
);
4052 isl_space_free(dim
);
4053 isl_qpolynomial_free(qp
);
4057 /* For each parameter or variable that does not appear in qp,
4058 * first eliminate the variable from all constraints and then set it to zero.
4060 static __isl_give isl_set
*fix_inactive(__isl_take isl_set
*set
,
4061 __isl_keep isl_qpolynomial
*qp
)
4072 d
= isl_space_dim(set
->dim
, isl_dim_all
);
4073 active
= isl_calloc_array(set
->ctx
, int, d
);
4074 if (set_active(qp
, active
) < 0)
4077 for (i
= 0; i
< d
; ++i
)
4086 nparam
= isl_space_dim(set
->dim
, isl_dim_param
);
4087 nvar
= isl_space_dim(set
->dim
, isl_dim_set
);
4088 for (i
= 0; i
< nparam
; ++i
) {
4091 set
= isl_set_eliminate(set
, isl_dim_param
, i
, 1);
4092 set
= isl_set_fix_si(set
, isl_dim_param
, i
, 0);
4094 for (i
= 0; i
< nvar
; ++i
) {
4095 if (active
[nparam
+ i
])
4097 set
= isl_set_eliminate(set
, isl_dim_set
, i
, 1);
4098 set
= isl_set_fix_si(set
, isl_dim_set
, i
, 0);
4110 struct isl_opt_data
{
4111 isl_qpolynomial
*qp
;
4117 static isl_stat
opt_fn(__isl_take isl_point
*pnt
, void *user
)
4119 struct isl_opt_data
*data
= (struct isl_opt_data
*)user
;
4122 val
= isl_qpolynomial_eval(isl_qpolynomial_copy(data
->qp
), pnt
);
4126 } else if (data
->max
) {
4127 data
->opt
= isl_val_max(data
->opt
, val
);
4129 data
->opt
= isl_val_min(data
->opt
, val
);
4135 __isl_give isl_val
*isl_qpolynomial_opt_on_domain(
4136 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*set
, int max
)
4138 struct isl_opt_data data
= { NULL
, 1, NULL
, max
};
4143 if (isl_upoly_is_cst(qp
->upoly
)) {
4145 data
.opt
= isl_qpolynomial_get_constant_val(qp
);
4146 isl_qpolynomial_free(qp
);
4150 set
= fix_inactive(set
, qp
);
4153 if (isl_set_foreach_point(set
, opt_fn
, &data
) < 0)
4157 data
.opt
= isl_val_zero(isl_set_get_ctx(set
));
4160 isl_qpolynomial_free(qp
);
4164 isl_qpolynomial_free(qp
);
4165 isl_val_free(data
.opt
);
4169 __isl_give isl_qpolynomial
*isl_qpolynomial_morph_domain(
4170 __isl_take isl_qpolynomial
*qp
, __isl_take isl_morph
*morph
)
4175 struct isl_upoly
**subs
;
4176 isl_mat
*mat
, *diag
;
4178 qp
= isl_qpolynomial_cow(qp
);
4183 isl_assert(ctx
, isl_space_is_equal(qp
->dim
, morph
->dom
->dim
), goto error
);
4185 n_sub
= morph
->inv
->n_row
- 1;
4186 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
4187 n_sub
+= qp
->div
->n_row
;
4188 subs
= isl_calloc_array(ctx
, struct isl_upoly
*, n_sub
);
4192 for (i
= 0; 1 + i
< morph
->inv
->n_row
; ++i
)
4193 subs
[i
] = isl_upoly_from_affine(ctx
, morph
->inv
->row
[1 + i
],
4194 morph
->inv
->row
[0][0], morph
->inv
->n_col
);
4195 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
4196 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4197 subs
[morph
->inv
->n_row
- 1 + i
] =
4198 isl_upoly_var_pow(ctx
, morph
->inv
->n_col
- 1 + i
, 1);
4200 qp
->upoly
= isl_upoly_subs(qp
->upoly
, 0, n_sub
, subs
);
4202 for (i
= 0; i
< n_sub
; ++i
)
4203 isl_upoly_free(subs
[i
]);
4206 diag
= isl_mat_diag(ctx
, 1, morph
->inv
->row
[0][0]);
4207 mat
= isl_mat_diagonal(diag
, isl_mat_copy(morph
->inv
));
4208 diag
= isl_mat_diag(ctx
, qp
->div
->n_row
, morph
->inv
->row
[0][0]);
4209 mat
= isl_mat_diagonal(mat
, diag
);
4210 qp
->div
= isl_mat_product(qp
->div
, mat
);
4211 isl_space_free(qp
->dim
);
4212 qp
->dim
= isl_space_copy(morph
->ran
->dim
);
4214 if (!qp
->upoly
|| !qp
->div
|| !qp
->dim
)
4217 isl_morph_free(morph
);
4221 isl_qpolynomial_free(qp
);
4222 isl_morph_free(morph
);
4226 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_mul(
4227 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
4228 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
4230 return isl_union_pw_qpolynomial_match_bin_op(upwqp1
, upwqp2
,
4231 &isl_pw_qpolynomial_mul
);
4234 /* Reorder the columns of the given div definitions according to the
4237 static __isl_give isl_mat
*reorder_divs(__isl_take isl_mat
*div
,
4238 __isl_take isl_reordering
*r
)
4247 extra
= isl_space_dim(r
->dim
, isl_dim_all
) + div
->n_row
- r
->len
;
4248 mat
= isl_mat_alloc(div
->ctx
, div
->n_row
, div
->n_col
+ extra
);
4252 for (i
= 0; i
< div
->n_row
; ++i
) {
4253 isl_seq_cpy(mat
->row
[i
], div
->row
[i
], 2);
4254 isl_seq_clr(mat
->row
[i
] + 2, mat
->n_col
- 2);
4255 for (j
= 0; j
< r
->len
; ++j
)
4256 isl_int_set(mat
->row
[i
][2 + r
->pos
[j
]],
4257 div
->row
[i
][2 + j
]);
4260 isl_reordering_free(r
);
4264 isl_reordering_free(r
);
4269 /* Reorder the dimension of "qp" according to the given reordering.
4271 __isl_give isl_qpolynomial
*isl_qpolynomial_realign_domain(
4272 __isl_take isl_qpolynomial
*qp
, __isl_take isl_reordering
*r
)
4274 qp
= isl_qpolynomial_cow(qp
);
4278 r
= isl_reordering_extend(r
, qp
->div
->n_row
);
4282 qp
->div
= reorder_divs(qp
->div
, isl_reordering_copy(r
));
4286 qp
->upoly
= reorder(qp
->upoly
, r
->pos
);
4290 qp
= isl_qpolynomial_reset_domain_space(qp
, isl_space_copy(r
->dim
));
4292 isl_reordering_free(r
);
4295 isl_qpolynomial_free(qp
);
4296 isl_reordering_free(r
);
4300 __isl_give isl_qpolynomial
*isl_qpolynomial_align_params(
4301 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*model
)
4306 if (!isl_space_match(qp
->dim
, isl_dim_param
, model
, isl_dim_param
)) {
4307 isl_reordering
*exp
;
4309 model
= isl_space_drop_dims(model
, isl_dim_in
,
4310 0, isl_space_dim(model
, isl_dim_in
));
4311 model
= isl_space_drop_dims(model
, isl_dim_out
,
4312 0, isl_space_dim(model
, isl_dim_out
));
4313 exp
= isl_parameter_alignment_reordering(qp
->dim
, model
);
4314 exp
= isl_reordering_extend_space(exp
,
4315 isl_qpolynomial_get_domain_space(qp
));
4316 qp
= isl_qpolynomial_realign_domain(qp
, exp
);
4319 isl_space_free(model
);
4322 isl_space_free(model
);
4323 isl_qpolynomial_free(qp
);
4327 struct isl_split_periods_data
{
4329 isl_pw_qpolynomial
*res
;
4332 /* Create a slice where the integer division "div" has the fixed value "v".
4333 * In particular, if "div" refers to floor(f/m), then create a slice
4335 * m v <= f <= m v + (m - 1)
4340 * -f + m v + (m - 1) >= 0
4342 static __isl_give isl_set
*set_div_slice(__isl_take isl_space
*dim
,
4343 __isl_keep isl_qpolynomial
*qp
, int div
, isl_int v
)
4346 isl_basic_set
*bset
= NULL
;
4352 total
= isl_space_dim(dim
, isl_dim_all
);
4353 bset
= isl_basic_set_alloc_space(isl_space_copy(dim
), 0, 0, 2);
4355 k
= isl_basic_set_alloc_inequality(bset
);
4358 isl_seq_cpy(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4359 isl_int_submul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4361 k
= isl_basic_set_alloc_inequality(bset
);
4364 isl_seq_neg(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4365 isl_int_addmul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4366 isl_int_add(bset
->ineq
[k
][0], bset
->ineq
[k
][0], qp
->div
->row
[div
][0]);
4367 isl_int_sub_ui(bset
->ineq
[k
][0], bset
->ineq
[k
][0], 1);
4369 isl_space_free(dim
);
4370 return isl_set_from_basic_set(bset
);
4372 isl_basic_set_free(bset
);
4373 isl_space_free(dim
);
4377 static isl_stat
split_periods(__isl_take isl_set
*set
,
4378 __isl_take isl_qpolynomial
*qp
, void *user
);
4380 /* Create a slice of the domain "set" such that integer division "div"
4381 * has the fixed value "v" and add the results to data->res,
4382 * replacing the integer division by "v" in "qp".
4384 static isl_stat
set_div(__isl_take isl_set
*set
,
4385 __isl_take isl_qpolynomial
*qp
, int div
, isl_int v
,
4386 struct isl_split_periods_data
*data
)
4391 struct isl_upoly
*cst
;
4393 slice
= set_div_slice(isl_set_get_space(set
), qp
, div
, v
);
4394 set
= isl_set_intersect(set
, slice
);
4399 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4401 for (i
= div
+ 1; i
< qp
->div
->n_row
; ++i
) {
4402 if (isl_int_is_zero(qp
->div
->row
[i
][2 + total
+ div
]))
4404 isl_int_addmul(qp
->div
->row
[i
][1],
4405 qp
->div
->row
[i
][2 + total
+ div
], v
);
4406 isl_int_set_si(qp
->div
->row
[i
][2 + total
+ div
], 0);
4409 cst
= isl_upoly_rat_cst(qp
->dim
->ctx
, v
, qp
->dim
->ctx
->one
);
4410 qp
= substitute_div(qp
, div
, cst
);
4412 return split_periods(set
, qp
, data
);
4415 isl_qpolynomial_free(qp
);
4419 /* Split the domain "set" such that integer division "div"
4420 * has a fixed value (ranging from "min" to "max") on each slice
4421 * and add the results to data->res.
4423 static isl_stat
split_div(__isl_take isl_set
*set
,
4424 __isl_take isl_qpolynomial
*qp
, int div
, isl_int min
, isl_int max
,
4425 struct isl_split_periods_data
*data
)
4427 for (; isl_int_le(min
, max
); isl_int_add_ui(min
, min
, 1)) {
4428 isl_set
*set_i
= isl_set_copy(set
);
4429 isl_qpolynomial
*qp_i
= isl_qpolynomial_copy(qp
);
4431 if (set_div(set_i
, qp_i
, div
, min
, data
) < 0)
4435 isl_qpolynomial_free(qp
);
4439 isl_qpolynomial_free(qp
);
4440 return isl_stat_error
;
4443 /* If "qp" refers to any integer division
4444 * that can only attain "max_periods" distinct values on "set"
4445 * then split the domain along those distinct values.
4446 * Add the results (or the original if no splitting occurs)
4449 static isl_stat
split_periods(__isl_take isl_set
*set
,
4450 __isl_take isl_qpolynomial
*qp
, void *user
)
4453 isl_pw_qpolynomial
*pwqp
;
4454 struct isl_split_periods_data
*data
;
4457 isl_stat r
= isl_stat_ok
;
4459 data
= (struct isl_split_periods_data
*)user
;
4464 if (qp
->div
->n_row
== 0) {
4465 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4466 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4472 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4473 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4474 enum isl_lp_result lp_res
;
4476 if (isl_seq_first_non_zero(qp
->div
->row
[i
] + 2 + total
,
4477 qp
->div
->n_row
) != -1)
4480 lp_res
= isl_set_solve_lp(set
, 0, qp
->div
->row
[i
] + 1,
4481 set
->ctx
->one
, &min
, NULL
, NULL
);
4482 if (lp_res
== isl_lp_error
)
4484 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4486 isl_int_fdiv_q(min
, min
, qp
->div
->row
[i
][0]);
4488 lp_res
= isl_set_solve_lp(set
, 1, qp
->div
->row
[i
] + 1,
4489 set
->ctx
->one
, &max
, NULL
, NULL
);
4490 if (lp_res
== isl_lp_error
)
4492 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4494 isl_int_fdiv_q(max
, max
, qp
->div
->row
[i
][0]);
4496 isl_int_sub(max
, max
, min
);
4497 if (isl_int_cmp_si(max
, data
->max_periods
) < 0) {
4498 isl_int_add(max
, max
, min
);
4503 if (i
< qp
->div
->n_row
) {
4504 r
= split_div(set
, qp
, i
, min
, max
, data
);
4506 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4507 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4519 isl_qpolynomial_free(qp
);
4520 return isl_stat_error
;
4523 /* If any quasi-polynomial in pwqp refers to any integer division
4524 * that can only attain "max_periods" distinct values on its domain
4525 * then split the domain along those distinct values.
4527 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_split_periods(
4528 __isl_take isl_pw_qpolynomial
*pwqp
, int max_periods
)
4530 struct isl_split_periods_data data
;
4532 data
.max_periods
= max_periods
;
4533 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp
));
4535 if (isl_pw_qpolynomial_foreach_piece(pwqp
, &split_periods
, &data
) < 0)
4538 isl_pw_qpolynomial_free(pwqp
);
4542 isl_pw_qpolynomial_free(data
.res
);
4543 isl_pw_qpolynomial_free(pwqp
);
4547 /* Construct a piecewise quasipolynomial that is constant on the given
4548 * domain. In particular, it is
4551 * infinity if cst == -1
4553 static __isl_give isl_pw_qpolynomial
*constant_on_domain(
4554 __isl_take isl_basic_set
*bset
, int cst
)
4557 isl_qpolynomial
*qp
;
4562 bset
= isl_basic_set_params(bset
);
4563 dim
= isl_basic_set_get_space(bset
);
4565 qp
= isl_qpolynomial_infty_on_domain(dim
);
4567 qp
= isl_qpolynomial_zero_on_domain(dim
);
4569 qp
= isl_qpolynomial_one_on_domain(dim
);
4570 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset
), qp
);
4573 /* Factor bset, call fn on each of the factors and return the product.
4575 * If no factors can be found, simply call fn on the input.
4576 * Otherwise, construct the factors based on the factorizer,
4577 * call fn on each factor and compute the product.
4579 static __isl_give isl_pw_qpolynomial
*compressed_multiplicative_call(
4580 __isl_take isl_basic_set
*bset
,
4581 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4587 isl_qpolynomial
*qp
;
4588 isl_pw_qpolynomial
*pwqp
;
4592 f
= isl_basic_set_factorizer(bset
);
4595 if (f
->n_group
== 0) {
4596 isl_factorizer_free(f
);
4600 nparam
= isl_basic_set_dim(bset
, isl_dim_param
);
4601 nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
4603 space
= isl_basic_set_get_space(bset
);
4604 space
= isl_space_domain(space
);
4605 set
= isl_set_universe(isl_space_copy(space
));
4606 qp
= isl_qpolynomial_one_on_domain(space
);
4607 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4609 bset
= isl_morph_basic_set(isl_morph_copy(f
->morph
), bset
);
4611 for (i
= 0, n
= 0; i
< f
->n_group
; ++i
) {
4612 isl_basic_set
*bset_i
;
4613 isl_pw_qpolynomial
*pwqp_i
;
4615 bset_i
= isl_basic_set_copy(bset
);
4616 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4617 nparam
+ n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4618 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4620 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
,
4621 n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4622 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
, 0, n
);
4624 pwqp_i
= fn(bset_i
);
4625 pwqp
= isl_pw_qpolynomial_mul(pwqp
, pwqp_i
);
4630 isl_basic_set_free(bset
);
4631 isl_factorizer_free(f
);
4635 isl_basic_set_free(bset
);
4639 /* Factor bset, call fn on each of the factors and return the product.
4640 * The function is assumed to evaluate to zero on empty domains,
4641 * to one on zero-dimensional domains and to infinity on unbounded domains
4642 * and will not be called explicitly on zero-dimensional or unbounded domains.
4644 * We first check for some special cases and remove all equalities.
4645 * Then we hand over control to compressed_multiplicative_call.
4647 __isl_give isl_pw_qpolynomial
*isl_basic_set_multiplicative_call(
4648 __isl_take isl_basic_set
*bset
,
4649 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4653 isl_pw_qpolynomial
*pwqp
;
4658 if (isl_basic_set_plain_is_empty(bset
))
4659 return constant_on_domain(bset
, 0);
4661 if (isl_basic_set_dim(bset
, isl_dim_set
) == 0)
4662 return constant_on_domain(bset
, 1);
4664 bounded
= isl_basic_set_is_bounded(bset
);
4668 return constant_on_domain(bset
, -1);
4670 if (bset
->n_eq
== 0)
4671 return compressed_multiplicative_call(bset
, fn
);
4673 morph
= isl_basic_set_full_compression(bset
);
4674 bset
= isl_morph_basic_set(isl_morph_copy(morph
), bset
);
4676 pwqp
= compressed_multiplicative_call(bset
, fn
);
4678 morph
= isl_morph_dom_params(morph
);
4679 morph
= isl_morph_ran_params(morph
);
4680 morph
= isl_morph_inverse(morph
);
4682 pwqp
= isl_pw_qpolynomial_morph_domain(pwqp
, morph
);
4686 isl_basic_set_free(bset
);
4690 /* Drop all floors in "qp", turning each integer division [a/m] into
4691 * a rational division a/m. If "down" is set, then the integer division
4692 * is replaced by (a-(m-1))/m instead.
4694 static __isl_give isl_qpolynomial
*qp_drop_floors(
4695 __isl_take isl_qpolynomial
*qp
, int down
)
4698 struct isl_upoly
*s
;
4702 if (qp
->div
->n_row
== 0)
4705 qp
= isl_qpolynomial_cow(qp
);
4709 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
4711 isl_int_sub(qp
->div
->row
[i
][1],
4712 qp
->div
->row
[i
][1], qp
->div
->row
[i
][0]);
4713 isl_int_add_ui(qp
->div
->row
[i
][1],
4714 qp
->div
->row
[i
][1], 1);
4716 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
4717 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
4718 qp
= substitute_div(qp
, i
, s
);
4726 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4727 * a rational division a/m.
4729 static __isl_give isl_pw_qpolynomial
*pwqp_drop_floors(
4730 __isl_take isl_pw_qpolynomial
*pwqp
)
4737 if (isl_pw_qpolynomial_is_zero(pwqp
))
4740 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
4744 for (i
= 0; i
< pwqp
->n
; ++i
) {
4745 pwqp
->p
[i
].qp
= qp_drop_floors(pwqp
->p
[i
].qp
, 0);
4752 isl_pw_qpolynomial_free(pwqp
);
4756 /* Adjust all the integer divisions in "qp" such that they are at least
4757 * one over the given orthant (identified by "signs"). This ensures
4758 * that they will still be non-negative even after subtracting (m-1)/m.
4760 * In particular, f is replaced by f' + v, changing f = [a/m]
4761 * to f' = [(a - m v)/m].
4762 * If the constant term k in a is smaller than m,
4763 * the constant term of v is set to floor(k/m) - 1.
4764 * For any other term, if the coefficient c and the variable x have
4765 * the same sign, then no changes are needed.
4766 * Otherwise, if the variable is positive (and c is negative),
4767 * then the coefficient of x in v is set to floor(c/m).
4768 * If the variable is negative (and c is positive),
4769 * then the coefficient of x in v is set to ceil(c/m).
4771 static __isl_give isl_qpolynomial
*make_divs_pos(__isl_take isl_qpolynomial
*qp
,
4777 struct isl_upoly
*s
;
4779 qp
= isl_qpolynomial_cow(qp
);
4782 qp
->div
= isl_mat_cow(qp
->div
);
4786 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4787 v
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
4789 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4790 isl_int
*row
= qp
->div
->row
[i
];
4794 if (isl_int_lt(row
[1], row
[0])) {
4795 isl_int_fdiv_q(v
->el
[0], row
[1], row
[0]);
4796 isl_int_sub_ui(v
->el
[0], v
->el
[0], 1);
4797 isl_int_submul(row
[1], row
[0], v
->el
[0]);
4799 for (j
= 0; j
< total
; ++j
) {
4800 if (isl_int_sgn(row
[2 + j
]) * signs
[j
] >= 0)
4803 isl_int_cdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4805 isl_int_fdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4806 isl_int_submul(row
[2 + j
], row
[0], v
->el
[1 + j
]);
4808 for (j
= 0; j
< i
; ++j
) {
4809 if (isl_int_sgn(row
[2 + total
+ j
]) >= 0)
4811 isl_int_fdiv_q(v
->el
[1 + total
+ j
],
4812 row
[2 + total
+ j
], row
[0]);
4813 isl_int_submul(row
[2 + total
+ j
],
4814 row
[0], v
->el
[1 + total
+ j
]);
4816 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
4817 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
4819 isl_seq_combine(qp
->div
->row
[j
] + 1,
4820 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
4821 qp
->div
->row
[j
][2 + total
+ i
], v
->el
, v
->size
);
4823 isl_int_set_si(v
->el
[1 + total
+ i
], 1);
4824 s
= isl_upoly_from_affine(qp
->dim
->ctx
, v
->el
,
4825 qp
->div
->ctx
->one
, v
->size
);
4826 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ i
, 1, &s
);
4836 isl_qpolynomial_free(qp
);
4840 struct isl_to_poly_data
{
4842 isl_pw_qpolynomial
*res
;
4843 isl_qpolynomial
*qp
;
4846 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4847 * We first make all integer divisions positive and then split the
4848 * quasipolynomials into terms with sign data->sign (the direction
4849 * of the requested approximation) and terms with the opposite sign.
4850 * In the first set of terms, each integer division [a/m] is
4851 * overapproximated by a/m, while in the second it is underapproximated
4854 static int to_polynomial_on_orthant(__isl_take isl_set
*orthant
, int *signs
,
4857 struct isl_to_poly_data
*data
= user
;
4858 isl_pw_qpolynomial
*t
;
4859 isl_qpolynomial
*qp
, *up
, *down
;
4861 qp
= isl_qpolynomial_copy(data
->qp
);
4862 qp
= make_divs_pos(qp
, signs
);
4864 up
= isl_qpolynomial_terms_of_sign(qp
, signs
, data
->sign
);
4865 up
= qp_drop_floors(up
, 0);
4866 down
= isl_qpolynomial_terms_of_sign(qp
, signs
, -data
->sign
);
4867 down
= qp_drop_floors(down
, 1);
4869 isl_qpolynomial_free(qp
);
4870 qp
= isl_qpolynomial_add(up
, down
);
4872 t
= isl_pw_qpolynomial_alloc(orthant
, qp
);
4873 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, t
);
4878 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4879 * the polynomial will be an overapproximation. If "sign" is negative,
4880 * it will be an underapproximation. If "sign" is zero, the approximation
4881 * will lie somewhere in between.
4883 * In particular, is sign == 0, we simply drop the floors, turning
4884 * the integer divisions into rational divisions.
4885 * Otherwise, we split the domains into orthants, make all integer divisions
4886 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4887 * depending on the requested sign and the sign of the term in which
4888 * the integer division appears.
4890 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_to_polynomial(
4891 __isl_take isl_pw_qpolynomial
*pwqp
, int sign
)
4894 struct isl_to_poly_data data
;
4897 return pwqp_drop_floors(pwqp
);
4903 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp
));
4905 for (i
= 0; i
< pwqp
->n
; ++i
) {
4906 if (pwqp
->p
[i
].qp
->div
->n_row
== 0) {
4907 isl_pw_qpolynomial
*t
;
4908 t
= isl_pw_qpolynomial_alloc(
4909 isl_set_copy(pwqp
->p
[i
].set
),
4910 isl_qpolynomial_copy(pwqp
->p
[i
].qp
));
4911 data
.res
= isl_pw_qpolynomial_add_disjoint(data
.res
, t
);
4914 data
.qp
= pwqp
->p
[i
].qp
;
4915 if (isl_set_foreach_orthant(pwqp
->p
[i
].set
,
4916 &to_polynomial_on_orthant
, &data
) < 0)
4920 isl_pw_qpolynomial_free(pwqp
);
4924 isl_pw_qpolynomial_free(pwqp
);
4925 isl_pw_qpolynomial_free(data
.res
);
4929 static __isl_give isl_pw_qpolynomial
*poly_entry(
4930 __isl_take isl_pw_qpolynomial
*pwqp
, void *user
)
4934 return isl_pw_qpolynomial_to_polynomial(pwqp
, *sign
);
4937 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_to_polynomial(
4938 __isl_take isl_union_pw_qpolynomial
*upwqp
, int sign
)
4940 return isl_union_pw_qpolynomial_transform_inplace(upwqp
,
4941 &poly_entry
, &sign
);
4944 __isl_give isl_basic_map
*isl_basic_map_from_qpolynomial(
4945 __isl_take isl_qpolynomial
*qp
)
4949 isl_vec
*aff
= NULL
;
4950 isl_basic_map
*bmap
= NULL
;
4956 if (!isl_upoly_is_affine(qp
->upoly
))
4957 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
4958 "input quasi-polynomial not affine", goto error
);
4959 aff
= isl_qpolynomial_extract_affine(qp
);
4962 dim
= isl_qpolynomial_get_space(qp
);
4963 pos
= 1 + isl_space_offset(dim
, isl_dim_out
);
4964 n_div
= qp
->div
->n_row
;
4965 bmap
= isl_basic_map_alloc_space(dim
, n_div
, 1, 2 * n_div
);
4967 for (i
= 0; i
< n_div
; ++i
) {
4968 k
= isl_basic_map_alloc_div(bmap
);
4971 isl_seq_cpy(bmap
->div
[k
], qp
->div
->row
[i
], qp
->div
->n_col
);
4972 isl_int_set_si(bmap
->div
[k
][qp
->div
->n_col
], 0);
4973 if (isl_basic_map_add_div_constraints(bmap
, k
) < 0)
4976 k
= isl_basic_map_alloc_equality(bmap
);
4979 isl_int_neg(bmap
->eq
[k
][pos
], aff
->el
[0]);
4980 isl_seq_cpy(bmap
->eq
[k
], aff
->el
+ 1, pos
);
4981 isl_seq_cpy(bmap
->eq
[k
] + pos
+ 1, aff
->el
+ 1 + pos
, n_div
);
4984 isl_qpolynomial_free(qp
);
4985 bmap
= isl_basic_map_finalize(bmap
);
4989 isl_qpolynomial_free(qp
);
4990 isl_basic_map_free(bmap
);