2 * Copyright 2011 INRIA Saclay
3 * Copyright 2011 Sven Verdoolaege
4 * Copyright 2012-2014 Ecole Normale Superieure
6 * Use of this software is governed by the MIT license
8 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
9 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
11 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
14 #include <isl_ctx_private.h>
16 #include <isl_map_private.h>
17 #include <isl_union_map_private.h>
18 #include <isl_aff_private.h>
19 #include <isl_space_private.h>
20 #include <isl_local_space_private.h>
21 #include <isl_vec_private.h>
22 #include <isl_mat_private.h>
23 #include <isl/constraint.h>
26 #include <isl_val_private.h>
27 #include <isl/deprecated/aff_int.h>
28 #include <isl_config.h>
33 #include <isl_list_templ.c>
38 #include <isl_list_templ.c>
40 __isl_give isl_aff
*isl_aff_alloc_vec(__isl_take isl_local_space
*ls
,
41 __isl_take isl_vec
*v
)
48 aff
= isl_calloc_type(v
->ctx
, struct isl_aff
);
58 isl_local_space_free(ls
);
63 __isl_give isl_aff
*isl_aff_alloc(__isl_take isl_local_space
*ls
)
72 ctx
= isl_local_space_get_ctx(ls
);
73 if (!isl_local_space_divs_known(ls
))
74 isl_die(ctx
, isl_error_invalid
, "local space has unknown divs",
76 if (!isl_local_space_is_set(ls
))
77 isl_die(ctx
, isl_error_invalid
,
78 "domain of affine expression should be a set",
81 total
= isl_local_space_dim(ls
, isl_dim_all
);
82 v
= isl_vec_alloc(ctx
, 1 + 1 + total
);
83 return isl_aff_alloc_vec(ls
, v
);
85 isl_local_space_free(ls
);
89 __isl_give isl_aff
*isl_aff_zero_on_domain(__isl_take isl_local_space
*ls
)
93 aff
= isl_aff_alloc(ls
);
97 isl_int_set_si(aff
->v
->el
[0], 1);
98 isl_seq_clr(aff
->v
->el
+ 1, aff
->v
->size
- 1);
103 /* Return a piecewise affine expression defined on the specified domain
104 * that is equal to zero.
106 __isl_give isl_pw_aff
*isl_pw_aff_zero_on_domain(__isl_take isl_local_space
*ls
)
108 return isl_pw_aff_from_aff(isl_aff_zero_on_domain(ls
));
111 /* Return an affine expression defined on the specified domain
112 * that represents NaN.
114 __isl_give isl_aff
*isl_aff_nan_on_domain(__isl_take isl_local_space
*ls
)
118 aff
= isl_aff_alloc(ls
);
122 isl_seq_clr(aff
->v
->el
, aff
->v
->size
);
127 /* Return a piecewise affine expression defined on the specified domain
128 * that represents NaN.
130 __isl_give isl_pw_aff
*isl_pw_aff_nan_on_domain(__isl_take isl_local_space
*ls
)
132 return isl_pw_aff_from_aff(isl_aff_nan_on_domain(ls
));
135 /* Return an affine expression that is equal to "val" on
136 * domain local space "ls".
138 __isl_give isl_aff
*isl_aff_val_on_domain(__isl_take isl_local_space
*ls
,
139 __isl_take isl_val
*val
)
145 if (!isl_val_is_rat(val
))
146 isl_die(isl_val_get_ctx(val
), isl_error_invalid
,
147 "expecting rational value", goto error
);
149 aff
= isl_aff_alloc(isl_local_space_copy(ls
));
153 isl_seq_clr(aff
->v
->el
+ 2, aff
->v
->size
- 2);
154 isl_int_set(aff
->v
->el
[1], val
->n
);
155 isl_int_set(aff
->v
->el
[0], val
->d
);
157 isl_local_space_free(ls
);
161 isl_local_space_free(ls
);
166 /* Return an affine expression that is equal to the specified dimension
169 __isl_give isl_aff
*isl_aff_var_on_domain(__isl_take isl_local_space
*ls
,
170 enum isl_dim_type type
, unsigned pos
)
178 space
= isl_local_space_get_space(ls
);
181 if (isl_space_is_map(space
))
182 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
183 "expecting (parameter) set space", goto error
);
184 if (pos
>= isl_local_space_dim(ls
, type
))
185 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
186 "position out of bounds", goto error
);
188 isl_space_free(space
);
189 aff
= isl_aff_alloc(ls
);
193 pos
+= isl_local_space_offset(aff
->ls
, type
);
195 isl_int_set_si(aff
->v
->el
[0], 1);
196 isl_seq_clr(aff
->v
->el
+ 1, aff
->v
->size
- 1);
197 isl_int_set_si(aff
->v
->el
[1 + pos
], 1);
201 isl_local_space_free(ls
);
202 isl_space_free(space
);
206 /* Return a piecewise affine expression that is equal to
207 * the specified dimension in "ls".
209 __isl_give isl_pw_aff
*isl_pw_aff_var_on_domain(__isl_take isl_local_space
*ls
,
210 enum isl_dim_type type
, unsigned pos
)
212 return isl_pw_aff_from_aff(isl_aff_var_on_domain(ls
, type
, pos
));
215 __isl_give isl_aff
*isl_aff_copy(__isl_keep isl_aff
*aff
)
224 __isl_give isl_aff
*isl_aff_dup(__isl_keep isl_aff
*aff
)
229 return isl_aff_alloc_vec(isl_local_space_copy(aff
->ls
),
230 isl_vec_copy(aff
->v
));
233 __isl_give isl_aff
*isl_aff_cow(__isl_take isl_aff
*aff
)
241 return isl_aff_dup(aff
);
244 __isl_null isl_aff
*isl_aff_free(__isl_take isl_aff
*aff
)
252 isl_local_space_free(aff
->ls
);
253 isl_vec_free(aff
->v
);
260 isl_ctx
*isl_aff_get_ctx(__isl_keep isl_aff
*aff
)
262 return aff
? isl_local_space_get_ctx(aff
->ls
) : NULL
;
265 /* Externally, an isl_aff has a map space, but internally, the
266 * ls field corresponds to the domain of that space.
268 int isl_aff_dim(__isl_keep isl_aff
*aff
, enum isl_dim_type type
)
272 if (type
== isl_dim_out
)
274 if (type
== isl_dim_in
)
276 return isl_local_space_dim(aff
->ls
, type
);
279 __isl_give isl_space
*isl_aff_get_domain_space(__isl_keep isl_aff
*aff
)
281 return aff
? isl_local_space_get_space(aff
->ls
) : NULL
;
284 __isl_give isl_space
*isl_aff_get_space(__isl_keep isl_aff
*aff
)
289 space
= isl_local_space_get_space(aff
->ls
);
290 space
= isl_space_from_domain(space
);
291 space
= isl_space_add_dims(space
, isl_dim_out
, 1);
295 __isl_give isl_local_space
*isl_aff_get_domain_local_space(
296 __isl_keep isl_aff
*aff
)
298 return aff
? isl_local_space_copy(aff
->ls
) : NULL
;
301 __isl_give isl_local_space
*isl_aff_get_local_space(__isl_keep isl_aff
*aff
)
306 ls
= isl_local_space_copy(aff
->ls
);
307 ls
= isl_local_space_from_domain(ls
);
308 ls
= isl_local_space_add_dims(ls
, isl_dim_out
, 1);
312 /* Externally, an isl_aff has a map space, but internally, the
313 * ls field corresponds to the domain of that space.
315 const char *isl_aff_get_dim_name(__isl_keep isl_aff
*aff
,
316 enum isl_dim_type type
, unsigned pos
)
320 if (type
== isl_dim_out
)
322 if (type
== isl_dim_in
)
324 return isl_local_space_get_dim_name(aff
->ls
, type
, pos
);
327 __isl_give isl_aff
*isl_aff_reset_domain_space(__isl_take isl_aff
*aff
,
328 __isl_take isl_space
*dim
)
330 aff
= isl_aff_cow(aff
);
334 aff
->ls
= isl_local_space_reset_space(aff
->ls
, dim
);
336 return isl_aff_free(aff
);
345 /* Reset the space of "aff". This function is called from isl_pw_templ.c
346 * and doesn't know if the space of an element object is represented
347 * directly or through its domain. It therefore passes along both.
349 __isl_give isl_aff
*isl_aff_reset_space_and_domain(__isl_take isl_aff
*aff
,
350 __isl_take isl_space
*space
, __isl_take isl_space
*domain
)
352 isl_space_free(space
);
353 return isl_aff_reset_domain_space(aff
, domain
);
356 /* Reorder the coefficients of the affine expression based
357 * on the given reodering.
358 * The reordering r is assumed to have been extended with the local
361 static __isl_give isl_vec
*vec_reorder(__isl_take isl_vec
*vec
,
362 __isl_take isl_reordering
*r
, int n_div
)
370 res
= isl_vec_alloc(vec
->ctx
,
371 2 + isl_space_dim(r
->dim
, isl_dim_all
) + n_div
);
372 isl_seq_cpy(res
->el
, vec
->el
, 2);
373 isl_seq_clr(res
->el
+ 2, res
->size
- 2);
374 for (i
= 0; i
< r
->len
; ++i
)
375 isl_int_set(res
->el
[2 + r
->pos
[i
]], vec
->el
[2 + i
]);
377 isl_reordering_free(r
);
382 isl_reordering_free(r
);
386 /* Reorder the dimensions of the domain of "aff" according
387 * to the given reordering.
389 __isl_give isl_aff
*isl_aff_realign_domain(__isl_take isl_aff
*aff
,
390 __isl_take isl_reordering
*r
)
392 aff
= isl_aff_cow(aff
);
396 r
= isl_reordering_extend(r
, aff
->ls
->div
->n_row
);
397 aff
->v
= vec_reorder(aff
->v
, isl_reordering_copy(r
),
398 aff
->ls
->div
->n_row
);
399 aff
->ls
= isl_local_space_realign(aff
->ls
, r
);
401 if (!aff
->v
|| !aff
->ls
)
402 return isl_aff_free(aff
);
407 isl_reordering_free(r
);
411 __isl_give isl_aff
*isl_aff_align_params(__isl_take isl_aff
*aff
,
412 __isl_take isl_space
*model
)
417 if (!isl_space_match(aff
->ls
->dim
, isl_dim_param
,
418 model
, isl_dim_param
)) {
421 model
= isl_space_drop_dims(model
, isl_dim_in
,
422 0, isl_space_dim(model
, isl_dim_in
));
423 model
= isl_space_drop_dims(model
, isl_dim_out
,
424 0, isl_space_dim(model
, isl_dim_out
));
425 exp
= isl_parameter_alignment_reordering(aff
->ls
->dim
, model
);
426 exp
= isl_reordering_extend_space(exp
,
427 isl_aff_get_domain_space(aff
));
428 aff
= isl_aff_realign_domain(aff
, exp
);
431 isl_space_free(model
);
434 isl_space_free(model
);
439 /* Is "aff" obviously equal to zero?
441 * If the denominator is zero, then "aff" is not equal to zero.
443 int isl_aff_plain_is_zero(__isl_keep isl_aff
*aff
)
448 if (isl_int_is_zero(aff
->v
->el
[0]))
450 return isl_seq_first_non_zero(aff
->v
->el
+ 1, aff
->v
->size
- 1) < 0;
453 /* Does "aff" represent NaN?
455 int isl_aff_is_nan(__isl_keep isl_aff
*aff
)
460 return isl_seq_first_non_zero(aff
->v
->el
, 2) < 0;
463 /* Does "pa" involve any NaNs?
465 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff
*pa
)
474 for (i
= 0; i
< pa
->n
; ++i
) {
475 int is_nan
= isl_aff_is_nan(pa
->p
[i
].aff
);
476 if (is_nan
< 0 || is_nan
)
483 /* Are "aff1" and "aff2" obviously equal?
485 * NaN is not equal to anything, not even to another NaN.
487 int isl_aff_plain_is_equal(__isl_keep isl_aff
*aff1
, __isl_keep isl_aff
*aff2
)
494 if (isl_aff_is_nan(aff1
) || isl_aff_is_nan(aff2
))
497 equal
= isl_local_space_is_equal(aff1
->ls
, aff2
->ls
);
498 if (equal
< 0 || !equal
)
501 return isl_vec_is_equal(aff1
->v
, aff2
->v
);
504 /* Return the common denominator of "aff" in "v".
506 * We cannot return anything meaningful in case of a NaN.
508 int isl_aff_get_denominator(__isl_keep isl_aff
*aff
, isl_int
*v
)
512 if (isl_aff_is_nan(aff
))
513 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
514 "cannot get denominator of NaN", return -1);
515 isl_int_set(*v
, aff
->v
->el
[0]);
519 /* Return the common denominator of "aff".
521 __isl_give isl_val
*isl_aff_get_denominator_val(__isl_keep isl_aff
*aff
)
528 ctx
= isl_aff_get_ctx(aff
);
529 if (isl_aff_is_nan(aff
))
530 return isl_val_nan(ctx
);
531 return isl_val_int_from_isl_int(ctx
, aff
->v
->el
[0]);
534 /* Return the constant term of "aff" in "v".
536 * We cannot return anything meaningful in case of a NaN.
538 int isl_aff_get_constant(__isl_keep isl_aff
*aff
, isl_int
*v
)
542 if (isl_aff_is_nan(aff
))
543 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
544 "cannot get constant term of NaN", return -1);
545 isl_int_set(*v
, aff
->v
->el
[1]);
549 /* Return the constant term of "aff".
551 __isl_give isl_val
*isl_aff_get_constant_val(__isl_keep isl_aff
*aff
)
559 ctx
= isl_aff_get_ctx(aff
);
560 if (isl_aff_is_nan(aff
))
561 return isl_val_nan(ctx
);
562 v
= isl_val_rat_from_isl_int(ctx
, aff
->v
->el
[1], aff
->v
->el
[0]);
563 return isl_val_normalize(v
);
566 /* Return the coefficient of the variable of type "type" at position "pos"
569 * We cannot return anything meaningful in case of a NaN.
571 int isl_aff_get_coefficient(__isl_keep isl_aff
*aff
,
572 enum isl_dim_type type
, int pos
, isl_int
*v
)
577 if (type
== isl_dim_out
)
578 isl_die(aff
->v
->ctx
, isl_error_invalid
,
579 "output/set dimension does not have a coefficient",
581 if (type
== isl_dim_in
)
584 if (pos
>= isl_local_space_dim(aff
->ls
, type
))
585 isl_die(aff
->v
->ctx
, isl_error_invalid
,
586 "position out of bounds", return -1);
588 if (isl_aff_is_nan(aff
))
589 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
590 "cannot get coefficient of NaN", return -1);
591 pos
+= isl_local_space_offset(aff
->ls
, type
);
592 isl_int_set(*v
, aff
->v
->el
[1 + pos
]);
597 /* Return the coefficient of the variable of type "type" at position "pos"
600 __isl_give isl_val
*isl_aff_get_coefficient_val(__isl_keep isl_aff
*aff
,
601 enum isl_dim_type type
, int pos
)
609 ctx
= isl_aff_get_ctx(aff
);
610 if (type
== isl_dim_out
)
611 isl_die(ctx
, isl_error_invalid
,
612 "output/set dimension does not have a coefficient",
614 if (type
== isl_dim_in
)
617 if (pos
>= isl_local_space_dim(aff
->ls
, type
))
618 isl_die(ctx
, isl_error_invalid
,
619 "position out of bounds", return NULL
);
621 if (isl_aff_is_nan(aff
))
622 return isl_val_nan(ctx
);
623 pos
+= isl_local_space_offset(aff
->ls
, type
);
624 v
= isl_val_rat_from_isl_int(ctx
, aff
->v
->el
[1 + pos
], aff
->v
->el
[0]);
625 return isl_val_normalize(v
);
628 /* Return the sign of the coefficient of the variable of type "type"
629 * at position "pos" of "aff".
631 int isl_aff_coefficient_sgn(__isl_keep isl_aff
*aff
, enum isl_dim_type type
,
639 ctx
= isl_aff_get_ctx(aff
);
640 if (type
== isl_dim_out
)
641 isl_die(ctx
, isl_error_invalid
,
642 "output/set dimension does not have a coefficient",
644 if (type
== isl_dim_in
)
647 if (pos
>= isl_local_space_dim(aff
->ls
, type
))
648 isl_die(ctx
, isl_error_invalid
,
649 "position out of bounds", return 0);
651 pos
+= isl_local_space_offset(aff
->ls
, type
);
652 return isl_int_sgn(aff
->v
->el
[1 + pos
]);
655 /* Replace the denominator of "aff" by "v".
657 * A NaN is unaffected by this operation.
659 __isl_give isl_aff
*isl_aff_set_denominator(__isl_take isl_aff
*aff
, isl_int v
)
663 if (isl_aff_is_nan(aff
))
665 aff
= isl_aff_cow(aff
);
669 aff
->v
= isl_vec_cow(aff
->v
);
671 return isl_aff_free(aff
);
673 isl_int_set(aff
->v
->el
[0], v
);
678 /* Replace the numerator of the constant term of "aff" by "v".
680 * A NaN is unaffected by this operation.
682 __isl_give isl_aff
*isl_aff_set_constant(__isl_take isl_aff
*aff
, isl_int v
)
686 if (isl_aff_is_nan(aff
))
688 aff
= isl_aff_cow(aff
);
692 aff
->v
= isl_vec_cow(aff
->v
);
694 return isl_aff_free(aff
);
696 isl_int_set(aff
->v
->el
[1], v
);
701 /* Replace the constant term of "aff" by "v".
703 * A NaN is unaffected by this operation.
705 __isl_give isl_aff
*isl_aff_set_constant_val(__isl_take isl_aff
*aff
,
706 __isl_take isl_val
*v
)
711 if (isl_aff_is_nan(aff
)) {
716 if (!isl_val_is_rat(v
))
717 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
718 "expecting rational value", goto error
);
720 if (isl_int_eq(aff
->v
->el
[1], v
->n
) &&
721 isl_int_eq(aff
->v
->el
[0], v
->d
)) {
726 aff
= isl_aff_cow(aff
);
729 aff
->v
= isl_vec_cow(aff
->v
);
733 if (isl_int_eq(aff
->v
->el
[0], v
->d
)) {
734 isl_int_set(aff
->v
->el
[1], v
->n
);
735 } else if (isl_int_is_one(v
->d
)) {
736 isl_int_mul(aff
->v
->el
[1], aff
->v
->el
[0], v
->n
);
738 isl_seq_scale(aff
->v
->el
+ 1,
739 aff
->v
->el
+ 1, v
->d
, aff
->v
->size
- 1);
740 isl_int_mul(aff
->v
->el
[1], aff
->v
->el
[0], v
->n
);
741 isl_int_mul(aff
->v
->el
[0], aff
->v
->el
[0], v
->d
);
742 aff
->v
= isl_vec_normalize(aff
->v
);
755 /* Add "v" to the constant term of "aff".
757 * A NaN is unaffected by this operation.
759 __isl_give isl_aff
*isl_aff_add_constant(__isl_take isl_aff
*aff
, isl_int v
)
761 if (isl_int_is_zero(v
))
766 if (isl_aff_is_nan(aff
))
768 aff
= isl_aff_cow(aff
);
772 aff
->v
= isl_vec_cow(aff
->v
);
774 return isl_aff_free(aff
);
776 isl_int_addmul(aff
->v
->el
[1], aff
->v
->el
[0], v
);
781 /* Add "v" to the constant term of "aff".
783 * A NaN is unaffected by this operation.
785 __isl_give isl_aff
*isl_aff_add_constant_val(__isl_take isl_aff
*aff
,
786 __isl_take isl_val
*v
)
791 if (isl_aff_is_nan(aff
) || isl_val_is_zero(v
)) {
796 if (!isl_val_is_rat(v
))
797 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
798 "expecting rational value", goto error
);
800 aff
= isl_aff_cow(aff
);
804 aff
->v
= isl_vec_cow(aff
->v
);
808 if (isl_int_is_one(v
->d
)) {
809 isl_int_addmul(aff
->v
->el
[1], aff
->v
->el
[0], v
->n
);
810 } else if (isl_int_eq(aff
->v
->el
[0], v
->d
)) {
811 isl_int_add(aff
->v
->el
[1], aff
->v
->el
[1], v
->n
);
812 aff
->v
= isl_vec_normalize(aff
->v
);
816 isl_seq_scale(aff
->v
->el
+ 1,
817 aff
->v
->el
+ 1, v
->d
, aff
->v
->size
- 1);
818 isl_int_addmul(aff
->v
->el
[1], aff
->v
->el
[0], v
->n
);
819 isl_int_mul(aff
->v
->el
[0], aff
->v
->el
[0], v
->d
);
820 aff
->v
= isl_vec_normalize(aff
->v
);
833 __isl_give isl_aff
*isl_aff_add_constant_si(__isl_take isl_aff
*aff
, int v
)
838 isl_int_set_si(t
, v
);
839 aff
= isl_aff_add_constant(aff
, t
);
845 /* Add "v" to the numerator of the constant term of "aff".
847 * A NaN is unaffected by this operation.
849 __isl_give isl_aff
*isl_aff_add_constant_num(__isl_take isl_aff
*aff
, isl_int v
)
851 if (isl_int_is_zero(v
))
856 if (isl_aff_is_nan(aff
))
858 aff
= isl_aff_cow(aff
);
862 aff
->v
= isl_vec_cow(aff
->v
);
864 return isl_aff_free(aff
);
866 isl_int_add(aff
->v
->el
[1], aff
->v
->el
[1], v
);
871 /* Add "v" to the numerator of the constant term of "aff".
873 * A NaN is unaffected by this operation.
875 __isl_give isl_aff
*isl_aff_add_constant_num_si(__isl_take isl_aff
*aff
, int v
)
883 isl_int_set_si(t
, v
);
884 aff
= isl_aff_add_constant_num(aff
, t
);
890 /* Replace the numerator of the constant term of "aff" by "v".
892 * A NaN is unaffected by this operation.
894 __isl_give isl_aff
*isl_aff_set_constant_si(__isl_take isl_aff
*aff
, int v
)
898 if (isl_aff_is_nan(aff
))
900 aff
= isl_aff_cow(aff
);
904 aff
->v
= isl_vec_cow(aff
->v
);
906 return isl_aff_free(aff
);
908 isl_int_set_si(aff
->v
->el
[1], v
);
913 /* Replace the numerator of the coefficient of the variable of type "type"
914 * at position "pos" of "aff" by "v".
916 * A NaN is unaffected by this operation.
918 __isl_give isl_aff
*isl_aff_set_coefficient(__isl_take isl_aff
*aff
,
919 enum isl_dim_type type
, int pos
, isl_int v
)
924 if (type
== isl_dim_out
)
925 isl_die(aff
->v
->ctx
, isl_error_invalid
,
926 "output/set dimension does not have a coefficient",
927 return isl_aff_free(aff
));
928 if (type
== isl_dim_in
)
931 if (pos
>= isl_local_space_dim(aff
->ls
, type
))
932 isl_die(aff
->v
->ctx
, isl_error_invalid
,
933 "position out of bounds", return isl_aff_free(aff
));
935 if (isl_aff_is_nan(aff
))
937 aff
= isl_aff_cow(aff
);
941 aff
->v
= isl_vec_cow(aff
->v
);
943 return isl_aff_free(aff
);
945 pos
+= isl_local_space_offset(aff
->ls
, type
);
946 isl_int_set(aff
->v
->el
[1 + pos
], v
);
951 /* Replace the numerator of the coefficient of the variable of type "type"
952 * at position "pos" of "aff" by "v".
954 * A NaN is unaffected by this operation.
956 __isl_give isl_aff
*isl_aff_set_coefficient_si(__isl_take isl_aff
*aff
,
957 enum isl_dim_type type
, int pos
, int v
)
962 if (type
== isl_dim_out
)
963 isl_die(aff
->v
->ctx
, isl_error_invalid
,
964 "output/set dimension does not have a coefficient",
965 return isl_aff_free(aff
));
966 if (type
== isl_dim_in
)
969 if (pos
< 0 || pos
>= isl_local_space_dim(aff
->ls
, type
))
970 isl_die(aff
->v
->ctx
, isl_error_invalid
,
971 "position out of bounds", return isl_aff_free(aff
));
973 if (isl_aff_is_nan(aff
))
975 pos
+= isl_local_space_offset(aff
->ls
, type
);
976 if (isl_int_cmp_si(aff
->v
->el
[1 + pos
], v
) == 0)
979 aff
= isl_aff_cow(aff
);
983 aff
->v
= isl_vec_cow(aff
->v
);
985 return isl_aff_free(aff
);
987 isl_int_set_si(aff
->v
->el
[1 + pos
], v
);
992 /* Replace the coefficient of the variable of type "type" at position "pos"
995 * A NaN is unaffected by this operation.
997 __isl_give isl_aff
*isl_aff_set_coefficient_val(__isl_take isl_aff
*aff
,
998 enum isl_dim_type type
, int pos
, __isl_take isl_val
*v
)
1003 if (type
== isl_dim_out
)
1004 isl_die(aff
->v
->ctx
, isl_error_invalid
,
1005 "output/set dimension does not have a coefficient",
1007 if (type
== isl_dim_in
)
1010 if (pos
>= isl_local_space_dim(aff
->ls
, type
))
1011 isl_die(aff
->v
->ctx
, isl_error_invalid
,
1012 "position out of bounds", goto error
);
1014 if (isl_aff_is_nan(aff
)) {
1018 if (!isl_val_is_rat(v
))
1019 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
1020 "expecting rational value", goto error
);
1022 pos
+= isl_local_space_offset(aff
->ls
, type
);
1023 if (isl_int_eq(aff
->v
->el
[1 + pos
], v
->n
) &&
1024 isl_int_eq(aff
->v
->el
[0], v
->d
)) {
1029 aff
= isl_aff_cow(aff
);
1032 aff
->v
= isl_vec_cow(aff
->v
);
1036 if (isl_int_eq(aff
->v
->el
[0], v
->d
)) {
1037 isl_int_set(aff
->v
->el
[1 + pos
], v
->n
);
1038 } else if (isl_int_is_one(v
->d
)) {
1039 isl_int_mul(aff
->v
->el
[1 + pos
], aff
->v
->el
[0], v
->n
);
1041 isl_seq_scale(aff
->v
->el
+ 1,
1042 aff
->v
->el
+ 1, v
->d
, aff
->v
->size
- 1);
1043 isl_int_mul(aff
->v
->el
[1 + pos
], aff
->v
->el
[0], v
->n
);
1044 isl_int_mul(aff
->v
->el
[0], aff
->v
->el
[0], v
->d
);
1045 aff
->v
= isl_vec_normalize(aff
->v
);
1058 /* Add "v" to the coefficient of the variable of type "type"
1059 * at position "pos" of "aff".
1061 * A NaN is unaffected by this operation.
1063 __isl_give isl_aff
*isl_aff_add_coefficient(__isl_take isl_aff
*aff
,
1064 enum isl_dim_type type
, int pos
, isl_int v
)
1069 if (type
== isl_dim_out
)
1070 isl_die(aff
->v
->ctx
, isl_error_invalid
,
1071 "output/set dimension does not have a coefficient",
1072 return isl_aff_free(aff
));
1073 if (type
== isl_dim_in
)
1076 if (pos
>= isl_local_space_dim(aff
->ls
, type
))
1077 isl_die(aff
->v
->ctx
, isl_error_invalid
,
1078 "position out of bounds", return isl_aff_free(aff
));
1080 if (isl_aff_is_nan(aff
))
1082 aff
= isl_aff_cow(aff
);
1086 aff
->v
= isl_vec_cow(aff
->v
);
1088 return isl_aff_free(aff
);
1090 pos
+= isl_local_space_offset(aff
->ls
, type
);
1091 isl_int_addmul(aff
->v
->el
[1 + pos
], aff
->v
->el
[0], v
);
1096 /* Add "v" to the coefficient of the variable of type "type"
1097 * at position "pos" of "aff".
1099 * A NaN is unaffected by this operation.
1101 __isl_give isl_aff
*isl_aff_add_coefficient_val(__isl_take isl_aff
*aff
,
1102 enum isl_dim_type type
, int pos
, __isl_take isl_val
*v
)
1107 if (isl_val_is_zero(v
)) {
1112 if (type
== isl_dim_out
)
1113 isl_die(aff
->v
->ctx
, isl_error_invalid
,
1114 "output/set dimension does not have a coefficient",
1116 if (type
== isl_dim_in
)
1119 if (pos
>= isl_local_space_dim(aff
->ls
, type
))
1120 isl_die(aff
->v
->ctx
, isl_error_invalid
,
1121 "position out of bounds", goto error
);
1123 if (isl_aff_is_nan(aff
)) {
1127 if (!isl_val_is_rat(v
))
1128 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
1129 "expecting rational value", goto error
);
1131 aff
= isl_aff_cow(aff
);
1135 aff
->v
= isl_vec_cow(aff
->v
);
1139 pos
+= isl_local_space_offset(aff
->ls
, type
);
1140 if (isl_int_is_one(v
->d
)) {
1141 isl_int_addmul(aff
->v
->el
[1 + pos
], aff
->v
->el
[0], v
->n
);
1142 } else if (isl_int_eq(aff
->v
->el
[0], v
->d
)) {
1143 isl_int_add(aff
->v
->el
[1 + pos
], aff
->v
->el
[1 + pos
], v
->n
);
1144 aff
->v
= isl_vec_normalize(aff
->v
);
1148 isl_seq_scale(aff
->v
->el
+ 1,
1149 aff
->v
->el
+ 1, v
->d
, aff
->v
->size
- 1);
1150 isl_int_addmul(aff
->v
->el
[1 + pos
], aff
->v
->el
[0], v
->n
);
1151 isl_int_mul(aff
->v
->el
[0], aff
->v
->el
[0], v
->d
);
1152 aff
->v
= isl_vec_normalize(aff
->v
);
1165 __isl_give isl_aff
*isl_aff_add_coefficient_si(__isl_take isl_aff
*aff
,
1166 enum isl_dim_type type
, int pos
, int v
)
1171 isl_int_set_si(t
, v
);
1172 aff
= isl_aff_add_coefficient(aff
, type
, pos
, t
);
1178 __isl_give isl_aff
*isl_aff_get_div(__isl_keep isl_aff
*aff
, int pos
)
1183 return isl_local_space_get_div(aff
->ls
, pos
);
1186 /* Return the negation of "aff".
1188 * As a special case, -NaN = NaN.
1190 __isl_give isl_aff
*isl_aff_neg(__isl_take isl_aff
*aff
)
1194 if (isl_aff_is_nan(aff
))
1196 aff
= isl_aff_cow(aff
);
1199 aff
->v
= isl_vec_cow(aff
->v
);
1201 return isl_aff_free(aff
);
1203 isl_seq_neg(aff
->v
->el
+ 1, aff
->v
->el
+ 1, aff
->v
->size
- 1);
1208 /* Remove divs from the local space that do not appear in the affine
1210 * We currently only remove divs at the end.
1211 * Some intermediate divs may also not appear directly in the affine
1212 * expression, but we would also need to check that no other divs are
1213 * defined in terms of them.
1215 __isl_give isl_aff
*isl_aff_remove_unused_divs( __isl_take isl_aff
*aff
)
1224 n
= isl_local_space_dim(aff
->ls
, isl_dim_div
);
1225 off
= isl_local_space_offset(aff
->ls
, isl_dim_div
);
1227 pos
= isl_seq_last_non_zero(aff
->v
->el
+ 1 + off
, n
) + 1;
1231 aff
= isl_aff_cow(aff
);
1235 aff
->ls
= isl_local_space_drop_dims(aff
->ls
, isl_dim_div
, pos
, n
- pos
);
1236 aff
->v
= isl_vec_drop_els(aff
->v
, 1 + off
+ pos
, n
- pos
);
1237 if (!aff
->ls
|| !aff
->v
)
1238 return isl_aff_free(aff
);
1243 /* Given two affine expressions "p" of length p_len (including the
1244 * denominator and the constant term) and "subs" of length subs_len,
1245 * plug in "subs" for the variable at position "pos".
1246 * The variables of "subs" and "p" are assumed to match up to subs_len,
1247 * but "p" may have additional variables.
1248 * "v" is an initialized isl_int that can be used internally.
1250 * In particular, if "p" represents the expression
1254 * with i the variable at position "pos" and "subs" represents the expression
1258 * then the result represents the expression
1263 void isl_seq_substitute(isl_int
*p
, int pos
, isl_int
*subs
,
1264 int p_len
, int subs_len
, isl_int v
)
1266 isl_int_set(v
, p
[1 + pos
]);
1267 isl_int_set_si(p
[1 + pos
], 0);
1268 isl_seq_combine(p
+ 1, subs
[0], p
+ 1, v
, subs
+ 1, subs_len
- 1);
1269 isl_seq_scale(p
+ subs_len
, p
+ subs_len
, subs
[0], p_len
- subs_len
);
1270 isl_int_mul(p
[0], p
[0], subs
[0]);
1273 /* Look for any divs in the aff->ls with a denominator equal to one
1274 * and plug them into the affine expression and any subsequent divs
1275 * that may reference the div.
1277 static __isl_give isl_aff
*plug_in_integral_divs(__isl_take isl_aff
*aff
)
1283 isl_local_space
*ls
;
1289 n
= isl_local_space_dim(aff
->ls
, isl_dim_div
);
1291 for (i
= 0; i
< n
; ++i
) {
1292 if (!isl_int_is_one(aff
->ls
->div
->row
[i
][0]))
1294 ls
= isl_local_space_copy(aff
->ls
);
1295 ls
= isl_local_space_substitute_seq(ls
, isl_dim_div
, i
,
1296 aff
->ls
->div
->row
[i
], len
, i
+ 1, n
- (i
+ 1));
1297 vec
= isl_vec_copy(aff
->v
);
1298 vec
= isl_vec_cow(vec
);
1304 pos
= isl_local_space_offset(aff
->ls
, isl_dim_div
) + i
;
1305 isl_seq_substitute(vec
->el
, pos
, aff
->ls
->div
->row
[i
],
1310 isl_vec_free(aff
->v
);
1312 isl_local_space_free(aff
->ls
);
1319 isl_local_space_free(ls
);
1320 return isl_aff_free(aff
);
1323 /* Look for any divs j that appear with a unit coefficient inside
1324 * the definitions of other divs i and plug them into the definitions
1327 * In particular, an expression of the form
1329 * floor((f(..) + floor(g(..)/n))/m)
1333 * floor((n * f(..) + g(..))/(n * m))
1335 * This simplification is correct because we can move the expression
1336 * f(..) into the inner floor in the original expression to obtain
1338 * floor(floor((n * f(..) + g(..))/n)/m)
1340 * from which we can derive the simplified expression.
1342 static __isl_give isl_aff
*plug_in_unit_divs(__isl_take isl_aff
*aff
)
1350 n
= isl_local_space_dim(aff
->ls
, isl_dim_div
);
1351 off
= isl_local_space_offset(aff
->ls
, isl_dim_div
);
1352 for (i
= 1; i
< n
; ++i
) {
1353 for (j
= 0; j
< i
; ++j
) {
1354 if (!isl_int_is_one(aff
->ls
->div
->row
[i
][1 + off
+ j
]))
1356 aff
->ls
= isl_local_space_substitute_seq(aff
->ls
,
1357 isl_dim_div
, j
, aff
->ls
->div
->row
[j
],
1358 aff
->v
->size
, i
, 1);
1360 return isl_aff_free(aff
);
1367 /* Swap divs "a" and "b" in "aff", which is assumed to be non-NULL.
1369 * Even though this function is only called on isl_affs with a single
1370 * reference, we are careful to only change aff->v and aff->ls together.
1372 static __isl_give isl_aff
*swap_div(__isl_take isl_aff
*aff
, int a
, int b
)
1374 unsigned off
= isl_local_space_offset(aff
->ls
, isl_dim_div
);
1375 isl_local_space
*ls
;
1378 ls
= isl_local_space_copy(aff
->ls
);
1379 ls
= isl_local_space_swap_div(ls
, a
, b
);
1380 v
= isl_vec_copy(aff
->v
);
1385 isl_int_swap(v
->el
[1 + off
+ a
], v
->el
[1 + off
+ b
]);
1386 isl_vec_free(aff
->v
);
1388 isl_local_space_free(aff
->ls
);
1394 isl_local_space_free(ls
);
1395 return isl_aff_free(aff
);
1398 /* Merge divs "a" and "b" in "aff", which is assumed to be non-NULL.
1400 * We currently do not actually remove div "b", but simply add its
1401 * coefficient to that of "a" and then zero it out.
1403 static __isl_give isl_aff
*merge_divs(__isl_take isl_aff
*aff
, int a
, int b
)
1405 unsigned off
= isl_local_space_offset(aff
->ls
, isl_dim_div
);
1407 if (isl_int_is_zero(aff
->v
->el
[1 + off
+ b
]))
1410 aff
->v
= isl_vec_cow(aff
->v
);
1412 return isl_aff_free(aff
);
1414 isl_int_add(aff
->v
->el
[1 + off
+ a
],
1415 aff
->v
->el
[1 + off
+ a
], aff
->v
->el
[1 + off
+ b
]);
1416 isl_int_set_si(aff
->v
->el
[1 + off
+ b
], 0);
1421 /* Sort the divs in the local space of "aff" according to
1422 * the comparison function "cmp_row" in isl_local_space.c,
1423 * combining the coefficients of identical divs.
1425 * Reordering divs does not change the semantics of "aff",
1426 * so there is no need to call isl_aff_cow.
1427 * Moreover, this function is currently only called on isl_affs
1428 * with a single reference.
1430 static __isl_give isl_aff
*sort_divs(__isl_take isl_aff
*aff
)
1438 off
= isl_local_space_offset(aff
->ls
, isl_dim_div
);
1439 n
= isl_aff_dim(aff
, isl_dim_div
);
1440 for (i
= 1; i
< n
; ++i
) {
1441 for (j
= i
- 1; j
>= 0; --j
) {
1442 int cmp
= isl_mat_cmp_div(aff
->ls
->div
, j
, j
+ 1);
1446 aff
= merge_divs(aff
, j
, j
+ 1);
1448 aff
= swap_div(aff
, j
, j
+ 1);
1457 /* Normalize the representation of "aff".
1459 * This function should only be called of "new" isl_affs, i.e.,
1460 * with only a single reference. We therefore do not need to
1461 * worry about affecting other instances.
1463 __isl_give isl_aff
*isl_aff_normalize(__isl_take isl_aff
*aff
)
1467 aff
->v
= isl_vec_normalize(aff
->v
);
1469 return isl_aff_free(aff
);
1470 aff
= plug_in_integral_divs(aff
);
1471 aff
= plug_in_unit_divs(aff
);
1472 aff
= sort_divs(aff
);
1473 aff
= isl_aff_remove_unused_divs(aff
);
1477 /* Given f, return floor(f).
1478 * If f is an integer expression, then just return f.
1479 * If f is a constant, then return the constant floor(f).
1480 * Otherwise, if f = g/m, write g = q m + r,
1481 * create a new div d = [r/m] and return the expression q + d.
1482 * The coefficients in r are taken to lie between -m/2 and m/2.
1484 * As a special case, floor(NaN) = NaN.
1486 __isl_give isl_aff
*isl_aff_floor(__isl_take isl_aff
*aff
)
1496 if (isl_aff_is_nan(aff
))
1498 if (isl_int_is_one(aff
->v
->el
[0]))
1501 aff
= isl_aff_cow(aff
);
1505 aff
->v
= isl_vec_cow(aff
->v
);
1507 return isl_aff_free(aff
);
1509 if (isl_aff_is_cst(aff
)) {
1510 isl_int_fdiv_q(aff
->v
->el
[1], aff
->v
->el
[1], aff
->v
->el
[0]);
1511 isl_int_set_si(aff
->v
->el
[0], 1);
1515 div
= isl_vec_copy(aff
->v
);
1516 div
= isl_vec_cow(div
);
1518 return isl_aff_free(aff
);
1520 ctx
= isl_aff_get_ctx(aff
);
1521 isl_int_fdiv_q(aff
->v
->el
[0], aff
->v
->el
[0], ctx
->two
);
1522 for (i
= 1; i
< aff
->v
->size
; ++i
) {
1523 isl_int_fdiv_r(div
->el
[i
], div
->el
[i
], div
->el
[0]);
1524 isl_int_fdiv_q(aff
->v
->el
[i
], aff
->v
->el
[i
], div
->el
[0]);
1525 if (isl_int_gt(div
->el
[i
], aff
->v
->el
[0])) {
1526 isl_int_sub(div
->el
[i
], div
->el
[i
], div
->el
[0]);
1527 isl_int_add_ui(aff
->v
->el
[i
], aff
->v
->el
[i
], 1);
1531 aff
->ls
= isl_local_space_add_div(aff
->ls
, div
);
1533 return isl_aff_free(aff
);
1535 size
= aff
->v
->size
;
1536 aff
->v
= isl_vec_extend(aff
->v
, size
+ 1);
1538 return isl_aff_free(aff
);
1539 isl_int_set_si(aff
->v
->el
[0], 1);
1540 isl_int_set_si(aff
->v
->el
[size
], 1);
1542 aff
= isl_aff_normalize(aff
);
1549 * aff mod m = aff - m * floor(aff/m)
1551 __isl_give isl_aff
*isl_aff_mod(__isl_take isl_aff
*aff
, isl_int m
)
1555 res
= isl_aff_copy(aff
);
1556 aff
= isl_aff_scale_down(aff
, m
);
1557 aff
= isl_aff_floor(aff
);
1558 aff
= isl_aff_scale(aff
, m
);
1559 res
= isl_aff_sub(res
, aff
);
1566 * aff mod m = aff - m * floor(aff/m)
1568 * with m an integer value.
1570 __isl_give isl_aff
*isl_aff_mod_val(__isl_take isl_aff
*aff
,
1571 __isl_take isl_val
*m
)
1578 if (!isl_val_is_int(m
))
1579 isl_die(isl_val_get_ctx(m
), isl_error_invalid
,
1580 "expecting integer modulo", goto error
);
1582 res
= isl_aff_copy(aff
);
1583 aff
= isl_aff_scale_down_val(aff
, isl_val_copy(m
));
1584 aff
= isl_aff_floor(aff
);
1585 aff
= isl_aff_scale_val(aff
, m
);
1586 res
= isl_aff_sub(res
, aff
);
1597 * pwaff mod m = pwaff - m * floor(pwaff/m)
1599 __isl_give isl_pw_aff
*isl_pw_aff_mod(__isl_take isl_pw_aff
*pwaff
, isl_int m
)
1603 res
= isl_pw_aff_copy(pwaff
);
1604 pwaff
= isl_pw_aff_scale_down(pwaff
, m
);
1605 pwaff
= isl_pw_aff_floor(pwaff
);
1606 pwaff
= isl_pw_aff_scale(pwaff
, m
);
1607 res
= isl_pw_aff_sub(res
, pwaff
);
1614 * pa mod m = pa - m * floor(pa/m)
1616 * with m an integer value.
1618 __isl_give isl_pw_aff
*isl_pw_aff_mod_val(__isl_take isl_pw_aff
*pa
,
1619 __isl_take isl_val
*m
)
1623 if (!isl_val_is_int(m
))
1624 isl_die(isl_pw_aff_get_ctx(pa
), isl_error_invalid
,
1625 "expecting integer modulo", goto error
);
1626 pa
= isl_pw_aff_mod(pa
, m
->n
);
1630 isl_pw_aff_free(pa
);
1635 /* Given f, return ceil(f).
1636 * If f is an integer expression, then just return f.
1637 * Otherwise, let f be the expression
1643 * floor((e + m - 1)/m)
1645 * As a special case, ceil(NaN) = NaN.
1647 __isl_give isl_aff
*isl_aff_ceil(__isl_take isl_aff
*aff
)
1652 if (isl_aff_is_nan(aff
))
1654 if (isl_int_is_one(aff
->v
->el
[0]))
1657 aff
= isl_aff_cow(aff
);
1660 aff
->v
= isl_vec_cow(aff
->v
);
1662 return isl_aff_free(aff
);
1664 isl_int_add(aff
->v
->el
[1], aff
->v
->el
[1], aff
->v
->el
[0]);
1665 isl_int_sub_ui(aff
->v
->el
[1], aff
->v
->el
[1], 1);
1666 aff
= isl_aff_floor(aff
);
1671 /* Apply the expansion computed by isl_merge_divs.
1672 * The expansion itself is given by "exp" while the resulting
1673 * list of divs is given by "div".
1675 __isl_give isl_aff
*isl_aff_expand_divs( __isl_take isl_aff
*aff
,
1676 __isl_take isl_mat
*div
, int *exp
)
1683 aff
= isl_aff_cow(aff
);
1687 old_n_div
= isl_local_space_dim(aff
->ls
, isl_dim_div
);
1688 new_n_div
= isl_mat_rows(div
);
1689 if (new_n_div
< old_n_div
)
1690 isl_die(isl_mat_get_ctx(div
), isl_error_invalid
,
1691 "not an expansion", goto error
);
1693 aff
->v
= isl_vec_extend(aff
->v
, aff
->v
->size
+ new_n_div
- old_n_div
);
1697 offset
= 1 + isl_local_space_offset(aff
->ls
, isl_dim_div
);
1699 for (i
= new_n_div
- 1; i
>= 0; --i
) {
1700 if (j
>= 0 && exp
[j
] == i
) {
1702 isl_int_swap(aff
->v
->el
[offset
+ i
],
1703 aff
->v
->el
[offset
+ j
]);
1706 isl_int_set_si(aff
->v
->el
[offset
+ i
], 0);
1709 aff
->ls
= isl_local_space_replace_divs(aff
->ls
, isl_mat_copy(div
));
1720 /* Add two affine expressions that live in the same local space.
1722 static __isl_give isl_aff
*add_expanded(__isl_take isl_aff
*aff1
,
1723 __isl_take isl_aff
*aff2
)
1727 aff1
= isl_aff_cow(aff1
);
1731 aff1
->v
= isl_vec_cow(aff1
->v
);
1737 isl_int_gcd(gcd
, aff1
->v
->el
[0], aff2
->v
->el
[0]);
1738 isl_int_divexact(f
, aff2
->v
->el
[0], gcd
);
1739 isl_seq_scale(aff1
->v
->el
+ 1, aff1
->v
->el
+ 1, f
, aff1
->v
->size
- 1);
1740 isl_int_divexact(f
, aff1
->v
->el
[0], gcd
);
1741 isl_seq_addmul(aff1
->v
->el
+ 1, f
, aff2
->v
->el
+ 1, aff1
->v
->size
- 1);
1742 isl_int_divexact(f
, aff2
->v
->el
[0], gcd
);
1743 isl_int_mul(aff1
->v
->el
[0], aff1
->v
->el
[0], f
);
1755 /* Return the sum of "aff1" and "aff2".
1757 * If either of the two is NaN, then the result is NaN.
1759 __isl_give isl_aff
*isl_aff_add(__isl_take isl_aff
*aff1
,
1760 __isl_take isl_aff
*aff2
)
1771 ctx
= isl_aff_get_ctx(aff1
);
1772 if (!isl_space_is_equal(aff1
->ls
->dim
, aff2
->ls
->dim
))
1773 isl_die(ctx
, isl_error_invalid
,
1774 "spaces don't match", goto error
);
1776 if (isl_aff_is_nan(aff1
)) {
1780 if (isl_aff_is_nan(aff2
)) {
1785 n_div1
= isl_aff_dim(aff1
, isl_dim_div
);
1786 n_div2
= isl_aff_dim(aff2
, isl_dim_div
);
1787 if (n_div1
== 0 && n_div2
== 0)
1788 return add_expanded(aff1
, aff2
);
1790 exp1
= isl_alloc_array(ctx
, int, n_div1
);
1791 exp2
= isl_alloc_array(ctx
, int, n_div2
);
1792 if ((n_div1
&& !exp1
) || (n_div2
&& !exp2
))
1795 div
= isl_merge_divs(aff1
->ls
->div
, aff2
->ls
->div
, exp1
, exp2
);
1796 aff1
= isl_aff_expand_divs(aff1
, isl_mat_copy(div
), exp1
);
1797 aff2
= isl_aff_expand_divs(aff2
, div
, exp2
);
1801 return add_expanded(aff1
, aff2
);
1810 __isl_give isl_aff
*isl_aff_sub(__isl_take isl_aff
*aff1
,
1811 __isl_take isl_aff
*aff2
)
1813 return isl_aff_add(aff1
, isl_aff_neg(aff2
));
1816 /* Return the result of scaling "aff" by a factor of "f".
1818 * As a special case, f * NaN = NaN.
1820 __isl_give isl_aff
*isl_aff_scale(__isl_take isl_aff
*aff
, isl_int f
)
1826 if (isl_aff_is_nan(aff
))
1829 if (isl_int_is_one(f
))
1832 aff
= isl_aff_cow(aff
);
1835 aff
->v
= isl_vec_cow(aff
->v
);
1837 return isl_aff_free(aff
);
1839 if (isl_int_is_pos(f
) && isl_int_is_divisible_by(aff
->v
->el
[0], f
)) {
1840 isl_int_divexact(aff
->v
->el
[0], aff
->v
->el
[0], f
);
1845 isl_int_gcd(gcd
, aff
->v
->el
[0], f
);
1846 isl_int_divexact(aff
->v
->el
[0], aff
->v
->el
[0], gcd
);
1847 isl_int_divexact(gcd
, f
, gcd
);
1848 isl_seq_scale(aff
->v
->el
+ 1, aff
->v
->el
+ 1, gcd
, aff
->v
->size
- 1);
1854 /* Multiple "aff" by "v".
1856 __isl_give isl_aff
*isl_aff_scale_val(__isl_take isl_aff
*aff
,
1857 __isl_take isl_val
*v
)
1862 if (isl_val_is_one(v
)) {
1867 if (!isl_val_is_rat(v
))
1868 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
1869 "expecting rational factor", goto error
);
1871 aff
= isl_aff_scale(aff
, v
->n
);
1872 aff
= isl_aff_scale_down(aff
, v
->d
);
1882 /* Return the result of scaling "aff" down by a factor of "f".
1884 * As a special case, NaN/f = NaN.
1886 __isl_give isl_aff
*isl_aff_scale_down(__isl_take isl_aff
*aff
, isl_int f
)
1892 if (isl_aff_is_nan(aff
))
1895 if (isl_int_is_one(f
))
1898 aff
= isl_aff_cow(aff
);
1902 if (isl_int_is_zero(f
))
1903 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
1904 "cannot scale down by zero", return isl_aff_free(aff
));
1906 aff
->v
= isl_vec_cow(aff
->v
);
1908 return isl_aff_free(aff
);
1911 isl_seq_gcd(aff
->v
->el
+ 1, aff
->v
->size
- 1, &gcd
);
1912 isl_int_gcd(gcd
, gcd
, f
);
1913 isl_seq_scale_down(aff
->v
->el
+ 1, aff
->v
->el
+ 1, gcd
, aff
->v
->size
- 1);
1914 isl_int_divexact(gcd
, f
, gcd
);
1915 isl_int_mul(aff
->v
->el
[0], aff
->v
->el
[0], gcd
);
1921 /* Divide "aff" by "v".
1923 __isl_give isl_aff
*isl_aff_scale_down_val(__isl_take isl_aff
*aff
,
1924 __isl_take isl_val
*v
)
1929 if (isl_val_is_one(v
)) {
1934 if (!isl_val_is_rat(v
))
1935 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
1936 "expecting rational factor", goto error
);
1937 if (!isl_val_is_pos(v
))
1938 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
1939 "factor needs to be positive", goto error
);
1941 aff
= isl_aff_scale(aff
, v
->d
);
1942 aff
= isl_aff_scale_down(aff
, v
->n
);
1952 __isl_give isl_aff
*isl_aff_scale_down_ui(__isl_take isl_aff
*aff
, unsigned f
)
1960 isl_int_set_ui(v
, f
);
1961 aff
= isl_aff_scale_down(aff
, v
);
1967 __isl_give isl_aff
*isl_aff_set_dim_name(__isl_take isl_aff
*aff
,
1968 enum isl_dim_type type
, unsigned pos
, const char *s
)
1970 aff
= isl_aff_cow(aff
);
1973 if (type
== isl_dim_out
)
1974 isl_die(aff
->v
->ctx
, isl_error_invalid
,
1975 "cannot set name of output/set dimension",
1976 return isl_aff_free(aff
));
1977 if (type
== isl_dim_in
)
1979 aff
->ls
= isl_local_space_set_dim_name(aff
->ls
, type
, pos
, s
);
1981 return isl_aff_free(aff
);
1986 __isl_give isl_aff
*isl_aff_set_dim_id(__isl_take isl_aff
*aff
,
1987 enum isl_dim_type type
, unsigned pos
, __isl_take isl_id
*id
)
1989 aff
= isl_aff_cow(aff
);
1992 if (type
== isl_dim_out
)
1993 isl_die(aff
->v
->ctx
, isl_error_invalid
,
1994 "cannot set name of output/set dimension",
1996 if (type
== isl_dim_in
)
1998 aff
->ls
= isl_local_space_set_dim_id(aff
->ls
, type
, pos
, id
);
2000 return isl_aff_free(aff
);
2009 /* Replace the identifier of the input tuple of "aff" by "id".
2010 * type is currently required to be equal to isl_dim_in
2012 __isl_give isl_aff
*isl_aff_set_tuple_id(__isl_take isl_aff
*aff
,
2013 enum isl_dim_type type
, __isl_take isl_id
*id
)
2015 aff
= isl_aff_cow(aff
);
2018 if (type
!= isl_dim_out
)
2019 isl_die(aff
->v
->ctx
, isl_error_invalid
,
2020 "cannot only set id of input tuple", goto error
);
2021 aff
->ls
= isl_local_space_set_tuple_id(aff
->ls
, isl_dim_set
, id
);
2023 return isl_aff_free(aff
);
2032 /* Exploit the equalities in "eq" to simplify the affine expression
2033 * and the expressions of the integer divisions in the local space.
2034 * The integer divisions in this local space are assumed to appear
2035 * as regular dimensions in "eq".
2037 static __isl_give isl_aff
*isl_aff_substitute_equalities_lifted(
2038 __isl_take isl_aff
*aff
, __isl_take isl_basic_set
*eq
)
2046 if (eq
->n_eq
== 0) {
2047 isl_basic_set_free(eq
);
2051 aff
= isl_aff_cow(aff
);
2055 aff
->ls
= isl_local_space_substitute_equalities(aff
->ls
,
2056 isl_basic_set_copy(eq
));
2057 aff
->v
= isl_vec_cow(aff
->v
);
2058 if (!aff
->ls
|| !aff
->v
)
2061 total
= 1 + isl_space_dim(eq
->dim
, isl_dim_all
);
2063 for (i
= 0; i
< eq
->n_eq
; ++i
) {
2064 j
= isl_seq_last_non_zero(eq
->eq
[i
], total
+ n_div
);
2065 if (j
< 0 || j
== 0 || j
>= total
)
2068 isl_seq_elim(aff
->v
->el
+ 1, eq
->eq
[i
], j
, total
,
2072 isl_basic_set_free(eq
);
2073 aff
= isl_aff_normalize(aff
);
2076 isl_basic_set_free(eq
);
2081 /* Exploit the equalities in "eq" to simplify the affine expression
2082 * and the expressions of the integer divisions in the local space.
2084 static __isl_give isl_aff
*isl_aff_substitute_equalities(
2085 __isl_take isl_aff
*aff
, __isl_take isl_basic_set
*eq
)
2091 n_div
= isl_local_space_dim(aff
->ls
, isl_dim_div
);
2093 eq
= isl_basic_set_add_dims(eq
, isl_dim_set
, n_div
);
2094 return isl_aff_substitute_equalities_lifted(aff
, eq
);
2096 isl_basic_set_free(eq
);
2101 /* Look for equalities among the variables shared by context and aff
2102 * and the integer divisions of aff, if any.
2103 * The equalities are then used to eliminate coefficients and/or integer
2104 * divisions from aff.
2106 __isl_give isl_aff
*isl_aff_gist(__isl_take isl_aff
*aff
,
2107 __isl_take isl_set
*context
)
2109 isl_basic_set
*hull
;
2114 n_div
= isl_local_space_dim(aff
->ls
, isl_dim_div
);
2116 isl_basic_set
*bset
;
2117 isl_local_space
*ls
;
2118 context
= isl_set_add_dims(context
, isl_dim_set
, n_div
);
2119 ls
= isl_aff_get_domain_local_space(aff
);
2120 bset
= isl_basic_set_from_local_space(ls
);
2121 bset
= isl_basic_set_lift(bset
);
2122 bset
= isl_basic_set_flatten(bset
);
2123 context
= isl_set_intersect(context
,
2124 isl_set_from_basic_set(bset
));
2127 hull
= isl_set_affine_hull(context
);
2128 return isl_aff_substitute_equalities_lifted(aff
, hull
);
2131 isl_set_free(context
);
2135 __isl_give isl_aff
*isl_aff_gist_params(__isl_take isl_aff
*aff
,
2136 __isl_take isl_set
*context
)
2138 isl_set
*dom_context
= isl_set_universe(isl_aff_get_domain_space(aff
));
2139 dom_context
= isl_set_intersect_params(dom_context
, context
);
2140 return isl_aff_gist(aff
, dom_context
);
2143 /* Return a basic set containing those elements in the space
2144 * of aff where it is non-negative.
2145 * If "rational" is set, then return a rational basic set.
2147 * If "aff" is NaN, then it is not non-negative (it's not negative either).
2149 static __isl_give isl_basic_set
*aff_nonneg_basic_set(
2150 __isl_take isl_aff
*aff
, int rational
)
2152 isl_constraint
*ineq
;
2153 isl_basic_set
*bset
;
2157 if (isl_aff_is_nan(aff
)) {
2158 isl_space
*space
= isl_aff_get_domain_space(aff
);
2160 return isl_basic_set_empty(space
);
2163 ineq
= isl_inequality_from_aff(aff
);
2165 bset
= isl_basic_set_from_constraint(ineq
);
2167 bset
= isl_basic_set_set_rational(bset
);
2168 bset
= isl_basic_set_simplify(bset
);
2172 /* Return a basic set containing those elements in the space
2173 * of aff where it is non-negative.
2175 __isl_give isl_basic_set
*isl_aff_nonneg_basic_set(__isl_take isl_aff
*aff
)
2177 return aff_nonneg_basic_set(aff
, 0);
2180 /* Return a basic set containing those elements in the domain space
2181 * of aff where it is negative.
2183 __isl_give isl_basic_set
*isl_aff_neg_basic_set(__isl_take isl_aff
*aff
)
2185 aff
= isl_aff_neg(aff
);
2186 aff
= isl_aff_add_constant_num_si(aff
, -1);
2187 return isl_aff_nonneg_basic_set(aff
);
2190 /* Return a basic set containing those elements in the space
2191 * of aff where it is zero.
2192 * If "rational" is set, then return a rational basic set.
2194 * If "aff" is NaN, then it is not zero.
2196 static __isl_give isl_basic_set
*aff_zero_basic_set(__isl_take isl_aff
*aff
,
2199 isl_constraint
*ineq
;
2200 isl_basic_set
*bset
;
2204 if (isl_aff_is_nan(aff
)) {
2205 isl_space
*space
= isl_aff_get_domain_space(aff
);
2207 return isl_basic_set_empty(space
);
2210 ineq
= isl_equality_from_aff(aff
);
2212 bset
= isl_basic_set_from_constraint(ineq
);
2214 bset
= isl_basic_set_set_rational(bset
);
2215 bset
= isl_basic_set_simplify(bset
);
2219 /* Return a basic set containing those elements in the space
2220 * of aff where it is zero.
2222 __isl_give isl_basic_set
*isl_aff_zero_basic_set(__isl_take isl_aff
*aff
)
2224 return aff_zero_basic_set(aff
, 0);
2227 /* Return a basic set containing those elements in the shared space
2228 * of aff1 and aff2 where aff1 is greater than or equal to aff2.
2230 __isl_give isl_basic_set
*isl_aff_ge_basic_set(__isl_take isl_aff
*aff1
,
2231 __isl_take isl_aff
*aff2
)
2233 aff1
= isl_aff_sub(aff1
, aff2
);
2235 return isl_aff_nonneg_basic_set(aff1
);
2238 /* Return a basic set containing those elements in the shared space
2239 * of aff1 and aff2 where aff1 is smaller than or equal to aff2.
2241 __isl_give isl_basic_set
*isl_aff_le_basic_set(__isl_take isl_aff
*aff1
,
2242 __isl_take isl_aff
*aff2
)
2244 return isl_aff_ge_basic_set(aff2
, aff1
);
2247 __isl_give isl_aff
*isl_aff_add_on_domain(__isl_keep isl_set
*dom
,
2248 __isl_take isl_aff
*aff1
, __isl_take isl_aff
*aff2
)
2250 aff1
= isl_aff_add(aff1
, aff2
);
2251 aff1
= isl_aff_gist(aff1
, isl_set_copy(dom
));
2255 int isl_aff_is_empty(__isl_keep isl_aff
*aff
)
2263 /* Check whether the given affine expression has non-zero coefficient
2264 * for any dimension in the given range or if any of these dimensions
2265 * appear with non-zero coefficients in any of the integer divisions
2266 * involved in the affine expression.
2268 int isl_aff_involves_dims(__isl_keep isl_aff
*aff
,
2269 enum isl_dim_type type
, unsigned first
, unsigned n
)
2281 ctx
= isl_aff_get_ctx(aff
);
2282 if (first
+ n
> isl_aff_dim(aff
, type
))
2283 isl_die(ctx
, isl_error_invalid
,
2284 "range out of bounds", return -1);
2286 active
= isl_local_space_get_active(aff
->ls
, aff
->v
->el
+ 2);
2290 first
+= isl_local_space_offset(aff
->ls
, type
) - 1;
2291 for (i
= 0; i
< n
; ++i
)
2292 if (active
[first
+ i
]) {
2305 __isl_give isl_aff
*isl_aff_drop_dims(__isl_take isl_aff
*aff
,
2306 enum isl_dim_type type
, unsigned first
, unsigned n
)
2312 if (type
== isl_dim_out
)
2313 isl_die(aff
->v
->ctx
, isl_error_invalid
,
2314 "cannot drop output/set dimension",
2315 return isl_aff_free(aff
));
2316 if (type
== isl_dim_in
)
2318 if (n
== 0 && !isl_local_space_is_named_or_nested(aff
->ls
, type
))
2321 ctx
= isl_aff_get_ctx(aff
);
2322 if (first
+ n
> isl_local_space_dim(aff
->ls
, type
))
2323 isl_die(ctx
, isl_error_invalid
, "range out of bounds",
2324 return isl_aff_free(aff
));
2326 aff
= isl_aff_cow(aff
);
2330 aff
->ls
= isl_local_space_drop_dims(aff
->ls
, type
, first
, n
);
2332 return isl_aff_free(aff
);
2334 first
+= 1 + isl_local_space_offset(aff
->ls
, type
);
2335 aff
->v
= isl_vec_drop_els(aff
->v
, first
, n
);
2337 return isl_aff_free(aff
);
2342 /* Project the domain of the affine expression onto its parameter space.
2343 * The affine expression may not involve any of the domain dimensions.
2345 __isl_give isl_aff
*isl_aff_project_domain_on_params(__isl_take isl_aff
*aff
)
2351 n
= isl_aff_dim(aff
, isl_dim_in
);
2352 involves
= isl_aff_involves_dims(aff
, isl_dim_in
, 0, n
);
2354 return isl_aff_free(aff
);
2356 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
2357 "affine expression involves some of the domain dimensions",
2358 return isl_aff_free(aff
));
2359 aff
= isl_aff_drop_dims(aff
, isl_dim_in
, 0, n
);
2360 space
= isl_aff_get_domain_space(aff
);
2361 space
= isl_space_params(space
);
2362 aff
= isl_aff_reset_domain_space(aff
, space
);
2366 __isl_give isl_aff
*isl_aff_insert_dims(__isl_take isl_aff
*aff
,
2367 enum isl_dim_type type
, unsigned first
, unsigned n
)
2373 if (type
== isl_dim_out
)
2374 isl_die(aff
->v
->ctx
, isl_error_invalid
,
2375 "cannot insert output/set dimensions",
2376 return isl_aff_free(aff
));
2377 if (type
== isl_dim_in
)
2379 if (n
== 0 && !isl_local_space_is_named_or_nested(aff
->ls
, type
))
2382 ctx
= isl_aff_get_ctx(aff
);
2383 if (first
> isl_local_space_dim(aff
->ls
, type
))
2384 isl_die(ctx
, isl_error_invalid
, "position out of bounds",
2385 return isl_aff_free(aff
));
2387 aff
= isl_aff_cow(aff
);
2391 aff
->ls
= isl_local_space_insert_dims(aff
->ls
, type
, first
, n
);
2393 return isl_aff_free(aff
);
2395 first
+= 1 + isl_local_space_offset(aff
->ls
, type
);
2396 aff
->v
= isl_vec_insert_zero_els(aff
->v
, first
, n
);
2398 return isl_aff_free(aff
);
2403 __isl_give isl_aff
*isl_aff_add_dims(__isl_take isl_aff
*aff
,
2404 enum isl_dim_type type
, unsigned n
)
2408 pos
= isl_aff_dim(aff
, type
);
2410 return isl_aff_insert_dims(aff
, type
, pos
, n
);
2413 __isl_give isl_pw_aff
*isl_pw_aff_add_dims(__isl_take isl_pw_aff
*pwaff
,
2414 enum isl_dim_type type
, unsigned n
)
2418 pos
= isl_pw_aff_dim(pwaff
, type
);
2420 return isl_pw_aff_insert_dims(pwaff
, type
, pos
, n
);
2423 /* Move the "n" dimensions of "src_type" starting at "src_pos" of "aff"
2424 * to dimensions of "dst_type" at "dst_pos".
2426 * We only support moving input dimensions to parameters and vice versa.
2428 __isl_give isl_aff
*isl_aff_move_dims(__isl_take isl_aff
*aff
,
2429 enum isl_dim_type dst_type
, unsigned dst_pos
,
2430 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
2438 !isl_local_space_is_named_or_nested(aff
->ls
, src_type
) &&
2439 !isl_local_space_is_named_or_nested(aff
->ls
, dst_type
))
2442 if (dst_type
== isl_dim_out
|| src_type
== isl_dim_out
)
2443 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
2444 "cannot move output/set dimension", isl_aff_free(aff
));
2445 if (dst_type
== isl_dim_div
|| src_type
== isl_dim_div
)
2446 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
2447 "cannot move divs", isl_aff_free(aff
));
2448 if (dst_type
== isl_dim_in
)
2449 dst_type
= isl_dim_set
;
2450 if (src_type
== isl_dim_in
)
2451 src_type
= isl_dim_set
;
2453 if (src_pos
+ n
> isl_local_space_dim(aff
->ls
, src_type
))
2454 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
2455 "range out of bounds", isl_aff_free(aff
));
2456 if (dst_type
== src_type
)
2457 isl_die(isl_aff_get_ctx(aff
), isl_error_unsupported
,
2458 "moving dims within the same type not supported",
2461 aff
= isl_aff_cow(aff
);
2465 g_src_pos
= 1 + isl_local_space_offset(aff
->ls
, src_type
) + src_pos
;
2466 g_dst_pos
= 1 + isl_local_space_offset(aff
->ls
, dst_type
) + dst_pos
;
2467 if (dst_type
> src_type
)
2470 aff
->v
= isl_vec_move_els(aff
->v
, g_dst_pos
, g_src_pos
, n
);
2471 aff
->ls
= isl_local_space_move_dims(aff
->ls
, dst_type
, dst_pos
,
2472 src_type
, src_pos
, n
);
2473 if (!aff
->v
|| !aff
->ls
)
2474 return isl_aff_free(aff
);
2476 aff
= sort_divs(aff
);
2481 __isl_give isl_pw_aff
*isl_pw_aff_from_aff(__isl_take isl_aff
*aff
)
2483 isl_set
*dom
= isl_set_universe(isl_aff_get_domain_space(aff
));
2484 return isl_pw_aff_alloc(dom
, aff
);
2488 #define PW isl_pw_aff
2492 #define EL_IS_ZERO is_empty
2496 #define IS_ZERO is_empty
2499 #undef DEFAULT_IS_ZERO
2500 #define DEFAULT_IS_ZERO 0
2507 #include <isl_pw_templ.c>
2509 static __isl_give isl_set
*align_params_pw_pw_set_and(
2510 __isl_take isl_pw_aff
*pwaff1
, __isl_take isl_pw_aff
*pwaff2
,
2511 __isl_give isl_set
*(*fn
)(__isl_take isl_pw_aff
*pwaff1
,
2512 __isl_take isl_pw_aff
*pwaff2
))
2514 if (!pwaff1
|| !pwaff2
)
2516 if (isl_space_match(pwaff1
->dim
, isl_dim_param
,
2517 pwaff2
->dim
, isl_dim_param
))
2518 return fn(pwaff1
, pwaff2
);
2519 if (!isl_space_has_named_params(pwaff1
->dim
) ||
2520 !isl_space_has_named_params(pwaff2
->dim
))
2521 isl_die(isl_pw_aff_get_ctx(pwaff1
), isl_error_invalid
,
2522 "unaligned unnamed parameters", goto error
);
2523 pwaff1
= isl_pw_aff_align_params(pwaff1
, isl_pw_aff_get_space(pwaff2
));
2524 pwaff2
= isl_pw_aff_align_params(pwaff2
, isl_pw_aff_get_space(pwaff1
));
2525 return fn(pwaff1
, pwaff2
);
2527 isl_pw_aff_free(pwaff1
);
2528 isl_pw_aff_free(pwaff2
);
2532 /* Compute a piecewise quasi-affine expression with a domain that
2533 * is the union of those of pwaff1 and pwaff2 and such that on each
2534 * cell, the quasi-affine expression is the better (according to cmp)
2535 * of those of pwaff1 and pwaff2. If only one of pwaff1 or pwaff2
2536 * is defined on a given cell, then the associated expression
2537 * is the defined one.
2539 static __isl_give isl_pw_aff
*pw_aff_union_opt(__isl_take isl_pw_aff
*pwaff1
,
2540 __isl_take isl_pw_aff
*pwaff2
,
2541 __isl_give isl_basic_set
*(*cmp
)(__isl_take isl_aff
*aff1
,
2542 __isl_take isl_aff
*aff2
))
2549 if (!pwaff1
|| !pwaff2
)
2552 ctx
= isl_space_get_ctx(pwaff1
->dim
);
2553 if (!isl_space_is_equal(pwaff1
->dim
, pwaff2
->dim
))
2554 isl_die(ctx
, isl_error_invalid
,
2555 "arguments should live in same space", goto error
);
2557 if (isl_pw_aff_is_empty(pwaff1
)) {
2558 isl_pw_aff_free(pwaff1
);
2562 if (isl_pw_aff_is_empty(pwaff2
)) {
2563 isl_pw_aff_free(pwaff2
);
2567 n
= 2 * (pwaff1
->n
+ 1) * (pwaff2
->n
+ 1);
2568 res
= isl_pw_aff_alloc_size(isl_space_copy(pwaff1
->dim
), n
);
2570 for (i
= 0; i
< pwaff1
->n
; ++i
) {
2571 set
= isl_set_copy(pwaff1
->p
[i
].set
);
2572 for (j
= 0; j
< pwaff2
->n
; ++j
) {
2573 struct isl_set
*common
;
2576 common
= isl_set_intersect(
2577 isl_set_copy(pwaff1
->p
[i
].set
),
2578 isl_set_copy(pwaff2
->p
[j
].set
));
2579 better
= isl_set_from_basic_set(cmp(
2580 isl_aff_copy(pwaff2
->p
[j
].aff
),
2581 isl_aff_copy(pwaff1
->p
[i
].aff
)));
2582 better
= isl_set_intersect(common
, better
);
2583 if (isl_set_plain_is_empty(better
)) {
2584 isl_set_free(better
);
2587 set
= isl_set_subtract(set
, isl_set_copy(better
));
2589 res
= isl_pw_aff_add_piece(res
, better
,
2590 isl_aff_copy(pwaff2
->p
[j
].aff
));
2592 res
= isl_pw_aff_add_piece(res
, set
,
2593 isl_aff_copy(pwaff1
->p
[i
].aff
));
2596 for (j
= 0; j
< pwaff2
->n
; ++j
) {
2597 set
= isl_set_copy(pwaff2
->p
[j
].set
);
2598 for (i
= 0; i
< pwaff1
->n
; ++i
)
2599 set
= isl_set_subtract(set
,
2600 isl_set_copy(pwaff1
->p
[i
].set
));
2601 res
= isl_pw_aff_add_piece(res
, set
,
2602 isl_aff_copy(pwaff2
->p
[j
].aff
));
2605 isl_pw_aff_free(pwaff1
);
2606 isl_pw_aff_free(pwaff2
);
2610 isl_pw_aff_free(pwaff1
);
2611 isl_pw_aff_free(pwaff2
);
2615 /* Compute a piecewise quasi-affine expression with a domain that
2616 * is the union of those of pwaff1 and pwaff2 and such that on each
2617 * cell, the quasi-affine expression is the maximum of those of pwaff1
2618 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
2619 * cell, then the associated expression is the defined one.
2621 static __isl_give isl_pw_aff
*pw_aff_union_max(__isl_take isl_pw_aff
*pwaff1
,
2622 __isl_take isl_pw_aff
*pwaff2
)
2624 return pw_aff_union_opt(pwaff1
, pwaff2
, &isl_aff_ge_basic_set
);
2627 __isl_give isl_pw_aff
*isl_pw_aff_union_max(__isl_take isl_pw_aff
*pwaff1
,
2628 __isl_take isl_pw_aff
*pwaff2
)
2630 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
,
2634 /* Compute a piecewise quasi-affine expression with a domain that
2635 * is the union of those of pwaff1 and pwaff2 and such that on each
2636 * cell, the quasi-affine expression is the minimum of those of pwaff1
2637 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
2638 * cell, then the associated expression is the defined one.
2640 static __isl_give isl_pw_aff
*pw_aff_union_min(__isl_take isl_pw_aff
*pwaff1
,
2641 __isl_take isl_pw_aff
*pwaff2
)
2643 return pw_aff_union_opt(pwaff1
, pwaff2
, &isl_aff_le_basic_set
);
2646 __isl_give isl_pw_aff
*isl_pw_aff_union_min(__isl_take isl_pw_aff
*pwaff1
,
2647 __isl_take isl_pw_aff
*pwaff2
)
2649 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
,
2653 __isl_give isl_pw_aff
*isl_pw_aff_union_opt(__isl_take isl_pw_aff
*pwaff1
,
2654 __isl_take isl_pw_aff
*pwaff2
, int max
)
2657 return isl_pw_aff_union_max(pwaff1
, pwaff2
);
2659 return isl_pw_aff_union_min(pwaff1
, pwaff2
);
2662 /* Construct a map with as domain the domain of pwaff and
2663 * one-dimensional range corresponding to the affine expressions.
2665 static __isl_give isl_map
*map_from_pw_aff(__isl_take isl_pw_aff
*pwaff
)
2674 dim
= isl_pw_aff_get_space(pwaff
);
2675 map
= isl_map_empty(dim
);
2677 for (i
= 0; i
< pwaff
->n
; ++i
) {
2678 isl_basic_map
*bmap
;
2681 bmap
= isl_basic_map_from_aff(isl_aff_copy(pwaff
->p
[i
].aff
));
2682 map_i
= isl_map_from_basic_map(bmap
);
2683 map_i
= isl_map_intersect_domain(map_i
,
2684 isl_set_copy(pwaff
->p
[i
].set
));
2685 map
= isl_map_union_disjoint(map
, map_i
);
2688 isl_pw_aff_free(pwaff
);
2693 /* Construct a map with as domain the domain of pwaff and
2694 * one-dimensional range corresponding to the affine expressions.
2696 __isl_give isl_map
*isl_map_from_pw_aff(__isl_take isl_pw_aff
*pwaff
)
2700 if (isl_space_is_set(pwaff
->dim
))
2701 isl_die(isl_pw_aff_get_ctx(pwaff
), isl_error_invalid
,
2702 "space of input is not a map", goto error
);
2703 return map_from_pw_aff(pwaff
);
2705 isl_pw_aff_free(pwaff
);
2709 /* Construct a one-dimensional set with as parameter domain
2710 * the domain of pwaff and the single set dimension
2711 * corresponding to the affine expressions.
2713 __isl_give isl_set
*isl_set_from_pw_aff(__isl_take isl_pw_aff
*pwaff
)
2717 if (!isl_space_is_set(pwaff
->dim
))
2718 isl_die(isl_pw_aff_get_ctx(pwaff
), isl_error_invalid
,
2719 "space of input is not a set", goto error
);
2720 return map_from_pw_aff(pwaff
);
2722 isl_pw_aff_free(pwaff
);
2726 /* Return a set containing those elements in the domain
2727 * of pwaff where it is non-negative.
2729 __isl_give isl_set
*isl_pw_aff_nonneg_set(__isl_take isl_pw_aff
*pwaff
)
2737 set
= isl_set_empty(isl_pw_aff_get_domain_space(pwaff
));
2739 for (i
= 0; i
< pwaff
->n
; ++i
) {
2740 isl_basic_set
*bset
;
2744 rational
= isl_set_has_rational(pwaff
->p
[i
].set
);
2745 bset
= aff_nonneg_basic_set(isl_aff_copy(pwaff
->p
[i
].aff
),
2747 set_i
= isl_set_from_basic_set(bset
);
2748 set_i
= isl_set_intersect(set_i
, isl_set_copy(pwaff
->p
[i
].set
));
2749 set
= isl_set_union_disjoint(set
, set_i
);
2752 isl_pw_aff_free(pwaff
);
2757 /* Return a set containing those elements in the domain
2758 * of pwaff where it is zero (if complement is 0) or not zero
2759 * (if complement is 1).
2761 * The pieces with a NaN never belong to the result since
2762 * NaN is neither zero nor non-zero.
2764 static __isl_give isl_set
*pw_aff_zero_set(__isl_take isl_pw_aff
*pwaff
,
2773 set
= isl_set_empty(isl_pw_aff_get_domain_space(pwaff
));
2775 for (i
= 0; i
< pwaff
->n
; ++i
) {
2776 isl_basic_set
*bset
;
2777 isl_set
*set_i
, *zero
;
2780 if (isl_aff_is_nan(pwaff
->p
[i
].aff
))
2783 rational
= isl_set_has_rational(pwaff
->p
[i
].set
);
2784 bset
= aff_zero_basic_set(isl_aff_copy(pwaff
->p
[i
].aff
),
2786 zero
= isl_set_from_basic_set(bset
);
2787 set_i
= isl_set_copy(pwaff
->p
[i
].set
);
2789 set_i
= isl_set_subtract(set_i
, zero
);
2791 set_i
= isl_set_intersect(set_i
, zero
);
2792 set
= isl_set_union_disjoint(set
, set_i
);
2795 isl_pw_aff_free(pwaff
);
2800 /* Return a set containing those elements in the domain
2801 * of pwaff where it is zero.
2803 __isl_give isl_set
*isl_pw_aff_zero_set(__isl_take isl_pw_aff
*pwaff
)
2805 return pw_aff_zero_set(pwaff
, 0);
2808 /* Return a set containing those elements in the domain
2809 * of pwaff where it is not zero.
2811 __isl_give isl_set
*isl_pw_aff_non_zero_set(__isl_take isl_pw_aff
*pwaff
)
2813 return pw_aff_zero_set(pwaff
, 1);
2816 /* Return a set containing those elements in the shared domain
2817 * of pwaff1 and pwaff2 where pwaff1 is greater than (or equal) to pwaff2.
2819 * We compute the difference on the shared domain and then construct
2820 * the set of values where this difference is non-negative.
2821 * If strict is set, we first subtract 1 from the difference.
2822 * If equal is set, we only return the elements where pwaff1 and pwaff2
2825 static __isl_give isl_set
*pw_aff_gte_set(__isl_take isl_pw_aff
*pwaff1
,
2826 __isl_take isl_pw_aff
*pwaff2
, int strict
, int equal
)
2828 isl_set
*set1
, *set2
;
2830 set1
= isl_pw_aff_domain(isl_pw_aff_copy(pwaff1
));
2831 set2
= isl_pw_aff_domain(isl_pw_aff_copy(pwaff2
));
2832 set1
= isl_set_intersect(set1
, set2
);
2833 pwaff1
= isl_pw_aff_intersect_domain(pwaff1
, isl_set_copy(set1
));
2834 pwaff2
= isl_pw_aff_intersect_domain(pwaff2
, isl_set_copy(set1
));
2835 pwaff1
= isl_pw_aff_add(pwaff1
, isl_pw_aff_neg(pwaff2
));
2838 isl_space
*dim
= isl_set_get_space(set1
);
2840 aff
= isl_aff_zero_on_domain(isl_local_space_from_space(dim
));
2841 aff
= isl_aff_add_constant_si(aff
, -1);
2842 pwaff1
= isl_pw_aff_add(pwaff1
, isl_pw_aff_alloc(set1
, aff
));
2847 return isl_pw_aff_zero_set(pwaff1
);
2848 return isl_pw_aff_nonneg_set(pwaff1
);
2851 /* Return a set containing those elements in the shared domain
2852 * of pwaff1 and pwaff2 where pwaff1 is equal to pwaff2.
2854 static __isl_give isl_set
*pw_aff_eq_set(__isl_take isl_pw_aff
*pwaff1
,
2855 __isl_take isl_pw_aff
*pwaff2
)
2857 return pw_aff_gte_set(pwaff1
, pwaff2
, 0, 1);
2860 __isl_give isl_set
*isl_pw_aff_eq_set(__isl_take isl_pw_aff
*pwaff1
,
2861 __isl_take isl_pw_aff
*pwaff2
)
2863 return align_params_pw_pw_set_and(pwaff1
, pwaff2
, &pw_aff_eq_set
);
2866 /* Return a set containing those elements in the shared domain
2867 * of pwaff1 and pwaff2 where pwaff1 is greater than or equal to pwaff2.
2869 static __isl_give isl_set
*pw_aff_ge_set(__isl_take isl_pw_aff
*pwaff1
,
2870 __isl_take isl_pw_aff
*pwaff2
)
2872 return pw_aff_gte_set(pwaff1
, pwaff2
, 0, 0);
2875 __isl_give isl_set
*isl_pw_aff_ge_set(__isl_take isl_pw_aff
*pwaff1
,
2876 __isl_take isl_pw_aff
*pwaff2
)
2878 return align_params_pw_pw_set_and(pwaff1
, pwaff2
, &pw_aff_ge_set
);
2881 /* Return a set containing those elements in the shared domain
2882 * of pwaff1 and pwaff2 where pwaff1 is strictly greater than pwaff2.
2884 static __isl_give isl_set
*pw_aff_gt_set(__isl_take isl_pw_aff
*pwaff1
,
2885 __isl_take isl_pw_aff
*pwaff2
)
2887 return pw_aff_gte_set(pwaff1
, pwaff2
, 1, 0);
2890 __isl_give isl_set
*isl_pw_aff_gt_set(__isl_take isl_pw_aff
*pwaff1
,
2891 __isl_take isl_pw_aff
*pwaff2
)
2893 return align_params_pw_pw_set_and(pwaff1
, pwaff2
, &pw_aff_gt_set
);
2896 __isl_give isl_set
*isl_pw_aff_le_set(__isl_take isl_pw_aff
*pwaff1
,
2897 __isl_take isl_pw_aff
*pwaff2
)
2899 return isl_pw_aff_ge_set(pwaff2
, pwaff1
);
2902 __isl_give isl_set
*isl_pw_aff_lt_set(__isl_take isl_pw_aff
*pwaff1
,
2903 __isl_take isl_pw_aff
*pwaff2
)
2905 return isl_pw_aff_gt_set(pwaff2
, pwaff1
);
2908 /* Return a set containing those elements in the shared domain
2909 * of the elements of list1 and list2 where each element in list1
2910 * has the relation specified by "fn" with each element in list2.
2912 static __isl_give isl_set
*pw_aff_list_set(__isl_take isl_pw_aff_list
*list1
,
2913 __isl_take isl_pw_aff_list
*list2
,
2914 __isl_give isl_set
*(*fn
)(__isl_take isl_pw_aff
*pwaff1
,
2915 __isl_take isl_pw_aff
*pwaff2
))
2921 if (!list1
|| !list2
)
2924 ctx
= isl_pw_aff_list_get_ctx(list1
);
2925 if (list1
->n
< 1 || list2
->n
< 1)
2926 isl_die(ctx
, isl_error_invalid
,
2927 "list should contain at least one element", goto error
);
2929 set
= isl_set_universe(isl_pw_aff_get_domain_space(list1
->p
[0]));
2930 for (i
= 0; i
< list1
->n
; ++i
)
2931 for (j
= 0; j
< list2
->n
; ++j
) {
2934 set_ij
= fn(isl_pw_aff_copy(list1
->p
[i
]),
2935 isl_pw_aff_copy(list2
->p
[j
]));
2936 set
= isl_set_intersect(set
, set_ij
);
2939 isl_pw_aff_list_free(list1
);
2940 isl_pw_aff_list_free(list2
);
2943 isl_pw_aff_list_free(list1
);
2944 isl_pw_aff_list_free(list2
);
2948 /* Return a set containing those elements in the shared domain
2949 * of the elements of list1 and list2 where each element in list1
2950 * is equal to each element in list2.
2952 __isl_give isl_set
*isl_pw_aff_list_eq_set(__isl_take isl_pw_aff_list
*list1
,
2953 __isl_take isl_pw_aff_list
*list2
)
2955 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_eq_set
);
2958 __isl_give isl_set
*isl_pw_aff_list_ne_set(__isl_take isl_pw_aff_list
*list1
,
2959 __isl_take isl_pw_aff_list
*list2
)
2961 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_ne_set
);
2964 /* Return a set containing those elements in the shared domain
2965 * of the elements of list1 and list2 where each element in list1
2966 * is less than or equal to each element in list2.
2968 __isl_give isl_set
*isl_pw_aff_list_le_set(__isl_take isl_pw_aff_list
*list1
,
2969 __isl_take isl_pw_aff_list
*list2
)
2971 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_le_set
);
2974 __isl_give isl_set
*isl_pw_aff_list_lt_set(__isl_take isl_pw_aff_list
*list1
,
2975 __isl_take isl_pw_aff_list
*list2
)
2977 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_lt_set
);
2980 __isl_give isl_set
*isl_pw_aff_list_ge_set(__isl_take isl_pw_aff_list
*list1
,
2981 __isl_take isl_pw_aff_list
*list2
)
2983 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_ge_set
);
2986 __isl_give isl_set
*isl_pw_aff_list_gt_set(__isl_take isl_pw_aff_list
*list1
,
2987 __isl_take isl_pw_aff_list
*list2
)
2989 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_gt_set
);
2993 /* Return a set containing those elements in the shared domain
2994 * of pwaff1 and pwaff2 where pwaff1 is not equal to pwaff2.
2996 static __isl_give isl_set
*pw_aff_ne_set(__isl_take isl_pw_aff
*pwaff1
,
2997 __isl_take isl_pw_aff
*pwaff2
)
2999 isl_set
*set_lt
, *set_gt
;
3001 set_lt
= isl_pw_aff_lt_set(isl_pw_aff_copy(pwaff1
),
3002 isl_pw_aff_copy(pwaff2
));
3003 set_gt
= isl_pw_aff_gt_set(pwaff1
, pwaff2
);
3004 return isl_set_union_disjoint(set_lt
, set_gt
);
3007 __isl_give isl_set
*isl_pw_aff_ne_set(__isl_take isl_pw_aff
*pwaff1
,
3008 __isl_take isl_pw_aff
*pwaff2
)
3010 return align_params_pw_pw_set_and(pwaff1
, pwaff2
, &pw_aff_ne_set
);
3013 __isl_give isl_pw_aff
*isl_pw_aff_scale_down(__isl_take isl_pw_aff
*pwaff
,
3018 if (isl_int_is_one(v
))
3020 if (!isl_int_is_pos(v
))
3021 isl_die(isl_pw_aff_get_ctx(pwaff
), isl_error_invalid
,
3022 "factor needs to be positive",
3023 return isl_pw_aff_free(pwaff
));
3024 pwaff
= isl_pw_aff_cow(pwaff
);
3030 for (i
= 0; i
< pwaff
->n
; ++i
) {
3031 pwaff
->p
[i
].aff
= isl_aff_scale_down(pwaff
->p
[i
].aff
, v
);
3032 if (!pwaff
->p
[i
].aff
)
3033 return isl_pw_aff_free(pwaff
);
3039 __isl_give isl_pw_aff
*isl_pw_aff_floor(__isl_take isl_pw_aff
*pwaff
)
3043 pwaff
= isl_pw_aff_cow(pwaff
);
3049 for (i
= 0; i
< pwaff
->n
; ++i
) {
3050 pwaff
->p
[i
].aff
= isl_aff_floor(pwaff
->p
[i
].aff
);
3051 if (!pwaff
->p
[i
].aff
)
3052 return isl_pw_aff_free(pwaff
);
3058 __isl_give isl_pw_aff
*isl_pw_aff_ceil(__isl_take isl_pw_aff
*pwaff
)
3062 pwaff
= isl_pw_aff_cow(pwaff
);
3068 for (i
= 0; i
< pwaff
->n
; ++i
) {
3069 pwaff
->p
[i
].aff
= isl_aff_ceil(pwaff
->p
[i
].aff
);
3070 if (!pwaff
->p
[i
].aff
)
3071 return isl_pw_aff_free(pwaff
);
3077 /* Assuming that "cond1" and "cond2" are disjoint,
3078 * return an affine expression that is equal to pwaff1 on cond1
3079 * and to pwaff2 on cond2.
3081 static __isl_give isl_pw_aff
*isl_pw_aff_select(
3082 __isl_take isl_set
*cond1
, __isl_take isl_pw_aff
*pwaff1
,
3083 __isl_take isl_set
*cond2
, __isl_take isl_pw_aff
*pwaff2
)
3085 pwaff1
= isl_pw_aff_intersect_domain(pwaff1
, cond1
);
3086 pwaff2
= isl_pw_aff_intersect_domain(pwaff2
, cond2
);
3088 return isl_pw_aff_add_disjoint(pwaff1
, pwaff2
);
3091 /* Return an affine expression that is equal to pwaff_true for elements
3092 * where "cond" is non-zero and to pwaff_false for elements where "cond"
3094 * That is, return cond ? pwaff_true : pwaff_false;
3096 * If "cond" involves and NaN, then we conservatively return a NaN
3097 * on its entire domain. In principle, we could consider the pieces
3098 * where it is NaN separately from those where it is not.
3100 __isl_give isl_pw_aff
*isl_pw_aff_cond(__isl_take isl_pw_aff
*cond
,
3101 __isl_take isl_pw_aff
*pwaff_true
, __isl_take isl_pw_aff
*pwaff_false
)
3103 isl_set
*cond_true
, *cond_false
;
3107 if (isl_pw_aff_involves_nan(cond
)) {
3108 isl_space
*space
= isl_pw_aff_get_domain_space(cond
);
3109 isl_local_space
*ls
= isl_local_space_from_space(space
);
3110 isl_pw_aff_free(cond
);
3111 isl_pw_aff_free(pwaff_true
);
3112 isl_pw_aff_free(pwaff_false
);
3113 return isl_pw_aff_nan_on_domain(ls
);
3116 cond_true
= isl_pw_aff_non_zero_set(isl_pw_aff_copy(cond
));
3117 cond_false
= isl_pw_aff_zero_set(cond
);
3118 return isl_pw_aff_select(cond_true
, pwaff_true
,
3119 cond_false
, pwaff_false
);
3121 isl_pw_aff_free(cond
);
3122 isl_pw_aff_free(pwaff_true
);
3123 isl_pw_aff_free(pwaff_false
);
3127 int isl_aff_is_cst(__isl_keep isl_aff
*aff
)
3132 return isl_seq_first_non_zero(aff
->v
->el
+ 2, aff
->v
->size
- 2) == -1;
3135 /* Check whether pwaff is a piecewise constant.
3137 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff
*pwaff
)
3144 for (i
= 0; i
< pwaff
->n
; ++i
) {
3145 int is_cst
= isl_aff_is_cst(pwaff
->p
[i
].aff
);
3146 if (is_cst
< 0 || !is_cst
)
3153 /* Return the product of "aff1" and "aff2".
3155 * If either of the two is NaN, then the result is NaN.
3157 * Otherwise, at least one of "aff1" or "aff2" needs to be a constant.
3159 __isl_give isl_aff
*isl_aff_mul(__isl_take isl_aff
*aff1
,
3160 __isl_take isl_aff
*aff2
)
3165 if (isl_aff_is_nan(aff1
)) {
3169 if (isl_aff_is_nan(aff2
)) {
3174 if (!isl_aff_is_cst(aff2
) && isl_aff_is_cst(aff1
))
3175 return isl_aff_mul(aff2
, aff1
);
3177 if (!isl_aff_is_cst(aff2
))
3178 isl_die(isl_aff_get_ctx(aff1
), isl_error_invalid
,
3179 "at least one affine expression should be constant",
3182 aff1
= isl_aff_cow(aff1
);
3186 aff1
= isl_aff_scale(aff1
, aff2
->v
->el
[1]);
3187 aff1
= isl_aff_scale_down(aff1
, aff2
->v
->el
[0]);
3197 /* Divide "aff1" by "aff2", assuming "aff2" is a constant.
3199 * If either of the two is NaN, then the result is NaN.
3201 __isl_give isl_aff
*isl_aff_div(__isl_take isl_aff
*aff1
,
3202 __isl_take isl_aff
*aff2
)
3210 if (isl_aff_is_nan(aff1
)) {
3214 if (isl_aff_is_nan(aff2
)) {
3219 is_cst
= isl_aff_is_cst(aff2
);
3223 isl_die(isl_aff_get_ctx(aff2
), isl_error_invalid
,
3224 "second argument should be a constant", goto error
);
3229 neg
= isl_int_is_neg(aff2
->v
->el
[1]);
3231 isl_int_neg(aff2
->v
->el
[0], aff2
->v
->el
[0]);
3232 isl_int_neg(aff2
->v
->el
[1], aff2
->v
->el
[1]);
3235 aff1
= isl_aff_scale(aff1
, aff2
->v
->el
[0]);
3236 aff1
= isl_aff_scale_down(aff1
, aff2
->v
->el
[1]);
3239 isl_int_neg(aff2
->v
->el
[0], aff2
->v
->el
[0]);
3240 isl_int_neg(aff2
->v
->el
[1], aff2
->v
->el
[1]);
3251 static __isl_give isl_pw_aff
*pw_aff_add(__isl_take isl_pw_aff
*pwaff1
,
3252 __isl_take isl_pw_aff
*pwaff2
)
3254 return isl_pw_aff_on_shared_domain(pwaff1
, pwaff2
, &isl_aff_add
);
3257 __isl_give isl_pw_aff
*isl_pw_aff_add(__isl_take isl_pw_aff
*pwaff1
,
3258 __isl_take isl_pw_aff
*pwaff2
)
3260 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
, &pw_aff_add
);
3263 __isl_give isl_pw_aff
*isl_pw_aff_union_add(__isl_take isl_pw_aff
*pwaff1
,
3264 __isl_take isl_pw_aff
*pwaff2
)
3266 return isl_pw_aff_union_add_(pwaff1
, pwaff2
);
3269 static __isl_give isl_pw_aff
*pw_aff_mul(__isl_take isl_pw_aff
*pwaff1
,
3270 __isl_take isl_pw_aff
*pwaff2
)
3272 return isl_pw_aff_on_shared_domain(pwaff1
, pwaff2
, &isl_aff_mul
);
3275 __isl_give isl_pw_aff
*isl_pw_aff_mul(__isl_take isl_pw_aff
*pwaff1
,
3276 __isl_take isl_pw_aff
*pwaff2
)
3278 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
, &pw_aff_mul
);
3281 static __isl_give isl_pw_aff
*pw_aff_div(__isl_take isl_pw_aff
*pa1
,
3282 __isl_take isl_pw_aff
*pa2
)
3284 return isl_pw_aff_on_shared_domain(pa1
, pa2
, &isl_aff_div
);
3287 /* Divide "pa1" by "pa2", assuming "pa2" is a piecewise constant.
3289 __isl_give isl_pw_aff
*isl_pw_aff_div(__isl_take isl_pw_aff
*pa1
,
3290 __isl_take isl_pw_aff
*pa2
)
3294 is_cst
= isl_pw_aff_is_cst(pa2
);
3298 isl_die(isl_pw_aff_get_ctx(pa2
), isl_error_invalid
,
3299 "second argument should be a piecewise constant",
3301 return isl_pw_aff_align_params_pw_pw_and(pa1
, pa2
, &pw_aff_div
);
3303 isl_pw_aff_free(pa1
);
3304 isl_pw_aff_free(pa2
);
3308 /* Compute the quotient of the integer division of "pa1" by "pa2"
3309 * with rounding towards zero.
3310 * "pa2" is assumed to be a piecewise constant.
3312 * In particular, return
3314 * pa1 >= 0 ? floor(pa1/pa2) : ceil(pa1/pa2)
3317 __isl_give isl_pw_aff
*isl_pw_aff_tdiv_q(__isl_take isl_pw_aff
*pa1
,
3318 __isl_take isl_pw_aff
*pa2
)
3324 is_cst
= isl_pw_aff_is_cst(pa2
);
3328 isl_die(isl_pw_aff_get_ctx(pa2
), isl_error_invalid
,
3329 "second argument should be a piecewise constant",
3332 pa1
= isl_pw_aff_div(pa1
, pa2
);
3334 cond
= isl_pw_aff_nonneg_set(isl_pw_aff_copy(pa1
));
3335 f
= isl_pw_aff_floor(isl_pw_aff_copy(pa1
));
3336 c
= isl_pw_aff_ceil(pa1
);
3337 return isl_pw_aff_cond(isl_set_indicator_function(cond
), f
, c
);
3339 isl_pw_aff_free(pa1
);
3340 isl_pw_aff_free(pa2
);
3344 /* Compute the remainder of the integer division of "pa1" by "pa2"
3345 * with rounding towards zero.
3346 * "pa2" is assumed to be a piecewise constant.
3348 * In particular, return
3350 * pa1 - pa2 * (pa1 >= 0 ? floor(pa1/pa2) : ceil(pa1/pa2))
3353 __isl_give isl_pw_aff
*isl_pw_aff_tdiv_r(__isl_take isl_pw_aff
*pa1
,
3354 __isl_take isl_pw_aff
*pa2
)
3359 is_cst
= isl_pw_aff_is_cst(pa2
);
3363 isl_die(isl_pw_aff_get_ctx(pa2
), isl_error_invalid
,
3364 "second argument should be a piecewise constant",
3366 res
= isl_pw_aff_tdiv_q(isl_pw_aff_copy(pa1
), isl_pw_aff_copy(pa2
));
3367 res
= isl_pw_aff_mul(pa2
, res
);
3368 res
= isl_pw_aff_sub(pa1
, res
);
3371 isl_pw_aff_free(pa1
);
3372 isl_pw_aff_free(pa2
);
3376 static __isl_give isl_pw_aff
*pw_aff_min(__isl_take isl_pw_aff
*pwaff1
,
3377 __isl_take isl_pw_aff
*pwaff2
)
3382 dom
= isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1
)),
3383 isl_pw_aff_domain(isl_pw_aff_copy(pwaff2
)));
3384 le
= isl_pw_aff_le_set(isl_pw_aff_copy(pwaff1
),
3385 isl_pw_aff_copy(pwaff2
));
3386 dom
= isl_set_subtract(dom
, isl_set_copy(le
));
3387 return isl_pw_aff_select(le
, pwaff1
, dom
, pwaff2
);
3390 __isl_give isl_pw_aff
*isl_pw_aff_min(__isl_take isl_pw_aff
*pwaff1
,
3391 __isl_take isl_pw_aff
*pwaff2
)
3393 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
, &pw_aff_min
);
3396 static __isl_give isl_pw_aff
*pw_aff_max(__isl_take isl_pw_aff
*pwaff1
,
3397 __isl_take isl_pw_aff
*pwaff2
)
3402 dom
= isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1
)),
3403 isl_pw_aff_domain(isl_pw_aff_copy(pwaff2
)));
3404 ge
= isl_pw_aff_ge_set(isl_pw_aff_copy(pwaff1
),
3405 isl_pw_aff_copy(pwaff2
));
3406 dom
= isl_set_subtract(dom
, isl_set_copy(ge
));
3407 return isl_pw_aff_select(ge
, pwaff1
, dom
, pwaff2
);
3410 __isl_give isl_pw_aff
*isl_pw_aff_max(__isl_take isl_pw_aff
*pwaff1
,
3411 __isl_take isl_pw_aff
*pwaff2
)
3413 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
, &pw_aff_max
);
3416 static __isl_give isl_pw_aff
*pw_aff_list_reduce(
3417 __isl_take isl_pw_aff_list
*list
,
3418 __isl_give isl_pw_aff
*(*fn
)(__isl_take isl_pw_aff
*pwaff1
,
3419 __isl_take isl_pw_aff
*pwaff2
))
3428 ctx
= isl_pw_aff_list_get_ctx(list
);
3430 isl_die(ctx
, isl_error_invalid
,
3431 "list should contain at least one element", goto error
);
3433 res
= isl_pw_aff_copy(list
->p
[0]);
3434 for (i
= 1; i
< list
->n
; ++i
)
3435 res
= fn(res
, isl_pw_aff_copy(list
->p
[i
]));
3437 isl_pw_aff_list_free(list
);
3440 isl_pw_aff_list_free(list
);
3444 /* Return an isl_pw_aff that maps each element in the intersection of the
3445 * domains of the elements of list to the minimal corresponding affine
3448 __isl_give isl_pw_aff
*isl_pw_aff_list_min(__isl_take isl_pw_aff_list
*list
)
3450 return pw_aff_list_reduce(list
, &isl_pw_aff_min
);
3453 /* Return an isl_pw_aff that maps each element in the intersection of the
3454 * domains of the elements of list to the maximal corresponding affine
3457 __isl_give isl_pw_aff
*isl_pw_aff_list_max(__isl_take isl_pw_aff_list
*list
)
3459 return pw_aff_list_reduce(list
, &isl_pw_aff_max
);
3462 /* Mark the domains of "pwaff" as rational.
3464 __isl_give isl_pw_aff
*isl_pw_aff_set_rational(__isl_take isl_pw_aff
*pwaff
)
3468 pwaff
= isl_pw_aff_cow(pwaff
);
3474 for (i
= 0; i
< pwaff
->n
; ++i
) {
3475 pwaff
->p
[i
].set
= isl_set_set_rational(pwaff
->p
[i
].set
);
3476 if (!pwaff
->p
[i
].set
)
3477 return isl_pw_aff_free(pwaff
);
3483 /* Mark the domains of the elements of "list" as rational.
3485 __isl_give isl_pw_aff_list
*isl_pw_aff_list_set_rational(
3486 __isl_take isl_pw_aff_list
*list
)
3496 for (i
= 0; i
< n
; ++i
) {
3499 pa
= isl_pw_aff_list_get_pw_aff(list
, i
);
3500 pa
= isl_pw_aff_set_rational(pa
);
3501 list
= isl_pw_aff_list_set_pw_aff(list
, i
, pa
);
3507 /* Do the parameters of "aff" match those of "space"?
3509 int isl_aff_matching_params(__isl_keep isl_aff
*aff
,
3510 __isl_keep isl_space
*space
)
3512 isl_space
*aff_space
;
3518 aff_space
= isl_aff_get_domain_space(aff
);
3520 match
= isl_space_match(space
, isl_dim_param
, aff_space
, isl_dim_param
);
3522 isl_space_free(aff_space
);
3526 /* Check that the domain space of "aff" matches "space".
3528 * Return 0 on success and -1 on error.
3530 int isl_aff_check_match_domain_space(__isl_keep isl_aff
*aff
,
3531 __isl_keep isl_space
*space
)
3533 isl_space
*aff_space
;
3539 aff_space
= isl_aff_get_domain_space(aff
);
3541 match
= isl_space_match(space
, isl_dim_param
, aff_space
, isl_dim_param
);
3545 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
3546 "parameters don't match", goto error
);
3547 match
= isl_space_tuple_is_equal(space
, isl_dim_in
,
3548 aff_space
, isl_dim_set
);
3552 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
3553 "domains don't match", goto error
);
3554 isl_space_free(aff_space
);
3557 isl_space_free(aff_space
);
3563 #define NO_INTERSECT_DOMAIN
3566 #include <isl_multi_templ.c>
3569 #undef NO_INTERSECT_DOMAIN
3571 /* Remove any internal structure of the domain of "ma".
3572 * If there is any such internal structure in the input,
3573 * then the name of the corresponding space is also removed.
3575 __isl_give isl_multi_aff
*isl_multi_aff_flatten_domain(
3576 __isl_take isl_multi_aff
*ma
)
3583 if (!ma
->space
->nested
[0])
3586 space
= isl_multi_aff_get_space(ma
);
3587 space
= isl_space_flatten_domain(space
);
3588 ma
= isl_multi_aff_reset_space(ma
, space
);
3593 /* Given a map space, return an isl_multi_aff that maps a wrapped copy
3594 * of the space to its domain.
3596 __isl_give isl_multi_aff
*isl_multi_aff_domain_map(__isl_take isl_space
*space
)
3599 isl_local_space
*ls
;
3604 if (!isl_space_is_map(space
))
3605 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
3606 "not a map space", goto error
);
3608 n_in
= isl_space_dim(space
, isl_dim_in
);
3609 space
= isl_space_domain_map(space
);
3611 ma
= isl_multi_aff_alloc(isl_space_copy(space
));
3613 isl_space_free(space
);
3617 space
= isl_space_domain(space
);
3618 ls
= isl_local_space_from_space(space
);
3619 for (i
= 0; i
< n_in
; ++i
) {
3622 aff
= isl_aff_var_on_domain(isl_local_space_copy(ls
),
3624 ma
= isl_multi_aff_set_aff(ma
, i
, aff
);
3626 isl_local_space_free(ls
);
3629 isl_space_free(space
);
3633 /* Given a map space, return an isl_multi_aff that maps a wrapped copy
3634 * of the space to its range.
3636 __isl_give isl_multi_aff
*isl_multi_aff_range_map(__isl_take isl_space
*space
)
3639 isl_local_space
*ls
;
3644 if (!isl_space_is_map(space
))
3645 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
3646 "not a map space", goto error
);
3648 n_in
= isl_space_dim(space
, isl_dim_in
);
3649 n_out
= isl_space_dim(space
, isl_dim_out
);
3650 space
= isl_space_range_map(space
);
3652 ma
= isl_multi_aff_alloc(isl_space_copy(space
));
3654 isl_space_free(space
);
3658 space
= isl_space_domain(space
);
3659 ls
= isl_local_space_from_space(space
);
3660 for (i
= 0; i
< n_out
; ++i
) {
3663 aff
= isl_aff_var_on_domain(isl_local_space_copy(ls
),
3664 isl_dim_set
, n_in
+ i
);
3665 ma
= isl_multi_aff_set_aff(ma
, i
, aff
);
3667 isl_local_space_free(ls
);
3670 isl_space_free(space
);
3674 /* Given the space of a set and a range of set dimensions,
3675 * construct an isl_multi_aff that projects out those dimensions.
3677 __isl_give isl_multi_aff
*isl_multi_aff_project_out_map(
3678 __isl_take isl_space
*space
, enum isl_dim_type type
,
3679 unsigned first
, unsigned n
)
3682 isl_local_space
*ls
;
3687 if (!isl_space_is_set(space
))
3688 isl_die(isl_space_get_ctx(space
), isl_error_unsupported
,
3689 "expecting set space", goto error
);
3690 if (type
!= isl_dim_set
)
3691 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
3692 "only set dimensions can be projected out", goto error
);
3694 dim
= isl_space_dim(space
, isl_dim_set
);
3695 if (first
+ n
> dim
)
3696 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
3697 "range out of bounds", goto error
);
3699 space
= isl_space_from_domain(space
);
3700 space
= isl_space_add_dims(space
, isl_dim_out
, dim
- n
);
3703 return isl_multi_aff_alloc(space
);
3705 ma
= isl_multi_aff_alloc(isl_space_copy(space
));
3706 space
= isl_space_domain(space
);
3707 ls
= isl_local_space_from_space(space
);
3709 for (i
= 0; i
< first
; ++i
) {
3712 aff
= isl_aff_var_on_domain(isl_local_space_copy(ls
),
3714 ma
= isl_multi_aff_set_aff(ma
, i
, aff
);
3717 for (i
= 0; i
< dim
- (first
+ n
); ++i
) {
3720 aff
= isl_aff_var_on_domain(isl_local_space_copy(ls
),
3721 isl_dim_set
, first
+ n
+ i
);
3722 ma
= isl_multi_aff_set_aff(ma
, first
+ i
, aff
);
3725 isl_local_space_free(ls
);
3728 isl_space_free(space
);
3732 /* Given the space of a set and a range of set dimensions,
3733 * construct an isl_pw_multi_aff that projects out those dimensions.
3735 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_project_out_map(
3736 __isl_take isl_space
*space
, enum isl_dim_type type
,
3737 unsigned first
, unsigned n
)
3741 ma
= isl_multi_aff_project_out_map(space
, type
, first
, n
);
3742 return isl_pw_multi_aff_from_multi_aff(ma
);
3745 /* Create an isl_pw_multi_aff with the given isl_multi_aff on a universe
3748 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_from_multi_aff(
3749 __isl_take isl_multi_aff
*ma
)
3751 isl_set
*dom
= isl_set_universe(isl_multi_aff_get_domain_space(ma
));
3752 return isl_pw_multi_aff_alloc(dom
, ma
);
3755 /* Create a piecewise multi-affine expression in the given space that maps each
3756 * input dimension to the corresponding output dimension.
3758 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_identity(
3759 __isl_take isl_space
*space
)
3761 return isl_pw_multi_aff_from_multi_aff(isl_multi_aff_identity(space
));
3764 /* Add "ma2" to "ma1" and return the result.
3766 * The parameters of "ma1" and "ma2" are assumed to have been aligned.
3768 static __isl_give isl_multi_aff
*isl_multi_aff_add_aligned(
3769 __isl_take isl_multi_aff
*maff1
, __isl_take isl_multi_aff
*maff2
)
3771 return isl_multi_aff_bin_op(maff1
, maff2
, &isl_aff_add
);
3774 /* Add "ma2" to "ma1" and return the result.
3776 __isl_give isl_multi_aff
*isl_multi_aff_add(__isl_take isl_multi_aff
*ma1
,
3777 __isl_take isl_multi_aff
*ma2
)
3779 return isl_multi_aff_align_params_multi_multi_and(ma1
, ma2
,
3780 &isl_multi_aff_add_aligned
);
3783 /* Subtract "ma2" from "ma1" and return the result.
3785 * The parameters of "ma1" and "ma2" are assumed to have been aligned.
3787 static __isl_give isl_multi_aff
*isl_multi_aff_sub_aligned(
3788 __isl_take isl_multi_aff
*ma1
, __isl_take isl_multi_aff
*ma2
)
3790 return isl_multi_aff_bin_op(ma1
, ma2
, &isl_aff_sub
);
3793 /* Subtract "ma2" from "ma1" and return the result.
3795 __isl_give isl_multi_aff
*isl_multi_aff_sub(__isl_take isl_multi_aff
*ma1
,
3796 __isl_take isl_multi_aff
*ma2
)
3798 return isl_multi_aff_align_params_multi_multi_and(ma1
, ma2
,
3799 &isl_multi_aff_sub_aligned
);
3802 /* Exploit the equalities in "eq" to simplify the affine expressions.
3804 static __isl_give isl_multi_aff
*isl_multi_aff_substitute_equalities(
3805 __isl_take isl_multi_aff
*maff
, __isl_take isl_basic_set
*eq
)
3809 maff
= isl_multi_aff_cow(maff
);
3813 for (i
= 0; i
< maff
->n
; ++i
) {
3814 maff
->p
[i
] = isl_aff_substitute_equalities(maff
->p
[i
],
3815 isl_basic_set_copy(eq
));
3820 isl_basic_set_free(eq
);
3823 isl_basic_set_free(eq
);
3824 isl_multi_aff_free(maff
);
3828 /* Given f, return floor(f).
3830 __isl_give isl_multi_aff
*isl_multi_aff_floor(__isl_take isl_multi_aff
*ma
)
3834 ma
= isl_multi_aff_cow(ma
);
3838 for (i
= 0; i
< ma
->n
; ++i
) {
3839 ma
->p
[i
] = isl_aff_floor(ma
->p
[i
]);
3841 return isl_multi_aff_free(ma
);
3847 __isl_give isl_multi_aff
*isl_multi_aff_scale(__isl_take isl_multi_aff
*maff
,
3852 maff
= isl_multi_aff_cow(maff
);
3856 for (i
= 0; i
< maff
->n
; ++i
) {
3857 maff
->p
[i
] = isl_aff_scale(maff
->p
[i
], f
);
3859 return isl_multi_aff_free(maff
);
3865 __isl_give isl_multi_aff
*isl_multi_aff_add_on_domain(__isl_keep isl_set
*dom
,
3866 __isl_take isl_multi_aff
*maff1
, __isl_take isl_multi_aff
*maff2
)
3868 maff1
= isl_multi_aff_add(maff1
, maff2
);
3869 maff1
= isl_multi_aff_gist(maff1
, isl_set_copy(dom
));
3873 int isl_multi_aff_is_empty(__isl_keep isl_multi_aff
*maff
)
3881 /* Return the set of domain elements where "ma1" is lexicographically
3882 * smaller than or equal to "ma2".
3884 __isl_give isl_set
*isl_multi_aff_lex_le_set(__isl_take isl_multi_aff
*ma1
,
3885 __isl_take isl_multi_aff
*ma2
)
3887 return isl_multi_aff_lex_ge_set(ma2
, ma1
);
3890 /* Return the set of domain elements where "ma1" is lexicographically
3891 * greater than or equal to "ma2".
3893 __isl_give isl_set
*isl_multi_aff_lex_ge_set(__isl_take isl_multi_aff
*ma1
,
3894 __isl_take isl_multi_aff
*ma2
)
3897 isl_map
*map1
, *map2
;
3900 map1
= isl_map_from_multi_aff(ma1
);
3901 map2
= isl_map_from_multi_aff(ma2
);
3902 map
= isl_map_range_product(map1
, map2
);
3903 space
= isl_space_range(isl_map_get_space(map
));
3904 space
= isl_space_domain(isl_space_unwrap(space
));
3905 ge
= isl_map_lex_ge(space
);
3906 map
= isl_map_intersect_range(map
, isl_map_wrap(ge
));
3908 return isl_map_domain(map
);
3912 #define PW isl_pw_multi_aff
3914 #define EL isl_multi_aff
3916 #define EL_IS_ZERO is_empty
3920 #define IS_ZERO is_empty
3923 #undef DEFAULT_IS_ZERO
3924 #define DEFAULT_IS_ZERO 0
3929 #define NO_INVOLVES_DIMS
3930 #define NO_INSERT_DIMS
3934 #include <isl_pw_templ.c>
3937 #define UNION isl_union_pw_multi_aff
3939 #define PART isl_pw_multi_aff
3941 #define PARTS pw_multi_aff
3942 #define ALIGN_DOMAIN
3946 #include <isl_union_templ.c>
3948 /* Given a function "cmp" that returns the set of elements where
3949 * "ma1" is "better" than "ma2", return the intersection of this
3950 * set with "dom1" and "dom2".
3952 static __isl_give isl_set
*shared_and_better(__isl_keep isl_set
*dom1
,
3953 __isl_keep isl_set
*dom2
, __isl_keep isl_multi_aff
*ma1
,
3954 __isl_keep isl_multi_aff
*ma2
,
3955 __isl_give isl_set
*(*cmp
)(__isl_take isl_multi_aff
*ma1
,
3956 __isl_take isl_multi_aff
*ma2
))
3962 common
= isl_set_intersect(isl_set_copy(dom1
), isl_set_copy(dom2
));
3963 is_empty
= isl_set_plain_is_empty(common
);
3964 if (is_empty
>= 0 && is_empty
)
3967 return isl_set_free(common
);
3968 better
= cmp(isl_multi_aff_copy(ma1
), isl_multi_aff_copy(ma2
));
3969 better
= isl_set_intersect(common
, better
);
3974 /* Given a function "cmp" that returns the set of elements where
3975 * "ma1" is "better" than "ma2", return a piecewise multi affine
3976 * expression defined on the union of the definition domains
3977 * of "pma1" and "pma2" that maps to the "best" of "pma1" and
3978 * "pma2" on each cell. If only one of the two input functions
3979 * is defined on a given cell, then it is considered the best.
3981 static __isl_give isl_pw_multi_aff
*pw_multi_aff_union_opt(
3982 __isl_take isl_pw_multi_aff
*pma1
,
3983 __isl_take isl_pw_multi_aff
*pma2
,
3984 __isl_give isl_set
*(*cmp
)(__isl_take isl_multi_aff
*ma1
,
3985 __isl_take isl_multi_aff
*ma2
))
3988 isl_pw_multi_aff
*res
= NULL
;
3990 isl_set
*set
= NULL
;
3995 ctx
= isl_space_get_ctx(pma1
->dim
);
3996 if (!isl_space_is_equal(pma1
->dim
, pma2
->dim
))
3997 isl_die(ctx
, isl_error_invalid
,
3998 "arguments should live in the same space", goto error
);
4000 if (isl_pw_multi_aff_is_empty(pma1
)) {
4001 isl_pw_multi_aff_free(pma1
);
4005 if (isl_pw_multi_aff_is_empty(pma2
)) {
4006 isl_pw_multi_aff_free(pma2
);
4010 n
= 2 * (pma1
->n
+ 1) * (pma2
->n
+ 1);
4011 res
= isl_pw_multi_aff_alloc_size(isl_space_copy(pma1
->dim
), n
);
4013 for (i
= 0; i
< pma1
->n
; ++i
) {
4014 set
= isl_set_copy(pma1
->p
[i
].set
);
4015 for (j
= 0; j
< pma2
->n
; ++j
) {
4019 better
= shared_and_better(pma2
->p
[j
].set
,
4020 pma1
->p
[i
].set
, pma2
->p
[j
].maff
,
4021 pma1
->p
[i
].maff
, cmp
);
4022 is_empty
= isl_set_plain_is_empty(better
);
4023 if (is_empty
< 0 || is_empty
) {
4024 isl_set_free(better
);
4029 set
= isl_set_subtract(set
, isl_set_copy(better
));
4031 res
= isl_pw_multi_aff_add_piece(res
, better
,
4032 isl_multi_aff_copy(pma2
->p
[j
].maff
));
4034 res
= isl_pw_multi_aff_add_piece(res
, set
,
4035 isl_multi_aff_copy(pma1
->p
[i
].maff
));
4038 for (j
= 0; j
< pma2
->n
; ++j
) {
4039 set
= isl_set_copy(pma2
->p
[j
].set
);
4040 for (i
= 0; i
< pma1
->n
; ++i
)
4041 set
= isl_set_subtract(set
,
4042 isl_set_copy(pma1
->p
[i
].set
));
4043 res
= isl_pw_multi_aff_add_piece(res
, set
,
4044 isl_multi_aff_copy(pma2
->p
[j
].maff
));
4047 isl_pw_multi_aff_free(pma1
);
4048 isl_pw_multi_aff_free(pma2
);
4052 isl_pw_multi_aff_free(pma1
);
4053 isl_pw_multi_aff_free(pma2
);
4055 return isl_pw_multi_aff_free(res
);
4058 static __isl_give isl_pw_multi_aff
*pw_multi_aff_union_lexmax(
4059 __isl_take isl_pw_multi_aff
*pma1
,
4060 __isl_take isl_pw_multi_aff
*pma2
)
4062 return pw_multi_aff_union_opt(pma1
, pma2
, &isl_multi_aff_lex_ge_set
);
4065 /* Given two piecewise multi affine expressions, return a piecewise
4066 * multi-affine expression defined on the union of the definition domains
4067 * of the inputs that is equal to the lexicographic maximum of the two
4068 * inputs on each cell. If only one of the two inputs is defined on
4069 * a given cell, then it is considered to be the maximum.
4071 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_union_lexmax(
4072 __isl_take isl_pw_multi_aff
*pma1
,
4073 __isl_take isl_pw_multi_aff
*pma2
)
4075 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
4076 &pw_multi_aff_union_lexmax
);
4079 static __isl_give isl_pw_multi_aff
*pw_multi_aff_union_lexmin(
4080 __isl_take isl_pw_multi_aff
*pma1
,
4081 __isl_take isl_pw_multi_aff
*pma2
)
4083 return pw_multi_aff_union_opt(pma1
, pma2
, &isl_multi_aff_lex_le_set
);
4086 /* Given two piecewise multi affine expressions, return a piecewise
4087 * multi-affine expression defined on the union of the definition domains
4088 * of the inputs that is equal to the lexicographic minimum of the two
4089 * inputs on each cell. If only one of the two inputs is defined on
4090 * a given cell, then it is considered to be the minimum.
4092 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_union_lexmin(
4093 __isl_take isl_pw_multi_aff
*pma1
,
4094 __isl_take isl_pw_multi_aff
*pma2
)
4096 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
4097 &pw_multi_aff_union_lexmin
);
4100 static __isl_give isl_pw_multi_aff
*pw_multi_aff_add(
4101 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
4103 return isl_pw_multi_aff_on_shared_domain(pma1
, pma2
,
4104 &isl_multi_aff_add
);
4107 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_add(
4108 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
4110 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
4114 static __isl_give isl_pw_multi_aff
*pw_multi_aff_sub(
4115 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
4117 return isl_pw_multi_aff_on_shared_domain(pma1
, pma2
,
4118 &isl_multi_aff_sub
);
4121 /* Subtract "pma2" from "pma1" and return the result.
4123 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_sub(
4124 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
4126 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
4130 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_union_add(
4131 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
4133 return isl_pw_multi_aff_union_add_(pma1
, pma2
);
4136 /* Compute the sum of "upma1" and "upma2" on the union of their domains,
4137 * with the actual sum on the shared domain and
4138 * the defined expression on the symmetric difference of the domains.
4140 __isl_give isl_union_pw_multi_aff
*isl_union_pw_multi_aff_union_add(
4141 __isl_take isl_union_pw_multi_aff
*upma1
,
4142 __isl_take isl_union_pw_multi_aff
*upma2
)
4144 return isl_union_pw_multi_aff_union_add_(upma1
, upma2
);
4147 /* Given two piecewise multi-affine expressions A -> B and C -> D,
4148 * construct a piecewise multi-affine expression [A -> C] -> [B -> D].
4150 static __isl_give isl_pw_multi_aff
*pw_multi_aff_product(
4151 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
4155 isl_pw_multi_aff
*res
;
4160 n
= pma1
->n
* pma2
->n
;
4161 space
= isl_space_product(isl_space_copy(pma1
->dim
),
4162 isl_space_copy(pma2
->dim
));
4163 res
= isl_pw_multi_aff_alloc_size(space
, n
);
4165 for (i
= 0; i
< pma1
->n
; ++i
) {
4166 for (j
= 0; j
< pma2
->n
; ++j
) {
4170 domain
= isl_set_product(isl_set_copy(pma1
->p
[i
].set
),
4171 isl_set_copy(pma2
->p
[j
].set
));
4172 ma
= isl_multi_aff_product(
4173 isl_multi_aff_copy(pma1
->p
[i
].maff
),
4174 isl_multi_aff_copy(pma2
->p
[j
].maff
));
4175 res
= isl_pw_multi_aff_add_piece(res
, domain
, ma
);
4179 isl_pw_multi_aff_free(pma1
);
4180 isl_pw_multi_aff_free(pma2
);
4183 isl_pw_multi_aff_free(pma1
);
4184 isl_pw_multi_aff_free(pma2
);
4188 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_product(
4189 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
4191 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
4192 &pw_multi_aff_product
);
4195 /* Construct a map mapping the domain of the piecewise multi-affine expression
4196 * to its range, with each dimension in the range equated to the
4197 * corresponding affine expression on its cell.
4199 __isl_give isl_map
*isl_map_from_pw_multi_aff(__isl_take isl_pw_multi_aff
*pma
)
4207 map
= isl_map_empty(isl_pw_multi_aff_get_space(pma
));
4209 for (i
= 0; i
< pma
->n
; ++i
) {
4210 isl_multi_aff
*maff
;
4211 isl_basic_map
*bmap
;
4214 maff
= isl_multi_aff_copy(pma
->p
[i
].maff
);
4215 bmap
= isl_basic_map_from_multi_aff(maff
);
4216 map_i
= isl_map_from_basic_map(bmap
);
4217 map_i
= isl_map_intersect_domain(map_i
,
4218 isl_set_copy(pma
->p
[i
].set
));
4219 map
= isl_map_union_disjoint(map
, map_i
);
4222 isl_pw_multi_aff_free(pma
);
4226 __isl_give isl_set
*isl_set_from_pw_multi_aff(__isl_take isl_pw_multi_aff
*pma
)
4231 if (!isl_space_is_set(pma
->dim
))
4232 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_invalid
,
4233 "isl_pw_multi_aff cannot be converted into an isl_set",
4236 return isl_map_from_pw_multi_aff(pma
);
4238 isl_pw_multi_aff_free(pma
);
4242 /* Given a basic map with a single output dimension that is defined
4243 * in terms of the parameters and input dimensions using an equality,
4244 * extract an isl_aff that expresses the output dimension in terms
4245 * of the parameters and input dimensions.
4246 * Note that this expression may involve integer divisions defined
4247 * in terms of parameters and input dimensions.
4249 * This function shares some similarities with
4250 * isl_basic_map_has_defining_equality and isl_constraint_get_bound.
4252 static __isl_give isl_aff
*extract_isl_aff_from_basic_map(
4253 __isl_take isl_basic_map
*bmap
)
4258 isl_local_space
*ls
;
4263 if (isl_basic_map_dim(bmap
, isl_dim_out
) != 1)
4264 isl_die(isl_basic_map_get_ctx(bmap
), isl_error_invalid
,
4265 "basic map should have a single output dimension",
4267 eq
= isl_basic_map_output_defining_equality(bmap
, 0);
4268 if (eq
>= bmap
->n_eq
)
4269 isl_die(isl_basic_map_get_ctx(bmap
), isl_error_invalid
,
4270 "unable to find suitable equality", goto error
);
4271 ls
= isl_basic_map_get_local_space(bmap
);
4272 aff
= isl_aff_alloc(isl_local_space_domain(ls
));
4275 offset
= isl_basic_map_offset(bmap
, isl_dim_out
);
4276 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
4277 if (isl_int_is_neg(bmap
->eq
[eq
][offset
])) {
4278 isl_seq_cpy(aff
->v
->el
+ 1, bmap
->eq
[eq
], offset
);
4279 isl_seq_cpy(aff
->v
->el
+ 1 + offset
, bmap
->eq
[eq
] + offset
+ 1,
4282 isl_seq_neg(aff
->v
->el
+ 1, bmap
->eq
[eq
], offset
);
4283 isl_seq_neg(aff
->v
->el
+ 1 + offset
, bmap
->eq
[eq
] + offset
+ 1,
4286 isl_int_abs(aff
->v
->el
[0], bmap
->eq
[eq
][offset
]);
4287 isl_basic_map_free(bmap
);
4289 aff
= isl_aff_remove_unused_divs(aff
);
4292 isl_basic_map_free(bmap
);
4296 /* Given a basic map where each output dimension is defined
4297 * in terms of the parameters and input dimensions using an equality,
4298 * extract an isl_multi_aff that expresses the output dimensions in terms
4299 * of the parameters and input dimensions.
4301 static __isl_give isl_multi_aff
*extract_isl_multi_aff_from_basic_map(
4302 __isl_take isl_basic_map
*bmap
)
4311 ma
= isl_multi_aff_alloc(isl_basic_map_get_space(bmap
));
4312 n_out
= isl_basic_map_dim(bmap
, isl_dim_out
);
4314 for (i
= 0; i
< n_out
; ++i
) {
4315 isl_basic_map
*bmap_i
;
4318 bmap_i
= isl_basic_map_copy(bmap
);
4319 bmap_i
= isl_basic_map_project_out(bmap_i
, isl_dim_out
,
4320 i
+ 1, n_out
- (1 + i
));
4321 bmap_i
= isl_basic_map_project_out(bmap_i
, isl_dim_out
, 0, i
);
4322 aff
= extract_isl_aff_from_basic_map(bmap_i
);
4323 ma
= isl_multi_aff_set_aff(ma
, i
, aff
);
4326 isl_basic_map_free(bmap
);
4331 /* Given a basic set where each set dimension is defined
4332 * in terms of the parameters using an equality,
4333 * extract an isl_multi_aff that expresses the set dimensions in terms
4334 * of the parameters.
4336 __isl_give isl_multi_aff
*isl_multi_aff_from_basic_set_equalities(
4337 __isl_take isl_basic_set
*bset
)
4339 return extract_isl_multi_aff_from_basic_map(bset
);
4342 /* Create an isl_pw_multi_aff that is equivalent to
4343 * isl_map_intersect_domain(isl_map_from_basic_map(bmap), domain).
4344 * The given basic map is such that each output dimension is defined
4345 * in terms of the parameters and input dimensions using an equality.
4347 * Since some applications expect the result of isl_pw_multi_aff_from_map
4348 * to only contain integer affine expressions, we compute the floor
4349 * of the expression before returning.
4351 static __isl_give isl_pw_multi_aff
*plain_pw_multi_aff_from_map(
4352 __isl_take isl_set
*domain
, __isl_take isl_basic_map
*bmap
)
4356 ma
= extract_isl_multi_aff_from_basic_map(bmap
);
4357 ma
= isl_multi_aff_floor(ma
);
4358 return isl_pw_multi_aff_alloc(domain
, ma
);
4361 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
4362 * This obviously only works if the input "map" is single-valued.
4363 * If so, we compute the lexicographic minimum of the image in the form
4364 * of an isl_pw_multi_aff. Since the image is unique, it is equal
4365 * to its lexicographic minimum.
4366 * If the input is not single-valued, we produce an error.
4368 static __isl_give isl_pw_multi_aff
*pw_multi_aff_from_map_base(
4369 __isl_take isl_map
*map
)
4373 isl_pw_multi_aff
*pma
;
4375 sv
= isl_map_is_single_valued(map
);
4379 isl_die(isl_map_get_ctx(map
), isl_error_invalid
,
4380 "map is not single-valued", goto error
);
4381 map
= isl_map_make_disjoint(map
);
4385 pma
= isl_pw_multi_aff_empty(isl_map_get_space(map
));
4387 for (i
= 0; i
< map
->n
; ++i
) {
4388 isl_pw_multi_aff
*pma_i
;
4389 isl_basic_map
*bmap
;
4390 bmap
= isl_basic_map_copy(map
->p
[i
]);
4391 pma_i
= isl_basic_map_lexmin_pw_multi_aff(bmap
);
4392 pma
= isl_pw_multi_aff_add_disjoint(pma
, pma_i
);
4402 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map,
4403 * taking into account that the output dimension at position "d"
4404 * can be represented as
4406 * x = floor((e(...) + c1) / m)
4408 * given that constraint "i" is of the form
4410 * e(...) + c1 - m x >= 0
4413 * Let "map" be of the form
4417 * We construct a mapping
4419 * A -> [A -> x = floor(...)]
4421 * apply that to the map, obtaining
4423 * [A -> x = floor(...)] -> B
4425 * and equate dimension "d" to x.
4426 * We then compute a isl_pw_multi_aff representation of the resulting map
4427 * and plug in the mapping above.
4429 static __isl_give isl_pw_multi_aff
*pw_multi_aff_from_map_div(
4430 __isl_take isl_map
*map
, __isl_take isl_basic_map
*hull
, int d
, int i
)
4434 isl_local_space
*ls
;
4442 isl_pw_multi_aff
*pma
;
4445 is_set
= isl_map_is_set(map
);
4447 offset
= isl_basic_map_offset(hull
, isl_dim_out
);
4448 ctx
= isl_map_get_ctx(map
);
4449 space
= isl_space_domain(isl_map_get_space(map
));
4450 n_in
= isl_space_dim(space
, isl_dim_set
);
4451 n
= isl_space_dim(space
, isl_dim_all
);
4453 v
= isl_vec_alloc(ctx
, 1 + 1 + n
);
4455 isl_int_neg(v
->el
[0], hull
->ineq
[i
][offset
+ d
]);
4456 isl_seq_cpy(v
->el
+ 1, hull
->ineq
[i
], 1 + n
);
4458 isl_basic_map_free(hull
);
4460 ls
= isl_local_space_from_space(isl_space_copy(space
));
4461 aff
= isl_aff_alloc_vec(ls
, v
);
4462 aff
= isl_aff_floor(aff
);
4464 isl_space_free(space
);
4465 ma
= isl_multi_aff_from_aff(aff
);
4467 ma
= isl_multi_aff_identity(isl_space_map_from_set(space
));
4468 ma
= isl_multi_aff_range_product(ma
,
4469 isl_multi_aff_from_aff(aff
));
4472 insert
= isl_map_from_multi_aff(isl_multi_aff_copy(ma
));
4473 map
= isl_map_apply_domain(map
, insert
);
4474 map
= isl_map_equate(map
, isl_dim_in
, n_in
, isl_dim_out
, d
);
4475 pma
= isl_pw_multi_aff_from_map(map
);
4476 pma
= isl_pw_multi_aff_pullback_multi_aff(pma
, ma
);
4481 /* Is constraint "c" of the form
4483 * e(...) + c1 - m x >= 0
4487 * -e(...) + c2 + m x >= 0
4489 * where m > 1 and e only depends on parameters and input dimemnsions?
4491 * "offset" is the offset of the output dimensions
4492 * "pos" is the position of output dimension x.
4494 static int is_potential_div_constraint(isl_int
*c
, int offset
, int d
, int total
)
4496 if (isl_int_is_zero(c
[offset
+ d
]))
4498 if (isl_int_is_one(c
[offset
+ d
]))
4500 if (isl_int_is_negone(c
[offset
+ d
]))
4502 if (isl_seq_first_non_zero(c
+ offset
, d
) != -1)
4504 if (isl_seq_first_non_zero(c
+ offset
+ d
+ 1,
4505 total
- (offset
+ d
+ 1)) != -1)
4510 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
4512 * As a special case, we first check if there is any pair of constraints,
4513 * shared by all the basic maps in "map" that force a given dimension
4514 * to be equal to the floor of some affine combination of the input dimensions.
4516 * In particular, if we can find two constraints
4518 * e(...) + c1 - m x >= 0 i.e., m x <= e(...) + c1
4522 * -e(...) + c2 + m x >= 0 i.e., m x >= e(...) - c2
4524 * where m > 1 and e only depends on parameters and input dimemnsions,
4527 * c1 + c2 < m i.e., -c2 >= c1 - (m - 1)
4529 * then we know that we can take
4531 * x = floor((e(...) + c1) / m)
4533 * without having to perform any computation.
4535 * Note that we know that
4539 * If c1 + c2 were 0, then we would have detected an equality during
4540 * simplification. If c1 + c2 were negative, then we would have detected
4543 static __isl_give isl_pw_multi_aff
*pw_multi_aff_from_map_check_div(
4544 __isl_take isl_map
*map
)
4550 isl_basic_map
*hull
;
4552 hull
= isl_map_unshifted_simple_hull(isl_map_copy(map
));
4557 dim
= isl_map_dim(map
, isl_dim_out
);
4558 offset
= isl_basic_map_offset(hull
, isl_dim_out
);
4559 total
= 1 + isl_basic_map_total_dim(hull
);
4561 for (d
= 0; d
< dim
; ++d
) {
4562 for (i
= 0; i
< n
; ++i
) {
4563 if (!is_potential_div_constraint(hull
->ineq
[i
],
4566 for (j
= i
+ 1; j
< n
; ++j
) {
4567 if (!isl_seq_is_neg(hull
->ineq
[i
] + 1,
4568 hull
->ineq
[j
] + 1, total
- 1))
4570 isl_int_add(sum
, hull
->ineq
[i
][0],
4572 if (isl_int_abs_lt(sum
,
4573 hull
->ineq
[i
][offset
+ d
]))
4580 if (isl_int_is_pos(hull
->ineq
[j
][offset
+ d
]))
4582 return pw_multi_aff_from_map_div(map
, hull
, d
, j
);
4586 isl_basic_map_free(hull
);
4587 return pw_multi_aff_from_map_base(map
);
4590 isl_basic_map_free(hull
);
4594 /* Given an affine expression
4596 * [A -> B] -> f(A,B)
4598 * construct an isl_multi_aff
4602 * such that dimension "d" in B' is set to "aff" and the remaining
4603 * dimensions are set equal to the corresponding dimensions in B.
4604 * "n_in" is the dimension of the space A.
4605 * "n_out" is the dimension of the space B.
4607 * If "is_set" is set, then the affine expression is of the form
4611 * and we construct an isl_multi_aff
4615 static __isl_give isl_multi_aff
*range_map(__isl_take isl_aff
*aff
, int d
,
4616 unsigned n_in
, unsigned n_out
, int is_set
)
4620 isl_space
*space
, *space2
;
4621 isl_local_space
*ls
;
4623 space
= isl_aff_get_domain_space(aff
);
4624 ls
= isl_local_space_from_space(isl_space_copy(space
));
4625 space2
= isl_space_copy(space
);
4627 space2
= isl_space_range(isl_space_unwrap(space2
));
4628 space
= isl_space_map_from_domain_and_range(space
, space2
);
4629 ma
= isl_multi_aff_alloc(space
);
4630 ma
= isl_multi_aff_set_aff(ma
, d
, aff
);
4632 for (i
= 0; i
< n_out
; ++i
) {
4635 aff
= isl_aff_var_on_domain(isl_local_space_copy(ls
),
4636 isl_dim_set
, n_in
+ i
);
4637 ma
= isl_multi_aff_set_aff(ma
, i
, aff
);
4640 isl_local_space_free(ls
);
4645 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map,
4646 * taking into account that the dimension at position "d" can be written as
4648 * x = m a + f(..) (1)
4650 * where m is equal to "gcd".
4651 * "i" is the index of the equality in "hull" that defines f(..).
4652 * In particular, the equality is of the form
4654 * f(..) - x + m g(existentials) = 0
4658 * -f(..) + x + m g(existentials) = 0
4660 * We basically plug (1) into "map", resulting in a map with "a"
4661 * in the range instead of "x". The corresponding isl_pw_multi_aff
4662 * defining "a" is then plugged back into (1) to obtain a definition fro "x".
4664 * Specifically, given the input map
4668 * We first wrap it into a set
4672 * and define (1) on top of the corresponding space, resulting in "aff".
4673 * We use this to create an isl_multi_aff that maps the output position "d"
4674 * from "a" to "x", leaving all other (intput and output) dimensions unchanged.
4675 * We plug this into the wrapped map, unwrap the result and compute the
4676 * corresponding isl_pw_multi_aff.
4677 * The result is an expression
4685 * so that we can plug that into "aff", after extending the latter to
4691 * If "map" is actually a set, then there is no "A" space, meaning
4692 * that we do not need to perform any wrapping, and that the result
4693 * of the recursive call is of the form
4697 * which is plugged into a mapping of the form
4701 static __isl_give isl_pw_multi_aff
*pw_multi_aff_from_map_stride(
4702 __isl_take isl_map
*map
, __isl_take isl_basic_map
*hull
, int d
, int i
,
4707 isl_local_space
*ls
;
4710 isl_pw_multi_aff
*pma
, *id
;
4716 is_set
= isl_map_is_set(map
);
4718 n_in
= isl_basic_map_dim(hull
, isl_dim_in
);
4719 n_out
= isl_basic_map_dim(hull
, isl_dim_out
);
4720 o_out
= isl_basic_map_offset(hull
, isl_dim_out
);
4725 set
= isl_map_wrap(map
);
4726 space
= isl_space_map_from_set(isl_set_get_space(set
));
4727 ma
= isl_multi_aff_identity(space
);
4728 ls
= isl_local_space_from_space(isl_set_get_space(set
));
4729 aff
= isl_aff_alloc(ls
);
4731 isl_int_set_si(aff
->v
->el
[0], 1);
4732 if (isl_int_is_one(hull
->eq
[i
][o_out
+ d
]))
4733 isl_seq_neg(aff
->v
->el
+ 1, hull
->eq
[i
],
4736 isl_seq_cpy(aff
->v
->el
+ 1, hull
->eq
[i
],
4738 isl_int_set(aff
->v
->el
[1 + o_out
+ d
], gcd
);
4740 ma
= isl_multi_aff_set_aff(ma
, n_in
+ d
, isl_aff_copy(aff
));
4741 set
= isl_set_preimage_multi_aff(set
, ma
);
4743 ma
= range_map(aff
, d
, n_in
, n_out
, is_set
);
4748 map
= isl_set_unwrap(set
);
4749 pma
= isl_pw_multi_aff_from_map(set
);
4752 space
= isl_pw_multi_aff_get_domain_space(pma
);
4753 space
= isl_space_map_from_set(space
);
4754 id
= isl_pw_multi_aff_identity(space
);
4755 pma
= isl_pw_multi_aff_range_product(id
, pma
);
4757 id
= isl_pw_multi_aff_from_multi_aff(ma
);
4758 pma
= isl_pw_multi_aff_pullback_pw_multi_aff(id
, pma
);
4760 isl_basic_map_free(hull
);
4764 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
4766 * As a special case, we first check if all output dimensions are uniquely
4767 * defined in terms of the parameters and input dimensions over the entire
4768 * domain. If so, we extract the desired isl_pw_multi_aff directly
4769 * from the affine hull of "map" and its domain.
4771 * Otherwise, we check if any of the output dimensions is "strided".
4772 * That is, we check if can be written as
4776 * with m greater than 1, a some combination of existentiall quantified
4777 * variables and f and expression in the parameters and input dimensions.
4778 * If so, we remove the stride in pw_multi_aff_from_map_stride.
4780 * Otherwise, we continue with pw_multi_aff_from_map_check_div for a further
4783 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_from_map(__isl_take isl_map
*map
)
4787 isl_basic_map
*hull
;
4797 hull
= isl_map_affine_hull(isl_map_copy(map
));
4798 sv
= isl_basic_map_plain_is_single_valued(hull
);
4800 return plain_pw_multi_aff_from_map(isl_map_domain(map
), hull
);
4802 hull
= isl_basic_map_free(hull
);
4806 n_div
= isl_basic_map_dim(hull
, isl_dim_div
);
4807 o_div
= isl_basic_map_offset(hull
, isl_dim_div
);
4810 isl_basic_map_free(hull
);
4811 return pw_multi_aff_from_map_check_div(map
);
4816 n_out
= isl_basic_map_dim(hull
, isl_dim_out
);
4817 o_out
= isl_basic_map_offset(hull
, isl_dim_out
);
4819 for (i
= 0; i
< n_out
; ++i
) {
4820 for (j
= 0; j
< hull
->n_eq
; ++j
) {
4821 isl_int
*eq
= hull
->eq
[j
];
4822 isl_pw_multi_aff
*res
;
4824 if (!isl_int_is_one(eq
[o_out
+ i
]) &&
4825 !isl_int_is_negone(eq
[o_out
+ i
]))
4827 if (isl_seq_first_non_zero(eq
+ o_out
, i
) != -1)
4829 if (isl_seq_first_non_zero(eq
+ o_out
+ i
+ 1,
4830 n_out
- (i
+ 1)) != -1)
4832 isl_seq_gcd(eq
+ o_div
, n_div
, &gcd
);
4833 if (isl_int_is_zero(gcd
))
4835 if (isl_int_is_one(gcd
))
4838 res
= pw_multi_aff_from_map_stride(map
, hull
,
4846 isl_basic_map_free(hull
);
4847 return pw_multi_aff_from_map_check_div(map
);
4853 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_from_set(__isl_take isl_set
*set
)
4855 return isl_pw_multi_aff_from_map(set
);
4858 /* Convert "map" into an isl_pw_multi_aff (if possible) and
4861 static int pw_multi_aff_from_map(__isl_take isl_map
*map
, void *user
)
4863 isl_union_pw_multi_aff
**upma
= user
;
4864 isl_pw_multi_aff
*pma
;
4866 pma
= isl_pw_multi_aff_from_map(map
);
4867 *upma
= isl_union_pw_multi_aff_add_pw_multi_aff(*upma
, pma
);
4869 return *upma
? 0 : -1;
4872 /* Try and create an isl_union_pw_multi_aff that is equivalent
4873 * to the given isl_union_map.
4874 * The isl_union_map is required to be single-valued in each space.
4875 * Otherwise, an error is produced.
4877 __isl_give isl_union_pw_multi_aff
*isl_union_pw_multi_aff_from_union_map(
4878 __isl_take isl_union_map
*umap
)
4881 isl_union_pw_multi_aff
*upma
;
4883 space
= isl_union_map_get_space(umap
);
4884 upma
= isl_union_pw_multi_aff_empty(space
);
4885 if (isl_union_map_foreach_map(umap
, &pw_multi_aff_from_map
, &upma
) < 0)
4886 upma
= isl_union_pw_multi_aff_free(upma
);
4887 isl_union_map_free(umap
);
4892 /* Try and create an isl_union_pw_multi_aff that is equivalent
4893 * to the given isl_union_set.
4894 * The isl_union_set is required to be a singleton in each space.
4895 * Otherwise, an error is produced.
4897 __isl_give isl_union_pw_multi_aff
*isl_union_pw_multi_aff_from_union_set(
4898 __isl_take isl_union_set
*uset
)
4900 return isl_union_pw_multi_aff_from_union_map(uset
);
4903 /* Return the piecewise affine expression "set ? 1 : 0".
4905 __isl_give isl_pw_aff
*isl_set_indicator_function(__isl_take isl_set
*set
)
4908 isl_space
*space
= isl_set_get_space(set
);
4909 isl_local_space
*ls
= isl_local_space_from_space(space
);
4910 isl_aff
*zero
= isl_aff_zero_on_domain(isl_local_space_copy(ls
));
4911 isl_aff
*one
= isl_aff_zero_on_domain(ls
);
4913 one
= isl_aff_add_constant_si(one
, 1);
4914 pa
= isl_pw_aff_alloc(isl_set_copy(set
), one
);
4915 set
= isl_set_complement(set
);
4916 pa
= isl_pw_aff_add_disjoint(pa
, isl_pw_aff_alloc(set
, zero
));
4921 /* Plug in "subs" for dimension "type", "pos" of "aff".
4923 * Let i be the dimension to replace and let "subs" be of the form
4927 * and "aff" of the form
4933 * (a f + d g')/(m d)
4935 * where g' is the result of plugging in "subs" in each of the integer
4938 __isl_give isl_aff
*isl_aff_substitute(__isl_take isl_aff
*aff
,
4939 enum isl_dim_type type
, unsigned pos
, __isl_keep isl_aff
*subs
)
4944 aff
= isl_aff_cow(aff
);
4946 return isl_aff_free(aff
);
4948 ctx
= isl_aff_get_ctx(aff
);
4949 if (!isl_space_is_equal(aff
->ls
->dim
, subs
->ls
->dim
))
4950 isl_die(ctx
, isl_error_invalid
,
4951 "spaces don't match", return isl_aff_free(aff
));
4952 if (isl_local_space_dim(subs
->ls
, isl_dim_div
) != 0)
4953 isl_die(ctx
, isl_error_unsupported
,
4954 "cannot handle divs yet", return isl_aff_free(aff
));
4956 aff
->ls
= isl_local_space_substitute(aff
->ls
, type
, pos
, subs
);
4958 return isl_aff_free(aff
);
4960 aff
->v
= isl_vec_cow(aff
->v
);
4962 return isl_aff_free(aff
);
4964 pos
+= isl_local_space_offset(aff
->ls
, type
);
4967 isl_seq_substitute(aff
->v
->el
, pos
, subs
->v
->el
,
4968 aff
->v
->size
, subs
->v
->size
, v
);
4974 /* Plug in "subs" for dimension "type", "pos" in each of the affine
4975 * expressions in "maff".
4977 __isl_give isl_multi_aff
*isl_multi_aff_substitute(
4978 __isl_take isl_multi_aff
*maff
, enum isl_dim_type type
, unsigned pos
,
4979 __isl_keep isl_aff
*subs
)
4983 maff
= isl_multi_aff_cow(maff
);
4985 return isl_multi_aff_free(maff
);
4987 if (type
== isl_dim_in
)
4990 for (i
= 0; i
< maff
->n
; ++i
) {
4991 maff
->p
[i
] = isl_aff_substitute(maff
->p
[i
], type
, pos
, subs
);
4993 return isl_multi_aff_free(maff
);
4999 /* Plug in "subs" for dimension "type", "pos" of "pma".
5001 * pma is of the form
5005 * while subs is of the form
5007 * v' = B_j(v) -> S_j
5009 * Each pair i,j such that C_ij = A_i \cap B_i is non-empty
5010 * has a contribution in the result, in particular
5012 * C_ij(S_j) -> M_i(S_j)
5014 * Note that plugging in S_j in C_ij may also result in an empty set
5015 * and this contribution should simply be discarded.
5017 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_substitute(
5018 __isl_take isl_pw_multi_aff
*pma
, enum isl_dim_type type
, unsigned pos
,
5019 __isl_keep isl_pw_aff
*subs
)
5022 isl_pw_multi_aff
*res
;
5025 return isl_pw_multi_aff_free(pma
);
5027 n
= pma
->n
* subs
->n
;
5028 res
= isl_pw_multi_aff_alloc_size(isl_space_copy(pma
->dim
), n
);
5030 for (i
= 0; i
< pma
->n
; ++i
) {
5031 for (j
= 0; j
< subs
->n
; ++j
) {
5033 isl_multi_aff
*res_ij
;
5036 common
= isl_set_intersect(
5037 isl_set_copy(pma
->p
[i
].set
),
5038 isl_set_copy(subs
->p
[j
].set
));
5039 common
= isl_set_substitute(common
,
5040 type
, pos
, subs
->p
[j
].aff
);
5041 empty
= isl_set_plain_is_empty(common
);
5042 if (empty
< 0 || empty
) {
5043 isl_set_free(common
);
5049 res_ij
= isl_multi_aff_substitute(
5050 isl_multi_aff_copy(pma
->p
[i
].maff
),
5051 type
, pos
, subs
->p
[j
].aff
);
5053 res
= isl_pw_multi_aff_add_piece(res
, common
, res_ij
);
5057 isl_pw_multi_aff_free(pma
);
5060 isl_pw_multi_aff_free(pma
);
5061 isl_pw_multi_aff_free(res
);
5065 /* Compute the preimage of a range of dimensions in the affine expression "src"
5066 * under "ma" and put the result in "dst". The number of dimensions in "src"
5067 * that precede the range is given by "n_before". The number of dimensions
5068 * in the range is given by the number of output dimensions of "ma".
5069 * The number of dimensions that follow the range is given by "n_after".
5070 * If "has_denom" is set (to one),
5071 * then "src" and "dst" have an extra initial denominator.
5072 * "n_div_ma" is the number of existentials in "ma"
5073 * "n_div_bset" is the number of existentials in "src"
5074 * The resulting "dst" (which is assumed to have been allocated by
5075 * the caller) contains coefficients for both sets of existentials,
5076 * first those in "ma" and then those in "src".
5077 * f, c1, c2 and g are temporary objects that have been initialized
5080 * Let src represent the expression
5082 * (a(p) + f_u u + b v + f_w w + c(divs))/d
5084 * and let ma represent the expressions
5086 * v_i = (r_i(p) + s_i(y) + t_i(divs'))/m_i
5088 * We start out with the following expression for dst:
5090 * (a(p) + f_u u + 0 y + f_w w + 0 divs' + c(divs) + f \sum_i b_i v_i)/d
5092 * with the multiplication factor f initially equal to 1
5093 * and f \sum_i b_i v_i kept separately.
5094 * For each x_i that we substitute, we multiply the numerator
5095 * (and denominator) of dst by c_1 = m_i and add the numerator
5096 * of the x_i expression multiplied by c_2 = f b_i,
5097 * after removing the common factors of c_1 and c_2.
5098 * The multiplication factor f also needs to be multiplied by c_1
5099 * for the next x_j, j > i.
5101 void isl_seq_preimage(isl_int
*dst
, isl_int
*src
,
5102 __isl_keep isl_multi_aff
*ma
, int n_before
, int n_after
,
5103 int n_div_ma
, int n_div_bmap
,
5104 isl_int f
, isl_int c1
, isl_int c2
, isl_int g
, int has_denom
)
5107 int n_param
, n_in
, n_out
;
5110 n_param
= isl_multi_aff_dim(ma
, isl_dim_param
);
5111 n_in
= isl_multi_aff_dim(ma
, isl_dim_in
);
5112 n_out
= isl_multi_aff_dim(ma
, isl_dim_out
);
5114 isl_seq_cpy(dst
, src
, has_denom
+ 1 + n_param
+ n_before
);
5115 o_dst
= o_src
= has_denom
+ 1 + n_param
+ n_before
;
5116 isl_seq_clr(dst
+ o_dst
, n_in
);
5119 isl_seq_cpy(dst
+ o_dst
, src
+ o_src
, n_after
);
5122 isl_seq_clr(dst
+ o_dst
, n_div_ma
);
5124 isl_seq_cpy(dst
+ o_dst
, src
+ o_src
, n_div_bmap
);
5126 isl_int_set_si(f
, 1);
5128 for (i
= 0; i
< n_out
; ++i
) {
5129 int offset
= has_denom
+ 1 + n_param
+ n_before
+ i
;
5131 if (isl_int_is_zero(src
[offset
]))
5133 isl_int_set(c1
, ma
->p
[i
]->v
->el
[0]);
5134 isl_int_mul(c2
, f
, src
[offset
]);
5135 isl_int_gcd(g
, c1
, c2
);
5136 isl_int_divexact(c1
, c1
, g
);
5137 isl_int_divexact(c2
, c2
, g
);
5139 isl_int_mul(f
, f
, c1
);
5142 isl_seq_combine(dst
+ o_dst
, c1
, dst
+ o_dst
,
5143 c2
, ma
->p
[i
]->v
->el
+ o_src
, 1 + n_param
);
5144 o_dst
+= 1 + n_param
;
5145 o_src
+= 1 + n_param
;
5146 isl_seq_scale(dst
+ o_dst
, dst
+ o_dst
, c1
, n_before
);
5148 isl_seq_combine(dst
+ o_dst
, c1
, dst
+ o_dst
,
5149 c2
, ma
->p
[i
]->v
->el
+ o_src
, n_in
);
5152 isl_seq_scale(dst
+ o_dst
, dst
+ o_dst
, c1
, n_after
);
5154 isl_seq_combine(dst
+ o_dst
, c1
, dst
+ o_dst
,
5155 c2
, ma
->p
[i
]->v
->el
+ o_src
, n_div_ma
);
5158 isl_seq_scale(dst
+ o_dst
, dst
+ o_dst
, c1
, n_div_bmap
);
5160 isl_int_mul(dst
[0], dst
[0], c1
);
5164 /* Compute the pullback of "aff" by the function represented by "ma".
5165 * In other words, plug in "ma" in "aff". The result is an affine expression
5166 * defined over the domain space of "ma".
5168 * If "aff" is represented by
5170 * (a(p) + b x + c(divs))/d
5172 * and ma is represented by
5174 * x = D(p) + F(y) + G(divs')
5176 * then the result is
5178 * (a(p) + b D(p) + b F(y) + b G(divs') + c(divs))/d
5180 * The divs in the local space of the input are similarly adjusted
5181 * through a call to isl_local_space_preimage_multi_aff.
5183 __isl_give isl_aff
*isl_aff_pullback_multi_aff(__isl_take isl_aff
*aff
,
5184 __isl_take isl_multi_aff
*ma
)
5186 isl_aff
*res
= NULL
;
5187 isl_local_space
*ls
;
5188 int n_div_aff
, n_div_ma
;
5189 isl_int f
, c1
, c2
, g
;
5191 ma
= isl_multi_aff_align_divs(ma
);
5195 n_div_aff
= isl_aff_dim(aff
, isl_dim_div
);
5196 n_div_ma
= ma
->n
? isl_aff_dim(ma
->p
[0], isl_dim_div
) : 0;
5198 ls
= isl_aff_get_domain_local_space(aff
);
5199 ls
= isl_local_space_preimage_multi_aff(ls
, isl_multi_aff_copy(ma
));
5200 res
= isl_aff_alloc(ls
);
5209 isl_seq_preimage(res
->v
->el
, aff
->v
->el
, ma
, 0, 0, n_div_ma
, n_div_aff
,
5218 isl_multi_aff_free(ma
);
5219 res
= isl_aff_normalize(res
);
5223 isl_multi_aff_free(ma
);
5228 /* Compute the pullback of "aff1" by the function represented by "aff2".
5229 * In other words, plug in "aff2" in "aff1". The result is an affine expression
5230 * defined over the domain space of "aff1".
5232 * The domain of "aff1" should match the range of "aff2", which means
5233 * that it should be single-dimensional.
5235 __isl_give isl_aff
*isl_aff_pullback_aff(__isl_take isl_aff
*aff1
,
5236 __isl_take isl_aff
*aff2
)
5240 ma
= isl_multi_aff_from_aff(aff2
);
5241 return isl_aff_pullback_multi_aff(aff1
, ma
);
5244 /* Compute the pullback of "ma1" by the function represented by "ma2".
5245 * In other words, plug in "ma2" in "ma1".
5247 * The parameters of "ma1" and "ma2" are assumed to have been aligned.
5249 static __isl_give isl_multi_aff
*isl_multi_aff_pullback_multi_aff_aligned(
5250 __isl_take isl_multi_aff
*ma1
, __isl_take isl_multi_aff
*ma2
)
5253 isl_space
*space
= NULL
;
5255 ma2
= isl_multi_aff_align_divs(ma2
);
5256 ma1
= isl_multi_aff_cow(ma1
);
5260 space
= isl_space_join(isl_multi_aff_get_space(ma2
),
5261 isl_multi_aff_get_space(ma1
));
5263 for (i
= 0; i
< ma1
->n
; ++i
) {
5264 ma1
->p
[i
] = isl_aff_pullback_multi_aff(ma1
->p
[i
],
5265 isl_multi_aff_copy(ma2
));
5270 ma1
= isl_multi_aff_reset_space(ma1
, space
);
5271 isl_multi_aff_free(ma2
);
5274 isl_space_free(space
);
5275 isl_multi_aff_free(ma2
);
5276 isl_multi_aff_free(ma1
);
5280 /* Compute the pullback of "ma1" by the function represented by "ma2".
5281 * In other words, plug in "ma2" in "ma1".
5283 __isl_give isl_multi_aff
*isl_multi_aff_pullback_multi_aff(
5284 __isl_take isl_multi_aff
*ma1
, __isl_take isl_multi_aff
*ma2
)
5286 return isl_multi_aff_align_params_multi_multi_and(ma1
, ma2
,
5287 &isl_multi_aff_pullback_multi_aff_aligned
);
5290 /* Extend the local space of "dst" to include the divs
5291 * in the local space of "src".
5293 __isl_give isl_aff
*isl_aff_align_divs(__isl_take isl_aff
*dst
,
5294 __isl_keep isl_aff
*src
)
5302 return isl_aff_free(dst
);
5304 ctx
= isl_aff_get_ctx(src
);
5305 if (!isl_space_is_equal(src
->ls
->dim
, dst
->ls
->dim
))
5306 isl_die(ctx
, isl_error_invalid
,
5307 "spaces don't match", goto error
);
5309 if (src
->ls
->div
->n_row
== 0)
5312 exp1
= isl_alloc_array(ctx
, int, src
->ls
->div
->n_row
);
5313 exp2
= isl_alloc_array(ctx
, int, dst
->ls
->div
->n_row
);
5314 if (!exp1
|| (dst
->ls
->div
->n_row
&& !exp2
))
5317 div
= isl_merge_divs(src
->ls
->div
, dst
->ls
->div
, exp1
, exp2
);
5318 dst
= isl_aff_expand_divs(dst
, div
, exp2
);
5326 return isl_aff_free(dst
);
5329 /* Adjust the local spaces of the affine expressions in "maff"
5330 * such that they all have the save divs.
5332 __isl_give isl_multi_aff
*isl_multi_aff_align_divs(
5333 __isl_take isl_multi_aff
*maff
)
5341 maff
= isl_multi_aff_cow(maff
);
5345 for (i
= 1; i
< maff
->n
; ++i
)
5346 maff
->p
[0] = isl_aff_align_divs(maff
->p
[0], maff
->p
[i
]);
5347 for (i
= 1; i
< maff
->n
; ++i
) {
5348 maff
->p
[i
] = isl_aff_align_divs(maff
->p
[i
], maff
->p
[0]);
5350 return isl_multi_aff_free(maff
);
5356 __isl_give isl_aff
*isl_aff_lift(__isl_take isl_aff
*aff
)
5358 aff
= isl_aff_cow(aff
);
5362 aff
->ls
= isl_local_space_lift(aff
->ls
);
5364 return isl_aff_free(aff
);
5369 /* Lift "maff" to a space with extra dimensions such that the result
5370 * has no more existentially quantified variables.
5371 * If "ls" is not NULL, then *ls is assigned the local space that lies
5372 * at the basis of the lifting applied to "maff".
5374 __isl_give isl_multi_aff
*isl_multi_aff_lift(__isl_take isl_multi_aff
*maff
,
5375 __isl_give isl_local_space
**ls
)
5389 isl_space
*space
= isl_multi_aff_get_domain_space(maff
);
5390 *ls
= isl_local_space_from_space(space
);
5392 return isl_multi_aff_free(maff
);
5397 maff
= isl_multi_aff_cow(maff
);
5398 maff
= isl_multi_aff_align_divs(maff
);
5402 n_div
= isl_aff_dim(maff
->p
[0], isl_dim_div
);
5403 space
= isl_multi_aff_get_space(maff
);
5404 space
= isl_space_lift(isl_space_domain(space
), n_div
);
5405 space
= isl_space_extend_domain_with_range(space
,
5406 isl_multi_aff_get_space(maff
));
5408 return isl_multi_aff_free(maff
);
5409 isl_space_free(maff
->space
);
5410 maff
->space
= space
;
5413 *ls
= isl_aff_get_domain_local_space(maff
->p
[0]);
5415 return isl_multi_aff_free(maff
);
5418 for (i
= 0; i
< maff
->n
; ++i
) {
5419 maff
->p
[i
] = isl_aff_lift(maff
->p
[i
]);
5427 isl_local_space_free(*ls
);
5428 return isl_multi_aff_free(maff
);
5432 /* Extract an isl_pw_aff corresponding to output dimension "pos" of "pma".
5434 __isl_give isl_pw_aff
*isl_pw_multi_aff_get_pw_aff(
5435 __isl_keep isl_pw_multi_aff
*pma
, int pos
)
5445 n_out
= isl_pw_multi_aff_dim(pma
, isl_dim_out
);
5446 if (pos
< 0 || pos
>= n_out
)
5447 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_invalid
,
5448 "index out of bounds", return NULL
);
5450 space
= isl_pw_multi_aff_get_space(pma
);
5451 space
= isl_space_drop_dims(space
, isl_dim_out
,
5452 pos
+ 1, n_out
- pos
- 1);
5453 space
= isl_space_drop_dims(space
, isl_dim_out
, 0, pos
);
5455 pa
= isl_pw_aff_alloc_size(space
, pma
->n
);
5456 for (i
= 0; i
< pma
->n
; ++i
) {
5458 aff
= isl_multi_aff_get_aff(pma
->p
[i
].maff
, pos
);
5459 pa
= isl_pw_aff_add_piece(pa
, isl_set_copy(pma
->p
[i
].set
), aff
);
5465 /* Return an isl_pw_multi_aff with the given "set" as domain and
5466 * an unnamed zero-dimensional range.
5468 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_from_domain(
5469 __isl_take isl_set
*set
)
5474 space
= isl_set_get_space(set
);
5475 space
= isl_space_from_domain(space
);
5476 ma
= isl_multi_aff_zero(space
);
5477 return isl_pw_multi_aff_alloc(set
, ma
);
5480 /* Add an isl_pw_multi_aff with the given "set" as domain and
5481 * an unnamed zero-dimensional range to *user.
5483 static int add_pw_multi_aff_from_domain(__isl_take isl_set
*set
, void *user
)
5485 isl_union_pw_multi_aff
**upma
= user
;
5486 isl_pw_multi_aff
*pma
;
5488 pma
= isl_pw_multi_aff_from_domain(set
);
5489 *upma
= isl_union_pw_multi_aff_add_pw_multi_aff(*upma
, pma
);
5494 /* Return an isl_union_pw_multi_aff with the given "uset" as domain and
5495 * an unnamed zero-dimensional range.
5497 __isl_give isl_union_pw_multi_aff
*isl_union_pw_multi_aff_from_domain(
5498 __isl_take isl_union_set
*uset
)
5501 isl_union_pw_multi_aff
*upma
;
5506 space
= isl_union_set_get_space(uset
);
5507 upma
= isl_union_pw_multi_aff_empty(space
);
5509 if (isl_union_set_foreach_set(uset
,
5510 &add_pw_multi_aff_from_domain
, &upma
) < 0)
5513 isl_union_set_free(uset
);
5516 isl_union_set_free(uset
);
5517 isl_union_pw_multi_aff_free(upma
);
5521 /* Convert "pma" to an isl_map and add it to *umap.
5523 static int map_from_pw_multi_aff(__isl_take isl_pw_multi_aff
*pma
, void *user
)
5525 isl_union_map
**umap
= user
;
5528 map
= isl_map_from_pw_multi_aff(pma
);
5529 *umap
= isl_union_map_add_map(*umap
, map
);
5534 /* Construct a union map mapping the domain of the union
5535 * piecewise multi-affine expression to its range, with each dimension
5536 * in the range equated to the corresponding affine expression on its cell.
5538 __isl_give isl_union_map
*isl_union_map_from_union_pw_multi_aff(
5539 __isl_take isl_union_pw_multi_aff
*upma
)
5542 isl_union_map
*umap
;
5547 space
= isl_union_pw_multi_aff_get_space(upma
);
5548 umap
= isl_union_map_empty(space
);
5550 if (isl_union_pw_multi_aff_foreach_pw_multi_aff(upma
,
5551 &map_from_pw_multi_aff
, &umap
) < 0)
5554 isl_union_pw_multi_aff_free(upma
);
5557 isl_union_pw_multi_aff_free(upma
);
5558 isl_union_map_free(umap
);
5562 /* Local data for bin_entry and the callback "fn".
5564 struct isl_union_pw_multi_aff_bin_data
{
5565 isl_union_pw_multi_aff
*upma2
;
5566 isl_union_pw_multi_aff
*res
;
5567 isl_pw_multi_aff
*pma
;
5568 int (*fn
)(void **entry
, void *user
);
5571 /* Given an isl_pw_multi_aff from upma1, store it in data->pma
5572 * and call data->fn for each isl_pw_multi_aff in data->upma2.
5574 static int bin_entry(void **entry
, void *user
)
5576 struct isl_union_pw_multi_aff_bin_data
*data
= user
;
5577 isl_pw_multi_aff
*pma
= *entry
;
5580 if (isl_hash_table_foreach(data
->upma2
->space
->ctx
, &data
->upma2
->table
,
5581 data
->fn
, data
) < 0)
5587 /* Call "fn" on each pair of isl_pw_multi_affs in "upma1" and "upma2".
5588 * The isl_pw_multi_aff from upma1 is stored in data->pma (where data is
5589 * passed as user field) and the isl_pw_multi_aff from upma2 is available
5590 * as *entry. The callback should adjust data->res if desired.
5592 static __isl_give isl_union_pw_multi_aff
*bin_op(
5593 __isl_take isl_union_pw_multi_aff
*upma1
,
5594 __isl_take isl_union_pw_multi_aff
*upma2
,
5595 int (*fn
)(void **entry
, void *user
))
5598 struct isl_union_pw_multi_aff_bin_data data
= { NULL
, NULL
, NULL
, fn
};
5600 space
= isl_union_pw_multi_aff_get_space(upma2
);
5601 upma1
= isl_union_pw_multi_aff_align_params(upma1
, space
);
5602 space
= isl_union_pw_multi_aff_get_space(upma1
);
5603 upma2
= isl_union_pw_multi_aff_align_params(upma2
, space
);
5605 if (!upma1
|| !upma2
)
5609 data
.res
= isl_union_pw_multi_aff_alloc(isl_space_copy(upma1
->space
),
5611 if (isl_hash_table_foreach(upma1
->space
->ctx
, &upma1
->table
,
5612 &bin_entry
, &data
) < 0)
5615 isl_union_pw_multi_aff_free(upma1
);
5616 isl_union_pw_multi_aff_free(upma2
);
5619 isl_union_pw_multi_aff_free(upma1
);
5620 isl_union_pw_multi_aff_free(upma2
);
5621 isl_union_pw_multi_aff_free(data
.res
);
5625 /* Given two aligned isl_pw_multi_affs A -> B and C -> D,
5626 * construct an isl_pw_multi_aff (A * C) -> [B -> D].
5628 static __isl_give isl_pw_multi_aff
*pw_multi_aff_range_product(
5629 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
5633 space
= isl_space_range_product(isl_pw_multi_aff_get_space(pma1
),
5634 isl_pw_multi_aff_get_space(pma2
));
5635 return isl_pw_multi_aff_on_shared_domain_in(pma1
, pma2
, space
,
5636 &isl_multi_aff_range_product
);
5639 /* Given two isl_pw_multi_affs A -> B and C -> D,
5640 * construct an isl_pw_multi_aff (A * C) -> [B -> D].
5642 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_range_product(
5643 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
5645 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
5646 &pw_multi_aff_range_product
);
5649 /* Given two aligned isl_pw_multi_affs A -> B and C -> D,
5650 * construct an isl_pw_multi_aff (A * C) -> (B, D).
5652 static __isl_give isl_pw_multi_aff
*pw_multi_aff_flat_range_product(
5653 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
5657 space
= isl_space_range_product(isl_pw_multi_aff_get_space(pma1
),
5658 isl_pw_multi_aff_get_space(pma2
));
5659 space
= isl_space_flatten_range(space
);
5660 return isl_pw_multi_aff_on_shared_domain_in(pma1
, pma2
, space
,
5661 &isl_multi_aff_flat_range_product
);
5664 /* Given two isl_pw_multi_affs A -> B and C -> D,
5665 * construct an isl_pw_multi_aff (A * C) -> (B, D).
5667 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_flat_range_product(
5668 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
5670 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
5671 &pw_multi_aff_flat_range_product
);
5674 /* If data->pma and *entry have the same domain space, then compute
5675 * their flat range product and the result to data->res.
5677 static int flat_range_product_entry(void **entry
, void *user
)
5679 struct isl_union_pw_multi_aff_bin_data
*data
= user
;
5680 isl_pw_multi_aff
*pma2
= *entry
;
5682 if (!isl_space_tuple_is_equal(data
->pma
->dim
, isl_dim_in
,
5683 pma2
->dim
, isl_dim_in
))
5686 pma2
= isl_pw_multi_aff_flat_range_product(
5687 isl_pw_multi_aff_copy(data
->pma
),
5688 isl_pw_multi_aff_copy(pma2
));
5690 data
->res
= isl_union_pw_multi_aff_add_pw_multi_aff(data
->res
, pma2
);
5695 /* Given two isl_union_pw_multi_affs A -> B and C -> D,
5696 * construct an isl_union_pw_multi_aff (A * C) -> (B, D).
5698 __isl_give isl_union_pw_multi_aff
*isl_union_pw_multi_aff_flat_range_product(
5699 __isl_take isl_union_pw_multi_aff
*upma1
,
5700 __isl_take isl_union_pw_multi_aff
*upma2
)
5702 return bin_op(upma1
, upma2
, &flat_range_product_entry
);
5705 /* Replace the affine expressions at position "pos" in "pma" by "pa".
5706 * The parameters are assumed to have been aligned.
5708 * The implementation essentially performs an isl_pw_*_on_shared_domain,
5709 * except that it works on two different isl_pw_* types.
5711 static __isl_give isl_pw_multi_aff
*pw_multi_aff_set_pw_aff(
5712 __isl_take isl_pw_multi_aff
*pma
, unsigned pos
,
5713 __isl_take isl_pw_aff
*pa
)
5716 isl_pw_multi_aff
*res
= NULL
;
5721 if (!isl_space_tuple_is_equal(pma
->dim
, isl_dim_in
,
5722 pa
->dim
, isl_dim_in
))
5723 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_invalid
,
5724 "domains don't match", goto error
);
5725 if (pos
>= isl_pw_multi_aff_dim(pma
, isl_dim_out
))
5726 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_invalid
,
5727 "index out of bounds", goto error
);
5730 res
= isl_pw_multi_aff_alloc_size(isl_pw_multi_aff_get_space(pma
), n
);
5732 for (i
= 0; i
< pma
->n
; ++i
) {
5733 for (j
= 0; j
< pa
->n
; ++j
) {
5735 isl_multi_aff
*res_ij
;
5738 common
= isl_set_intersect(isl_set_copy(pma
->p
[i
].set
),
5739 isl_set_copy(pa
->p
[j
].set
));
5740 empty
= isl_set_plain_is_empty(common
);
5741 if (empty
< 0 || empty
) {
5742 isl_set_free(common
);
5748 res_ij
= isl_multi_aff_set_aff(
5749 isl_multi_aff_copy(pma
->p
[i
].maff
), pos
,
5750 isl_aff_copy(pa
->p
[j
].aff
));
5751 res_ij
= isl_multi_aff_gist(res_ij
,
5752 isl_set_copy(common
));
5754 res
= isl_pw_multi_aff_add_piece(res
, common
, res_ij
);
5758 isl_pw_multi_aff_free(pma
);
5759 isl_pw_aff_free(pa
);
5762 isl_pw_multi_aff_free(pma
);
5763 isl_pw_aff_free(pa
);
5764 return isl_pw_multi_aff_free(res
);
5767 /* Replace the affine expressions at position "pos" in "pma" by "pa".
5769 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_set_pw_aff(
5770 __isl_take isl_pw_multi_aff
*pma
, unsigned pos
,
5771 __isl_take isl_pw_aff
*pa
)
5775 if (isl_space_match(pma
->dim
, isl_dim_param
, pa
->dim
, isl_dim_param
))
5776 return pw_multi_aff_set_pw_aff(pma
, pos
, pa
);
5777 if (!isl_space_has_named_params(pma
->dim
) ||
5778 !isl_space_has_named_params(pa
->dim
))
5779 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_invalid
,
5780 "unaligned unnamed parameters", goto error
);
5781 pma
= isl_pw_multi_aff_align_params(pma
, isl_pw_aff_get_space(pa
));
5782 pa
= isl_pw_aff_align_params(pa
, isl_pw_multi_aff_get_space(pma
));
5783 return pw_multi_aff_set_pw_aff(pma
, pos
, pa
);
5785 isl_pw_multi_aff_free(pma
);
5786 isl_pw_aff_free(pa
);
5790 /* Do the parameters of "pa" match those of "space"?
5792 int isl_pw_aff_matching_params(__isl_keep isl_pw_aff
*pa
,
5793 __isl_keep isl_space
*space
)
5795 isl_space
*pa_space
;
5801 pa_space
= isl_pw_aff_get_space(pa
);
5803 match
= isl_space_match(space
, isl_dim_param
, pa_space
, isl_dim_param
);
5805 isl_space_free(pa_space
);
5809 /* Check that the domain space of "pa" matches "space".
5811 * Return 0 on success and -1 on error.
5813 int isl_pw_aff_check_match_domain_space(__isl_keep isl_pw_aff
*pa
,
5814 __isl_keep isl_space
*space
)
5816 isl_space
*pa_space
;
5822 pa_space
= isl_pw_aff_get_space(pa
);
5824 match
= isl_space_match(space
, isl_dim_param
, pa_space
, isl_dim_param
);
5828 isl_die(isl_pw_aff_get_ctx(pa
), isl_error_invalid
,
5829 "parameters don't match", goto error
);
5830 match
= isl_space_tuple_is_equal(space
, isl_dim_in
,
5831 pa_space
, isl_dim_in
);
5835 isl_die(isl_pw_aff_get_ctx(pa
), isl_error_invalid
,
5836 "domains don't match", goto error
);
5837 isl_space_free(pa_space
);
5840 isl_space_free(pa_space
);
5847 #include <isl_multi_templ.c>
5849 /* Scale the elements of "pma" by the corresponding elements of "mv".
5851 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_scale_multi_val(
5852 __isl_take isl_pw_multi_aff
*pma
, __isl_take isl_multi_val
*mv
)
5856 pma
= isl_pw_multi_aff_cow(pma
);
5859 if (!isl_space_tuple_is_equal(pma
->dim
, isl_dim_out
,
5860 mv
->space
, isl_dim_set
))
5861 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_invalid
,
5862 "spaces don't match", goto error
);
5863 if (!isl_space_match(pma
->dim
, isl_dim_param
,
5864 mv
->space
, isl_dim_param
)) {
5865 pma
= isl_pw_multi_aff_align_params(pma
,
5866 isl_multi_val_get_space(mv
));
5867 mv
= isl_multi_val_align_params(mv
,
5868 isl_pw_multi_aff_get_space(pma
));
5873 for (i
= 0; i
< pma
->n
; ++i
) {
5874 pma
->p
[i
].maff
= isl_multi_aff_scale_multi_val(pma
->p
[i
].maff
,
5875 isl_multi_val_copy(mv
));
5876 if (!pma
->p
[i
].maff
)
5880 isl_multi_val_free(mv
);
5883 isl_multi_val_free(mv
);
5884 isl_pw_multi_aff_free(pma
);
5888 /* Internal data structure for isl_union_pw_multi_aff_scale_multi_val.
5889 * mv contains the mv argument.
5890 * res collects the results.
5892 struct isl_union_pw_multi_aff_scale_multi_val_data
{
5894 isl_union_pw_multi_aff
*res
;
5897 /* This function is called for each entry of an isl_union_pw_multi_aff.
5898 * If the space of the entry matches that of data->mv,
5899 * then apply isl_pw_multi_aff_scale_multi_val and add the result
5902 static int union_pw_multi_aff_scale_multi_val_entry(void **entry
, void *user
)
5904 struct isl_union_pw_multi_aff_scale_multi_val_data
*data
= user
;
5905 isl_pw_multi_aff
*pma
= *entry
;
5909 if (!isl_space_tuple_is_equal(pma
->dim
, isl_dim_out
,
5910 data
->mv
->space
, isl_dim_set
))
5913 pma
= isl_pw_multi_aff_copy(pma
);
5914 pma
= isl_pw_multi_aff_scale_multi_val(pma
,
5915 isl_multi_val_copy(data
->mv
));
5916 data
->res
= isl_union_pw_multi_aff_add_pw_multi_aff(data
->res
, pma
);
5923 /* Scale the elements of "upma" by the corresponding elements of "mv",
5924 * for those entries that match the space of "mv".
5926 __isl_give isl_union_pw_multi_aff
*isl_union_pw_multi_aff_scale_multi_val(
5927 __isl_take isl_union_pw_multi_aff
*upma
, __isl_take isl_multi_val
*mv
)
5929 struct isl_union_pw_multi_aff_scale_multi_val_data data
;
5931 upma
= isl_union_pw_multi_aff_align_params(upma
,
5932 isl_multi_val_get_space(mv
));
5933 mv
= isl_multi_val_align_params(mv
,
5934 isl_union_pw_multi_aff_get_space(upma
));
5939 data
.res
= isl_union_pw_multi_aff_alloc(isl_space_copy(upma
->space
),
5941 if (isl_hash_table_foreach(upma
->space
->ctx
, &upma
->table
,
5942 &union_pw_multi_aff_scale_multi_val_entry
, &data
) < 0)
5945 isl_multi_val_free(mv
);
5946 isl_union_pw_multi_aff_free(upma
);
5949 isl_multi_val_free(mv
);
5950 isl_union_pw_multi_aff_free(upma
);
5954 /* Construct and return a piecewise multi affine expression
5955 * in the given space with value zero in each of the output dimensions and
5956 * a universe domain.
5958 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_zero(__isl_take isl_space
*space
)
5960 return isl_pw_multi_aff_from_multi_aff(isl_multi_aff_zero(space
));
5963 /* Construct and return a piecewise multi affine expression
5964 * that is equal to the given piecewise affine expression.
5966 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_from_pw_aff(
5967 __isl_take isl_pw_aff
*pa
)
5971 isl_pw_multi_aff
*pma
;
5976 space
= isl_pw_aff_get_space(pa
);
5977 pma
= isl_pw_multi_aff_alloc_size(space
, pa
->n
);
5979 for (i
= 0; i
< pa
->n
; ++i
) {
5983 set
= isl_set_copy(pa
->p
[i
].set
);
5984 ma
= isl_multi_aff_from_aff(isl_aff_copy(pa
->p
[i
].aff
));
5985 pma
= isl_pw_multi_aff_add_piece(pma
, set
, ma
);
5988 isl_pw_aff_free(pa
);
5992 /* Construct a set or map mapping the shared (parameter) domain
5993 * of the piecewise affine expressions to the range of "mpa"
5994 * with each dimension in the range equated to the
5995 * corresponding piecewise affine expression.
5997 static __isl_give isl_map
*map_from_multi_pw_aff(
5998 __isl_take isl_multi_pw_aff
*mpa
)
6007 if (isl_space_dim(mpa
->space
, isl_dim_out
) != mpa
->n
)
6008 isl_die(isl_multi_pw_aff_get_ctx(mpa
), isl_error_internal
,
6009 "invalid space", goto error
);
6011 space
= isl_multi_pw_aff_get_domain_space(mpa
);
6012 map
= isl_map_universe(isl_space_from_domain(space
));
6014 for (i
= 0; i
< mpa
->n
; ++i
) {
6018 pa
= isl_pw_aff_copy(mpa
->p
[i
]);
6019 map_i
= map_from_pw_aff(pa
);
6021 map
= isl_map_flat_range_product(map
, map_i
);
6024 map
= isl_map_reset_space(map
, isl_multi_pw_aff_get_space(mpa
));
6026 isl_multi_pw_aff_free(mpa
);
6029 isl_multi_pw_aff_free(mpa
);
6033 /* Construct a map mapping the shared domain
6034 * of the piecewise affine expressions to the range of "mpa"
6035 * with each dimension in the range equated to the
6036 * corresponding piecewise affine expression.
6038 __isl_give isl_map
*isl_map_from_multi_pw_aff(__isl_take isl_multi_pw_aff
*mpa
)
6042 if (isl_space_is_set(mpa
->space
))
6043 isl_die(isl_multi_pw_aff_get_ctx(mpa
), isl_error_internal
,
6044 "space of input is not a map", goto error
);
6046 return map_from_multi_pw_aff(mpa
);
6048 isl_multi_pw_aff_free(mpa
);
6052 /* Construct a set mapping the shared parameter domain
6053 * of the piecewise affine expressions to the space of "mpa"
6054 * with each dimension in the range equated to the
6055 * corresponding piecewise affine expression.
6057 __isl_give isl_set
*isl_set_from_multi_pw_aff(__isl_take isl_multi_pw_aff
*mpa
)
6061 if (!isl_space_is_set(mpa
->space
))
6062 isl_die(isl_multi_pw_aff_get_ctx(mpa
), isl_error_internal
,
6063 "space of input is not a set", goto error
);
6065 return map_from_multi_pw_aff(mpa
);
6067 isl_multi_pw_aff_free(mpa
);
6071 /* Construct and return a piecewise multi affine expression
6072 * that is equal to the given multi piecewise affine expression
6073 * on the shared domain of the piecewise affine expressions.
6075 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_from_multi_pw_aff(
6076 __isl_take isl_multi_pw_aff
*mpa
)
6081 isl_pw_multi_aff
*pma
;
6086 space
= isl_multi_pw_aff_get_space(mpa
);
6089 isl_multi_pw_aff_free(mpa
);
6090 return isl_pw_multi_aff_zero(space
);
6093 pa
= isl_multi_pw_aff_get_pw_aff(mpa
, 0);
6094 pma
= isl_pw_multi_aff_from_pw_aff(pa
);
6096 for (i
= 1; i
< mpa
->n
; ++i
) {
6097 isl_pw_multi_aff
*pma_i
;
6099 pa
= isl_multi_pw_aff_get_pw_aff(mpa
, i
);
6100 pma_i
= isl_pw_multi_aff_from_pw_aff(pa
);
6101 pma
= isl_pw_multi_aff_range_product(pma
, pma_i
);
6104 pma
= isl_pw_multi_aff_reset_space(pma
, space
);
6106 isl_multi_pw_aff_free(mpa
);
6110 /* Construct and return a multi piecewise affine expression
6111 * that is equal to the given multi affine expression.
6113 __isl_give isl_multi_pw_aff
*isl_multi_pw_aff_from_multi_aff(
6114 __isl_take isl_multi_aff
*ma
)
6117 isl_multi_pw_aff
*mpa
;
6122 n
= isl_multi_aff_dim(ma
, isl_dim_out
);
6123 mpa
= isl_multi_pw_aff_alloc(isl_multi_aff_get_space(ma
));
6125 for (i
= 0; i
< n
; ++i
) {
6128 pa
= isl_pw_aff_from_aff(isl_multi_aff_get_aff(ma
, i
));
6129 mpa
= isl_multi_pw_aff_set_pw_aff(mpa
, i
, pa
);
6132 isl_multi_aff_free(ma
);
6136 /* Construct and return a multi piecewise affine expression
6137 * that is equal to the given piecewise multi affine expression.
6139 __isl_give isl_multi_pw_aff
*isl_multi_pw_aff_from_pw_multi_aff(
6140 __isl_take isl_pw_multi_aff
*pma
)
6144 isl_multi_pw_aff
*mpa
;
6149 n
= isl_pw_multi_aff_dim(pma
, isl_dim_out
);
6150 space
= isl_pw_multi_aff_get_space(pma
);
6151 mpa
= isl_multi_pw_aff_alloc(space
);
6153 for (i
= 0; i
< n
; ++i
) {
6156 pa
= isl_pw_multi_aff_get_pw_aff(pma
, i
);
6157 mpa
= isl_multi_pw_aff_set_pw_aff(mpa
, i
, pa
);
6160 isl_pw_multi_aff_free(pma
);
6164 /* Do "pa1" and "pa2" represent the same function?
6166 * We first check if they are obviously equal.
6167 * If not, we convert them to maps and check if those are equal.
6169 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff
*pa1
, __isl_keep isl_pw_aff
*pa2
)
6172 isl_map
*map1
, *map2
;
6177 equal
= isl_pw_aff_plain_is_equal(pa1
, pa2
);
6178 if (equal
< 0 || equal
)
6181 map1
= map_from_pw_aff(isl_pw_aff_copy(pa1
));
6182 map2
= map_from_pw_aff(isl_pw_aff_copy(pa2
));
6183 equal
= isl_map_is_equal(map1
, map2
);
6190 /* Do "mpa1" and "mpa2" represent the same function?
6192 * Note that we cannot convert the entire isl_multi_pw_aff
6193 * to a map because the domains of the piecewise affine expressions
6194 * may not be the same.
6196 int isl_multi_pw_aff_is_equal(__isl_keep isl_multi_pw_aff
*mpa1
,
6197 __isl_keep isl_multi_pw_aff
*mpa2
)
6205 if (!isl_space_match(mpa1
->space
, isl_dim_param
,
6206 mpa2
->space
, isl_dim_param
)) {
6207 if (!isl_space_has_named_params(mpa1
->space
))
6209 if (!isl_space_has_named_params(mpa2
->space
))
6211 mpa1
= isl_multi_pw_aff_copy(mpa1
);
6212 mpa2
= isl_multi_pw_aff_copy(mpa2
);
6213 mpa1
= isl_multi_pw_aff_align_params(mpa1
,
6214 isl_multi_pw_aff_get_space(mpa2
));
6215 mpa2
= isl_multi_pw_aff_align_params(mpa2
,
6216 isl_multi_pw_aff_get_space(mpa1
));
6217 equal
= isl_multi_pw_aff_is_equal(mpa1
, mpa2
);
6218 isl_multi_pw_aff_free(mpa1
);
6219 isl_multi_pw_aff_free(mpa2
);
6223 equal
= isl_space_is_equal(mpa1
->space
, mpa2
->space
);
6224 if (equal
< 0 || !equal
)
6227 for (i
= 0; i
< mpa1
->n
; ++i
) {
6228 equal
= isl_pw_aff_is_equal(mpa1
->p
[i
], mpa2
->p
[i
]);
6229 if (equal
< 0 || !equal
)
6236 /* Coalesce the elements of "mpa".
6238 * Note that such coalescing does not change the meaning of "mpa"
6239 * so there is no need to cow. We do need to be careful not to
6240 * destroy any other copies of "mpa" in case of failure.
6242 __isl_give isl_multi_pw_aff
*isl_multi_pw_aff_coalesce(
6243 __isl_take isl_multi_pw_aff
*mpa
)
6250 for (i
= 0; i
< mpa
->n
; ++i
) {
6251 isl_pw_aff
*pa
= isl_pw_aff_copy(mpa
->p
[i
]);
6252 pa
= isl_pw_aff_coalesce(pa
);
6254 return isl_multi_pw_aff_free(mpa
);
6255 isl_pw_aff_free(mpa
->p
[i
]);
6262 /* Compute the pullback of "mpa" by the function represented by "ma".
6263 * In other words, plug in "ma" in "mpa".
6265 * The parameters of "mpa" and "ma" are assumed to have been aligned.
6267 static __isl_give isl_multi_pw_aff
*isl_multi_pw_aff_pullback_multi_aff_aligned(
6268 __isl_take isl_multi_pw_aff
*mpa
, __isl_take isl_multi_aff
*ma
)
6271 isl_space
*space
= NULL
;
6273 mpa
= isl_multi_pw_aff_cow(mpa
);
6277 space
= isl_space_join(isl_multi_aff_get_space(ma
),
6278 isl_multi_pw_aff_get_space(mpa
));
6282 for (i
= 0; i
< mpa
->n
; ++i
) {
6283 mpa
->p
[i
] = isl_pw_aff_pullback_multi_aff(mpa
->p
[i
],
6284 isl_multi_aff_copy(ma
));
6289 isl_multi_aff_free(ma
);
6290 isl_space_free(mpa
->space
);
6294 isl_space_free(space
);
6295 isl_multi_pw_aff_free(mpa
);
6296 isl_multi_aff_free(ma
);
6300 /* Compute the pullback of "mpa" by the function represented by "ma".
6301 * In other words, plug in "ma" in "mpa".
6303 __isl_give isl_multi_pw_aff
*isl_multi_pw_aff_pullback_multi_aff(
6304 __isl_take isl_multi_pw_aff
*mpa
, __isl_take isl_multi_aff
*ma
)
6308 if (isl_space_match(mpa
->space
, isl_dim_param
,
6309 ma
->space
, isl_dim_param
))
6310 return isl_multi_pw_aff_pullback_multi_aff_aligned(mpa
, ma
);
6311 mpa
= isl_multi_pw_aff_align_params(mpa
, isl_multi_aff_get_space(ma
));
6312 ma
= isl_multi_aff_align_params(ma
, isl_multi_pw_aff_get_space(mpa
));
6313 return isl_multi_pw_aff_pullback_multi_aff_aligned(mpa
, ma
);
6315 isl_multi_pw_aff_free(mpa
);
6316 isl_multi_aff_free(ma
);
6320 /* Compute the pullback of "mpa" by the function represented by "pma".
6321 * In other words, plug in "pma" in "mpa".
6323 * The parameters of "mpa" and "mpa" are assumed to have been aligned.
6325 static __isl_give isl_multi_pw_aff
*
6326 isl_multi_pw_aff_pullback_pw_multi_aff_aligned(
6327 __isl_take isl_multi_pw_aff
*mpa
, __isl_take isl_pw_multi_aff
*pma
)
6330 isl_space
*space
= NULL
;
6332 mpa
= isl_multi_pw_aff_cow(mpa
);
6336 space
= isl_space_join(isl_pw_multi_aff_get_space(pma
),
6337 isl_multi_pw_aff_get_space(mpa
));
6339 for (i
= 0; i
< mpa
->n
; ++i
) {
6340 mpa
->p
[i
] = isl_pw_aff_pullback_pw_multi_aff_aligned(mpa
->p
[i
],
6341 isl_pw_multi_aff_copy(pma
));
6346 isl_pw_multi_aff_free(pma
);
6347 isl_space_free(mpa
->space
);
6351 isl_space_free(space
);
6352 isl_multi_pw_aff_free(mpa
);
6353 isl_pw_multi_aff_free(pma
);
6357 /* Compute the pullback of "mpa" by the function represented by "pma".
6358 * In other words, plug in "pma" in "mpa".
6360 __isl_give isl_multi_pw_aff
*isl_multi_pw_aff_pullback_pw_multi_aff(
6361 __isl_take isl_multi_pw_aff
*mpa
, __isl_take isl_pw_multi_aff
*pma
)
6365 if (isl_space_match(mpa
->space
, isl_dim_param
, pma
->dim
, isl_dim_param
))
6366 return isl_multi_pw_aff_pullback_pw_multi_aff_aligned(mpa
, pma
);
6367 mpa
= isl_multi_pw_aff_align_params(mpa
,
6368 isl_pw_multi_aff_get_space(pma
));
6369 pma
= isl_pw_multi_aff_align_params(pma
,
6370 isl_multi_pw_aff_get_space(mpa
));
6371 return isl_multi_pw_aff_pullback_pw_multi_aff_aligned(mpa
, pma
);
6373 isl_multi_pw_aff_free(mpa
);
6374 isl_pw_multi_aff_free(pma
);
6378 /* Apply "aff" to "mpa". The range of "mpa" needs to be compatible
6379 * with the domain of "aff". The domain of the result is the same
6381 * "mpa" and "aff" are assumed to have been aligned.
6383 * We first extract the parametric constant from "aff", defined
6384 * over the correct domain.
6385 * Then we add the appropriate combinations of the members of "mpa".
6386 * Finally, we add the integer divisions through recursive calls.
6388 static __isl_give isl_pw_aff
*isl_multi_pw_aff_apply_aff_aligned(
6389 __isl_take isl_multi_pw_aff
*mpa
, __isl_take isl_aff
*aff
)
6391 int i
, n_param
, n_in
, n_div
;
6397 n_param
= isl_aff_dim(aff
, isl_dim_param
);
6398 n_in
= isl_aff_dim(aff
, isl_dim_in
);
6399 n_div
= isl_aff_dim(aff
, isl_dim_div
);
6401 space
= isl_space_domain(isl_multi_pw_aff_get_space(mpa
));
6402 tmp
= isl_aff_copy(aff
);
6403 tmp
= isl_aff_drop_dims(tmp
, isl_dim_div
, 0, n_div
);
6404 tmp
= isl_aff_drop_dims(tmp
, isl_dim_in
, 0, n_in
);
6405 tmp
= isl_aff_add_dims(tmp
, isl_dim_in
,
6406 isl_space_dim(space
, isl_dim_set
));
6407 tmp
= isl_aff_reset_domain_space(tmp
, space
);
6408 pa
= isl_pw_aff_from_aff(tmp
);
6410 for (i
= 0; i
< n_in
; ++i
) {
6413 if (!isl_aff_involves_dims(aff
, isl_dim_in
, i
, 1))
6415 v
= isl_aff_get_coefficient_val(aff
, isl_dim_in
, i
);
6416 pa_i
= isl_multi_pw_aff_get_pw_aff(mpa
, i
);
6417 pa_i
= isl_pw_aff_scale_val(pa_i
, v
);
6418 pa
= isl_pw_aff_add(pa
, pa_i
);
6421 for (i
= 0; i
< n_div
; ++i
) {
6425 if (!isl_aff_involves_dims(aff
, isl_dim_div
, i
, 1))
6427 div
= isl_aff_get_div(aff
, i
);
6428 pa_i
= isl_multi_pw_aff_apply_aff_aligned(
6429 isl_multi_pw_aff_copy(mpa
), div
);
6430 pa_i
= isl_pw_aff_floor(pa_i
);
6431 v
= isl_aff_get_coefficient_val(aff
, isl_dim_div
, i
);
6432 pa_i
= isl_pw_aff_scale_val(pa_i
, v
);
6433 pa
= isl_pw_aff_add(pa
, pa_i
);
6436 isl_multi_pw_aff_free(mpa
);
6442 /* Apply "aff" to "mpa". The range of "mpa" needs to be compatible
6443 * with the domain of "aff". The domain of the result is the same
6446 __isl_give isl_pw_aff
*isl_multi_pw_aff_apply_aff(
6447 __isl_take isl_multi_pw_aff
*mpa
, __isl_take isl_aff
*aff
)
6451 if (isl_space_match(aff
->ls
->dim
, isl_dim_param
,
6452 mpa
->space
, isl_dim_param
))
6453 return isl_multi_pw_aff_apply_aff_aligned(mpa
, aff
);
6455 aff
= isl_aff_align_params(aff
, isl_multi_pw_aff_get_space(mpa
));
6456 mpa
= isl_multi_pw_aff_align_params(mpa
, isl_aff_get_space(aff
));
6458 return isl_multi_pw_aff_apply_aff_aligned(mpa
, aff
);
6461 isl_multi_pw_aff_free(mpa
);
6465 /* Apply "pa" to "mpa". The range of "mpa" needs to be compatible
6466 * with the domain of "pa". The domain of the result is the same
6468 * "mpa" and "pa" are assumed to have been aligned.
6470 * We consider each piece in turn. Note that the domains of the
6471 * pieces are assumed to be disjoint and they remain disjoint
6472 * after taking the preimage (over the same function).
6474 static __isl_give isl_pw_aff
*isl_multi_pw_aff_apply_pw_aff_aligned(
6475 __isl_take isl_multi_pw_aff
*mpa
, __isl_take isl_pw_aff
*pa
)
6484 space
= isl_space_join(isl_multi_pw_aff_get_space(mpa
),
6485 isl_pw_aff_get_space(pa
));
6486 res
= isl_pw_aff_empty(space
);
6488 for (i
= 0; i
< pa
->n
; ++i
) {
6492 pa_i
= isl_multi_pw_aff_apply_aff_aligned(
6493 isl_multi_pw_aff_copy(mpa
),
6494 isl_aff_copy(pa
->p
[i
].aff
));
6495 domain
= isl_set_copy(pa
->p
[i
].set
);
6496 domain
= isl_set_preimage_multi_pw_aff(domain
,
6497 isl_multi_pw_aff_copy(mpa
));
6498 pa_i
= isl_pw_aff_intersect_domain(pa_i
, domain
);
6499 res
= isl_pw_aff_add_disjoint(res
, pa_i
);
6502 isl_pw_aff_free(pa
);
6503 isl_multi_pw_aff_free(mpa
);
6506 isl_pw_aff_free(pa
);
6507 isl_multi_pw_aff_free(mpa
);
6511 /* Apply "pa" to "mpa". The range of "mpa" needs to be compatible
6512 * with the domain of "pa". The domain of the result is the same
6515 __isl_give isl_pw_aff
*isl_multi_pw_aff_apply_pw_aff(
6516 __isl_take isl_multi_pw_aff
*mpa
, __isl_take isl_pw_aff
*pa
)
6520 if (isl_space_match(pa
->dim
, isl_dim_param
, mpa
->space
, isl_dim_param
))
6521 return isl_multi_pw_aff_apply_pw_aff_aligned(mpa
, pa
);
6523 pa
= isl_pw_aff_align_params(pa
, isl_multi_pw_aff_get_space(mpa
));
6524 mpa
= isl_multi_pw_aff_align_params(mpa
, isl_pw_aff_get_space(pa
));
6526 return isl_multi_pw_aff_apply_pw_aff_aligned(mpa
, pa
);
6528 isl_pw_aff_free(pa
);
6529 isl_multi_pw_aff_free(mpa
);
6533 /* Compute the pullback of "pa" by the function represented by "mpa".
6534 * In other words, plug in "mpa" in "pa".
6535 * "pa" and "mpa" are assumed to have been aligned.
6537 * The pullback is computed by applying "pa" to "mpa".
6539 static __isl_give isl_pw_aff
*isl_pw_aff_pullback_multi_pw_aff_aligned(
6540 __isl_take isl_pw_aff
*pa
, __isl_take isl_multi_pw_aff
*mpa
)
6542 return isl_multi_pw_aff_apply_pw_aff_aligned(mpa
, pa
);
6545 /* Compute the pullback of "pa" by the function represented by "mpa".
6546 * In other words, plug in "mpa" in "pa".
6548 * The pullback is computed by applying "pa" to "mpa".
6550 __isl_give isl_pw_aff
*isl_pw_aff_pullback_multi_pw_aff(
6551 __isl_take isl_pw_aff
*pa
, __isl_take isl_multi_pw_aff
*mpa
)
6553 return isl_multi_pw_aff_apply_pw_aff(mpa
, pa
);
6556 /* Compute the pullback of "mpa1" by the function represented by "mpa2".
6557 * In other words, plug in "mpa2" in "mpa1".
6559 * The parameters of "mpa1" and "mpa2" are assumed to have been aligned.
6561 * We pullback each member of "mpa1" in turn.
6563 static __isl_give isl_multi_pw_aff
*
6564 isl_multi_pw_aff_pullback_multi_pw_aff_aligned(
6565 __isl_take isl_multi_pw_aff
*mpa1
, __isl_take isl_multi_pw_aff
*mpa2
)
6568 isl_space
*space
= NULL
;
6570 mpa1
= isl_multi_pw_aff_cow(mpa1
);
6574 space
= isl_space_join(isl_multi_pw_aff_get_space(mpa2
),
6575 isl_multi_pw_aff_get_space(mpa1
));
6577 for (i
= 0; i
< mpa1
->n
; ++i
) {
6578 mpa1
->p
[i
] = isl_pw_aff_pullback_multi_pw_aff_aligned(
6579 mpa1
->p
[i
], isl_multi_pw_aff_copy(mpa2
));
6584 mpa1
= isl_multi_pw_aff_reset_space(mpa1
, space
);
6586 isl_multi_pw_aff_free(mpa2
);
6589 isl_space_free(space
);
6590 isl_multi_pw_aff_free(mpa1
);
6591 isl_multi_pw_aff_free(mpa2
);
6595 /* Compute the pullback of "mpa1" by the function represented by "mpa2".
6596 * In other words, plug in "mpa2" in "mpa1".
6598 __isl_give isl_multi_pw_aff
*isl_multi_pw_aff_pullback_multi_pw_aff(
6599 __isl_take isl_multi_pw_aff
*mpa1
, __isl_take isl_multi_pw_aff
*mpa2
)
6601 return isl_multi_pw_aff_align_params_multi_multi_and(mpa1
, mpa2
,
6602 &isl_multi_pw_aff_pullback_multi_pw_aff_aligned
);
6605 /* Compare two isl_affs.
6607 * Return -1 if "aff1" is "smaller" than "aff2", 1 if "aff1" is "greater"
6608 * than "aff2" and 0 if they are equal.
6610 * The order is fairly arbitrary. We do consider expressions that only involve
6611 * earlier dimensions as "smaller".
6613 int isl_aff_plain_cmp(__isl_keep isl_aff
*aff1
, __isl_keep isl_aff
*aff2
)
6626 cmp
= isl_local_space_cmp(aff1
->ls
, aff2
->ls
);
6630 last1
= isl_seq_last_non_zero(aff1
->v
->el
+ 1, aff1
->v
->size
- 1);
6631 last2
= isl_seq_last_non_zero(aff2
->v
->el
+ 1, aff1
->v
->size
- 1);
6633 return last1
- last2
;
6635 return isl_seq_cmp(aff1
->v
->el
, aff2
->v
->el
, aff1
->v
->size
);
6638 /* Compare two isl_pw_affs.
6640 * Return -1 if "pa1" is "smaller" than "pa2", 1 if "pa1" is "greater"
6641 * than "pa2" and 0 if they are equal.
6643 * The order is fairly arbitrary. We do consider expressions that only involve
6644 * earlier dimensions as "smaller".
6646 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff
*pa1
,
6647 __isl_keep isl_pw_aff
*pa2
)
6660 cmp
= isl_space_cmp(pa1
->dim
, pa2
->dim
);
6664 if (pa1
->n
!= pa2
->n
)
6665 return pa1
->n
- pa2
->n
;
6667 for (i
= 0; i
< pa1
->n
; ++i
) {
6668 cmp
= isl_set_plain_cmp(pa1
->p
[i
].set
, pa2
->p
[i
].set
);
6671 cmp
= isl_aff_plain_cmp(pa1
->p
[i
].aff
, pa2
->p
[i
].aff
);
6679 /* Return a piecewise affine expression that is equal to "v" on "domain".
6681 __isl_give isl_pw_aff
*isl_pw_aff_val_on_domain(__isl_take isl_set
*domain
,
6682 __isl_take isl_val
*v
)
6685 isl_local_space
*ls
;
6688 space
= isl_set_get_space(domain
);
6689 ls
= isl_local_space_from_space(space
);
6690 aff
= isl_aff_val_on_domain(ls
, v
);
6692 return isl_pw_aff_alloc(domain
, aff
);
6695 /* Return a multi affine expression that is equal to "mv" on domain
6698 __isl_give isl_multi_aff
*isl_multi_aff_multi_val_on_space(
6699 __isl_take isl_space
*space
, __isl_take isl_multi_val
*mv
)
6703 isl_local_space
*ls
;
6709 n
= isl_multi_val_dim(mv
, isl_dim_set
);
6710 space2
= isl_multi_val_get_space(mv
);
6711 space2
= isl_space_align_params(space2
, isl_space_copy(space
));
6712 space
= isl_space_align_params(space
, isl_space_copy(space2
));
6713 space
= isl_space_map_from_domain_and_range(space
, space2
);
6714 ma
= isl_multi_aff_alloc(isl_space_copy(space
));
6715 ls
= isl_local_space_from_space(isl_space_domain(space
));
6716 for (i
= 0; i
< n
; ++i
) {
6720 v
= isl_multi_val_get_val(mv
, i
);
6721 aff
= isl_aff_val_on_domain(isl_local_space_copy(ls
), v
);
6722 ma
= isl_multi_aff_set_aff(ma
, i
, aff
);
6724 isl_local_space_free(ls
);
6726 isl_multi_val_free(mv
);
6729 isl_space_free(space
);
6730 isl_multi_val_free(mv
);
6734 /* Return a piecewise multi-affine expression
6735 * that is equal to "mv" on "domain".
6737 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_multi_val_on_domain(
6738 __isl_take isl_set
*domain
, __isl_take isl_multi_val
*mv
)
6743 space
= isl_set_get_space(domain
);
6744 ma
= isl_multi_aff_multi_val_on_space(space
, mv
);
6746 return isl_pw_multi_aff_alloc(domain
, ma
);
6749 /* Internal data structure for isl_union_pw_multi_aff_multi_val_on_domain.
6750 * mv is the value that should be attained on each domain set
6751 * res collects the results
6753 struct isl_union_pw_multi_aff_multi_val_on_domain_data
{
6755 isl_union_pw_multi_aff
*res
;
6758 /* Create an isl_pw_multi_aff equal to data->mv on "domain"
6759 * and add it to data->res.
6761 static int pw_multi_aff_multi_val_on_domain(__isl_take isl_set
*domain
,
6764 struct isl_union_pw_multi_aff_multi_val_on_domain_data
*data
= user
;
6765 isl_pw_multi_aff
*pma
;
6768 mv
= isl_multi_val_copy(data
->mv
);
6769 pma
= isl_pw_multi_aff_multi_val_on_domain(domain
, mv
);
6770 data
->res
= isl_union_pw_multi_aff_add_pw_multi_aff(data
->res
, pma
);
6772 return data
->res
? 0 : -1;
6775 /* Return a union piecewise multi-affine expression
6776 * that is equal to "mv" on "domain".
6778 __isl_give isl_union_pw_multi_aff
*isl_union_pw_multi_aff_multi_val_on_domain(
6779 __isl_take isl_union_set
*domain
, __isl_take isl_multi_val
*mv
)
6781 struct isl_union_pw_multi_aff_multi_val_on_domain_data data
;
6784 space
= isl_union_set_get_space(domain
);
6785 data
.res
= isl_union_pw_multi_aff_empty(space
);
6787 if (isl_union_set_foreach_set(domain
,
6788 &pw_multi_aff_multi_val_on_domain
, &data
) < 0)
6789 data
.res
= isl_union_pw_multi_aff_free(data
.res
);
6790 isl_union_set_free(domain
);
6791 isl_multi_val_free(mv
);