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>
41 #define BASE union_pw_aff
43 #include <isl_list_templ.c>
46 #define BASE union_pw_multi_aff
48 #include <isl_list_templ.c>
50 __isl_give isl_aff
*isl_aff_alloc_vec(__isl_take isl_local_space
*ls
,
51 __isl_take isl_vec
*v
)
58 aff
= isl_calloc_type(v
->ctx
, struct isl_aff
);
68 isl_local_space_free(ls
);
73 __isl_give isl_aff
*isl_aff_alloc(__isl_take isl_local_space
*ls
)
82 ctx
= isl_local_space_get_ctx(ls
);
83 if (!isl_local_space_divs_known(ls
))
84 isl_die(ctx
, isl_error_invalid
, "local space has unknown divs",
86 if (!isl_local_space_is_set(ls
))
87 isl_die(ctx
, isl_error_invalid
,
88 "domain of affine expression should be a set",
91 total
= isl_local_space_dim(ls
, isl_dim_all
);
92 v
= isl_vec_alloc(ctx
, 1 + 1 + total
);
93 return isl_aff_alloc_vec(ls
, v
);
95 isl_local_space_free(ls
);
99 __isl_give isl_aff
*isl_aff_zero_on_domain(__isl_take isl_local_space
*ls
)
103 aff
= isl_aff_alloc(ls
);
107 isl_int_set_si(aff
->v
->el
[0], 1);
108 isl_seq_clr(aff
->v
->el
+ 1, aff
->v
->size
- 1);
113 /* Return a piecewise affine expression defined on the specified domain
114 * that is equal to zero.
116 __isl_give isl_pw_aff
*isl_pw_aff_zero_on_domain(__isl_take isl_local_space
*ls
)
118 return isl_pw_aff_from_aff(isl_aff_zero_on_domain(ls
));
121 /* Return an affine expression defined on the specified domain
122 * that represents NaN.
124 __isl_give isl_aff
*isl_aff_nan_on_domain(__isl_take isl_local_space
*ls
)
128 aff
= isl_aff_alloc(ls
);
132 isl_seq_clr(aff
->v
->el
, aff
->v
->size
);
137 /* Return a piecewise affine expression defined on the specified domain
138 * that represents NaN.
140 __isl_give isl_pw_aff
*isl_pw_aff_nan_on_domain(__isl_take isl_local_space
*ls
)
142 return isl_pw_aff_from_aff(isl_aff_nan_on_domain(ls
));
145 /* Return an affine expression that is equal to "val" on
146 * domain local space "ls".
148 __isl_give isl_aff
*isl_aff_val_on_domain(__isl_take isl_local_space
*ls
,
149 __isl_take isl_val
*val
)
155 if (!isl_val_is_rat(val
))
156 isl_die(isl_val_get_ctx(val
), isl_error_invalid
,
157 "expecting rational value", goto error
);
159 aff
= isl_aff_alloc(isl_local_space_copy(ls
));
163 isl_seq_clr(aff
->v
->el
+ 2, aff
->v
->size
- 2);
164 isl_int_set(aff
->v
->el
[1], val
->n
);
165 isl_int_set(aff
->v
->el
[0], val
->d
);
167 isl_local_space_free(ls
);
171 isl_local_space_free(ls
);
176 /* Return an affine expression that is equal to the specified dimension
179 __isl_give isl_aff
*isl_aff_var_on_domain(__isl_take isl_local_space
*ls
,
180 enum isl_dim_type type
, unsigned pos
)
188 space
= isl_local_space_get_space(ls
);
191 if (isl_space_is_map(space
))
192 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
193 "expecting (parameter) set space", goto error
);
194 if (pos
>= isl_local_space_dim(ls
, type
))
195 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
196 "position out of bounds", goto error
);
198 isl_space_free(space
);
199 aff
= isl_aff_alloc(ls
);
203 pos
+= isl_local_space_offset(aff
->ls
, type
);
205 isl_int_set_si(aff
->v
->el
[0], 1);
206 isl_seq_clr(aff
->v
->el
+ 1, aff
->v
->size
- 1);
207 isl_int_set_si(aff
->v
->el
[1 + pos
], 1);
211 isl_local_space_free(ls
);
212 isl_space_free(space
);
216 /* Return a piecewise affine expression that is equal to
217 * the specified dimension in "ls".
219 __isl_give isl_pw_aff
*isl_pw_aff_var_on_domain(__isl_take isl_local_space
*ls
,
220 enum isl_dim_type type
, unsigned pos
)
222 return isl_pw_aff_from_aff(isl_aff_var_on_domain(ls
, type
, pos
));
225 __isl_give isl_aff
*isl_aff_copy(__isl_keep isl_aff
*aff
)
234 __isl_give isl_aff
*isl_aff_dup(__isl_keep isl_aff
*aff
)
239 return isl_aff_alloc_vec(isl_local_space_copy(aff
->ls
),
240 isl_vec_copy(aff
->v
));
243 __isl_give isl_aff
*isl_aff_cow(__isl_take isl_aff
*aff
)
251 return isl_aff_dup(aff
);
254 __isl_null isl_aff
*isl_aff_free(__isl_take isl_aff
*aff
)
262 isl_local_space_free(aff
->ls
);
263 isl_vec_free(aff
->v
);
270 isl_ctx
*isl_aff_get_ctx(__isl_keep isl_aff
*aff
)
272 return aff
? isl_local_space_get_ctx(aff
->ls
) : NULL
;
275 /* Externally, an isl_aff has a map space, but internally, the
276 * ls field corresponds to the domain of that space.
278 int isl_aff_dim(__isl_keep isl_aff
*aff
, enum isl_dim_type type
)
282 if (type
== isl_dim_out
)
284 if (type
== isl_dim_in
)
286 return isl_local_space_dim(aff
->ls
, type
);
289 /* Return the position of the dimension of the given type and name
291 * Return -1 if no such dimension can be found.
293 int isl_aff_find_dim_by_name(__isl_keep isl_aff
*aff
, enum isl_dim_type type
,
298 if (type
== isl_dim_out
)
300 if (type
== isl_dim_in
)
302 return isl_local_space_find_dim_by_name(aff
->ls
, type
, name
);
305 __isl_give isl_space
*isl_aff_get_domain_space(__isl_keep isl_aff
*aff
)
307 return aff
? isl_local_space_get_space(aff
->ls
) : NULL
;
310 __isl_give isl_space
*isl_aff_get_space(__isl_keep isl_aff
*aff
)
315 space
= isl_local_space_get_space(aff
->ls
);
316 space
= isl_space_from_domain(space
);
317 space
= isl_space_add_dims(space
, isl_dim_out
, 1);
321 __isl_give isl_local_space
*isl_aff_get_domain_local_space(
322 __isl_keep isl_aff
*aff
)
324 return aff
? isl_local_space_copy(aff
->ls
) : NULL
;
327 __isl_give isl_local_space
*isl_aff_get_local_space(__isl_keep isl_aff
*aff
)
332 ls
= isl_local_space_copy(aff
->ls
);
333 ls
= isl_local_space_from_domain(ls
);
334 ls
= isl_local_space_add_dims(ls
, isl_dim_out
, 1);
338 /* Externally, an isl_aff has a map space, but internally, the
339 * ls field corresponds to the domain of that space.
341 const char *isl_aff_get_dim_name(__isl_keep isl_aff
*aff
,
342 enum isl_dim_type type
, unsigned pos
)
346 if (type
== isl_dim_out
)
348 if (type
== isl_dim_in
)
350 return isl_local_space_get_dim_name(aff
->ls
, type
, pos
);
353 __isl_give isl_aff
*isl_aff_reset_domain_space(__isl_take isl_aff
*aff
,
354 __isl_take isl_space
*dim
)
356 aff
= isl_aff_cow(aff
);
360 aff
->ls
= isl_local_space_reset_space(aff
->ls
, dim
);
362 return isl_aff_free(aff
);
371 /* Reset the space of "aff". This function is called from isl_pw_templ.c
372 * and doesn't know if the space of an element object is represented
373 * directly or through its domain. It therefore passes along both.
375 __isl_give isl_aff
*isl_aff_reset_space_and_domain(__isl_take isl_aff
*aff
,
376 __isl_take isl_space
*space
, __isl_take isl_space
*domain
)
378 isl_space_free(space
);
379 return isl_aff_reset_domain_space(aff
, domain
);
382 /* Reorder the coefficients of the affine expression based
383 * on the given reodering.
384 * The reordering r is assumed to have been extended with the local
387 static __isl_give isl_vec
*vec_reorder(__isl_take isl_vec
*vec
,
388 __isl_take isl_reordering
*r
, int n_div
)
396 res
= isl_vec_alloc(vec
->ctx
,
397 2 + isl_space_dim(r
->dim
, isl_dim_all
) + n_div
);
398 isl_seq_cpy(res
->el
, vec
->el
, 2);
399 isl_seq_clr(res
->el
+ 2, res
->size
- 2);
400 for (i
= 0; i
< r
->len
; ++i
)
401 isl_int_set(res
->el
[2 + r
->pos
[i
]], vec
->el
[2 + i
]);
403 isl_reordering_free(r
);
408 isl_reordering_free(r
);
412 /* Reorder the dimensions of the domain of "aff" according
413 * to the given reordering.
415 __isl_give isl_aff
*isl_aff_realign_domain(__isl_take isl_aff
*aff
,
416 __isl_take isl_reordering
*r
)
418 aff
= isl_aff_cow(aff
);
422 r
= isl_reordering_extend(r
, aff
->ls
->div
->n_row
);
423 aff
->v
= vec_reorder(aff
->v
, isl_reordering_copy(r
),
424 aff
->ls
->div
->n_row
);
425 aff
->ls
= isl_local_space_realign(aff
->ls
, r
);
427 if (!aff
->v
|| !aff
->ls
)
428 return isl_aff_free(aff
);
433 isl_reordering_free(r
);
437 __isl_give isl_aff
*isl_aff_align_params(__isl_take isl_aff
*aff
,
438 __isl_take isl_space
*model
)
443 if (!isl_space_match(aff
->ls
->dim
, isl_dim_param
,
444 model
, isl_dim_param
)) {
447 model
= isl_space_drop_dims(model
, isl_dim_in
,
448 0, isl_space_dim(model
, isl_dim_in
));
449 model
= isl_space_drop_dims(model
, isl_dim_out
,
450 0, isl_space_dim(model
, isl_dim_out
));
451 exp
= isl_parameter_alignment_reordering(aff
->ls
->dim
, model
);
452 exp
= isl_reordering_extend_space(exp
,
453 isl_aff_get_domain_space(aff
));
454 aff
= isl_aff_realign_domain(aff
, exp
);
457 isl_space_free(model
);
460 isl_space_free(model
);
465 /* Is "aff" obviously equal to zero?
467 * If the denominator is zero, then "aff" is not equal to zero.
469 int isl_aff_plain_is_zero(__isl_keep isl_aff
*aff
)
474 if (isl_int_is_zero(aff
->v
->el
[0]))
476 return isl_seq_first_non_zero(aff
->v
->el
+ 1, aff
->v
->size
- 1) < 0;
479 /* Does "aff" represent NaN?
481 int isl_aff_is_nan(__isl_keep isl_aff
*aff
)
486 return isl_seq_first_non_zero(aff
->v
->el
, 2) < 0;
489 /* Does "pa" involve any NaNs?
491 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff
*pa
)
500 for (i
= 0; i
< pa
->n
; ++i
) {
501 int is_nan
= isl_aff_is_nan(pa
->p
[i
].aff
);
502 if (is_nan
< 0 || is_nan
)
509 /* Are "aff1" and "aff2" obviously equal?
511 * NaN is not equal to anything, not even to another NaN.
513 int isl_aff_plain_is_equal(__isl_keep isl_aff
*aff1
, __isl_keep isl_aff
*aff2
)
520 if (isl_aff_is_nan(aff1
) || isl_aff_is_nan(aff2
))
523 equal
= isl_local_space_is_equal(aff1
->ls
, aff2
->ls
);
524 if (equal
< 0 || !equal
)
527 return isl_vec_is_equal(aff1
->v
, aff2
->v
);
530 /* Return the common denominator of "aff" in "v".
532 * We cannot return anything meaningful in case of a NaN.
534 int isl_aff_get_denominator(__isl_keep isl_aff
*aff
, isl_int
*v
)
538 if (isl_aff_is_nan(aff
))
539 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
540 "cannot get denominator of NaN", return -1);
541 isl_int_set(*v
, aff
->v
->el
[0]);
545 /* Return the common denominator of "aff".
547 __isl_give isl_val
*isl_aff_get_denominator_val(__isl_keep isl_aff
*aff
)
554 ctx
= isl_aff_get_ctx(aff
);
555 if (isl_aff_is_nan(aff
))
556 return isl_val_nan(ctx
);
557 return isl_val_int_from_isl_int(ctx
, aff
->v
->el
[0]);
560 /* Return the constant term of "aff" in "v".
562 * We cannot return anything meaningful in case of a NaN.
564 int isl_aff_get_constant(__isl_keep isl_aff
*aff
, isl_int
*v
)
568 if (isl_aff_is_nan(aff
))
569 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
570 "cannot get constant term of NaN", return -1);
571 isl_int_set(*v
, aff
->v
->el
[1]);
575 /* Return the constant term of "aff".
577 __isl_give isl_val
*isl_aff_get_constant_val(__isl_keep isl_aff
*aff
)
585 ctx
= isl_aff_get_ctx(aff
);
586 if (isl_aff_is_nan(aff
))
587 return isl_val_nan(ctx
);
588 v
= isl_val_rat_from_isl_int(ctx
, aff
->v
->el
[1], aff
->v
->el
[0]);
589 return isl_val_normalize(v
);
592 /* Return the coefficient of the variable of type "type" at position "pos"
595 * We cannot return anything meaningful in case of a NaN.
597 int isl_aff_get_coefficient(__isl_keep isl_aff
*aff
,
598 enum isl_dim_type type
, int pos
, isl_int
*v
)
603 if (type
== isl_dim_out
)
604 isl_die(aff
->v
->ctx
, isl_error_invalid
,
605 "output/set dimension does not have a coefficient",
607 if (type
== isl_dim_in
)
610 if (pos
>= isl_local_space_dim(aff
->ls
, type
))
611 isl_die(aff
->v
->ctx
, isl_error_invalid
,
612 "position out of bounds", return -1);
614 if (isl_aff_is_nan(aff
))
615 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
616 "cannot get coefficient of NaN", return -1);
617 pos
+= isl_local_space_offset(aff
->ls
, type
);
618 isl_int_set(*v
, aff
->v
->el
[1 + pos
]);
623 /* Return the coefficient of the variable of type "type" at position "pos"
626 __isl_give isl_val
*isl_aff_get_coefficient_val(__isl_keep isl_aff
*aff
,
627 enum isl_dim_type type
, int pos
)
635 ctx
= isl_aff_get_ctx(aff
);
636 if (type
== isl_dim_out
)
637 isl_die(ctx
, isl_error_invalid
,
638 "output/set dimension does not have a coefficient",
640 if (type
== isl_dim_in
)
643 if (pos
>= isl_local_space_dim(aff
->ls
, type
))
644 isl_die(ctx
, isl_error_invalid
,
645 "position out of bounds", return NULL
);
647 if (isl_aff_is_nan(aff
))
648 return isl_val_nan(ctx
);
649 pos
+= isl_local_space_offset(aff
->ls
, type
);
650 v
= isl_val_rat_from_isl_int(ctx
, aff
->v
->el
[1 + pos
], aff
->v
->el
[0]);
651 return isl_val_normalize(v
);
654 /* Return the sign of the coefficient of the variable of type "type"
655 * at position "pos" of "aff".
657 int isl_aff_coefficient_sgn(__isl_keep isl_aff
*aff
, enum isl_dim_type type
,
665 ctx
= isl_aff_get_ctx(aff
);
666 if (type
== isl_dim_out
)
667 isl_die(ctx
, isl_error_invalid
,
668 "output/set dimension does not have a coefficient",
670 if (type
== isl_dim_in
)
673 if (pos
>= isl_local_space_dim(aff
->ls
, type
))
674 isl_die(ctx
, isl_error_invalid
,
675 "position out of bounds", return 0);
677 pos
+= isl_local_space_offset(aff
->ls
, type
);
678 return isl_int_sgn(aff
->v
->el
[1 + pos
]);
681 /* Replace the denominator of "aff" by "v".
683 * A NaN is unaffected by this operation.
685 __isl_give isl_aff
*isl_aff_set_denominator(__isl_take isl_aff
*aff
, isl_int v
)
689 if (isl_aff_is_nan(aff
))
691 aff
= isl_aff_cow(aff
);
695 aff
->v
= isl_vec_cow(aff
->v
);
697 return isl_aff_free(aff
);
699 isl_int_set(aff
->v
->el
[0], v
);
704 /* Replace the numerator of the constant term of "aff" by "v".
706 * A NaN is unaffected by this operation.
708 __isl_give isl_aff
*isl_aff_set_constant(__isl_take isl_aff
*aff
, isl_int v
)
712 if (isl_aff_is_nan(aff
))
714 aff
= isl_aff_cow(aff
);
718 aff
->v
= isl_vec_cow(aff
->v
);
720 return isl_aff_free(aff
);
722 isl_int_set(aff
->v
->el
[1], v
);
727 /* Replace the constant term of "aff" by "v".
729 * A NaN is unaffected by this operation.
731 __isl_give isl_aff
*isl_aff_set_constant_val(__isl_take isl_aff
*aff
,
732 __isl_take isl_val
*v
)
737 if (isl_aff_is_nan(aff
)) {
742 if (!isl_val_is_rat(v
))
743 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
744 "expecting rational value", goto error
);
746 if (isl_int_eq(aff
->v
->el
[1], v
->n
) &&
747 isl_int_eq(aff
->v
->el
[0], v
->d
)) {
752 aff
= isl_aff_cow(aff
);
755 aff
->v
= isl_vec_cow(aff
->v
);
759 if (isl_int_eq(aff
->v
->el
[0], v
->d
)) {
760 isl_int_set(aff
->v
->el
[1], v
->n
);
761 } else if (isl_int_is_one(v
->d
)) {
762 isl_int_mul(aff
->v
->el
[1], aff
->v
->el
[0], v
->n
);
764 isl_seq_scale(aff
->v
->el
+ 1,
765 aff
->v
->el
+ 1, v
->d
, aff
->v
->size
- 1);
766 isl_int_mul(aff
->v
->el
[1], aff
->v
->el
[0], v
->n
);
767 isl_int_mul(aff
->v
->el
[0], aff
->v
->el
[0], v
->d
);
768 aff
->v
= isl_vec_normalize(aff
->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(__isl_take isl_aff
*aff
, isl_int v
)
787 if (isl_int_is_zero(v
))
792 if (isl_aff_is_nan(aff
))
794 aff
= isl_aff_cow(aff
);
798 aff
->v
= isl_vec_cow(aff
->v
);
800 return isl_aff_free(aff
);
802 isl_int_addmul(aff
->v
->el
[1], aff
->v
->el
[0], v
);
807 /* Add "v" to the constant term of "aff".
809 * A NaN is unaffected by this operation.
811 __isl_give isl_aff
*isl_aff_add_constant_val(__isl_take isl_aff
*aff
,
812 __isl_take isl_val
*v
)
817 if (isl_aff_is_nan(aff
) || isl_val_is_zero(v
)) {
822 if (!isl_val_is_rat(v
))
823 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
824 "expecting rational value", goto error
);
826 aff
= isl_aff_cow(aff
);
830 aff
->v
= isl_vec_cow(aff
->v
);
834 if (isl_int_is_one(v
->d
)) {
835 isl_int_addmul(aff
->v
->el
[1], aff
->v
->el
[0], v
->n
);
836 } else if (isl_int_eq(aff
->v
->el
[0], v
->d
)) {
837 isl_int_add(aff
->v
->el
[1], aff
->v
->el
[1], v
->n
);
838 aff
->v
= isl_vec_normalize(aff
->v
);
842 isl_seq_scale(aff
->v
->el
+ 1,
843 aff
->v
->el
+ 1, v
->d
, aff
->v
->size
- 1);
844 isl_int_addmul(aff
->v
->el
[1], aff
->v
->el
[0], v
->n
);
845 isl_int_mul(aff
->v
->el
[0], aff
->v
->el
[0], v
->d
);
846 aff
->v
= isl_vec_normalize(aff
->v
);
859 __isl_give isl_aff
*isl_aff_add_constant_si(__isl_take isl_aff
*aff
, int v
)
864 isl_int_set_si(t
, v
);
865 aff
= isl_aff_add_constant(aff
, t
);
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(__isl_take isl_aff
*aff
, isl_int v
)
877 if (isl_int_is_zero(v
))
882 if (isl_aff_is_nan(aff
))
884 aff
= isl_aff_cow(aff
);
888 aff
->v
= isl_vec_cow(aff
->v
);
890 return isl_aff_free(aff
);
892 isl_int_add(aff
->v
->el
[1], aff
->v
->el
[1], v
);
897 /* Add "v" to the numerator of the constant term of "aff".
899 * A NaN is unaffected by this operation.
901 __isl_give isl_aff
*isl_aff_add_constant_num_si(__isl_take isl_aff
*aff
, int v
)
909 isl_int_set_si(t
, v
);
910 aff
= isl_aff_add_constant_num(aff
, t
);
916 /* Replace the numerator of the constant term of "aff" by "v".
918 * A NaN is unaffected by this operation.
920 __isl_give isl_aff
*isl_aff_set_constant_si(__isl_take isl_aff
*aff
, int v
)
924 if (isl_aff_is_nan(aff
))
926 aff
= isl_aff_cow(aff
);
930 aff
->v
= isl_vec_cow(aff
->v
);
932 return isl_aff_free(aff
);
934 isl_int_set_si(aff
->v
->el
[1], v
);
939 /* Replace the numerator of the coefficient of the variable of type "type"
940 * at position "pos" of "aff" by "v".
942 * A NaN is unaffected by this operation.
944 __isl_give isl_aff
*isl_aff_set_coefficient(__isl_take isl_aff
*aff
,
945 enum isl_dim_type type
, int pos
, isl_int v
)
950 if (type
== isl_dim_out
)
951 isl_die(aff
->v
->ctx
, isl_error_invalid
,
952 "output/set dimension does not have a coefficient",
953 return isl_aff_free(aff
));
954 if (type
== isl_dim_in
)
957 if (pos
>= isl_local_space_dim(aff
->ls
, type
))
958 isl_die(aff
->v
->ctx
, isl_error_invalid
,
959 "position out of bounds", return isl_aff_free(aff
));
961 if (isl_aff_is_nan(aff
))
963 aff
= isl_aff_cow(aff
);
967 aff
->v
= isl_vec_cow(aff
->v
);
969 return isl_aff_free(aff
);
971 pos
+= isl_local_space_offset(aff
->ls
, type
);
972 isl_int_set(aff
->v
->el
[1 + pos
], v
);
977 /* Replace the numerator of the coefficient of the variable of type "type"
978 * at position "pos" of "aff" by "v".
980 * A NaN is unaffected by this operation.
982 __isl_give isl_aff
*isl_aff_set_coefficient_si(__isl_take isl_aff
*aff
,
983 enum isl_dim_type type
, int pos
, int v
)
988 if (type
== isl_dim_out
)
989 isl_die(aff
->v
->ctx
, isl_error_invalid
,
990 "output/set dimension does not have a coefficient",
991 return isl_aff_free(aff
));
992 if (type
== isl_dim_in
)
995 if (pos
< 0 || pos
>= isl_local_space_dim(aff
->ls
, type
))
996 isl_die(aff
->v
->ctx
, isl_error_invalid
,
997 "position out of bounds", return isl_aff_free(aff
));
999 if (isl_aff_is_nan(aff
))
1001 pos
+= isl_local_space_offset(aff
->ls
, type
);
1002 if (isl_int_cmp_si(aff
->v
->el
[1 + pos
], v
) == 0)
1005 aff
= isl_aff_cow(aff
);
1009 aff
->v
= isl_vec_cow(aff
->v
);
1011 return isl_aff_free(aff
);
1013 isl_int_set_si(aff
->v
->el
[1 + pos
], v
);
1018 /* Replace the coefficient of the variable of type "type" at position "pos"
1021 * A NaN is unaffected by this operation.
1023 __isl_give isl_aff
*isl_aff_set_coefficient_val(__isl_take isl_aff
*aff
,
1024 enum isl_dim_type type
, int pos
, __isl_take isl_val
*v
)
1029 if (type
== isl_dim_out
)
1030 isl_die(aff
->v
->ctx
, isl_error_invalid
,
1031 "output/set dimension does not have a coefficient",
1033 if (type
== isl_dim_in
)
1036 if (pos
>= isl_local_space_dim(aff
->ls
, type
))
1037 isl_die(aff
->v
->ctx
, isl_error_invalid
,
1038 "position out of bounds", goto error
);
1040 if (isl_aff_is_nan(aff
)) {
1044 if (!isl_val_is_rat(v
))
1045 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
1046 "expecting rational value", goto error
);
1048 pos
+= isl_local_space_offset(aff
->ls
, type
);
1049 if (isl_int_eq(aff
->v
->el
[1 + pos
], v
->n
) &&
1050 isl_int_eq(aff
->v
->el
[0], v
->d
)) {
1055 aff
= isl_aff_cow(aff
);
1058 aff
->v
= isl_vec_cow(aff
->v
);
1062 if (isl_int_eq(aff
->v
->el
[0], v
->d
)) {
1063 isl_int_set(aff
->v
->el
[1 + pos
], v
->n
);
1064 } else if (isl_int_is_one(v
->d
)) {
1065 isl_int_mul(aff
->v
->el
[1 + pos
], aff
->v
->el
[0], v
->n
);
1067 isl_seq_scale(aff
->v
->el
+ 1,
1068 aff
->v
->el
+ 1, v
->d
, aff
->v
->size
- 1);
1069 isl_int_mul(aff
->v
->el
[1 + pos
], aff
->v
->el
[0], v
->n
);
1070 isl_int_mul(aff
->v
->el
[0], aff
->v
->el
[0], v
->d
);
1071 aff
->v
= isl_vec_normalize(aff
->v
);
1084 /* Add "v" to the coefficient of the variable of type "type"
1085 * at position "pos" of "aff".
1087 * A NaN is unaffected by this operation.
1089 __isl_give isl_aff
*isl_aff_add_coefficient(__isl_take isl_aff
*aff
,
1090 enum isl_dim_type type
, int pos
, isl_int v
)
1095 if (type
== isl_dim_out
)
1096 isl_die(aff
->v
->ctx
, isl_error_invalid
,
1097 "output/set dimension does not have a coefficient",
1098 return isl_aff_free(aff
));
1099 if (type
== isl_dim_in
)
1102 if (pos
>= isl_local_space_dim(aff
->ls
, type
))
1103 isl_die(aff
->v
->ctx
, isl_error_invalid
,
1104 "position out of bounds", return isl_aff_free(aff
));
1106 if (isl_aff_is_nan(aff
))
1108 aff
= isl_aff_cow(aff
);
1112 aff
->v
= isl_vec_cow(aff
->v
);
1114 return isl_aff_free(aff
);
1116 pos
+= isl_local_space_offset(aff
->ls
, type
);
1117 isl_int_addmul(aff
->v
->el
[1 + pos
], aff
->v
->el
[0], v
);
1122 /* Add "v" to the coefficient of the variable of type "type"
1123 * at position "pos" of "aff".
1125 * A NaN is unaffected by this operation.
1127 __isl_give isl_aff
*isl_aff_add_coefficient_val(__isl_take isl_aff
*aff
,
1128 enum isl_dim_type type
, int pos
, __isl_take isl_val
*v
)
1133 if (isl_val_is_zero(v
)) {
1138 if (type
== isl_dim_out
)
1139 isl_die(aff
->v
->ctx
, isl_error_invalid
,
1140 "output/set dimension does not have a coefficient",
1142 if (type
== isl_dim_in
)
1145 if (pos
>= isl_local_space_dim(aff
->ls
, type
))
1146 isl_die(aff
->v
->ctx
, isl_error_invalid
,
1147 "position out of bounds", goto error
);
1149 if (isl_aff_is_nan(aff
)) {
1153 if (!isl_val_is_rat(v
))
1154 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
1155 "expecting rational value", goto error
);
1157 aff
= isl_aff_cow(aff
);
1161 aff
->v
= isl_vec_cow(aff
->v
);
1165 pos
+= isl_local_space_offset(aff
->ls
, type
);
1166 if (isl_int_is_one(v
->d
)) {
1167 isl_int_addmul(aff
->v
->el
[1 + pos
], aff
->v
->el
[0], v
->n
);
1168 } else if (isl_int_eq(aff
->v
->el
[0], v
->d
)) {
1169 isl_int_add(aff
->v
->el
[1 + pos
], aff
->v
->el
[1 + pos
], v
->n
);
1170 aff
->v
= isl_vec_normalize(aff
->v
);
1174 isl_seq_scale(aff
->v
->el
+ 1,
1175 aff
->v
->el
+ 1, v
->d
, aff
->v
->size
- 1);
1176 isl_int_addmul(aff
->v
->el
[1 + pos
], aff
->v
->el
[0], v
->n
);
1177 isl_int_mul(aff
->v
->el
[0], aff
->v
->el
[0], v
->d
);
1178 aff
->v
= isl_vec_normalize(aff
->v
);
1191 __isl_give isl_aff
*isl_aff_add_coefficient_si(__isl_take isl_aff
*aff
,
1192 enum isl_dim_type type
, int pos
, int v
)
1197 isl_int_set_si(t
, v
);
1198 aff
= isl_aff_add_coefficient(aff
, type
, pos
, t
);
1204 __isl_give isl_aff
*isl_aff_get_div(__isl_keep isl_aff
*aff
, int pos
)
1209 return isl_local_space_get_div(aff
->ls
, pos
);
1212 /* Return the negation of "aff".
1214 * As a special case, -NaN = NaN.
1216 __isl_give isl_aff
*isl_aff_neg(__isl_take isl_aff
*aff
)
1220 if (isl_aff_is_nan(aff
))
1222 aff
= isl_aff_cow(aff
);
1225 aff
->v
= isl_vec_cow(aff
->v
);
1227 return isl_aff_free(aff
);
1229 isl_seq_neg(aff
->v
->el
+ 1, aff
->v
->el
+ 1, aff
->v
->size
- 1);
1234 /* Remove divs from the local space that do not appear in the affine
1236 * We currently only remove divs at the end.
1237 * Some intermediate divs may also not appear directly in the affine
1238 * expression, but we would also need to check that no other divs are
1239 * defined in terms of them.
1241 __isl_give isl_aff
*isl_aff_remove_unused_divs( __isl_take isl_aff
*aff
)
1250 n
= isl_local_space_dim(aff
->ls
, isl_dim_div
);
1251 off
= isl_local_space_offset(aff
->ls
, isl_dim_div
);
1253 pos
= isl_seq_last_non_zero(aff
->v
->el
+ 1 + off
, n
) + 1;
1257 aff
= isl_aff_cow(aff
);
1261 aff
->ls
= isl_local_space_drop_dims(aff
->ls
, isl_dim_div
, pos
, n
- pos
);
1262 aff
->v
= isl_vec_drop_els(aff
->v
, 1 + off
+ pos
, n
- pos
);
1263 if (!aff
->ls
|| !aff
->v
)
1264 return isl_aff_free(aff
);
1269 /* Given two affine expressions "p" of length p_len (including the
1270 * denominator and the constant term) and "subs" of length subs_len,
1271 * plug in "subs" for the variable at position "pos".
1272 * The variables of "subs" and "p" are assumed to match up to subs_len,
1273 * but "p" may have additional variables.
1274 * "v" is an initialized isl_int that can be used internally.
1276 * In particular, if "p" represents the expression
1280 * with i the variable at position "pos" and "subs" represents the expression
1284 * then the result represents the expression
1289 void isl_seq_substitute(isl_int
*p
, int pos
, isl_int
*subs
,
1290 int p_len
, int subs_len
, isl_int v
)
1292 isl_int_set(v
, p
[1 + pos
]);
1293 isl_int_set_si(p
[1 + pos
], 0);
1294 isl_seq_combine(p
+ 1, subs
[0], p
+ 1, v
, subs
+ 1, subs_len
- 1);
1295 isl_seq_scale(p
+ subs_len
, p
+ subs_len
, subs
[0], p_len
- subs_len
);
1296 isl_int_mul(p
[0], p
[0], subs
[0]);
1299 /* Look for any divs in the aff->ls with a denominator equal to one
1300 * and plug them into the affine expression and any subsequent divs
1301 * that may reference the div.
1303 static __isl_give isl_aff
*plug_in_integral_divs(__isl_take isl_aff
*aff
)
1309 isl_local_space
*ls
;
1315 n
= isl_local_space_dim(aff
->ls
, isl_dim_div
);
1317 for (i
= 0; i
< n
; ++i
) {
1318 if (!isl_int_is_one(aff
->ls
->div
->row
[i
][0]))
1320 ls
= isl_local_space_copy(aff
->ls
);
1321 ls
= isl_local_space_substitute_seq(ls
, isl_dim_div
, i
,
1322 aff
->ls
->div
->row
[i
], len
, i
+ 1, n
- (i
+ 1));
1323 vec
= isl_vec_copy(aff
->v
);
1324 vec
= isl_vec_cow(vec
);
1330 pos
= isl_local_space_offset(aff
->ls
, isl_dim_div
) + i
;
1331 isl_seq_substitute(vec
->el
, pos
, aff
->ls
->div
->row
[i
],
1336 isl_vec_free(aff
->v
);
1338 isl_local_space_free(aff
->ls
);
1345 isl_local_space_free(ls
);
1346 return isl_aff_free(aff
);
1349 /* Look for any divs j that appear with a unit coefficient inside
1350 * the definitions of other divs i and plug them into the definitions
1353 * In particular, an expression of the form
1355 * floor((f(..) + floor(g(..)/n))/m)
1359 * floor((n * f(..) + g(..))/(n * m))
1361 * This simplification is correct because we can move the expression
1362 * f(..) into the inner floor in the original expression to obtain
1364 * floor(floor((n * f(..) + g(..))/n)/m)
1366 * from which we can derive the simplified expression.
1368 static __isl_give isl_aff
*plug_in_unit_divs(__isl_take isl_aff
*aff
)
1376 n
= isl_local_space_dim(aff
->ls
, isl_dim_div
);
1377 off
= isl_local_space_offset(aff
->ls
, isl_dim_div
);
1378 for (i
= 1; i
< n
; ++i
) {
1379 for (j
= 0; j
< i
; ++j
) {
1380 if (!isl_int_is_one(aff
->ls
->div
->row
[i
][1 + off
+ j
]))
1382 aff
->ls
= isl_local_space_substitute_seq(aff
->ls
,
1383 isl_dim_div
, j
, aff
->ls
->div
->row
[j
],
1384 aff
->v
->size
, i
, 1);
1386 return isl_aff_free(aff
);
1393 /* Swap divs "a" and "b" in "aff", which is assumed to be non-NULL.
1395 * Even though this function is only called on isl_affs with a single
1396 * reference, we are careful to only change aff->v and aff->ls together.
1398 static __isl_give isl_aff
*swap_div(__isl_take isl_aff
*aff
, int a
, int b
)
1400 unsigned off
= isl_local_space_offset(aff
->ls
, isl_dim_div
);
1401 isl_local_space
*ls
;
1404 ls
= isl_local_space_copy(aff
->ls
);
1405 ls
= isl_local_space_swap_div(ls
, a
, b
);
1406 v
= isl_vec_copy(aff
->v
);
1411 isl_int_swap(v
->el
[1 + off
+ a
], v
->el
[1 + off
+ b
]);
1412 isl_vec_free(aff
->v
);
1414 isl_local_space_free(aff
->ls
);
1420 isl_local_space_free(ls
);
1421 return isl_aff_free(aff
);
1424 /* Merge divs "a" and "b" in "aff", which is assumed to be non-NULL.
1426 * We currently do not actually remove div "b", but simply add its
1427 * coefficient to that of "a" and then zero it out.
1429 static __isl_give isl_aff
*merge_divs(__isl_take isl_aff
*aff
, int a
, int b
)
1431 unsigned off
= isl_local_space_offset(aff
->ls
, isl_dim_div
);
1433 if (isl_int_is_zero(aff
->v
->el
[1 + off
+ b
]))
1436 aff
->v
= isl_vec_cow(aff
->v
);
1438 return isl_aff_free(aff
);
1440 isl_int_add(aff
->v
->el
[1 + off
+ a
],
1441 aff
->v
->el
[1 + off
+ a
], aff
->v
->el
[1 + off
+ b
]);
1442 isl_int_set_si(aff
->v
->el
[1 + off
+ b
], 0);
1447 /* Sort the divs in the local space of "aff" according to
1448 * the comparison function "cmp_row" in isl_local_space.c,
1449 * combining the coefficients of identical divs.
1451 * Reordering divs does not change the semantics of "aff",
1452 * so there is no need to call isl_aff_cow.
1453 * Moreover, this function is currently only called on isl_affs
1454 * with a single reference.
1456 static __isl_give isl_aff
*sort_divs(__isl_take isl_aff
*aff
)
1464 off
= isl_local_space_offset(aff
->ls
, isl_dim_div
);
1465 n
= isl_aff_dim(aff
, isl_dim_div
);
1466 for (i
= 1; i
< n
; ++i
) {
1467 for (j
= i
- 1; j
>= 0; --j
) {
1468 int cmp
= isl_mat_cmp_div(aff
->ls
->div
, j
, j
+ 1);
1472 aff
= merge_divs(aff
, j
, j
+ 1);
1474 aff
= swap_div(aff
, j
, j
+ 1);
1483 /* Normalize the representation of "aff".
1485 * This function should only be called of "new" isl_affs, i.e.,
1486 * with only a single reference. We therefore do not need to
1487 * worry about affecting other instances.
1489 __isl_give isl_aff
*isl_aff_normalize(__isl_take isl_aff
*aff
)
1493 aff
->v
= isl_vec_normalize(aff
->v
);
1495 return isl_aff_free(aff
);
1496 aff
= plug_in_integral_divs(aff
);
1497 aff
= plug_in_unit_divs(aff
);
1498 aff
= sort_divs(aff
);
1499 aff
= isl_aff_remove_unused_divs(aff
);
1503 /* Given f, return floor(f).
1504 * If f is an integer expression, then just return f.
1505 * If f is a constant, then return the constant floor(f).
1506 * Otherwise, if f = g/m, write g = q m + r,
1507 * create a new div d = [r/m] and return the expression q + d.
1508 * The coefficients in r are taken to lie between -m/2 and m/2.
1510 * As a special case, floor(NaN) = NaN.
1512 __isl_give isl_aff
*isl_aff_floor(__isl_take isl_aff
*aff
)
1522 if (isl_aff_is_nan(aff
))
1524 if (isl_int_is_one(aff
->v
->el
[0]))
1527 aff
= isl_aff_cow(aff
);
1531 aff
->v
= isl_vec_cow(aff
->v
);
1533 return isl_aff_free(aff
);
1535 if (isl_aff_is_cst(aff
)) {
1536 isl_int_fdiv_q(aff
->v
->el
[1], aff
->v
->el
[1], aff
->v
->el
[0]);
1537 isl_int_set_si(aff
->v
->el
[0], 1);
1541 div
= isl_vec_copy(aff
->v
);
1542 div
= isl_vec_cow(div
);
1544 return isl_aff_free(aff
);
1546 ctx
= isl_aff_get_ctx(aff
);
1547 isl_int_fdiv_q(aff
->v
->el
[0], aff
->v
->el
[0], ctx
->two
);
1548 for (i
= 1; i
< aff
->v
->size
; ++i
) {
1549 isl_int_fdiv_r(div
->el
[i
], div
->el
[i
], div
->el
[0]);
1550 isl_int_fdiv_q(aff
->v
->el
[i
], aff
->v
->el
[i
], div
->el
[0]);
1551 if (isl_int_gt(div
->el
[i
], aff
->v
->el
[0])) {
1552 isl_int_sub(div
->el
[i
], div
->el
[i
], div
->el
[0]);
1553 isl_int_add_ui(aff
->v
->el
[i
], aff
->v
->el
[i
], 1);
1557 aff
->ls
= isl_local_space_add_div(aff
->ls
, div
);
1559 return isl_aff_free(aff
);
1561 size
= aff
->v
->size
;
1562 aff
->v
= isl_vec_extend(aff
->v
, size
+ 1);
1564 return isl_aff_free(aff
);
1565 isl_int_set_si(aff
->v
->el
[0], 1);
1566 isl_int_set_si(aff
->v
->el
[size
], 1);
1568 aff
= isl_aff_normalize(aff
);
1575 * aff mod m = aff - m * floor(aff/m)
1577 __isl_give isl_aff
*isl_aff_mod(__isl_take isl_aff
*aff
, isl_int m
)
1581 res
= isl_aff_copy(aff
);
1582 aff
= isl_aff_scale_down(aff
, m
);
1583 aff
= isl_aff_floor(aff
);
1584 aff
= isl_aff_scale(aff
, m
);
1585 res
= isl_aff_sub(res
, aff
);
1592 * aff mod m = aff - m * floor(aff/m)
1594 * with m an integer value.
1596 __isl_give isl_aff
*isl_aff_mod_val(__isl_take isl_aff
*aff
,
1597 __isl_take isl_val
*m
)
1604 if (!isl_val_is_int(m
))
1605 isl_die(isl_val_get_ctx(m
), isl_error_invalid
,
1606 "expecting integer modulo", goto error
);
1608 res
= isl_aff_copy(aff
);
1609 aff
= isl_aff_scale_down_val(aff
, isl_val_copy(m
));
1610 aff
= isl_aff_floor(aff
);
1611 aff
= isl_aff_scale_val(aff
, m
);
1612 res
= isl_aff_sub(res
, aff
);
1623 * pwaff mod m = pwaff - m * floor(pwaff/m)
1625 __isl_give isl_pw_aff
*isl_pw_aff_mod(__isl_take isl_pw_aff
*pwaff
, isl_int m
)
1629 res
= isl_pw_aff_copy(pwaff
);
1630 pwaff
= isl_pw_aff_scale_down(pwaff
, m
);
1631 pwaff
= isl_pw_aff_floor(pwaff
);
1632 pwaff
= isl_pw_aff_scale(pwaff
, m
);
1633 res
= isl_pw_aff_sub(res
, pwaff
);
1640 * pa mod m = pa - m * floor(pa/m)
1642 * with m an integer value.
1644 __isl_give isl_pw_aff
*isl_pw_aff_mod_val(__isl_take isl_pw_aff
*pa
,
1645 __isl_take isl_val
*m
)
1649 if (!isl_val_is_int(m
))
1650 isl_die(isl_pw_aff_get_ctx(pa
), isl_error_invalid
,
1651 "expecting integer modulo", goto error
);
1652 pa
= isl_pw_aff_mod(pa
, m
->n
);
1656 isl_pw_aff_free(pa
);
1661 /* Given f, return ceil(f).
1662 * If f is an integer expression, then just return f.
1663 * Otherwise, let f be the expression
1669 * floor((e + m - 1)/m)
1671 * As a special case, ceil(NaN) = NaN.
1673 __isl_give isl_aff
*isl_aff_ceil(__isl_take isl_aff
*aff
)
1678 if (isl_aff_is_nan(aff
))
1680 if (isl_int_is_one(aff
->v
->el
[0]))
1683 aff
= isl_aff_cow(aff
);
1686 aff
->v
= isl_vec_cow(aff
->v
);
1688 return isl_aff_free(aff
);
1690 isl_int_add(aff
->v
->el
[1], aff
->v
->el
[1], aff
->v
->el
[0]);
1691 isl_int_sub_ui(aff
->v
->el
[1], aff
->v
->el
[1], 1);
1692 aff
= isl_aff_floor(aff
);
1697 /* Apply the expansion computed by isl_merge_divs.
1698 * The expansion itself is given by "exp" while the resulting
1699 * list of divs is given by "div".
1701 __isl_give isl_aff
*isl_aff_expand_divs( __isl_take isl_aff
*aff
,
1702 __isl_take isl_mat
*div
, int *exp
)
1709 aff
= isl_aff_cow(aff
);
1713 old_n_div
= isl_local_space_dim(aff
->ls
, isl_dim_div
);
1714 new_n_div
= isl_mat_rows(div
);
1715 if (new_n_div
< old_n_div
)
1716 isl_die(isl_mat_get_ctx(div
), isl_error_invalid
,
1717 "not an expansion", goto error
);
1719 aff
->v
= isl_vec_extend(aff
->v
, aff
->v
->size
+ new_n_div
- old_n_div
);
1723 offset
= 1 + isl_local_space_offset(aff
->ls
, isl_dim_div
);
1725 for (i
= new_n_div
- 1; i
>= 0; --i
) {
1726 if (j
>= 0 && exp
[j
] == i
) {
1728 isl_int_swap(aff
->v
->el
[offset
+ i
],
1729 aff
->v
->el
[offset
+ j
]);
1732 isl_int_set_si(aff
->v
->el
[offset
+ i
], 0);
1735 aff
->ls
= isl_local_space_replace_divs(aff
->ls
, isl_mat_copy(div
));
1746 /* Add two affine expressions that live in the same local space.
1748 static __isl_give isl_aff
*add_expanded(__isl_take isl_aff
*aff1
,
1749 __isl_take isl_aff
*aff2
)
1753 aff1
= isl_aff_cow(aff1
);
1757 aff1
->v
= isl_vec_cow(aff1
->v
);
1763 isl_int_gcd(gcd
, aff1
->v
->el
[0], aff2
->v
->el
[0]);
1764 isl_int_divexact(f
, aff2
->v
->el
[0], gcd
);
1765 isl_seq_scale(aff1
->v
->el
+ 1, aff1
->v
->el
+ 1, f
, aff1
->v
->size
- 1);
1766 isl_int_divexact(f
, aff1
->v
->el
[0], gcd
);
1767 isl_seq_addmul(aff1
->v
->el
+ 1, f
, aff2
->v
->el
+ 1, aff1
->v
->size
- 1);
1768 isl_int_divexact(f
, aff2
->v
->el
[0], gcd
);
1769 isl_int_mul(aff1
->v
->el
[0], aff1
->v
->el
[0], f
);
1781 /* Return the sum of "aff1" and "aff2".
1783 * If either of the two is NaN, then the result is NaN.
1785 __isl_give isl_aff
*isl_aff_add(__isl_take isl_aff
*aff1
,
1786 __isl_take isl_aff
*aff2
)
1797 ctx
= isl_aff_get_ctx(aff1
);
1798 if (!isl_space_is_equal(aff1
->ls
->dim
, aff2
->ls
->dim
))
1799 isl_die(ctx
, isl_error_invalid
,
1800 "spaces don't match", goto error
);
1802 if (isl_aff_is_nan(aff1
)) {
1806 if (isl_aff_is_nan(aff2
)) {
1811 n_div1
= isl_aff_dim(aff1
, isl_dim_div
);
1812 n_div2
= isl_aff_dim(aff2
, isl_dim_div
);
1813 if (n_div1
== 0 && n_div2
== 0)
1814 return add_expanded(aff1
, aff2
);
1816 exp1
= isl_alloc_array(ctx
, int, n_div1
);
1817 exp2
= isl_alloc_array(ctx
, int, n_div2
);
1818 if ((n_div1
&& !exp1
) || (n_div2
&& !exp2
))
1821 div
= isl_merge_divs(aff1
->ls
->div
, aff2
->ls
->div
, exp1
, exp2
);
1822 aff1
= isl_aff_expand_divs(aff1
, isl_mat_copy(div
), exp1
);
1823 aff2
= isl_aff_expand_divs(aff2
, div
, exp2
);
1827 return add_expanded(aff1
, aff2
);
1836 __isl_give isl_aff
*isl_aff_sub(__isl_take isl_aff
*aff1
,
1837 __isl_take isl_aff
*aff2
)
1839 return isl_aff_add(aff1
, isl_aff_neg(aff2
));
1842 /* Return the result of scaling "aff" by a factor of "f".
1844 * As a special case, f * NaN = NaN.
1846 __isl_give isl_aff
*isl_aff_scale(__isl_take isl_aff
*aff
, isl_int f
)
1852 if (isl_aff_is_nan(aff
))
1855 if (isl_int_is_one(f
))
1858 aff
= isl_aff_cow(aff
);
1861 aff
->v
= isl_vec_cow(aff
->v
);
1863 return isl_aff_free(aff
);
1865 if (isl_int_is_pos(f
) && isl_int_is_divisible_by(aff
->v
->el
[0], f
)) {
1866 isl_int_divexact(aff
->v
->el
[0], aff
->v
->el
[0], f
);
1871 isl_int_gcd(gcd
, aff
->v
->el
[0], f
);
1872 isl_int_divexact(aff
->v
->el
[0], aff
->v
->el
[0], gcd
);
1873 isl_int_divexact(gcd
, f
, gcd
);
1874 isl_seq_scale(aff
->v
->el
+ 1, aff
->v
->el
+ 1, gcd
, aff
->v
->size
- 1);
1880 /* Multiple "aff" by "v".
1882 __isl_give isl_aff
*isl_aff_scale_val(__isl_take isl_aff
*aff
,
1883 __isl_take isl_val
*v
)
1888 if (isl_val_is_one(v
)) {
1893 if (!isl_val_is_rat(v
))
1894 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
1895 "expecting rational factor", goto error
);
1897 aff
= isl_aff_scale(aff
, v
->n
);
1898 aff
= isl_aff_scale_down(aff
, v
->d
);
1908 /* Return the result of scaling "aff" down by a factor of "f".
1910 * As a special case, NaN/f = NaN.
1912 __isl_give isl_aff
*isl_aff_scale_down(__isl_take isl_aff
*aff
, isl_int f
)
1918 if (isl_aff_is_nan(aff
))
1921 if (isl_int_is_one(f
))
1924 aff
= isl_aff_cow(aff
);
1928 if (isl_int_is_zero(f
))
1929 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
1930 "cannot scale down by zero", return isl_aff_free(aff
));
1932 aff
->v
= isl_vec_cow(aff
->v
);
1934 return isl_aff_free(aff
);
1937 isl_seq_gcd(aff
->v
->el
+ 1, aff
->v
->size
- 1, &gcd
);
1938 isl_int_gcd(gcd
, gcd
, f
);
1939 isl_seq_scale_down(aff
->v
->el
+ 1, aff
->v
->el
+ 1, gcd
, aff
->v
->size
- 1);
1940 isl_int_divexact(gcd
, f
, gcd
);
1941 isl_int_mul(aff
->v
->el
[0], aff
->v
->el
[0], gcd
);
1947 /* Divide "aff" by "v".
1949 __isl_give isl_aff
*isl_aff_scale_down_val(__isl_take isl_aff
*aff
,
1950 __isl_take isl_val
*v
)
1955 if (isl_val_is_one(v
)) {
1960 if (!isl_val_is_rat(v
))
1961 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
1962 "expecting rational factor", goto error
);
1963 if (!isl_val_is_pos(v
))
1964 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
1965 "factor needs to be positive", goto error
);
1967 aff
= isl_aff_scale(aff
, v
->d
);
1968 aff
= isl_aff_scale_down(aff
, v
->n
);
1978 __isl_give isl_aff
*isl_aff_scale_down_ui(__isl_take isl_aff
*aff
, unsigned f
)
1986 isl_int_set_ui(v
, f
);
1987 aff
= isl_aff_scale_down(aff
, v
);
1993 __isl_give isl_aff
*isl_aff_set_dim_name(__isl_take isl_aff
*aff
,
1994 enum isl_dim_type type
, unsigned pos
, const char *s
)
1996 aff
= isl_aff_cow(aff
);
1999 if (type
== isl_dim_out
)
2000 isl_die(aff
->v
->ctx
, isl_error_invalid
,
2001 "cannot set name of output/set dimension",
2002 return isl_aff_free(aff
));
2003 if (type
== isl_dim_in
)
2005 aff
->ls
= isl_local_space_set_dim_name(aff
->ls
, type
, pos
, s
);
2007 return isl_aff_free(aff
);
2012 __isl_give isl_aff
*isl_aff_set_dim_id(__isl_take isl_aff
*aff
,
2013 enum isl_dim_type type
, unsigned pos
, __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 set name of output/set dimension",
2022 if (type
== isl_dim_in
)
2024 aff
->ls
= isl_local_space_set_dim_id(aff
->ls
, type
, pos
, id
);
2026 return isl_aff_free(aff
);
2035 /* Replace the identifier of the input tuple of "aff" by "id".
2036 * type is currently required to be equal to isl_dim_in
2038 __isl_give isl_aff
*isl_aff_set_tuple_id(__isl_take isl_aff
*aff
,
2039 enum isl_dim_type type
, __isl_take isl_id
*id
)
2041 aff
= isl_aff_cow(aff
);
2044 if (type
!= isl_dim_out
)
2045 isl_die(aff
->v
->ctx
, isl_error_invalid
,
2046 "cannot only set id of input tuple", goto error
);
2047 aff
->ls
= isl_local_space_set_tuple_id(aff
->ls
, isl_dim_set
, id
);
2049 return isl_aff_free(aff
);
2058 /* Exploit the equalities in "eq" to simplify the affine expression
2059 * and the expressions of the integer divisions in the local space.
2060 * The integer divisions in this local space are assumed to appear
2061 * as regular dimensions in "eq".
2063 static __isl_give isl_aff
*isl_aff_substitute_equalities_lifted(
2064 __isl_take isl_aff
*aff
, __isl_take isl_basic_set
*eq
)
2072 if (eq
->n_eq
== 0) {
2073 isl_basic_set_free(eq
);
2077 aff
= isl_aff_cow(aff
);
2081 aff
->ls
= isl_local_space_substitute_equalities(aff
->ls
,
2082 isl_basic_set_copy(eq
));
2083 aff
->v
= isl_vec_cow(aff
->v
);
2084 if (!aff
->ls
|| !aff
->v
)
2087 total
= 1 + isl_space_dim(eq
->dim
, isl_dim_all
);
2089 for (i
= 0; i
< eq
->n_eq
; ++i
) {
2090 j
= isl_seq_last_non_zero(eq
->eq
[i
], total
+ n_div
);
2091 if (j
< 0 || j
== 0 || j
>= total
)
2094 isl_seq_elim(aff
->v
->el
+ 1, eq
->eq
[i
], j
, total
,
2098 isl_basic_set_free(eq
);
2099 aff
= isl_aff_normalize(aff
);
2102 isl_basic_set_free(eq
);
2107 /* Exploit the equalities in "eq" to simplify the affine expression
2108 * and the expressions of the integer divisions in the local space.
2110 __isl_give isl_aff
*isl_aff_substitute_equalities(__isl_take isl_aff
*aff
,
2111 __isl_take isl_basic_set
*eq
)
2117 n_div
= isl_local_space_dim(aff
->ls
, isl_dim_div
);
2119 eq
= isl_basic_set_add_dims(eq
, isl_dim_set
, n_div
);
2120 return isl_aff_substitute_equalities_lifted(aff
, eq
);
2122 isl_basic_set_free(eq
);
2127 /* Look for equalities among the variables shared by context and aff
2128 * and the integer divisions of aff, if any.
2129 * The equalities are then used to eliminate coefficients and/or integer
2130 * divisions from aff.
2132 __isl_give isl_aff
*isl_aff_gist(__isl_take isl_aff
*aff
,
2133 __isl_take isl_set
*context
)
2135 isl_basic_set
*hull
;
2140 n_div
= isl_local_space_dim(aff
->ls
, isl_dim_div
);
2142 isl_basic_set
*bset
;
2143 isl_local_space
*ls
;
2144 context
= isl_set_add_dims(context
, isl_dim_set
, n_div
);
2145 ls
= isl_aff_get_domain_local_space(aff
);
2146 bset
= isl_basic_set_from_local_space(ls
);
2147 bset
= isl_basic_set_lift(bset
);
2148 bset
= isl_basic_set_flatten(bset
);
2149 context
= isl_set_intersect(context
,
2150 isl_set_from_basic_set(bset
));
2153 hull
= isl_set_affine_hull(context
);
2154 return isl_aff_substitute_equalities_lifted(aff
, hull
);
2157 isl_set_free(context
);
2161 __isl_give isl_aff
*isl_aff_gist_params(__isl_take isl_aff
*aff
,
2162 __isl_take isl_set
*context
)
2164 isl_set
*dom_context
= isl_set_universe(isl_aff_get_domain_space(aff
));
2165 dom_context
= isl_set_intersect_params(dom_context
, context
);
2166 return isl_aff_gist(aff
, dom_context
);
2169 /* Return a basic set containing those elements in the space
2170 * of aff where it is positive. "rational" should not be set.
2172 * If "aff" is NaN, then it is not positive.
2174 static __isl_give isl_basic_set
*aff_pos_basic_set(__isl_take isl_aff
*aff
,
2177 isl_constraint
*ineq
;
2178 isl_basic_set
*bset
;
2183 if (isl_aff_is_nan(aff
)) {
2184 isl_space
*space
= isl_aff_get_domain_space(aff
);
2186 return isl_basic_set_empty(space
);
2189 isl_die(isl_aff_get_ctx(aff
), isl_error_unsupported
,
2190 "rational sets not supported", goto error
);
2192 ineq
= isl_inequality_from_aff(aff
);
2193 c
= isl_constraint_get_constant_val(ineq
);
2194 c
= isl_val_sub_ui(c
, 1);
2195 ineq
= isl_constraint_set_constant_val(ineq
, c
);
2197 bset
= isl_basic_set_from_constraint(ineq
);
2198 bset
= isl_basic_set_simplify(bset
);
2205 /* Return a basic set containing those elements in the space
2206 * of aff where it is non-negative.
2207 * If "rational" is set, then return a rational basic set.
2209 * If "aff" is NaN, then it is not non-negative (it's not negative either).
2211 static __isl_give isl_basic_set
*aff_nonneg_basic_set(
2212 __isl_take isl_aff
*aff
, int rational
)
2214 isl_constraint
*ineq
;
2215 isl_basic_set
*bset
;
2219 if (isl_aff_is_nan(aff
)) {
2220 isl_space
*space
= isl_aff_get_domain_space(aff
);
2222 return isl_basic_set_empty(space
);
2225 ineq
= isl_inequality_from_aff(aff
);
2227 bset
= isl_basic_set_from_constraint(ineq
);
2229 bset
= isl_basic_set_set_rational(bset
);
2230 bset
= isl_basic_set_simplify(bset
);
2234 /* Return a basic set containing those elements in the space
2235 * of aff where it is non-negative.
2237 __isl_give isl_basic_set
*isl_aff_nonneg_basic_set(__isl_take isl_aff
*aff
)
2239 return aff_nonneg_basic_set(aff
, 0);
2242 /* Return a basic set containing those elements in the domain space
2243 * of aff where it is negative.
2245 __isl_give isl_basic_set
*isl_aff_neg_basic_set(__isl_take isl_aff
*aff
)
2247 aff
= isl_aff_neg(aff
);
2248 aff
= isl_aff_add_constant_num_si(aff
, -1);
2249 return isl_aff_nonneg_basic_set(aff
);
2252 /* Return a basic set containing those elements in the space
2253 * of aff where it is zero.
2254 * If "rational" is set, then return a rational basic set.
2256 * If "aff" is NaN, then it is not zero.
2258 static __isl_give isl_basic_set
*aff_zero_basic_set(__isl_take isl_aff
*aff
,
2261 isl_constraint
*ineq
;
2262 isl_basic_set
*bset
;
2266 if (isl_aff_is_nan(aff
)) {
2267 isl_space
*space
= isl_aff_get_domain_space(aff
);
2269 return isl_basic_set_empty(space
);
2272 ineq
= isl_equality_from_aff(aff
);
2274 bset
= isl_basic_set_from_constraint(ineq
);
2276 bset
= isl_basic_set_set_rational(bset
);
2277 bset
= isl_basic_set_simplify(bset
);
2281 /* Return a basic set containing those elements in the space
2282 * of aff where it is zero.
2284 __isl_give isl_basic_set
*isl_aff_zero_basic_set(__isl_take isl_aff
*aff
)
2286 return aff_zero_basic_set(aff
, 0);
2289 /* Return a basic set containing those elements in the shared space
2290 * of aff1 and aff2 where aff1 is greater than or equal to aff2.
2292 __isl_give isl_basic_set
*isl_aff_ge_basic_set(__isl_take isl_aff
*aff1
,
2293 __isl_take isl_aff
*aff2
)
2295 aff1
= isl_aff_sub(aff1
, aff2
);
2297 return isl_aff_nonneg_basic_set(aff1
);
2300 /* Return a basic set containing those elements in the shared space
2301 * of aff1 and aff2 where aff1 is smaller than or equal to aff2.
2303 __isl_give isl_basic_set
*isl_aff_le_basic_set(__isl_take isl_aff
*aff1
,
2304 __isl_take isl_aff
*aff2
)
2306 return isl_aff_ge_basic_set(aff2
, aff1
);
2309 __isl_give isl_aff
*isl_aff_add_on_domain(__isl_keep isl_set
*dom
,
2310 __isl_take isl_aff
*aff1
, __isl_take isl_aff
*aff2
)
2312 aff1
= isl_aff_add(aff1
, aff2
);
2313 aff1
= isl_aff_gist(aff1
, isl_set_copy(dom
));
2317 int isl_aff_is_empty(__isl_keep isl_aff
*aff
)
2325 /* Check whether the given affine expression has non-zero coefficient
2326 * for any dimension in the given range or if any of these dimensions
2327 * appear with non-zero coefficients in any of the integer divisions
2328 * involved in the affine expression.
2330 int isl_aff_involves_dims(__isl_keep isl_aff
*aff
,
2331 enum isl_dim_type type
, unsigned first
, unsigned n
)
2343 ctx
= isl_aff_get_ctx(aff
);
2344 if (first
+ n
> isl_aff_dim(aff
, type
))
2345 isl_die(ctx
, isl_error_invalid
,
2346 "range out of bounds", return -1);
2348 active
= isl_local_space_get_active(aff
->ls
, aff
->v
->el
+ 2);
2352 first
+= isl_local_space_offset(aff
->ls
, type
) - 1;
2353 for (i
= 0; i
< n
; ++i
)
2354 if (active
[first
+ i
]) {
2367 __isl_give isl_aff
*isl_aff_drop_dims(__isl_take isl_aff
*aff
,
2368 enum isl_dim_type type
, unsigned first
, unsigned n
)
2374 if (type
== isl_dim_out
)
2375 isl_die(aff
->v
->ctx
, isl_error_invalid
,
2376 "cannot drop output/set dimension",
2377 return isl_aff_free(aff
));
2378 if (type
== isl_dim_in
)
2380 if (n
== 0 && !isl_local_space_is_named_or_nested(aff
->ls
, type
))
2383 ctx
= isl_aff_get_ctx(aff
);
2384 if (first
+ n
> isl_local_space_dim(aff
->ls
, type
))
2385 isl_die(ctx
, isl_error_invalid
, "range out of bounds",
2386 return isl_aff_free(aff
));
2388 aff
= isl_aff_cow(aff
);
2392 aff
->ls
= isl_local_space_drop_dims(aff
->ls
, type
, first
, n
);
2394 return isl_aff_free(aff
);
2396 first
+= 1 + isl_local_space_offset(aff
->ls
, type
);
2397 aff
->v
= isl_vec_drop_els(aff
->v
, first
, n
);
2399 return isl_aff_free(aff
);
2404 /* Project the domain of the affine expression onto its parameter space.
2405 * The affine expression may not involve any of the domain dimensions.
2407 __isl_give isl_aff
*isl_aff_project_domain_on_params(__isl_take isl_aff
*aff
)
2413 n
= isl_aff_dim(aff
, isl_dim_in
);
2414 involves
= isl_aff_involves_dims(aff
, isl_dim_in
, 0, n
);
2416 return isl_aff_free(aff
);
2418 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
2419 "affine expression involves some of the domain dimensions",
2420 return isl_aff_free(aff
));
2421 aff
= isl_aff_drop_dims(aff
, isl_dim_in
, 0, n
);
2422 space
= isl_aff_get_domain_space(aff
);
2423 space
= isl_space_params(space
);
2424 aff
= isl_aff_reset_domain_space(aff
, space
);
2428 __isl_give isl_aff
*isl_aff_insert_dims(__isl_take isl_aff
*aff
,
2429 enum isl_dim_type type
, unsigned first
, unsigned n
)
2435 if (type
== isl_dim_out
)
2436 isl_die(aff
->v
->ctx
, isl_error_invalid
,
2437 "cannot insert output/set dimensions",
2438 return isl_aff_free(aff
));
2439 if (type
== isl_dim_in
)
2441 if (n
== 0 && !isl_local_space_is_named_or_nested(aff
->ls
, type
))
2444 ctx
= isl_aff_get_ctx(aff
);
2445 if (first
> isl_local_space_dim(aff
->ls
, type
))
2446 isl_die(ctx
, isl_error_invalid
, "position out of bounds",
2447 return isl_aff_free(aff
));
2449 aff
= isl_aff_cow(aff
);
2453 aff
->ls
= isl_local_space_insert_dims(aff
->ls
, type
, first
, n
);
2455 return isl_aff_free(aff
);
2457 first
+= 1 + isl_local_space_offset(aff
->ls
, type
);
2458 aff
->v
= isl_vec_insert_zero_els(aff
->v
, first
, n
);
2460 return isl_aff_free(aff
);
2465 __isl_give isl_aff
*isl_aff_add_dims(__isl_take isl_aff
*aff
,
2466 enum isl_dim_type type
, unsigned n
)
2470 pos
= isl_aff_dim(aff
, type
);
2472 return isl_aff_insert_dims(aff
, type
, pos
, n
);
2475 __isl_give isl_pw_aff
*isl_pw_aff_add_dims(__isl_take isl_pw_aff
*pwaff
,
2476 enum isl_dim_type type
, unsigned n
)
2480 pos
= isl_pw_aff_dim(pwaff
, type
);
2482 return isl_pw_aff_insert_dims(pwaff
, type
, pos
, n
);
2485 /* Move the "n" dimensions of "src_type" starting at "src_pos" of "aff"
2486 * to dimensions of "dst_type" at "dst_pos".
2488 * We only support moving input dimensions to parameters and vice versa.
2490 __isl_give isl_aff
*isl_aff_move_dims(__isl_take isl_aff
*aff
,
2491 enum isl_dim_type dst_type
, unsigned dst_pos
,
2492 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
2500 !isl_local_space_is_named_or_nested(aff
->ls
, src_type
) &&
2501 !isl_local_space_is_named_or_nested(aff
->ls
, dst_type
))
2504 if (dst_type
== isl_dim_out
|| src_type
== isl_dim_out
)
2505 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
2506 "cannot move output/set dimension", isl_aff_free(aff
));
2507 if (dst_type
== isl_dim_div
|| src_type
== isl_dim_div
)
2508 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
2509 "cannot move divs", isl_aff_free(aff
));
2510 if (dst_type
== isl_dim_in
)
2511 dst_type
= isl_dim_set
;
2512 if (src_type
== isl_dim_in
)
2513 src_type
= isl_dim_set
;
2515 if (src_pos
+ n
> isl_local_space_dim(aff
->ls
, src_type
))
2516 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
2517 "range out of bounds", isl_aff_free(aff
));
2518 if (dst_type
== src_type
)
2519 isl_die(isl_aff_get_ctx(aff
), isl_error_unsupported
,
2520 "moving dims within the same type not supported",
2523 aff
= isl_aff_cow(aff
);
2527 g_src_pos
= 1 + isl_local_space_offset(aff
->ls
, src_type
) + src_pos
;
2528 g_dst_pos
= 1 + isl_local_space_offset(aff
->ls
, dst_type
) + dst_pos
;
2529 if (dst_type
> src_type
)
2532 aff
->v
= isl_vec_move_els(aff
->v
, g_dst_pos
, g_src_pos
, n
);
2533 aff
->ls
= isl_local_space_move_dims(aff
->ls
, dst_type
, dst_pos
,
2534 src_type
, src_pos
, n
);
2535 if (!aff
->v
|| !aff
->ls
)
2536 return isl_aff_free(aff
);
2538 aff
= sort_divs(aff
);
2543 __isl_give isl_pw_aff
*isl_pw_aff_from_aff(__isl_take isl_aff
*aff
)
2545 isl_set
*dom
= isl_set_universe(isl_aff_get_domain_space(aff
));
2546 return isl_pw_aff_alloc(dom
, aff
);
2550 #define PW isl_pw_aff
2554 #define EL_IS_ZERO is_empty
2558 #define IS_ZERO is_empty
2561 #undef DEFAULT_IS_ZERO
2562 #define DEFAULT_IS_ZERO 0
2569 #include <isl_pw_templ.c>
2572 #define UNION isl_union_pw_aff
2574 #define PART isl_pw_aff
2576 #define PARTS pw_aff
2577 #define ALIGN_DOMAIN
2581 #include <isl_union_templ.c>
2583 static __isl_give isl_set
*align_params_pw_pw_set_and(
2584 __isl_take isl_pw_aff
*pwaff1
, __isl_take isl_pw_aff
*pwaff2
,
2585 __isl_give isl_set
*(*fn
)(__isl_take isl_pw_aff
*pwaff1
,
2586 __isl_take isl_pw_aff
*pwaff2
))
2588 if (!pwaff1
|| !pwaff2
)
2590 if (isl_space_match(pwaff1
->dim
, isl_dim_param
,
2591 pwaff2
->dim
, isl_dim_param
))
2592 return fn(pwaff1
, pwaff2
);
2593 if (!isl_space_has_named_params(pwaff1
->dim
) ||
2594 !isl_space_has_named_params(pwaff2
->dim
))
2595 isl_die(isl_pw_aff_get_ctx(pwaff1
), isl_error_invalid
,
2596 "unaligned unnamed parameters", goto error
);
2597 pwaff1
= isl_pw_aff_align_params(pwaff1
, isl_pw_aff_get_space(pwaff2
));
2598 pwaff2
= isl_pw_aff_align_params(pwaff2
, isl_pw_aff_get_space(pwaff1
));
2599 return fn(pwaff1
, pwaff2
);
2601 isl_pw_aff_free(pwaff1
);
2602 isl_pw_aff_free(pwaff2
);
2606 /* Compute a piecewise quasi-affine expression with a domain that
2607 * is the union of those of pwaff1 and pwaff2 and such that on each
2608 * cell, the quasi-affine expression is the better (according to cmp)
2609 * of those of pwaff1 and pwaff2. If only one of pwaff1 or pwaff2
2610 * is defined on a given cell, then the associated expression
2611 * is the defined one.
2613 static __isl_give isl_pw_aff
*pw_aff_union_opt(__isl_take isl_pw_aff
*pwaff1
,
2614 __isl_take isl_pw_aff
*pwaff2
,
2615 __isl_give isl_basic_set
*(*cmp
)(__isl_take isl_aff
*aff1
,
2616 __isl_take isl_aff
*aff2
))
2623 if (!pwaff1
|| !pwaff2
)
2626 ctx
= isl_space_get_ctx(pwaff1
->dim
);
2627 if (!isl_space_is_equal(pwaff1
->dim
, pwaff2
->dim
))
2628 isl_die(ctx
, isl_error_invalid
,
2629 "arguments should live in same space", goto error
);
2631 if (isl_pw_aff_is_empty(pwaff1
)) {
2632 isl_pw_aff_free(pwaff1
);
2636 if (isl_pw_aff_is_empty(pwaff2
)) {
2637 isl_pw_aff_free(pwaff2
);
2641 n
= 2 * (pwaff1
->n
+ 1) * (pwaff2
->n
+ 1);
2642 res
= isl_pw_aff_alloc_size(isl_space_copy(pwaff1
->dim
), n
);
2644 for (i
= 0; i
< pwaff1
->n
; ++i
) {
2645 set
= isl_set_copy(pwaff1
->p
[i
].set
);
2646 for (j
= 0; j
< pwaff2
->n
; ++j
) {
2647 struct isl_set
*common
;
2650 common
= isl_set_intersect(
2651 isl_set_copy(pwaff1
->p
[i
].set
),
2652 isl_set_copy(pwaff2
->p
[j
].set
));
2653 better
= isl_set_from_basic_set(cmp(
2654 isl_aff_copy(pwaff2
->p
[j
].aff
),
2655 isl_aff_copy(pwaff1
->p
[i
].aff
)));
2656 better
= isl_set_intersect(common
, better
);
2657 if (isl_set_plain_is_empty(better
)) {
2658 isl_set_free(better
);
2661 set
= isl_set_subtract(set
, isl_set_copy(better
));
2663 res
= isl_pw_aff_add_piece(res
, better
,
2664 isl_aff_copy(pwaff2
->p
[j
].aff
));
2666 res
= isl_pw_aff_add_piece(res
, set
,
2667 isl_aff_copy(pwaff1
->p
[i
].aff
));
2670 for (j
= 0; j
< pwaff2
->n
; ++j
) {
2671 set
= isl_set_copy(pwaff2
->p
[j
].set
);
2672 for (i
= 0; i
< pwaff1
->n
; ++i
)
2673 set
= isl_set_subtract(set
,
2674 isl_set_copy(pwaff1
->p
[i
].set
));
2675 res
= isl_pw_aff_add_piece(res
, set
,
2676 isl_aff_copy(pwaff2
->p
[j
].aff
));
2679 isl_pw_aff_free(pwaff1
);
2680 isl_pw_aff_free(pwaff2
);
2684 isl_pw_aff_free(pwaff1
);
2685 isl_pw_aff_free(pwaff2
);
2689 /* Compute a piecewise quasi-affine expression with a domain that
2690 * is the union of those of pwaff1 and pwaff2 and such that on each
2691 * cell, the quasi-affine expression is the maximum of those of pwaff1
2692 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
2693 * cell, then the associated expression is the defined one.
2695 static __isl_give isl_pw_aff
*pw_aff_union_max(__isl_take isl_pw_aff
*pwaff1
,
2696 __isl_take isl_pw_aff
*pwaff2
)
2698 return pw_aff_union_opt(pwaff1
, pwaff2
, &isl_aff_ge_basic_set
);
2701 __isl_give isl_pw_aff
*isl_pw_aff_union_max(__isl_take isl_pw_aff
*pwaff1
,
2702 __isl_take isl_pw_aff
*pwaff2
)
2704 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
,
2708 /* Compute a piecewise quasi-affine expression with a domain that
2709 * is the union of those of pwaff1 and pwaff2 and such that on each
2710 * cell, the quasi-affine expression is the minimum of those of pwaff1
2711 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
2712 * cell, then the associated expression is the defined one.
2714 static __isl_give isl_pw_aff
*pw_aff_union_min(__isl_take isl_pw_aff
*pwaff1
,
2715 __isl_take isl_pw_aff
*pwaff2
)
2717 return pw_aff_union_opt(pwaff1
, pwaff2
, &isl_aff_le_basic_set
);
2720 __isl_give isl_pw_aff
*isl_pw_aff_union_min(__isl_take isl_pw_aff
*pwaff1
,
2721 __isl_take isl_pw_aff
*pwaff2
)
2723 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
,
2727 __isl_give isl_pw_aff
*isl_pw_aff_union_opt(__isl_take isl_pw_aff
*pwaff1
,
2728 __isl_take isl_pw_aff
*pwaff2
, int max
)
2731 return isl_pw_aff_union_max(pwaff1
, pwaff2
);
2733 return isl_pw_aff_union_min(pwaff1
, pwaff2
);
2736 /* Construct a map with as domain the domain of pwaff and
2737 * one-dimensional range corresponding to the affine expressions.
2739 static __isl_give isl_map
*map_from_pw_aff(__isl_take isl_pw_aff
*pwaff
)
2748 dim
= isl_pw_aff_get_space(pwaff
);
2749 map
= isl_map_empty(dim
);
2751 for (i
= 0; i
< pwaff
->n
; ++i
) {
2752 isl_basic_map
*bmap
;
2755 bmap
= isl_basic_map_from_aff(isl_aff_copy(pwaff
->p
[i
].aff
));
2756 map_i
= isl_map_from_basic_map(bmap
);
2757 map_i
= isl_map_intersect_domain(map_i
,
2758 isl_set_copy(pwaff
->p
[i
].set
));
2759 map
= isl_map_union_disjoint(map
, map_i
);
2762 isl_pw_aff_free(pwaff
);
2767 /* Construct a map with as domain the domain of pwaff and
2768 * one-dimensional range corresponding to the affine expressions.
2770 __isl_give isl_map
*isl_map_from_pw_aff(__isl_take isl_pw_aff
*pwaff
)
2774 if (isl_space_is_set(pwaff
->dim
))
2775 isl_die(isl_pw_aff_get_ctx(pwaff
), isl_error_invalid
,
2776 "space of input is not a map", goto error
);
2777 return map_from_pw_aff(pwaff
);
2779 isl_pw_aff_free(pwaff
);
2783 /* Construct a one-dimensional set with as parameter domain
2784 * the domain of pwaff and the single set dimension
2785 * corresponding to the affine expressions.
2787 __isl_give isl_set
*isl_set_from_pw_aff(__isl_take isl_pw_aff
*pwaff
)
2791 if (!isl_space_is_set(pwaff
->dim
))
2792 isl_die(isl_pw_aff_get_ctx(pwaff
), isl_error_invalid
,
2793 "space of input is not a set", goto error
);
2794 return map_from_pw_aff(pwaff
);
2796 isl_pw_aff_free(pwaff
);
2800 /* Return a set containing those elements in the domain
2801 * of "pwaff" where it satisfies "fn" (if complement is 0) or
2802 * does not satisfy "fn" (if complement is 1).
2804 * The pieces with a NaN never belong to the result since
2805 * NaN does not satisfy any property.
2807 static __isl_give isl_set
*pw_aff_locus(__isl_take isl_pw_aff
*pwaff
,
2808 __isl_give isl_basic_set
*(*fn
)(__isl_take isl_aff
*aff
, int rational
),
2817 set
= isl_set_empty(isl_pw_aff_get_domain_space(pwaff
));
2819 for (i
= 0; i
< pwaff
->n
; ++i
) {
2820 isl_basic_set
*bset
;
2821 isl_set
*set_i
, *locus
;
2824 if (isl_aff_is_nan(pwaff
->p
[i
].aff
))
2827 rational
= isl_set_has_rational(pwaff
->p
[i
].set
);
2828 bset
= fn(isl_aff_copy(pwaff
->p
[i
].aff
), rational
);
2829 locus
= isl_set_from_basic_set(bset
);
2830 set_i
= isl_set_copy(pwaff
->p
[i
].set
);
2832 set_i
= isl_set_subtract(set_i
, locus
);
2834 set_i
= isl_set_intersect(set_i
, locus
);
2835 set
= isl_set_union_disjoint(set
, set_i
);
2838 isl_pw_aff_free(pwaff
);
2843 /* Return a set containing those elements in the domain
2844 * of "pa" where it is positive.
2846 __isl_give isl_set
*isl_pw_aff_pos_set(__isl_take isl_pw_aff
*pa
)
2848 return pw_aff_locus(pa
, &aff_pos_basic_set
, 0);
2851 /* Return a set containing those elements in the domain
2852 * of pwaff where it is non-negative.
2854 __isl_give isl_set
*isl_pw_aff_nonneg_set(__isl_take isl_pw_aff
*pwaff
)
2856 return pw_aff_locus(pwaff
, &aff_nonneg_basic_set
, 0);
2859 /* Return a set containing those elements in the domain
2860 * of pwaff where it is zero.
2862 __isl_give isl_set
*isl_pw_aff_zero_set(__isl_take isl_pw_aff
*pwaff
)
2864 return pw_aff_locus(pwaff
, &aff_zero_basic_set
, 0);
2867 /* Return a set containing those elements in the domain
2868 * of pwaff where it is not zero.
2870 __isl_give isl_set
*isl_pw_aff_non_zero_set(__isl_take isl_pw_aff
*pwaff
)
2872 return pw_aff_locus(pwaff
, &aff_zero_basic_set
, 1);
2875 /* Return a set containing those elements in the shared domain
2876 * of pwaff1 and pwaff2 where pwaff1 is greater than (or equal) to pwaff2.
2878 * We compute the difference on the shared domain and then construct
2879 * the set of values where this difference is non-negative.
2880 * If strict is set, we first subtract 1 from the difference.
2881 * If equal is set, we only return the elements where pwaff1 and pwaff2
2884 static __isl_give isl_set
*pw_aff_gte_set(__isl_take isl_pw_aff
*pwaff1
,
2885 __isl_take isl_pw_aff
*pwaff2
, int strict
, int equal
)
2887 isl_set
*set1
, *set2
;
2889 set1
= isl_pw_aff_domain(isl_pw_aff_copy(pwaff1
));
2890 set2
= isl_pw_aff_domain(isl_pw_aff_copy(pwaff2
));
2891 set1
= isl_set_intersect(set1
, set2
);
2892 pwaff1
= isl_pw_aff_intersect_domain(pwaff1
, isl_set_copy(set1
));
2893 pwaff2
= isl_pw_aff_intersect_domain(pwaff2
, isl_set_copy(set1
));
2894 pwaff1
= isl_pw_aff_add(pwaff1
, isl_pw_aff_neg(pwaff2
));
2897 isl_space
*dim
= isl_set_get_space(set1
);
2899 aff
= isl_aff_zero_on_domain(isl_local_space_from_space(dim
));
2900 aff
= isl_aff_add_constant_si(aff
, -1);
2901 pwaff1
= isl_pw_aff_add(pwaff1
, isl_pw_aff_alloc(set1
, aff
));
2906 return isl_pw_aff_zero_set(pwaff1
);
2907 return isl_pw_aff_nonneg_set(pwaff1
);
2910 /* Return a set containing those elements in the shared domain
2911 * of pwaff1 and pwaff2 where pwaff1 is equal to pwaff2.
2913 static __isl_give isl_set
*pw_aff_eq_set(__isl_take isl_pw_aff
*pwaff1
,
2914 __isl_take isl_pw_aff
*pwaff2
)
2916 return pw_aff_gte_set(pwaff1
, pwaff2
, 0, 1);
2919 __isl_give isl_set
*isl_pw_aff_eq_set(__isl_take isl_pw_aff
*pwaff1
,
2920 __isl_take isl_pw_aff
*pwaff2
)
2922 return align_params_pw_pw_set_and(pwaff1
, pwaff2
, &pw_aff_eq_set
);
2925 /* Return a set containing those elements in the shared domain
2926 * of pwaff1 and pwaff2 where pwaff1 is greater than or equal to pwaff2.
2928 static __isl_give isl_set
*pw_aff_ge_set(__isl_take isl_pw_aff
*pwaff1
,
2929 __isl_take isl_pw_aff
*pwaff2
)
2931 return pw_aff_gte_set(pwaff1
, pwaff2
, 0, 0);
2934 __isl_give isl_set
*isl_pw_aff_ge_set(__isl_take isl_pw_aff
*pwaff1
,
2935 __isl_take isl_pw_aff
*pwaff2
)
2937 return align_params_pw_pw_set_and(pwaff1
, pwaff2
, &pw_aff_ge_set
);
2940 /* Return a set containing those elements in the shared domain
2941 * of pwaff1 and pwaff2 where pwaff1 is strictly greater than pwaff2.
2943 static __isl_give isl_set
*pw_aff_gt_set(__isl_take isl_pw_aff
*pwaff1
,
2944 __isl_take isl_pw_aff
*pwaff2
)
2946 return pw_aff_gte_set(pwaff1
, pwaff2
, 1, 0);
2949 __isl_give isl_set
*isl_pw_aff_gt_set(__isl_take isl_pw_aff
*pwaff1
,
2950 __isl_take isl_pw_aff
*pwaff2
)
2952 return align_params_pw_pw_set_and(pwaff1
, pwaff2
, &pw_aff_gt_set
);
2955 __isl_give isl_set
*isl_pw_aff_le_set(__isl_take isl_pw_aff
*pwaff1
,
2956 __isl_take isl_pw_aff
*pwaff2
)
2958 return isl_pw_aff_ge_set(pwaff2
, pwaff1
);
2961 __isl_give isl_set
*isl_pw_aff_lt_set(__isl_take isl_pw_aff
*pwaff1
,
2962 __isl_take isl_pw_aff
*pwaff2
)
2964 return isl_pw_aff_gt_set(pwaff2
, pwaff1
);
2967 /* Return a set containing those elements in the shared domain
2968 * of the elements of list1 and list2 where each element in list1
2969 * has the relation specified by "fn" with each element in list2.
2971 static __isl_give isl_set
*pw_aff_list_set(__isl_take isl_pw_aff_list
*list1
,
2972 __isl_take isl_pw_aff_list
*list2
,
2973 __isl_give isl_set
*(*fn
)(__isl_take isl_pw_aff
*pwaff1
,
2974 __isl_take isl_pw_aff
*pwaff2
))
2980 if (!list1
|| !list2
)
2983 ctx
= isl_pw_aff_list_get_ctx(list1
);
2984 if (list1
->n
< 1 || list2
->n
< 1)
2985 isl_die(ctx
, isl_error_invalid
,
2986 "list should contain at least one element", goto error
);
2988 set
= isl_set_universe(isl_pw_aff_get_domain_space(list1
->p
[0]));
2989 for (i
= 0; i
< list1
->n
; ++i
)
2990 for (j
= 0; j
< list2
->n
; ++j
) {
2993 set_ij
= fn(isl_pw_aff_copy(list1
->p
[i
]),
2994 isl_pw_aff_copy(list2
->p
[j
]));
2995 set
= isl_set_intersect(set
, set_ij
);
2998 isl_pw_aff_list_free(list1
);
2999 isl_pw_aff_list_free(list2
);
3002 isl_pw_aff_list_free(list1
);
3003 isl_pw_aff_list_free(list2
);
3007 /* Return a set containing those elements in the shared domain
3008 * of the elements of list1 and list2 where each element in list1
3009 * is equal to each element in list2.
3011 __isl_give isl_set
*isl_pw_aff_list_eq_set(__isl_take isl_pw_aff_list
*list1
,
3012 __isl_take isl_pw_aff_list
*list2
)
3014 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_eq_set
);
3017 __isl_give isl_set
*isl_pw_aff_list_ne_set(__isl_take isl_pw_aff_list
*list1
,
3018 __isl_take isl_pw_aff_list
*list2
)
3020 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_ne_set
);
3023 /* Return a set containing those elements in the shared domain
3024 * of the elements of list1 and list2 where each element in list1
3025 * is less than or equal to each element in list2.
3027 __isl_give isl_set
*isl_pw_aff_list_le_set(__isl_take isl_pw_aff_list
*list1
,
3028 __isl_take isl_pw_aff_list
*list2
)
3030 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_le_set
);
3033 __isl_give isl_set
*isl_pw_aff_list_lt_set(__isl_take isl_pw_aff_list
*list1
,
3034 __isl_take isl_pw_aff_list
*list2
)
3036 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_lt_set
);
3039 __isl_give isl_set
*isl_pw_aff_list_ge_set(__isl_take isl_pw_aff_list
*list1
,
3040 __isl_take isl_pw_aff_list
*list2
)
3042 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_ge_set
);
3045 __isl_give isl_set
*isl_pw_aff_list_gt_set(__isl_take isl_pw_aff_list
*list1
,
3046 __isl_take isl_pw_aff_list
*list2
)
3048 return pw_aff_list_set(list1
, list2
, &isl_pw_aff_gt_set
);
3052 /* Return a set containing those elements in the shared domain
3053 * of pwaff1 and pwaff2 where pwaff1 is not equal to pwaff2.
3055 static __isl_give isl_set
*pw_aff_ne_set(__isl_take isl_pw_aff
*pwaff1
,
3056 __isl_take isl_pw_aff
*pwaff2
)
3058 isl_set
*set_lt
, *set_gt
;
3060 set_lt
= isl_pw_aff_lt_set(isl_pw_aff_copy(pwaff1
),
3061 isl_pw_aff_copy(pwaff2
));
3062 set_gt
= isl_pw_aff_gt_set(pwaff1
, pwaff2
);
3063 return isl_set_union_disjoint(set_lt
, set_gt
);
3066 __isl_give isl_set
*isl_pw_aff_ne_set(__isl_take isl_pw_aff
*pwaff1
,
3067 __isl_take isl_pw_aff
*pwaff2
)
3069 return align_params_pw_pw_set_and(pwaff1
, pwaff2
, &pw_aff_ne_set
);
3072 __isl_give isl_pw_aff
*isl_pw_aff_scale_down(__isl_take isl_pw_aff
*pwaff
,
3077 if (isl_int_is_one(v
))
3079 if (!isl_int_is_pos(v
))
3080 isl_die(isl_pw_aff_get_ctx(pwaff
), isl_error_invalid
,
3081 "factor needs to be positive",
3082 return isl_pw_aff_free(pwaff
));
3083 pwaff
= isl_pw_aff_cow(pwaff
);
3089 for (i
= 0; i
< pwaff
->n
; ++i
) {
3090 pwaff
->p
[i
].aff
= isl_aff_scale_down(pwaff
->p
[i
].aff
, v
);
3091 if (!pwaff
->p
[i
].aff
)
3092 return isl_pw_aff_free(pwaff
);
3098 __isl_give isl_pw_aff
*isl_pw_aff_floor(__isl_take isl_pw_aff
*pwaff
)
3102 pwaff
= isl_pw_aff_cow(pwaff
);
3108 for (i
= 0; i
< pwaff
->n
; ++i
) {
3109 pwaff
->p
[i
].aff
= isl_aff_floor(pwaff
->p
[i
].aff
);
3110 if (!pwaff
->p
[i
].aff
)
3111 return isl_pw_aff_free(pwaff
);
3117 __isl_give isl_pw_aff
*isl_pw_aff_ceil(__isl_take isl_pw_aff
*pwaff
)
3121 pwaff
= isl_pw_aff_cow(pwaff
);
3127 for (i
= 0; i
< pwaff
->n
; ++i
) {
3128 pwaff
->p
[i
].aff
= isl_aff_ceil(pwaff
->p
[i
].aff
);
3129 if (!pwaff
->p
[i
].aff
)
3130 return isl_pw_aff_free(pwaff
);
3136 /* Assuming that "cond1" and "cond2" are disjoint,
3137 * return an affine expression that is equal to pwaff1 on cond1
3138 * and to pwaff2 on cond2.
3140 static __isl_give isl_pw_aff
*isl_pw_aff_select(
3141 __isl_take isl_set
*cond1
, __isl_take isl_pw_aff
*pwaff1
,
3142 __isl_take isl_set
*cond2
, __isl_take isl_pw_aff
*pwaff2
)
3144 pwaff1
= isl_pw_aff_intersect_domain(pwaff1
, cond1
);
3145 pwaff2
= isl_pw_aff_intersect_domain(pwaff2
, cond2
);
3147 return isl_pw_aff_add_disjoint(pwaff1
, pwaff2
);
3150 /* Return an affine expression that is equal to pwaff_true for elements
3151 * where "cond" is non-zero and to pwaff_false for elements where "cond"
3153 * That is, return cond ? pwaff_true : pwaff_false;
3155 * If "cond" involves and NaN, then we conservatively return a NaN
3156 * on its entire domain. In principle, we could consider the pieces
3157 * where it is NaN separately from those where it is not.
3159 __isl_give isl_pw_aff
*isl_pw_aff_cond(__isl_take isl_pw_aff
*cond
,
3160 __isl_take isl_pw_aff
*pwaff_true
, __isl_take isl_pw_aff
*pwaff_false
)
3162 isl_set
*cond_true
, *cond_false
;
3166 if (isl_pw_aff_involves_nan(cond
)) {
3167 isl_space
*space
= isl_pw_aff_get_domain_space(cond
);
3168 isl_local_space
*ls
= isl_local_space_from_space(space
);
3169 isl_pw_aff_free(cond
);
3170 isl_pw_aff_free(pwaff_true
);
3171 isl_pw_aff_free(pwaff_false
);
3172 return isl_pw_aff_nan_on_domain(ls
);
3175 cond_true
= isl_pw_aff_non_zero_set(isl_pw_aff_copy(cond
));
3176 cond_false
= isl_pw_aff_zero_set(cond
);
3177 return isl_pw_aff_select(cond_true
, pwaff_true
,
3178 cond_false
, pwaff_false
);
3180 isl_pw_aff_free(cond
);
3181 isl_pw_aff_free(pwaff_true
);
3182 isl_pw_aff_free(pwaff_false
);
3186 int isl_aff_is_cst(__isl_keep isl_aff
*aff
)
3191 return isl_seq_first_non_zero(aff
->v
->el
+ 2, aff
->v
->size
- 2) == -1;
3194 /* Check whether pwaff is a piecewise constant.
3196 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff
*pwaff
)
3203 for (i
= 0; i
< pwaff
->n
; ++i
) {
3204 int is_cst
= isl_aff_is_cst(pwaff
->p
[i
].aff
);
3205 if (is_cst
< 0 || !is_cst
)
3212 /* Return the product of "aff1" and "aff2".
3214 * If either of the two is NaN, then the result is NaN.
3216 * Otherwise, at least one of "aff1" or "aff2" needs to be a constant.
3218 __isl_give isl_aff
*isl_aff_mul(__isl_take isl_aff
*aff1
,
3219 __isl_take isl_aff
*aff2
)
3224 if (isl_aff_is_nan(aff1
)) {
3228 if (isl_aff_is_nan(aff2
)) {
3233 if (!isl_aff_is_cst(aff2
) && isl_aff_is_cst(aff1
))
3234 return isl_aff_mul(aff2
, aff1
);
3236 if (!isl_aff_is_cst(aff2
))
3237 isl_die(isl_aff_get_ctx(aff1
), isl_error_invalid
,
3238 "at least one affine expression should be constant",
3241 aff1
= isl_aff_cow(aff1
);
3245 aff1
= isl_aff_scale(aff1
, aff2
->v
->el
[1]);
3246 aff1
= isl_aff_scale_down(aff1
, aff2
->v
->el
[0]);
3256 /* Divide "aff1" by "aff2", assuming "aff2" is a constant.
3258 * If either of the two is NaN, then the result is NaN.
3260 __isl_give isl_aff
*isl_aff_div(__isl_take isl_aff
*aff1
,
3261 __isl_take isl_aff
*aff2
)
3269 if (isl_aff_is_nan(aff1
)) {
3273 if (isl_aff_is_nan(aff2
)) {
3278 is_cst
= isl_aff_is_cst(aff2
);
3282 isl_die(isl_aff_get_ctx(aff2
), isl_error_invalid
,
3283 "second argument should be a constant", goto error
);
3288 neg
= isl_int_is_neg(aff2
->v
->el
[1]);
3290 isl_int_neg(aff2
->v
->el
[0], aff2
->v
->el
[0]);
3291 isl_int_neg(aff2
->v
->el
[1], aff2
->v
->el
[1]);
3294 aff1
= isl_aff_scale(aff1
, aff2
->v
->el
[0]);
3295 aff1
= isl_aff_scale_down(aff1
, aff2
->v
->el
[1]);
3298 isl_int_neg(aff2
->v
->el
[0], aff2
->v
->el
[0]);
3299 isl_int_neg(aff2
->v
->el
[1], aff2
->v
->el
[1]);
3310 static __isl_give isl_pw_aff
*pw_aff_add(__isl_take isl_pw_aff
*pwaff1
,
3311 __isl_take isl_pw_aff
*pwaff2
)
3313 return isl_pw_aff_on_shared_domain(pwaff1
, pwaff2
, &isl_aff_add
);
3316 __isl_give isl_pw_aff
*isl_pw_aff_add(__isl_take isl_pw_aff
*pwaff1
,
3317 __isl_take isl_pw_aff
*pwaff2
)
3319 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
, &pw_aff_add
);
3322 __isl_give isl_pw_aff
*isl_pw_aff_union_add(__isl_take isl_pw_aff
*pwaff1
,
3323 __isl_take isl_pw_aff
*pwaff2
)
3325 return isl_pw_aff_union_add_(pwaff1
, pwaff2
);
3328 static __isl_give isl_pw_aff
*pw_aff_mul(__isl_take isl_pw_aff
*pwaff1
,
3329 __isl_take isl_pw_aff
*pwaff2
)
3331 return isl_pw_aff_on_shared_domain(pwaff1
, pwaff2
, &isl_aff_mul
);
3334 __isl_give isl_pw_aff
*isl_pw_aff_mul(__isl_take isl_pw_aff
*pwaff1
,
3335 __isl_take isl_pw_aff
*pwaff2
)
3337 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
, &pw_aff_mul
);
3340 static __isl_give isl_pw_aff
*pw_aff_div(__isl_take isl_pw_aff
*pa1
,
3341 __isl_take isl_pw_aff
*pa2
)
3343 return isl_pw_aff_on_shared_domain(pa1
, pa2
, &isl_aff_div
);
3346 /* Divide "pa1" by "pa2", assuming "pa2" is a piecewise constant.
3348 __isl_give isl_pw_aff
*isl_pw_aff_div(__isl_take isl_pw_aff
*pa1
,
3349 __isl_take isl_pw_aff
*pa2
)
3353 is_cst
= isl_pw_aff_is_cst(pa2
);
3357 isl_die(isl_pw_aff_get_ctx(pa2
), isl_error_invalid
,
3358 "second argument should be a piecewise constant",
3360 return isl_pw_aff_align_params_pw_pw_and(pa1
, pa2
, &pw_aff_div
);
3362 isl_pw_aff_free(pa1
);
3363 isl_pw_aff_free(pa2
);
3367 /* Compute the quotient of the integer division of "pa1" by "pa2"
3368 * with rounding towards zero.
3369 * "pa2" is assumed to be a piecewise constant.
3371 * In particular, return
3373 * pa1 >= 0 ? floor(pa1/pa2) : ceil(pa1/pa2)
3376 __isl_give isl_pw_aff
*isl_pw_aff_tdiv_q(__isl_take isl_pw_aff
*pa1
,
3377 __isl_take isl_pw_aff
*pa2
)
3383 is_cst
= isl_pw_aff_is_cst(pa2
);
3387 isl_die(isl_pw_aff_get_ctx(pa2
), isl_error_invalid
,
3388 "second argument should be a piecewise constant",
3391 pa1
= isl_pw_aff_div(pa1
, pa2
);
3393 cond
= isl_pw_aff_nonneg_set(isl_pw_aff_copy(pa1
));
3394 f
= isl_pw_aff_floor(isl_pw_aff_copy(pa1
));
3395 c
= isl_pw_aff_ceil(pa1
);
3396 return isl_pw_aff_cond(isl_set_indicator_function(cond
), f
, c
);
3398 isl_pw_aff_free(pa1
);
3399 isl_pw_aff_free(pa2
);
3403 /* Compute the remainder of the integer division of "pa1" by "pa2"
3404 * with rounding towards zero.
3405 * "pa2" is assumed to be a piecewise constant.
3407 * In particular, return
3409 * pa1 - pa2 * (pa1 >= 0 ? floor(pa1/pa2) : ceil(pa1/pa2))
3412 __isl_give isl_pw_aff
*isl_pw_aff_tdiv_r(__isl_take isl_pw_aff
*pa1
,
3413 __isl_take isl_pw_aff
*pa2
)
3418 is_cst
= isl_pw_aff_is_cst(pa2
);
3422 isl_die(isl_pw_aff_get_ctx(pa2
), isl_error_invalid
,
3423 "second argument should be a piecewise constant",
3425 res
= isl_pw_aff_tdiv_q(isl_pw_aff_copy(pa1
), isl_pw_aff_copy(pa2
));
3426 res
= isl_pw_aff_mul(pa2
, res
);
3427 res
= isl_pw_aff_sub(pa1
, res
);
3430 isl_pw_aff_free(pa1
);
3431 isl_pw_aff_free(pa2
);
3435 static __isl_give isl_pw_aff
*pw_aff_min(__isl_take isl_pw_aff
*pwaff1
,
3436 __isl_take isl_pw_aff
*pwaff2
)
3441 dom
= isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1
)),
3442 isl_pw_aff_domain(isl_pw_aff_copy(pwaff2
)));
3443 le
= isl_pw_aff_le_set(isl_pw_aff_copy(pwaff1
),
3444 isl_pw_aff_copy(pwaff2
));
3445 dom
= isl_set_subtract(dom
, isl_set_copy(le
));
3446 return isl_pw_aff_select(le
, pwaff1
, dom
, pwaff2
);
3449 __isl_give isl_pw_aff
*isl_pw_aff_min(__isl_take isl_pw_aff
*pwaff1
,
3450 __isl_take isl_pw_aff
*pwaff2
)
3452 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
, &pw_aff_min
);
3455 static __isl_give isl_pw_aff
*pw_aff_max(__isl_take isl_pw_aff
*pwaff1
,
3456 __isl_take isl_pw_aff
*pwaff2
)
3461 dom
= isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1
)),
3462 isl_pw_aff_domain(isl_pw_aff_copy(pwaff2
)));
3463 ge
= isl_pw_aff_ge_set(isl_pw_aff_copy(pwaff1
),
3464 isl_pw_aff_copy(pwaff2
));
3465 dom
= isl_set_subtract(dom
, isl_set_copy(ge
));
3466 return isl_pw_aff_select(ge
, pwaff1
, dom
, pwaff2
);
3469 __isl_give isl_pw_aff
*isl_pw_aff_max(__isl_take isl_pw_aff
*pwaff1
,
3470 __isl_take isl_pw_aff
*pwaff2
)
3472 return isl_pw_aff_align_params_pw_pw_and(pwaff1
, pwaff2
, &pw_aff_max
);
3475 static __isl_give isl_pw_aff
*pw_aff_list_reduce(
3476 __isl_take isl_pw_aff_list
*list
,
3477 __isl_give isl_pw_aff
*(*fn
)(__isl_take isl_pw_aff
*pwaff1
,
3478 __isl_take isl_pw_aff
*pwaff2
))
3487 ctx
= isl_pw_aff_list_get_ctx(list
);
3489 isl_die(ctx
, isl_error_invalid
,
3490 "list should contain at least one element", goto error
);
3492 res
= isl_pw_aff_copy(list
->p
[0]);
3493 for (i
= 1; i
< list
->n
; ++i
)
3494 res
= fn(res
, isl_pw_aff_copy(list
->p
[i
]));
3496 isl_pw_aff_list_free(list
);
3499 isl_pw_aff_list_free(list
);
3503 /* Return an isl_pw_aff that maps each element in the intersection of the
3504 * domains of the elements of list to the minimal corresponding affine
3507 __isl_give isl_pw_aff
*isl_pw_aff_list_min(__isl_take isl_pw_aff_list
*list
)
3509 return pw_aff_list_reduce(list
, &isl_pw_aff_min
);
3512 /* Return an isl_pw_aff that maps each element in the intersection of the
3513 * domains of the elements of list to the maximal corresponding affine
3516 __isl_give isl_pw_aff
*isl_pw_aff_list_max(__isl_take isl_pw_aff_list
*list
)
3518 return pw_aff_list_reduce(list
, &isl_pw_aff_max
);
3521 /* Mark the domains of "pwaff" as rational.
3523 __isl_give isl_pw_aff
*isl_pw_aff_set_rational(__isl_take isl_pw_aff
*pwaff
)
3527 pwaff
= isl_pw_aff_cow(pwaff
);
3533 for (i
= 0; i
< pwaff
->n
; ++i
) {
3534 pwaff
->p
[i
].set
= isl_set_set_rational(pwaff
->p
[i
].set
);
3535 if (!pwaff
->p
[i
].set
)
3536 return isl_pw_aff_free(pwaff
);
3542 /* Mark the domains of the elements of "list" as rational.
3544 __isl_give isl_pw_aff_list
*isl_pw_aff_list_set_rational(
3545 __isl_take isl_pw_aff_list
*list
)
3555 for (i
= 0; i
< n
; ++i
) {
3558 pa
= isl_pw_aff_list_get_pw_aff(list
, i
);
3559 pa
= isl_pw_aff_set_rational(pa
);
3560 list
= isl_pw_aff_list_set_pw_aff(list
, i
, pa
);
3566 /* Do the parameters of "aff" match those of "space"?
3568 int isl_aff_matching_params(__isl_keep isl_aff
*aff
,
3569 __isl_keep isl_space
*space
)
3571 isl_space
*aff_space
;
3577 aff_space
= isl_aff_get_domain_space(aff
);
3579 match
= isl_space_match(space
, isl_dim_param
, aff_space
, isl_dim_param
);
3581 isl_space_free(aff_space
);
3585 /* Check that the domain space of "aff" matches "space".
3587 * Return 0 on success and -1 on error.
3589 int isl_aff_check_match_domain_space(__isl_keep isl_aff
*aff
,
3590 __isl_keep isl_space
*space
)
3592 isl_space
*aff_space
;
3598 aff_space
= isl_aff_get_domain_space(aff
);
3600 match
= isl_space_match(space
, isl_dim_param
, aff_space
, isl_dim_param
);
3604 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
3605 "parameters don't match", goto error
);
3606 match
= isl_space_tuple_is_equal(space
, isl_dim_in
,
3607 aff_space
, isl_dim_set
);
3611 isl_die(isl_aff_get_ctx(aff
), isl_error_invalid
,
3612 "domains don't match", goto error
);
3613 isl_space_free(aff_space
);
3616 isl_space_free(aff_space
);
3622 #define NO_INTERSECT_DOMAIN
3625 #include <isl_multi_templ.c>
3628 #undef NO_INTERSECT_DOMAIN
3630 /* Remove any internal structure of the domain of "ma".
3631 * If there is any such internal structure in the input,
3632 * then the name of the corresponding space is also removed.
3634 __isl_give isl_multi_aff
*isl_multi_aff_flatten_domain(
3635 __isl_take isl_multi_aff
*ma
)
3642 if (!ma
->space
->nested
[0])
3645 space
= isl_multi_aff_get_space(ma
);
3646 space
= isl_space_flatten_domain(space
);
3647 ma
= isl_multi_aff_reset_space(ma
, space
);
3652 /* Given a map space, return an isl_multi_aff that maps a wrapped copy
3653 * of the space to its domain.
3655 __isl_give isl_multi_aff
*isl_multi_aff_domain_map(__isl_take isl_space
*space
)
3658 isl_local_space
*ls
;
3663 if (!isl_space_is_map(space
))
3664 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
3665 "not a map space", goto error
);
3667 n_in
= isl_space_dim(space
, isl_dim_in
);
3668 space
= isl_space_domain_map(space
);
3670 ma
= isl_multi_aff_alloc(isl_space_copy(space
));
3672 isl_space_free(space
);
3676 space
= isl_space_domain(space
);
3677 ls
= isl_local_space_from_space(space
);
3678 for (i
= 0; i
< n_in
; ++i
) {
3681 aff
= isl_aff_var_on_domain(isl_local_space_copy(ls
),
3683 ma
= isl_multi_aff_set_aff(ma
, i
, aff
);
3685 isl_local_space_free(ls
);
3688 isl_space_free(space
);
3692 /* Given a map space, return an isl_multi_aff that maps a wrapped copy
3693 * of the space to its range.
3695 __isl_give isl_multi_aff
*isl_multi_aff_range_map(__isl_take isl_space
*space
)
3698 isl_local_space
*ls
;
3703 if (!isl_space_is_map(space
))
3704 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
3705 "not a map space", goto error
);
3707 n_in
= isl_space_dim(space
, isl_dim_in
);
3708 n_out
= isl_space_dim(space
, isl_dim_out
);
3709 space
= isl_space_range_map(space
);
3711 ma
= isl_multi_aff_alloc(isl_space_copy(space
));
3713 isl_space_free(space
);
3717 space
= isl_space_domain(space
);
3718 ls
= isl_local_space_from_space(space
);
3719 for (i
= 0; i
< n_out
; ++i
) {
3722 aff
= isl_aff_var_on_domain(isl_local_space_copy(ls
),
3723 isl_dim_set
, n_in
+ i
);
3724 ma
= isl_multi_aff_set_aff(ma
, i
, aff
);
3726 isl_local_space_free(ls
);
3729 isl_space_free(space
);
3733 /* Given a map space, return an isl_pw_multi_aff that maps a wrapped copy
3734 * of the space to its range.
3736 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_range_map(
3737 __isl_take isl_space
*space
)
3739 return isl_pw_multi_aff_from_multi_aff(isl_multi_aff_range_map(space
));
3742 /* Given the space of a set and a range of set dimensions,
3743 * construct an isl_multi_aff that projects out those dimensions.
3745 __isl_give isl_multi_aff
*isl_multi_aff_project_out_map(
3746 __isl_take isl_space
*space
, enum isl_dim_type type
,
3747 unsigned first
, unsigned n
)
3750 isl_local_space
*ls
;
3755 if (!isl_space_is_set(space
))
3756 isl_die(isl_space_get_ctx(space
), isl_error_unsupported
,
3757 "expecting set space", goto error
);
3758 if (type
!= isl_dim_set
)
3759 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
3760 "only set dimensions can be projected out", goto error
);
3762 dim
= isl_space_dim(space
, isl_dim_set
);
3763 if (first
+ n
> dim
)
3764 isl_die(isl_space_get_ctx(space
), isl_error_invalid
,
3765 "range out of bounds", goto error
);
3767 space
= isl_space_from_domain(space
);
3768 space
= isl_space_add_dims(space
, isl_dim_out
, dim
- n
);
3771 return isl_multi_aff_alloc(space
);
3773 ma
= isl_multi_aff_alloc(isl_space_copy(space
));
3774 space
= isl_space_domain(space
);
3775 ls
= isl_local_space_from_space(space
);
3777 for (i
= 0; i
< first
; ++i
) {
3780 aff
= isl_aff_var_on_domain(isl_local_space_copy(ls
),
3782 ma
= isl_multi_aff_set_aff(ma
, i
, aff
);
3785 for (i
= 0; i
< dim
- (first
+ n
); ++i
) {
3788 aff
= isl_aff_var_on_domain(isl_local_space_copy(ls
),
3789 isl_dim_set
, first
+ n
+ i
);
3790 ma
= isl_multi_aff_set_aff(ma
, first
+ i
, aff
);
3793 isl_local_space_free(ls
);
3796 isl_space_free(space
);
3800 /* Given the space of a set and a range of set dimensions,
3801 * construct an isl_pw_multi_aff that projects out those dimensions.
3803 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_project_out_map(
3804 __isl_take isl_space
*space
, enum isl_dim_type type
,
3805 unsigned first
, unsigned n
)
3809 ma
= isl_multi_aff_project_out_map(space
, type
, first
, n
);
3810 return isl_pw_multi_aff_from_multi_aff(ma
);
3813 /* Create an isl_pw_multi_aff with the given isl_multi_aff on a universe
3816 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_from_multi_aff(
3817 __isl_take isl_multi_aff
*ma
)
3819 isl_set
*dom
= isl_set_universe(isl_multi_aff_get_domain_space(ma
));
3820 return isl_pw_multi_aff_alloc(dom
, ma
);
3823 /* Create a piecewise multi-affine expression in the given space that maps each
3824 * input dimension to the corresponding output dimension.
3826 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_identity(
3827 __isl_take isl_space
*space
)
3829 return isl_pw_multi_aff_from_multi_aff(isl_multi_aff_identity(space
));
3832 /* Add "ma2" to "ma1" and return the result.
3834 * The parameters of "ma1" and "ma2" are assumed to have been aligned.
3836 static __isl_give isl_multi_aff
*isl_multi_aff_add_aligned(
3837 __isl_take isl_multi_aff
*maff1
, __isl_take isl_multi_aff
*maff2
)
3839 return isl_multi_aff_bin_op(maff1
, maff2
, &isl_aff_add
);
3842 /* Add "ma2" to "ma1" and return the result.
3844 __isl_give isl_multi_aff
*isl_multi_aff_add(__isl_take isl_multi_aff
*ma1
,
3845 __isl_take isl_multi_aff
*ma2
)
3847 return isl_multi_aff_align_params_multi_multi_and(ma1
, ma2
,
3848 &isl_multi_aff_add_aligned
);
3851 /* Exploit the equalities in "eq" to simplify the affine expressions.
3853 static __isl_give isl_multi_aff
*isl_multi_aff_substitute_equalities(
3854 __isl_take isl_multi_aff
*maff
, __isl_take isl_basic_set
*eq
)
3858 maff
= isl_multi_aff_cow(maff
);
3862 for (i
= 0; i
< maff
->n
; ++i
) {
3863 maff
->p
[i
] = isl_aff_substitute_equalities(maff
->p
[i
],
3864 isl_basic_set_copy(eq
));
3869 isl_basic_set_free(eq
);
3872 isl_basic_set_free(eq
);
3873 isl_multi_aff_free(maff
);
3877 /* Given f, return floor(f).
3879 __isl_give isl_multi_aff
*isl_multi_aff_floor(__isl_take isl_multi_aff
*ma
)
3883 ma
= isl_multi_aff_cow(ma
);
3887 for (i
= 0; i
< ma
->n
; ++i
) {
3888 ma
->p
[i
] = isl_aff_floor(ma
->p
[i
]);
3890 return isl_multi_aff_free(ma
);
3896 __isl_give isl_multi_aff
*isl_multi_aff_scale(__isl_take isl_multi_aff
*maff
,
3901 maff
= isl_multi_aff_cow(maff
);
3905 for (i
= 0; i
< maff
->n
; ++i
) {
3906 maff
->p
[i
] = isl_aff_scale(maff
->p
[i
], f
);
3908 return isl_multi_aff_free(maff
);
3914 __isl_give isl_multi_aff
*isl_multi_aff_add_on_domain(__isl_keep isl_set
*dom
,
3915 __isl_take isl_multi_aff
*maff1
, __isl_take isl_multi_aff
*maff2
)
3917 maff1
= isl_multi_aff_add(maff1
, maff2
);
3918 maff1
= isl_multi_aff_gist(maff1
, isl_set_copy(dom
));
3922 int isl_multi_aff_is_empty(__isl_keep isl_multi_aff
*maff
)
3930 /* Return the set of domain elements where "ma1" is lexicographically
3931 * smaller than or equal to "ma2".
3933 __isl_give isl_set
*isl_multi_aff_lex_le_set(__isl_take isl_multi_aff
*ma1
,
3934 __isl_take isl_multi_aff
*ma2
)
3936 return isl_multi_aff_lex_ge_set(ma2
, ma1
);
3939 /* Return the set of domain elements where "ma1" is lexicographically
3940 * greater than or equal to "ma2".
3942 __isl_give isl_set
*isl_multi_aff_lex_ge_set(__isl_take isl_multi_aff
*ma1
,
3943 __isl_take isl_multi_aff
*ma2
)
3946 isl_map
*map1
, *map2
;
3949 map1
= isl_map_from_multi_aff(ma1
);
3950 map2
= isl_map_from_multi_aff(ma2
);
3951 map
= isl_map_range_product(map1
, map2
);
3952 space
= isl_space_range(isl_map_get_space(map
));
3953 space
= isl_space_domain(isl_space_unwrap(space
));
3954 ge
= isl_map_lex_ge(space
);
3955 map
= isl_map_intersect_range(map
, isl_map_wrap(ge
));
3957 return isl_map_domain(map
);
3961 #define PW isl_pw_multi_aff
3963 #define EL isl_multi_aff
3965 #define EL_IS_ZERO is_empty
3969 #define IS_ZERO is_empty
3972 #undef DEFAULT_IS_ZERO
3973 #define DEFAULT_IS_ZERO 0
3978 #define NO_INVOLVES_DIMS
3979 #define NO_INSERT_DIMS
3983 #include <isl_pw_templ.c>
3988 #define UNION isl_union_pw_multi_aff
3990 #define PART isl_pw_multi_aff
3992 #define PARTS pw_multi_aff
3993 #define ALIGN_DOMAIN
3997 #include <isl_union_templ.c>
3999 /* Given a function "cmp" that returns the set of elements where
4000 * "ma1" is "better" than "ma2", return the intersection of this
4001 * set with "dom1" and "dom2".
4003 static __isl_give isl_set
*shared_and_better(__isl_keep isl_set
*dom1
,
4004 __isl_keep isl_set
*dom2
, __isl_keep isl_multi_aff
*ma1
,
4005 __isl_keep isl_multi_aff
*ma2
,
4006 __isl_give isl_set
*(*cmp
)(__isl_take isl_multi_aff
*ma1
,
4007 __isl_take isl_multi_aff
*ma2
))
4013 common
= isl_set_intersect(isl_set_copy(dom1
), isl_set_copy(dom2
));
4014 is_empty
= isl_set_plain_is_empty(common
);
4015 if (is_empty
>= 0 && is_empty
)
4018 return isl_set_free(common
);
4019 better
= cmp(isl_multi_aff_copy(ma1
), isl_multi_aff_copy(ma2
));
4020 better
= isl_set_intersect(common
, better
);
4025 /* Given a function "cmp" that returns the set of elements where
4026 * "ma1" is "better" than "ma2", return a piecewise multi affine
4027 * expression defined on the union of the definition domains
4028 * of "pma1" and "pma2" that maps to the "best" of "pma1" and
4029 * "pma2" on each cell. If only one of the two input functions
4030 * is defined on a given cell, then it is considered the best.
4032 static __isl_give isl_pw_multi_aff
*pw_multi_aff_union_opt(
4033 __isl_take isl_pw_multi_aff
*pma1
,
4034 __isl_take isl_pw_multi_aff
*pma2
,
4035 __isl_give isl_set
*(*cmp
)(__isl_take isl_multi_aff
*ma1
,
4036 __isl_take isl_multi_aff
*ma2
))
4039 isl_pw_multi_aff
*res
= NULL
;
4041 isl_set
*set
= NULL
;
4046 ctx
= isl_space_get_ctx(pma1
->dim
);
4047 if (!isl_space_is_equal(pma1
->dim
, pma2
->dim
))
4048 isl_die(ctx
, isl_error_invalid
,
4049 "arguments should live in the same space", goto error
);
4051 if (isl_pw_multi_aff_is_empty(pma1
)) {
4052 isl_pw_multi_aff_free(pma1
);
4056 if (isl_pw_multi_aff_is_empty(pma2
)) {
4057 isl_pw_multi_aff_free(pma2
);
4061 n
= 2 * (pma1
->n
+ 1) * (pma2
->n
+ 1);
4062 res
= isl_pw_multi_aff_alloc_size(isl_space_copy(pma1
->dim
), n
);
4064 for (i
= 0; i
< pma1
->n
; ++i
) {
4065 set
= isl_set_copy(pma1
->p
[i
].set
);
4066 for (j
= 0; j
< pma2
->n
; ++j
) {
4070 better
= shared_and_better(pma2
->p
[j
].set
,
4071 pma1
->p
[i
].set
, pma2
->p
[j
].maff
,
4072 pma1
->p
[i
].maff
, cmp
);
4073 is_empty
= isl_set_plain_is_empty(better
);
4074 if (is_empty
< 0 || is_empty
) {
4075 isl_set_free(better
);
4080 set
= isl_set_subtract(set
, isl_set_copy(better
));
4082 res
= isl_pw_multi_aff_add_piece(res
, better
,
4083 isl_multi_aff_copy(pma2
->p
[j
].maff
));
4085 res
= isl_pw_multi_aff_add_piece(res
, set
,
4086 isl_multi_aff_copy(pma1
->p
[i
].maff
));
4089 for (j
= 0; j
< pma2
->n
; ++j
) {
4090 set
= isl_set_copy(pma2
->p
[j
].set
);
4091 for (i
= 0; i
< pma1
->n
; ++i
)
4092 set
= isl_set_subtract(set
,
4093 isl_set_copy(pma1
->p
[i
].set
));
4094 res
= isl_pw_multi_aff_add_piece(res
, set
,
4095 isl_multi_aff_copy(pma2
->p
[j
].maff
));
4098 isl_pw_multi_aff_free(pma1
);
4099 isl_pw_multi_aff_free(pma2
);
4103 isl_pw_multi_aff_free(pma1
);
4104 isl_pw_multi_aff_free(pma2
);
4106 return isl_pw_multi_aff_free(res
);
4109 static __isl_give isl_pw_multi_aff
*pw_multi_aff_union_lexmax(
4110 __isl_take isl_pw_multi_aff
*pma1
,
4111 __isl_take isl_pw_multi_aff
*pma2
)
4113 return pw_multi_aff_union_opt(pma1
, pma2
, &isl_multi_aff_lex_ge_set
);
4116 /* Given two piecewise multi affine expressions, return a piecewise
4117 * multi-affine expression defined on the union of the definition domains
4118 * of the inputs that is equal to the lexicographic maximum of the two
4119 * inputs on each cell. If only one of the two inputs is defined on
4120 * a given cell, then it is considered to be the maximum.
4122 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_union_lexmax(
4123 __isl_take isl_pw_multi_aff
*pma1
,
4124 __isl_take isl_pw_multi_aff
*pma2
)
4126 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
4127 &pw_multi_aff_union_lexmax
);
4130 static __isl_give isl_pw_multi_aff
*pw_multi_aff_union_lexmin(
4131 __isl_take isl_pw_multi_aff
*pma1
,
4132 __isl_take isl_pw_multi_aff
*pma2
)
4134 return pw_multi_aff_union_opt(pma1
, pma2
, &isl_multi_aff_lex_le_set
);
4137 /* Given two piecewise multi affine expressions, return a piecewise
4138 * multi-affine expression defined on the union of the definition domains
4139 * of the inputs that is equal to the lexicographic minimum of the two
4140 * inputs on each cell. If only one of the two inputs is defined on
4141 * a given cell, then it is considered to be the minimum.
4143 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_union_lexmin(
4144 __isl_take isl_pw_multi_aff
*pma1
,
4145 __isl_take isl_pw_multi_aff
*pma2
)
4147 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
4148 &pw_multi_aff_union_lexmin
);
4151 static __isl_give isl_pw_multi_aff
*pw_multi_aff_add(
4152 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
4154 return isl_pw_multi_aff_on_shared_domain(pma1
, pma2
,
4155 &isl_multi_aff_add
);
4158 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_add(
4159 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
4161 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
4165 static __isl_give isl_pw_multi_aff
*pw_multi_aff_sub(
4166 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
4168 return isl_pw_multi_aff_on_shared_domain(pma1
, pma2
,
4169 &isl_multi_aff_sub
);
4172 /* Subtract "pma2" from "pma1" and return the result.
4174 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_sub(
4175 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
4177 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
4181 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_union_add(
4182 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
4184 return isl_pw_multi_aff_union_add_(pma1
, pma2
);
4187 /* Compute the sum of "upa1" and "upa2" on the union of their domains,
4188 * with the actual sum on the shared domain and
4189 * the defined expression on the symmetric difference of the domains.
4191 __isl_give isl_union_pw_aff
*isl_union_pw_aff_union_add(
4192 __isl_take isl_union_pw_aff
*upa1
, __isl_take isl_union_pw_aff
*upa2
)
4194 return isl_union_pw_aff_union_add_(upa1
, upa2
);
4197 /* Compute the sum of "upma1" and "upma2" on the union of their domains,
4198 * with the actual sum on the shared domain and
4199 * the defined expression on the symmetric difference of the domains.
4201 __isl_give isl_union_pw_multi_aff
*isl_union_pw_multi_aff_union_add(
4202 __isl_take isl_union_pw_multi_aff
*upma1
,
4203 __isl_take isl_union_pw_multi_aff
*upma2
)
4205 return isl_union_pw_multi_aff_union_add_(upma1
, upma2
);
4208 /* Given two piecewise multi-affine expressions A -> B and C -> D,
4209 * construct a piecewise multi-affine expression [A -> C] -> [B -> D].
4211 static __isl_give isl_pw_multi_aff
*pw_multi_aff_product(
4212 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
4216 isl_pw_multi_aff
*res
;
4221 n
= pma1
->n
* pma2
->n
;
4222 space
= isl_space_product(isl_space_copy(pma1
->dim
),
4223 isl_space_copy(pma2
->dim
));
4224 res
= isl_pw_multi_aff_alloc_size(space
, n
);
4226 for (i
= 0; i
< pma1
->n
; ++i
) {
4227 for (j
= 0; j
< pma2
->n
; ++j
) {
4231 domain
= isl_set_product(isl_set_copy(pma1
->p
[i
].set
),
4232 isl_set_copy(pma2
->p
[j
].set
));
4233 ma
= isl_multi_aff_product(
4234 isl_multi_aff_copy(pma1
->p
[i
].maff
),
4235 isl_multi_aff_copy(pma2
->p
[j
].maff
));
4236 res
= isl_pw_multi_aff_add_piece(res
, domain
, ma
);
4240 isl_pw_multi_aff_free(pma1
);
4241 isl_pw_multi_aff_free(pma2
);
4244 isl_pw_multi_aff_free(pma1
);
4245 isl_pw_multi_aff_free(pma2
);
4249 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_product(
4250 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
4252 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
4253 &pw_multi_aff_product
);
4256 /* Construct a map mapping the domain of the piecewise multi-affine expression
4257 * to its range, with each dimension in the range equated to the
4258 * corresponding affine expression on its cell.
4260 __isl_give isl_map
*isl_map_from_pw_multi_aff(__isl_take isl_pw_multi_aff
*pma
)
4268 map
= isl_map_empty(isl_pw_multi_aff_get_space(pma
));
4270 for (i
= 0; i
< pma
->n
; ++i
) {
4271 isl_multi_aff
*maff
;
4272 isl_basic_map
*bmap
;
4275 maff
= isl_multi_aff_copy(pma
->p
[i
].maff
);
4276 bmap
= isl_basic_map_from_multi_aff(maff
);
4277 map_i
= isl_map_from_basic_map(bmap
);
4278 map_i
= isl_map_intersect_domain(map_i
,
4279 isl_set_copy(pma
->p
[i
].set
));
4280 map
= isl_map_union_disjoint(map
, map_i
);
4283 isl_pw_multi_aff_free(pma
);
4287 __isl_give isl_set
*isl_set_from_pw_multi_aff(__isl_take isl_pw_multi_aff
*pma
)
4292 if (!isl_space_is_set(pma
->dim
))
4293 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_invalid
,
4294 "isl_pw_multi_aff cannot be converted into an isl_set",
4297 return isl_map_from_pw_multi_aff(pma
);
4299 isl_pw_multi_aff_free(pma
);
4303 /* Given a basic map with a single output dimension that is defined
4304 * in terms of the parameters and input dimensions using an equality,
4305 * extract an isl_aff that expresses the output dimension in terms
4306 * of the parameters and input dimensions.
4307 * Note that this expression may involve integer divisions defined
4308 * in terms of parameters and input dimensions.
4310 * This function shares some similarities with
4311 * isl_basic_map_has_defining_equality and isl_constraint_get_bound.
4313 static __isl_give isl_aff
*extract_isl_aff_from_basic_map(
4314 __isl_take isl_basic_map
*bmap
)
4319 isl_local_space
*ls
;
4324 if (isl_basic_map_dim(bmap
, isl_dim_out
) != 1)
4325 isl_die(isl_basic_map_get_ctx(bmap
), isl_error_invalid
,
4326 "basic map should have a single output dimension",
4328 eq
= isl_basic_map_output_defining_equality(bmap
, 0);
4329 if (eq
>= bmap
->n_eq
)
4330 isl_die(isl_basic_map_get_ctx(bmap
), isl_error_invalid
,
4331 "unable to find suitable equality", goto error
);
4332 ls
= isl_basic_map_get_local_space(bmap
);
4333 aff
= isl_aff_alloc(isl_local_space_domain(ls
));
4336 offset
= isl_basic_map_offset(bmap
, isl_dim_out
);
4337 n_div
= isl_basic_map_dim(bmap
, isl_dim_div
);
4338 if (isl_int_is_neg(bmap
->eq
[eq
][offset
])) {
4339 isl_seq_cpy(aff
->v
->el
+ 1, bmap
->eq
[eq
], offset
);
4340 isl_seq_cpy(aff
->v
->el
+ 1 + offset
, bmap
->eq
[eq
] + offset
+ 1,
4343 isl_seq_neg(aff
->v
->el
+ 1, bmap
->eq
[eq
], offset
);
4344 isl_seq_neg(aff
->v
->el
+ 1 + offset
, bmap
->eq
[eq
] + offset
+ 1,
4347 isl_int_abs(aff
->v
->el
[0], bmap
->eq
[eq
][offset
]);
4348 isl_basic_map_free(bmap
);
4350 aff
= isl_aff_remove_unused_divs(aff
);
4353 isl_basic_map_free(bmap
);
4357 /* Given a basic map where each output dimension is defined
4358 * in terms of the parameters and input dimensions using an equality,
4359 * extract an isl_multi_aff that expresses the output dimensions in terms
4360 * of the parameters and input dimensions.
4362 static __isl_give isl_multi_aff
*extract_isl_multi_aff_from_basic_map(
4363 __isl_take isl_basic_map
*bmap
)
4372 ma
= isl_multi_aff_alloc(isl_basic_map_get_space(bmap
));
4373 n_out
= isl_basic_map_dim(bmap
, isl_dim_out
);
4375 for (i
= 0; i
< n_out
; ++i
) {
4376 isl_basic_map
*bmap_i
;
4379 bmap_i
= isl_basic_map_copy(bmap
);
4380 bmap_i
= isl_basic_map_project_out(bmap_i
, isl_dim_out
,
4381 i
+ 1, n_out
- (1 + i
));
4382 bmap_i
= isl_basic_map_project_out(bmap_i
, isl_dim_out
, 0, i
);
4383 aff
= extract_isl_aff_from_basic_map(bmap_i
);
4384 ma
= isl_multi_aff_set_aff(ma
, i
, aff
);
4387 isl_basic_map_free(bmap
);
4392 /* Given a basic set where each set dimension is defined
4393 * in terms of the parameters using an equality,
4394 * extract an isl_multi_aff that expresses the set dimensions in terms
4395 * of the parameters.
4397 __isl_give isl_multi_aff
*isl_multi_aff_from_basic_set_equalities(
4398 __isl_take isl_basic_set
*bset
)
4400 return extract_isl_multi_aff_from_basic_map(bset
);
4403 /* Create an isl_pw_multi_aff that is equivalent to
4404 * isl_map_intersect_domain(isl_map_from_basic_map(bmap), domain).
4405 * The given basic map is such that each output dimension is defined
4406 * in terms of the parameters and input dimensions using an equality.
4408 * Since some applications expect the result of isl_pw_multi_aff_from_map
4409 * to only contain integer affine expressions, we compute the floor
4410 * of the expression before returning.
4412 static __isl_give isl_pw_multi_aff
*plain_pw_multi_aff_from_map(
4413 __isl_take isl_set
*domain
, __isl_take isl_basic_map
*bmap
)
4417 ma
= extract_isl_multi_aff_from_basic_map(bmap
);
4418 ma
= isl_multi_aff_floor(ma
);
4419 return isl_pw_multi_aff_alloc(domain
, ma
);
4422 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
4423 * This obviously only works if the input "map" is single-valued.
4424 * If so, we compute the lexicographic minimum of the image in the form
4425 * of an isl_pw_multi_aff. Since the image is unique, it is equal
4426 * to its lexicographic minimum.
4427 * If the input is not single-valued, we produce an error.
4429 static __isl_give isl_pw_multi_aff
*pw_multi_aff_from_map_base(
4430 __isl_take isl_map
*map
)
4434 isl_pw_multi_aff
*pma
;
4436 sv
= isl_map_is_single_valued(map
);
4440 isl_die(isl_map_get_ctx(map
), isl_error_invalid
,
4441 "map is not single-valued", goto error
);
4442 map
= isl_map_make_disjoint(map
);
4446 pma
= isl_pw_multi_aff_empty(isl_map_get_space(map
));
4448 for (i
= 0; i
< map
->n
; ++i
) {
4449 isl_pw_multi_aff
*pma_i
;
4450 isl_basic_map
*bmap
;
4451 bmap
= isl_basic_map_copy(map
->p
[i
]);
4452 pma_i
= isl_basic_map_lexmin_pw_multi_aff(bmap
);
4453 pma
= isl_pw_multi_aff_add_disjoint(pma
, pma_i
);
4463 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map,
4464 * taking into account that the output dimension at position "d"
4465 * can be represented as
4467 * x = floor((e(...) + c1) / m)
4469 * given that constraint "i" is of the form
4471 * e(...) + c1 - m x >= 0
4474 * Let "map" be of the form
4478 * We construct a mapping
4480 * A -> [A -> x = floor(...)]
4482 * apply that to the map, obtaining
4484 * [A -> x = floor(...)] -> B
4486 * and equate dimension "d" to x.
4487 * We then compute a isl_pw_multi_aff representation of the resulting map
4488 * and plug in the mapping above.
4490 static __isl_give isl_pw_multi_aff
*pw_multi_aff_from_map_div(
4491 __isl_take isl_map
*map
, __isl_take isl_basic_map
*hull
, int d
, int i
)
4495 isl_local_space
*ls
;
4503 isl_pw_multi_aff
*pma
;
4506 is_set
= isl_map_is_set(map
);
4508 offset
= isl_basic_map_offset(hull
, isl_dim_out
);
4509 ctx
= isl_map_get_ctx(map
);
4510 space
= isl_space_domain(isl_map_get_space(map
));
4511 n_in
= isl_space_dim(space
, isl_dim_set
);
4512 n
= isl_space_dim(space
, isl_dim_all
);
4514 v
= isl_vec_alloc(ctx
, 1 + 1 + n
);
4516 isl_int_neg(v
->el
[0], hull
->ineq
[i
][offset
+ d
]);
4517 isl_seq_cpy(v
->el
+ 1, hull
->ineq
[i
], 1 + n
);
4519 isl_basic_map_free(hull
);
4521 ls
= isl_local_space_from_space(isl_space_copy(space
));
4522 aff
= isl_aff_alloc_vec(ls
, v
);
4523 aff
= isl_aff_floor(aff
);
4525 isl_space_free(space
);
4526 ma
= isl_multi_aff_from_aff(aff
);
4528 ma
= isl_multi_aff_identity(isl_space_map_from_set(space
));
4529 ma
= isl_multi_aff_range_product(ma
,
4530 isl_multi_aff_from_aff(aff
));
4533 insert
= isl_map_from_multi_aff(isl_multi_aff_copy(ma
));
4534 map
= isl_map_apply_domain(map
, insert
);
4535 map
= isl_map_equate(map
, isl_dim_in
, n_in
, isl_dim_out
, d
);
4536 pma
= isl_pw_multi_aff_from_map(map
);
4537 pma
= isl_pw_multi_aff_pullback_multi_aff(pma
, ma
);
4542 /* Is constraint "c" of the form
4544 * e(...) + c1 - m x >= 0
4548 * -e(...) + c2 + m x >= 0
4550 * where m > 1 and e only depends on parameters and input dimemnsions?
4552 * "offset" is the offset of the output dimensions
4553 * "pos" is the position of output dimension x.
4555 static int is_potential_div_constraint(isl_int
*c
, int offset
, int d
, int total
)
4557 if (isl_int_is_zero(c
[offset
+ d
]))
4559 if (isl_int_is_one(c
[offset
+ d
]))
4561 if (isl_int_is_negone(c
[offset
+ d
]))
4563 if (isl_seq_first_non_zero(c
+ offset
, d
) != -1)
4565 if (isl_seq_first_non_zero(c
+ offset
+ d
+ 1,
4566 total
- (offset
+ d
+ 1)) != -1)
4571 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
4573 * As a special case, we first check if there is any pair of constraints,
4574 * shared by all the basic maps in "map" that force a given dimension
4575 * to be equal to the floor of some affine combination of the input dimensions.
4577 * In particular, if we can find two constraints
4579 * e(...) + c1 - m x >= 0 i.e., m x <= e(...) + c1
4583 * -e(...) + c2 + m x >= 0 i.e., m x >= e(...) - c2
4585 * where m > 1 and e only depends on parameters and input dimemnsions,
4588 * c1 + c2 < m i.e., -c2 >= c1 - (m - 1)
4590 * then we know that we can take
4592 * x = floor((e(...) + c1) / m)
4594 * without having to perform any computation.
4596 * Note that we know that
4600 * If c1 + c2 were 0, then we would have detected an equality during
4601 * simplification. If c1 + c2 were negative, then we would have detected
4604 static __isl_give isl_pw_multi_aff
*pw_multi_aff_from_map_check_div(
4605 __isl_take isl_map
*map
)
4611 isl_basic_map
*hull
;
4613 hull
= isl_map_unshifted_simple_hull(isl_map_copy(map
));
4618 dim
= isl_map_dim(map
, isl_dim_out
);
4619 offset
= isl_basic_map_offset(hull
, isl_dim_out
);
4620 total
= 1 + isl_basic_map_total_dim(hull
);
4622 for (d
= 0; d
< dim
; ++d
) {
4623 for (i
= 0; i
< n
; ++i
) {
4624 if (!is_potential_div_constraint(hull
->ineq
[i
],
4627 for (j
= i
+ 1; j
< n
; ++j
) {
4628 if (!isl_seq_is_neg(hull
->ineq
[i
] + 1,
4629 hull
->ineq
[j
] + 1, total
- 1))
4631 isl_int_add(sum
, hull
->ineq
[i
][0],
4633 if (isl_int_abs_lt(sum
,
4634 hull
->ineq
[i
][offset
+ d
]))
4641 if (isl_int_is_pos(hull
->ineq
[j
][offset
+ d
]))
4643 return pw_multi_aff_from_map_div(map
, hull
, d
, j
);
4647 isl_basic_map_free(hull
);
4648 return pw_multi_aff_from_map_base(map
);
4651 isl_basic_map_free(hull
);
4655 /* Given an affine expression
4657 * [A -> B] -> f(A,B)
4659 * construct an isl_multi_aff
4663 * such that dimension "d" in B' is set to "aff" and the remaining
4664 * dimensions are set equal to the corresponding dimensions in B.
4665 * "n_in" is the dimension of the space A.
4666 * "n_out" is the dimension of the space B.
4668 * If "is_set" is set, then the affine expression is of the form
4672 * and we construct an isl_multi_aff
4676 static __isl_give isl_multi_aff
*range_map(__isl_take isl_aff
*aff
, int d
,
4677 unsigned n_in
, unsigned n_out
, int is_set
)
4681 isl_space
*space
, *space2
;
4682 isl_local_space
*ls
;
4684 space
= isl_aff_get_domain_space(aff
);
4685 ls
= isl_local_space_from_space(isl_space_copy(space
));
4686 space2
= isl_space_copy(space
);
4688 space2
= isl_space_range(isl_space_unwrap(space2
));
4689 space
= isl_space_map_from_domain_and_range(space
, space2
);
4690 ma
= isl_multi_aff_alloc(space
);
4691 ma
= isl_multi_aff_set_aff(ma
, d
, aff
);
4693 for (i
= 0; i
< n_out
; ++i
) {
4696 aff
= isl_aff_var_on_domain(isl_local_space_copy(ls
),
4697 isl_dim_set
, n_in
+ i
);
4698 ma
= isl_multi_aff_set_aff(ma
, i
, aff
);
4701 isl_local_space_free(ls
);
4706 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map,
4707 * taking into account that the dimension at position "d" can be written as
4709 * x = m a + f(..) (1)
4711 * where m is equal to "gcd".
4712 * "i" is the index of the equality in "hull" that defines f(..).
4713 * In particular, the equality is of the form
4715 * f(..) - x + m g(existentials) = 0
4719 * -f(..) + x + m g(existentials) = 0
4721 * We basically plug (1) into "map", resulting in a map with "a"
4722 * in the range instead of "x". The corresponding isl_pw_multi_aff
4723 * defining "a" is then plugged back into (1) to obtain a definition fro "x".
4725 * Specifically, given the input map
4729 * We first wrap it into a set
4733 * and define (1) on top of the corresponding space, resulting in "aff".
4734 * We use this to create an isl_multi_aff that maps the output position "d"
4735 * from "a" to "x", leaving all other (intput and output) dimensions unchanged.
4736 * We plug this into the wrapped map, unwrap the result and compute the
4737 * corresponding isl_pw_multi_aff.
4738 * The result is an expression
4746 * so that we can plug that into "aff", after extending the latter to
4752 * If "map" is actually a set, then there is no "A" space, meaning
4753 * that we do not need to perform any wrapping, and that the result
4754 * of the recursive call is of the form
4758 * which is plugged into a mapping of the form
4762 static __isl_give isl_pw_multi_aff
*pw_multi_aff_from_map_stride(
4763 __isl_take isl_map
*map
, __isl_take isl_basic_map
*hull
, int d
, int i
,
4768 isl_local_space
*ls
;
4771 isl_pw_multi_aff
*pma
, *id
;
4777 is_set
= isl_map_is_set(map
);
4779 n_in
= isl_basic_map_dim(hull
, isl_dim_in
);
4780 n_out
= isl_basic_map_dim(hull
, isl_dim_out
);
4781 o_out
= isl_basic_map_offset(hull
, isl_dim_out
);
4786 set
= isl_map_wrap(map
);
4787 space
= isl_space_map_from_set(isl_set_get_space(set
));
4788 ma
= isl_multi_aff_identity(space
);
4789 ls
= isl_local_space_from_space(isl_set_get_space(set
));
4790 aff
= isl_aff_alloc(ls
);
4792 isl_int_set_si(aff
->v
->el
[0], 1);
4793 if (isl_int_is_one(hull
->eq
[i
][o_out
+ d
]))
4794 isl_seq_neg(aff
->v
->el
+ 1, hull
->eq
[i
],
4797 isl_seq_cpy(aff
->v
->el
+ 1, hull
->eq
[i
],
4799 isl_int_set(aff
->v
->el
[1 + o_out
+ d
], gcd
);
4801 ma
= isl_multi_aff_set_aff(ma
, n_in
+ d
, isl_aff_copy(aff
));
4802 set
= isl_set_preimage_multi_aff(set
, ma
);
4804 ma
= range_map(aff
, d
, n_in
, n_out
, is_set
);
4809 map
= isl_set_unwrap(set
);
4810 pma
= isl_pw_multi_aff_from_map(set
);
4813 space
= isl_pw_multi_aff_get_domain_space(pma
);
4814 space
= isl_space_map_from_set(space
);
4815 id
= isl_pw_multi_aff_identity(space
);
4816 pma
= isl_pw_multi_aff_range_product(id
, pma
);
4818 id
= isl_pw_multi_aff_from_multi_aff(ma
);
4819 pma
= isl_pw_multi_aff_pullback_pw_multi_aff(id
, pma
);
4821 isl_basic_map_free(hull
);
4825 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
4827 * As a special case, we first check if all output dimensions are uniquely
4828 * defined in terms of the parameters and input dimensions over the entire
4829 * domain. If so, we extract the desired isl_pw_multi_aff directly
4830 * from the affine hull of "map" and its domain.
4832 * Otherwise, we check if any of the output dimensions is "strided".
4833 * That is, we check if can be written as
4837 * with m greater than 1, a some combination of existentiall quantified
4838 * variables and f and expression in the parameters and input dimensions.
4839 * If so, we remove the stride in pw_multi_aff_from_map_stride.
4841 * Otherwise, we continue with pw_multi_aff_from_map_check_div for a further
4844 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_from_map(__isl_take isl_map
*map
)
4848 isl_basic_map
*hull
;
4858 hull
= isl_map_affine_hull(isl_map_copy(map
));
4859 sv
= isl_basic_map_plain_is_single_valued(hull
);
4861 return plain_pw_multi_aff_from_map(isl_map_domain(map
), hull
);
4863 hull
= isl_basic_map_free(hull
);
4867 n_div
= isl_basic_map_dim(hull
, isl_dim_div
);
4868 o_div
= isl_basic_map_offset(hull
, isl_dim_div
);
4871 isl_basic_map_free(hull
);
4872 return pw_multi_aff_from_map_check_div(map
);
4877 n_out
= isl_basic_map_dim(hull
, isl_dim_out
);
4878 o_out
= isl_basic_map_offset(hull
, isl_dim_out
);
4880 for (i
= 0; i
< n_out
; ++i
) {
4881 for (j
= 0; j
< hull
->n_eq
; ++j
) {
4882 isl_int
*eq
= hull
->eq
[j
];
4883 isl_pw_multi_aff
*res
;
4885 if (!isl_int_is_one(eq
[o_out
+ i
]) &&
4886 !isl_int_is_negone(eq
[o_out
+ i
]))
4888 if (isl_seq_first_non_zero(eq
+ o_out
, i
) != -1)
4890 if (isl_seq_first_non_zero(eq
+ o_out
+ i
+ 1,
4891 n_out
- (i
+ 1)) != -1)
4893 isl_seq_gcd(eq
+ o_div
, n_div
, &gcd
);
4894 if (isl_int_is_zero(gcd
))
4896 if (isl_int_is_one(gcd
))
4899 res
= pw_multi_aff_from_map_stride(map
, hull
,
4907 isl_basic_map_free(hull
);
4908 return pw_multi_aff_from_map_check_div(map
);
4914 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_from_set(__isl_take isl_set
*set
)
4916 return isl_pw_multi_aff_from_map(set
);
4919 /* Convert "map" into an isl_pw_multi_aff (if possible) and
4922 static int pw_multi_aff_from_map(__isl_take isl_map
*map
, void *user
)
4924 isl_union_pw_multi_aff
**upma
= user
;
4925 isl_pw_multi_aff
*pma
;
4927 pma
= isl_pw_multi_aff_from_map(map
);
4928 *upma
= isl_union_pw_multi_aff_add_pw_multi_aff(*upma
, pma
);
4930 return *upma
? 0 : -1;
4933 /* Create an isl_union_pw_multi_aff with the given isl_aff on a universe
4936 __isl_give isl_union_pw_multi_aff
*isl_union_pw_multi_aff_from_aff(
4937 __isl_take isl_aff
*aff
)
4940 isl_pw_multi_aff
*pma
;
4942 ma
= isl_multi_aff_from_aff(aff
);
4943 pma
= isl_pw_multi_aff_from_multi_aff(ma
);
4944 return isl_union_pw_multi_aff_from_pw_multi_aff(pma
);
4947 /* Try and create an isl_union_pw_multi_aff that is equivalent
4948 * to the given isl_union_map.
4949 * The isl_union_map is required to be single-valued in each space.
4950 * Otherwise, an error is produced.
4952 __isl_give isl_union_pw_multi_aff
*isl_union_pw_multi_aff_from_union_map(
4953 __isl_take isl_union_map
*umap
)
4956 isl_union_pw_multi_aff
*upma
;
4958 space
= isl_union_map_get_space(umap
);
4959 upma
= isl_union_pw_multi_aff_empty(space
);
4960 if (isl_union_map_foreach_map(umap
, &pw_multi_aff_from_map
, &upma
) < 0)
4961 upma
= isl_union_pw_multi_aff_free(upma
);
4962 isl_union_map_free(umap
);
4967 /* Try and create an isl_union_pw_multi_aff that is equivalent
4968 * to the given isl_union_set.
4969 * The isl_union_set is required to be a singleton in each space.
4970 * Otherwise, an error is produced.
4972 __isl_give isl_union_pw_multi_aff
*isl_union_pw_multi_aff_from_union_set(
4973 __isl_take isl_union_set
*uset
)
4975 return isl_union_pw_multi_aff_from_union_map(uset
);
4978 /* Return the piecewise affine expression "set ? 1 : 0".
4980 __isl_give isl_pw_aff
*isl_set_indicator_function(__isl_take isl_set
*set
)
4983 isl_space
*space
= isl_set_get_space(set
);
4984 isl_local_space
*ls
= isl_local_space_from_space(space
);
4985 isl_aff
*zero
= isl_aff_zero_on_domain(isl_local_space_copy(ls
));
4986 isl_aff
*one
= isl_aff_zero_on_domain(ls
);
4988 one
= isl_aff_add_constant_si(one
, 1);
4989 pa
= isl_pw_aff_alloc(isl_set_copy(set
), one
);
4990 set
= isl_set_complement(set
);
4991 pa
= isl_pw_aff_add_disjoint(pa
, isl_pw_aff_alloc(set
, zero
));
4996 /* Plug in "subs" for dimension "type", "pos" of "aff".
4998 * Let i be the dimension to replace and let "subs" be of the form
5002 * and "aff" of the form
5008 * (a f + d g')/(m d)
5010 * where g' is the result of plugging in "subs" in each of the integer
5013 __isl_give isl_aff
*isl_aff_substitute(__isl_take isl_aff
*aff
,
5014 enum isl_dim_type type
, unsigned pos
, __isl_keep isl_aff
*subs
)
5019 aff
= isl_aff_cow(aff
);
5021 return isl_aff_free(aff
);
5023 ctx
= isl_aff_get_ctx(aff
);
5024 if (!isl_space_is_equal(aff
->ls
->dim
, subs
->ls
->dim
))
5025 isl_die(ctx
, isl_error_invalid
,
5026 "spaces don't match", return isl_aff_free(aff
));
5027 if (isl_local_space_dim(subs
->ls
, isl_dim_div
) != 0)
5028 isl_die(ctx
, isl_error_unsupported
,
5029 "cannot handle divs yet", return isl_aff_free(aff
));
5031 aff
->ls
= isl_local_space_substitute(aff
->ls
, type
, pos
, subs
);
5033 return isl_aff_free(aff
);
5035 aff
->v
= isl_vec_cow(aff
->v
);
5037 return isl_aff_free(aff
);
5039 pos
+= isl_local_space_offset(aff
->ls
, type
);
5042 isl_seq_substitute(aff
->v
->el
, pos
, subs
->v
->el
,
5043 aff
->v
->size
, subs
->v
->size
, v
);
5049 /* Plug in "subs" for dimension "type", "pos" in each of the affine
5050 * expressions in "maff".
5052 __isl_give isl_multi_aff
*isl_multi_aff_substitute(
5053 __isl_take isl_multi_aff
*maff
, enum isl_dim_type type
, unsigned pos
,
5054 __isl_keep isl_aff
*subs
)
5058 maff
= isl_multi_aff_cow(maff
);
5060 return isl_multi_aff_free(maff
);
5062 if (type
== isl_dim_in
)
5065 for (i
= 0; i
< maff
->n
; ++i
) {
5066 maff
->p
[i
] = isl_aff_substitute(maff
->p
[i
], type
, pos
, subs
);
5068 return isl_multi_aff_free(maff
);
5074 /* Plug in "subs" for dimension "type", "pos" of "pma".
5076 * pma is of the form
5080 * while subs is of the form
5082 * v' = B_j(v) -> S_j
5084 * Each pair i,j such that C_ij = A_i \cap B_i is non-empty
5085 * has a contribution in the result, in particular
5087 * C_ij(S_j) -> M_i(S_j)
5089 * Note that plugging in S_j in C_ij may also result in an empty set
5090 * and this contribution should simply be discarded.
5092 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_substitute(
5093 __isl_take isl_pw_multi_aff
*pma
, enum isl_dim_type type
, unsigned pos
,
5094 __isl_keep isl_pw_aff
*subs
)
5097 isl_pw_multi_aff
*res
;
5100 return isl_pw_multi_aff_free(pma
);
5102 n
= pma
->n
* subs
->n
;
5103 res
= isl_pw_multi_aff_alloc_size(isl_space_copy(pma
->dim
), n
);
5105 for (i
= 0; i
< pma
->n
; ++i
) {
5106 for (j
= 0; j
< subs
->n
; ++j
) {
5108 isl_multi_aff
*res_ij
;
5111 common
= isl_set_intersect(
5112 isl_set_copy(pma
->p
[i
].set
),
5113 isl_set_copy(subs
->p
[j
].set
));
5114 common
= isl_set_substitute(common
,
5115 type
, pos
, subs
->p
[j
].aff
);
5116 empty
= isl_set_plain_is_empty(common
);
5117 if (empty
< 0 || empty
) {
5118 isl_set_free(common
);
5124 res_ij
= isl_multi_aff_substitute(
5125 isl_multi_aff_copy(pma
->p
[i
].maff
),
5126 type
, pos
, subs
->p
[j
].aff
);
5128 res
= isl_pw_multi_aff_add_piece(res
, common
, res_ij
);
5132 isl_pw_multi_aff_free(pma
);
5135 isl_pw_multi_aff_free(pma
);
5136 isl_pw_multi_aff_free(res
);
5140 /* Compute the preimage of a range of dimensions in the affine expression "src"
5141 * under "ma" and put the result in "dst". The number of dimensions in "src"
5142 * that precede the range is given by "n_before". The number of dimensions
5143 * in the range is given by the number of output dimensions of "ma".
5144 * The number of dimensions that follow the range is given by "n_after".
5145 * If "has_denom" is set (to one),
5146 * then "src" and "dst" have an extra initial denominator.
5147 * "n_div_ma" is the number of existentials in "ma"
5148 * "n_div_bset" is the number of existentials in "src"
5149 * The resulting "dst" (which is assumed to have been allocated by
5150 * the caller) contains coefficients for both sets of existentials,
5151 * first those in "ma" and then those in "src".
5152 * f, c1, c2 and g are temporary objects that have been initialized
5155 * Let src represent the expression
5157 * (a(p) + f_u u + b v + f_w w + c(divs))/d
5159 * and let ma represent the expressions
5161 * v_i = (r_i(p) + s_i(y) + t_i(divs'))/m_i
5163 * We start out with the following expression for dst:
5165 * (a(p) + f_u u + 0 y + f_w w + 0 divs' + c(divs) + f \sum_i b_i v_i)/d
5167 * with the multiplication factor f initially equal to 1
5168 * and f \sum_i b_i v_i kept separately.
5169 * For each x_i that we substitute, we multiply the numerator
5170 * (and denominator) of dst by c_1 = m_i and add the numerator
5171 * of the x_i expression multiplied by c_2 = f b_i,
5172 * after removing the common factors of c_1 and c_2.
5173 * The multiplication factor f also needs to be multiplied by c_1
5174 * for the next x_j, j > i.
5176 void isl_seq_preimage(isl_int
*dst
, isl_int
*src
,
5177 __isl_keep isl_multi_aff
*ma
, int n_before
, int n_after
,
5178 int n_div_ma
, int n_div_bmap
,
5179 isl_int f
, isl_int c1
, isl_int c2
, isl_int g
, int has_denom
)
5182 int n_param
, n_in
, n_out
;
5185 n_param
= isl_multi_aff_dim(ma
, isl_dim_param
);
5186 n_in
= isl_multi_aff_dim(ma
, isl_dim_in
);
5187 n_out
= isl_multi_aff_dim(ma
, isl_dim_out
);
5189 isl_seq_cpy(dst
, src
, has_denom
+ 1 + n_param
+ n_before
);
5190 o_dst
= o_src
= has_denom
+ 1 + n_param
+ n_before
;
5191 isl_seq_clr(dst
+ o_dst
, n_in
);
5194 isl_seq_cpy(dst
+ o_dst
, src
+ o_src
, n_after
);
5197 isl_seq_clr(dst
+ o_dst
, n_div_ma
);
5199 isl_seq_cpy(dst
+ o_dst
, src
+ o_src
, n_div_bmap
);
5201 isl_int_set_si(f
, 1);
5203 for (i
= 0; i
< n_out
; ++i
) {
5204 int offset
= has_denom
+ 1 + n_param
+ n_before
+ i
;
5206 if (isl_int_is_zero(src
[offset
]))
5208 isl_int_set(c1
, ma
->p
[i
]->v
->el
[0]);
5209 isl_int_mul(c2
, f
, src
[offset
]);
5210 isl_int_gcd(g
, c1
, c2
);
5211 isl_int_divexact(c1
, c1
, g
);
5212 isl_int_divexact(c2
, c2
, g
);
5214 isl_int_mul(f
, f
, c1
);
5217 isl_seq_combine(dst
+ o_dst
, c1
, dst
+ o_dst
,
5218 c2
, ma
->p
[i
]->v
->el
+ o_src
, 1 + n_param
);
5219 o_dst
+= 1 + n_param
;
5220 o_src
+= 1 + n_param
;
5221 isl_seq_scale(dst
+ o_dst
, dst
+ o_dst
, c1
, n_before
);
5223 isl_seq_combine(dst
+ o_dst
, c1
, dst
+ o_dst
,
5224 c2
, ma
->p
[i
]->v
->el
+ o_src
, n_in
);
5227 isl_seq_scale(dst
+ o_dst
, dst
+ o_dst
, c1
, n_after
);
5229 isl_seq_combine(dst
+ o_dst
, c1
, dst
+ o_dst
,
5230 c2
, ma
->p
[i
]->v
->el
+ o_src
, n_div_ma
);
5233 isl_seq_scale(dst
+ o_dst
, dst
+ o_dst
, c1
, n_div_bmap
);
5235 isl_int_mul(dst
[0], dst
[0], c1
);
5239 /* Compute the pullback of "aff" by the function represented by "ma".
5240 * In other words, plug in "ma" in "aff". The result is an affine expression
5241 * defined over the domain space of "ma".
5243 * If "aff" is represented by
5245 * (a(p) + b x + c(divs))/d
5247 * and ma is represented by
5249 * x = D(p) + F(y) + G(divs')
5251 * then the result is
5253 * (a(p) + b D(p) + b F(y) + b G(divs') + c(divs))/d
5255 * The divs in the local space of the input are similarly adjusted
5256 * through a call to isl_local_space_preimage_multi_aff.
5258 __isl_give isl_aff
*isl_aff_pullback_multi_aff(__isl_take isl_aff
*aff
,
5259 __isl_take isl_multi_aff
*ma
)
5261 isl_aff
*res
= NULL
;
5262 isl_local_space
*ls
;
5263 int n_div_aff
, n_div_ma
;
5264 isl_int f
, c1
, c2
, g
;
5266 ma
= isl_multi_aff_align_divs(ma
);
5270 n_div_aff
= isl_aff_dim(aff
, isl_dim_div
);
5271 n_div_ma
= ma
->n
? isl_aff_dim(ma
->p
[0], isl_dim_div
) : 0;
5273 ls
= isl_aff_get_domain_local_space(aff
);
5274 ls
= isl_local_space_preimage_multi_aff(ls
, isl_multi_aff_copy(ma
));
5275 res
= isl_aff_alloc(ls
);
5284 isl_seq_preimage(res
->v
->el
, aff
->v
->el
, ma
, 0, 0, n_div_ma
, n_div_aff
,
5293 isl_multi_aff_free(ma
);
5294 res
= isl_aff_normalize(res
);
5298 isl_multi_aff_free(ma
);
5303 /* Compute the pullback of "aff1" by the function represented by "aff2".
5304 * In other words, plug in "aff2" in "aff1". The result is an affine expression
5305 * defined over the domain space of "aff1".
5307 * The domain of "aff1" should match the range of "aff2", which means
5308 * that it should be single-dimensional.
5310 __isl_give isl_aff
*isl_aff_pullback_aff(__isl_take isl_aff
*aff1
,
5311 __isl_take isl_aff
*aff2
)
5315 ma
= isl_multi_aff_from_aff(aff2
);
5316 return isl_aff_pullback_multi_aff(aff1
, ma
);
5319 /* Compute the pullback of "ma1" by the function represented by "ma2".
5320 * In other words, plug in "ma2" in "ma1".
5322 * The parameters of "ma1" and "ma2" are assumed to have been aligned.
5324 static __isl_give isl_multi_aff
*isl_multi_aff_pullback_multi_aff_aligned(
5325 __isl_take isl_multi_aff
*ma1
, __isl_take isl_multi_aff
*ma2
)
5328 isl_space
*space
= NULL
;
5330 ma2
= isl_multi_aff_align_divs(ma2
);
5331 ma1
= isl_multi_aff_cow(ma1
);
5335 space
= isl_space_join(isl_multi_aff_get_space(ma2
),
5336 isl_multi_aff_get_space(ma1
));
5338 for (i
= 0; i
< ma1
->n
; ++i
) {
5339 ma1
->p
[i
] = isl_aff_pullback_multi_aff(ma1
->p
[i
],
5340 isl_multi_aff_copy(ma2
));
5345 ma1
= isl_multi_aff_reset_space(ma1
, space
);
5346 isl_multi_aff_free(ma2
);
5349 isl_space_free(space
);
5350 isl_multi_aff_free(ma2
);
5351 isl_multi_aff_free(ma1
);
5355 /* Compute the pullback of "ma1" by the function represented by "ma2".
5356 * In other words, plug in "ma2" in "ma1".
5358 __isl_give isl_multi_aff
*isl_multi_aff_pullback_multi_aff(
5359 __isl_take isl_multi_aff
*ma1
, __isl_take isl_multi_aff
*ma2
)
5361 return isl_multi_aff_align_params_multi_multi_and(ma1
, ma2
,
5362 &isl_multi_aff_pullback_multi_aff_aligned
);
5365 /* Extend the local space of "dst" to include the divs
5366 * in the local space of "src".
5368 __isl_give isl_aff
*isl_aff_align_divs(__isl_take isl_aff
*dst
,
5369 __isl_keep isl_aff
*src
)
5377 return isl_aff_free(dst
);
5379 ctx
= isl_aff_get_ctx(src
);
5380 if (!isl_space_is_equal(src
->ls
->dim
, dst
->ls
->dim
))
5381 isl_die(ctx
, isl_error_invalid
,
5382 "spaces don't match", goto error
);
5384 if (src
->ls
->div
->n_row
== 0)
5387 exp1
= isl_alloc_array(ctx
, int, src
->ls
->div
->n_row
);
5388 exp2
= isl_alloc_array(ctx
, int, dst
->ls
->div
->n_row
);
5389 if (!exp1
|| (dst
->ls
->div
->n_row
&& !exp2
))
5392 div
= isl_merge_divs(src
->ls
->div
, dst
->ls
->div
, exp1
, exp2
);
5393 dst
= isl_aff_expand_divs(dst
, div
, exp2
);
5401 return isl_aff_free(dst
);
5404 /* Adjust the local spaces of the affine expressions in "maff"
5405 * such that they all have the save divs.
5407 __isl_give isl_multi_aff
*isl_multi_aff_align_divs(
5408 __isl_take isl_multi_aff
*maff
)
5416 maff
= isl_multi_aff_cow(maff
);
5420 for (i
= 1; i
< maff
->n
; ++i
)
5421 maff
->p
[0] = isl_aff_align_divs(maff
->p
[0], maff
->p
[i
]);
5422 for (i
= 1; i
< maff
->n
; ++i
) {
5423 maff
->p
[i
] = isl_aff_align_divs(maff
->p
[i
], maff
->p
[0]);
5425 return isl_multi_aff_free(maff
);
5431 __isl_give isl_aff
*isl_aff_lift(__isl_take isl_aff
*aff
)
5433 aff
= isl_aff_cow(aff
);
5437 aff
->ls
= isl_local_space_lift(aff
->ls
);
5439 return isl_aff_free(aff
);
5444 /* Lift "maff" to a space with extra dimensions such that the result
5445 * has no more existentially quantified variables.
5446 * If "ls" is not NULL, then *ls is assigned the local space that lies
5447 * at the basis of the lifting applied to "maff".
5449 __isl_give isl_multi_aff
*isl_multi_aff_lift(__isl_take isl_multi_aff
*maff
,
5450 __isl_give isl_local_space
**ls
)
5464 isl_space
*space
= isl_multi_aff_get_domain_space(maff
);
5465 *ls
= isl_local_space_from_space(space
);
5467 return isl_multi_aff_free(maff
);
5472 maff
= isl_multi_aff_cow(maff
);
5473 maff
= isl_multi_aff_align_divs(maff
);
5477 n_div
= isl_aff_dim(maff
->p
[0], isl_dim_div
);
5478 space
= isl_multi_aff_get_space(maff
);
5479 space
= isl_space_lift(isl_space_domain(space
), n_div
);
5480 space
= isl_space_extend_domain_with_range(space
,
5481 isl_multi_aff_get_space(maff
));
5483 return isl_multi_aff_free(maff
);
5484 isl_space_free(maff
->space
);
5485 maff
->space
= space
;
5488 *ls
= isl_aff_get_domain_local_space(maff
->p
[0]);
5490 return isl_multi_aff_free(maff
);
5493 for (i
= 0; i
< maff
->n
; ++i
) {
5494 maff
->p
[i
] = isl_aff_lift(maff
->p
[i
]);
5502 isl_local_space_free(*ls
);
5503 return isl_multi_aff_free(maff
);
5507 /* Extract an isl_pw_aff corresponding to output dimension "pos" of "pma".
5509 __isl_give isl_pw_aff
*isl_pw_multi_aff_get_pw_aff(
5510 __isl_keep isl_pw_multi_aff
*pma
, int pos
)
5520 n_out
= isl_pw_multi_aff_dim(pma
, isl_dim_out
);
5521 if (pos
< 0 || pos
>= n_out
)
5522 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_invalid
,
5523 "index out of bounds", return NULL
);
5525 space
= isl_pw_multi_aff_get_space(pma
);
5526 space
= isl_space_drop_dims(space
, isl_dim_out
,
5527 pos
+ 1, n_out
- pos
- 1);
5528 space
= isl_space_drop_dims(space
, isl_dim_out
, 0, pos
);
5530 pa
= isl_pw_aff_alloc_size(space
, pma
->n
);
5531 for (i
= 0; i
< pma
->n
; ++i
) {
5533 aff
= isl_multi_aff_get_aff(pma
->p
[i
].maff
, pos
);
5534 pa
= isl_pw_aff_add_piece(pa
, isl_set_copy(pma
->p
[i
].set
), aff
);
5540 /* Return an isl_pw_multi_aff with the given "set" as domain and
5541 * an unnamed zero-dimensional range.
5543 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_from_domain(
5544 __isl_take isl_set
*set
)
5549 space
= isl_set_get_space(set
);
5550 space
= isl_space_from_domain(space
);
5551 ma
= isl_multi_aff_zero(space
);
5552 return isl_pw_multi_aff_alloc(set
, ma
);
5555 /* Add an isl_pw_multi_aff with the given "set" as domain and
5556 * an unnamed zero-dimensional range to *user.
5558 static int add_pw_multi_aff_from_domain(__isl_take isl_set
*set
, void *user
)
5560 isl_union_pw_multi_aff
**upma
= user
;
5561 isl_pw_multi_aff
*pma
;
5563 pma
= isl_pw_multi_aff_from_domain(set
);
5564 *upma
= isl_union_pw_multi_aff_add_pw_multi_aff(*upma
, pma
);
5569 /* Return an isl_union_pw_multi_aff with the given "uset" as domain and
5570 * an unnamed zero-dimensional range.
5572 __isl_give isl_union_pw_multi_aff
*isl_union_pw_multi_aff_from_domain(
5573 __isl_take isl_union_set
*uset
)
5576 isl_union_pw_multi_aff
*upma
;
5581 space
= isl_union_set_get_space(uset
);
5582 upma
= isl_union_pw_multi_aff_empty(space
);
5584 if (isl_union_set_foreach_set(uset
,
5585 &add_pw_multi_aff_from_domain
, &upma
) < 0)
5588 isl_union_set_free(uset
);
5591 isl_union_set_free(uset
);
5592 isl_union_pw_multi_aff_free(upma
);
5596 /* Convert "pma" to an isl_map and add it to *umap.
5598 static int map_from_pw_multi_aff(__isl_take isl_pw_multi_aff
*pma
, void *user
)
5600 isl_union_map
**umap
= user
;
5603 map
= isl_map_from_pw_multi_aff(pma
);
5604 *umap
= isl_union_map_add_map(*umap
, map
);
5609 /* Construct a union map mapping the domain of the union
5610 * piecewise multi-affine expression to its range, with each dimension
5611 * in the range equated to the corresponding affine expression on its cell.
5613 __isl_give isl_union_map
*isl_union_map_from_union_pw_multi_aff(
5614 __isl_take isl_union_pw_multi_aff
*upma
)
5617 isl_union_map
*umap
;
5622 space
= isl_union_pw_multi_aff_get_space(upma
);
5623 umap
= isl_union_map_empty(space
);
5625 if (isl_union_pw_multi_aff_foreach_pw_multi_aff(upma
,
5626 &map_from_pw_multi_aff
, &umap
) < 0)
5629 isl_union_pw_multi_aff_free(upma
);
5632 isl_union_pw_multi_aff_free(upma
);
5633 isl_union_map_free(umap
);
5637 /* Local data for bin_entry and the callback "fn".
5639 struct isl_union_pw_multi_aff_bin_data
{
5640 isl_union_pw_multi_aff
*upma2
;
5641 isl_union_pw_multi_aff
*res
;
5642 isl_pw_multi_aff
*pma
;
5643 int (*fn
)(void **entry
, void *user
);
5646 /* Given an isl_pw_multi_aff from upma1, store it in data->pma
5647 * and call data->fn for each isl_pw_multi_aff in data->upma2.
5649 static int bin_entry(void **entry
, void *user
)
5651 struct isl_union_pw_multi_aff_bin_data
*data
= user
;
5652 isl_pw_multi_aff
*pma
= *entry
;
5655 if (isl_hash_table_foreach(data
->upma2
->space
->ctx
, &data
->upma2
->table
,
5656 data
->fn
, data
) < 0)
5662 /* Call "fn" on each pair of isl_pw_multi_affs in "upma1" and "upma2".
5663 * The isl_pw_multi_aff from upma1 is stored in data->pma (where data is
5664 * passed as user field) and the isl_pw_multi_aff from upma2 is available
5665 * as *entry. The callback should adjust data->res if desired.
5667 static __isl_give isl_union_pw_multi_aff
*bin_op(
5668 __isl_take isl_union_pw_multi_aff
*upma1
,
5669 __isl_take isl_union_pw_multi_aff
*upma2
,
5670 int (*fn
)(void **entry
, void *user
))
5673 struct isl_union_pw_multi_aff_bin_data data
= { NULL
, NULL
, NULL
, fn
};
5675 space
= isl_union_pw_multi_aff_get_space(upma2
);
5676 upma1
= isl_union_pw_multi_aff_align_params(upma1
, space
);
5677 space
= isl_union_pw_multi_aff_get_space(upma1
);
5678 upma2
= isl_union_pw_multi_aff_align_params(upma2
, space
);
5680 if (!upma1
|| !upma2
)
5684 data
.res
= isl_union_pw_multi_aff_alloc(isl_space_copy(upma1
->space
),
5686 if (isl_hash_table_foreach(upma1
->space
->ctx
, &upma1
->table
,
5687 &bin_entry
, &data
) < 0)
5690 isl_union_pw_multi_aff_free(upma1
);
5691 isl_union_pw_multi_aff_free(upma2
);
5694 isl_union_pw_multi_aff_free(upma1
);
5695 isl_union_pw_multi_aff_free(upma2
);
5696 isl_union_pw_multi_aff_free(data
.res
);
5700 /* Given two aligned isl_pw_multi_affs A -> B and C -> D,
5701 * construct an isl_pw_multi_aff (A * C) -> [B -> D].
5703 static __isl_give isl_pw_multi_aff
*pw_multi_aff_range_product(
5704 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
5708 space
= isl_space_range_product(isl_pw_multi_aff_get_space(pma1
),
5709 isl_pw_multi_aff_get_space(pma2
));
5710 return isl_pw_multi_aff_on_shared_domain_in(pma1
, pma2
, space
,
5711 &isl_multi_aff_range_product
);
5714 /* Given two isl_pw_multi_affs A -> B and C -> D,
5715 * construct an isl_pw_multi_aff (A * C) -> [B -> D].
5717 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_range_product(
5718 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
5720 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
5721 &pw_multi_aff_range_product
);
5724 /* Given two aligned isl_pw_multi_affs A -> B and C -> D,
5725 * construct an isl_pw_multi_aff (A * C) -> (B, D).
5727 static __isl_give isl_pw_multi_aff
*pw_multi_aff_flat_range_product(
5728 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
5732 space
= isl_space_range_product(isl_pw_multi_aff_get_space(pma1
),
5733 isl_pw_multi_aff_get_space(pma2
));
5734 space
= isl_space_flatten_range(space
);
5735 return isl_pw_multi_aff_on_shared_domain_in(pma1
, pma2
, space
,
5736 &isl_multi_aff_flat_range_product
);
5739 /* Given two isl_pw_multi_affs A -> B and C -> D,
5740 * construct an isl_pw_multi_aff (A * C) -> (B, D).
5742 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_flat_range_product(
5743 __isl_take isl_pw_multi_aff
*pma1
, __isl_take isl_pw_multi_aff
*pma2
)
5745 return isl_pw_multi_aff_align_params_pw_pw_and(pma1
, pma2
,
5746 &pw_multi_aff_flat_range_product
);
5749 /* If data->pma and *entry have the same domain space, then compute
5750 * their flat range product and the result to data->res.
5752 static int flat_range_product_entry(void **entry
, void *user
)
5754 struct isl_union_pw_multi_aff_bin_data
*data
= user
;
5755 isl_pw_multi_aff
*pma2
= *entry
;
5757 if (!isl_space_tuple_is_equal(data
->pma
->dim
, isl_dim_in
,
5758 pma2
->dim
, isl_dim_in
))
5761 pma2
= isl_pw_multi_aff_flat_range_product(
5762 isl_pw_multi_aff_copy(data
->pma
),
5763 isl_pw_multi_aff_copy(pma2
));
5765 data
->res
= isl_union_pw_multi_aff_add_pw_multi_aff(data
->res
, pma2
);
5770 /* Given two isl_union_pw_multi_affs A -> B and C -> D,
5771 * construct an isl_union_pw_multi_aff (A * C) -> (B, D).
5773 __isl_give isl_union_pw_multi_aff
*isl_union_pw_multi_aff_flat_range_product(
5774 __isl_take isl_union_pw_multi_aff
*upma1
,
5775 __isl_take isl_union_pw_multi_aff
*upma2
)
5777 return bin_op(upma1
, upma2
, &flat_range_product_entry
);
5780 /* Replace the affine expressions at position "pos" in "pma" by "pa".
5781 * The parameters are assumed to have been aligned.
5783 * The implementation essentially performs an isl_pw_*_on_shared_domain,
5784 * except that it works on two different isl_pw_* types.
5786 static __isl_give isl_pw_multi_aff
*pw_multi_aff_set_pw_aff(
5787 __isl_take isl_pw_multi_aff
*pma
, unsigned pos
,
5788 __isl_take isl_pw_aff
*pa
)
5791 isl_pw_multi_aff
*res
= NULL
;
5796 if (!isl_space_tuple_is_equal(pma
->dim
, isl_dim_in
,
5797 pa
->dim
, isl_dim_in
))
5798 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_invalid
,
5799 "domains don't match", goto error
);
5800 if (pos
>= isl_pw_multi_aff_dim(pma
, isl_dim_out
))
5801 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_invalid
,
5802 "index out of bounds", goto error
);
5805 res
= isl_pw_multi_aff_alloc_size(isl_pw_multi_aff_get_space(pma
), n
);
5807 for (i
= 0; i
< pma
->n
; ++i
) {
5808 for (j
= 0; j
< pa
->n
; ++j
) {
5810 isl_multi_aff
*res_ij
;
5813 common
= isl_set_intersect(isl_set_copy(pma
->p
[i
].set
),
5814 isl_set_copy(pa
->p
[j
].set
));
5815 empty
= isl_set_plain_is_empty(common
);
5816 if (empty
< 0 || empty
) {
5817 isl_set_free(common
);
5823 res_ij
= isl_multi_aff_set_aff(
5824 isl_multi_aff_copy(pma
->p
[i
].maff
), pos
,
5825 isl_aff_copy(pa
->p
[j
].aff
));
5826 res_ij
= isl_multi_aff_gist(res_ij
,
5827 isl_set_copy(common
));
5829 res
= isl_pw_multi_aff_add_piece(res
, common
, res_ij
);
5833 isl_pw_multi_aff_free(pma
);
5834 isl_pw_aff_free(pa
);
5837 isl_pw_multi_aff_free(pma
);
5838 isl_pw_aff_free(pa
);
5839 return isl_pw_multi_aff_free(res
);
5842 /* Replace the affine expressions at position "pos" in "pma" by "pa".
5844 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_set_pw_aff(
5845 __isl_take isl_pw_multi_aff
*pma
, unsigned pos
,
5846 __isl_take isl_pw_aff
*pa
)
5850 if (isl_space_match(pma
->dim
, isl_dim_param
, pa
->dim
, isl_dim_param
))
5851 return pw_multi_aff_set_pw_aff(pma
, pos
, pa
);
5852 if (!isl_space_has_named_params(pma
->dim
) ||
5853 !isl_space_has_named_params(pa
->dim
))
5854 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_invalid
,
5855 "unaligned unnamed parameters", goto error
);
5856 pma
= isl_pw_multi_aff_align_params(pma
, isl_pw_aff_get_space(pa
));
5857 pa
= isl_pw_aff_align_params(pa
, isl_pw_multi_aff_get_space(pma
));
5858 return pw_multi_aff_set_pw_aff(pma
, pos
, pa
);
5860 isl_pw_multi_aff_free(pma
);
5861 isl_pw_aff_free(pa
);
5865 /* Do the parameters of "pa" match those of "space"?
5867 int isl_pw_aff_matching_params(__isl_keep isl_pw_aff
*pa
,
5868 __isl_keep isl_space
*space
)
5870 isl_space
*pa_space
;
5876 pa_space
= isl_pw_aff_get_space(pa
);
5878 match
= isl_space_match(space
, isl_dim_param
, pa_space
, isl_dim_param
);
5880 isl_space_free(pa_space
);
5884 /* Check that the domain space of "pa" matches "space".
5886 * Return 0 on success and -1 on error.
5888 int isl_pw_aff_check_match_domain_space(__isl_keep isl_pw_aff
*pa
,
5889 __isl_keep isl_space
*space
)
5891 isl_space
*pa_space
;
5897 pa_space
= isl_pw_aff_get_space(pa
);
5899 match
= isl_space_match(space
, isl_dim_param
, pa_space
, isl_dim_param
);
5903 isl_die(isl_pw_aff_get_ctx(pa
), isl_error_invalid
,
5904 "parameters don't match", goto error
);
5905 match
= isl_space_tuple_is_equal(space
, isl_dim_in
,
5906 pa_space
, isl_dim_in
);
5910 isl_die(isl_pw_aff_get_ctx(pa
), isl_error_invalid
,
5911 "domains don't match", goto error
);
5912 isl_space_free(pa_space
);
5915 isl_space_free(pa_space
);
5922 #include <isl_multi_templ.c>
5924 /* Scale the elements of "pma" by the corresponding elements of "mv".
5926 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_scale_multi_val(
5927 __isl_take isl_pw_multi_aff
*pma
, __isl_take isl_multi_val
*mv
)
5931 pma
= isl_pw_multi_aff_cow(pma
);
5934 if (!isl_space_tuple_is_equal(pma
->dim
, isl_dim_out
,
5935 mv
->space
, isl_dim_set
))
5936 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_invalid
,
5937 "spaces don't match", goto error
);
5938 if (!isl_space_match(pma
->dim
, isl_dim_param
,
5939 mv
->space
, isl_dim_param
)) {
5940 pma
= isl_pw_multi_aff_align_params(pma
,
5941 isl_multi_val_get_space(mv
));
5942 mv
= isl_multi_val_align_params(mv
,
5943 isl_pw_multi_aff_get_space(pma
));
5948 for (i
= 0; i
< pma
->n
; ++i
) {
5949 pma
->p
[i
].maff
= isl_multi_aff_scale_multi_val(pma
->p
[i
].maff
,
5950 isl_multi_val_copy(mv
));
5951 if (!pma
->p
[i
].maff
)
5955 isl_multi_val_free(mv
);
5958 isl_multi_val_free(mv
);
5959 isl_pw_multi_aff_free(pma
);
5963 /* Internal data structure for isl_union_pw_multi_aff_scale_multi_val.
5964 * mv contains the mv argument.
5965 * res collects the results.
5967 struct isl_union_pw_multi_aff_scale_multi_val_data
{
5969 isl_union_pw_multi_aff
*res
;
5972 /* This function is called for each entry of an isl_union_pw_multi_aff.
5973 * If the space of the entry matches that of data->mv,
5974 * then apply isl_pw_multi_aff_scale_multi_val and add the result
5977 static int union_pw_multi_aff_scale_multi_val_entry(void **entry
, void *user
)
5979 struct isl_union_pw_multi_aff_scale_multi_val_data
*data
= user
;
5980 isl_pw_multi_aff
*pma
= *entry
;
5984 if (!isl_space_tuple_is_equal(pma
->dim
, isl_dim_out
,
5985 data
->mv
->space
, isl_dim_set
))
5988 pma
= isl_pw_multi_aff_copy(pma
);
5989 pma
= isl_pw_multi_aff_scale_multi_val(pma
,
5990 isl_multi_val_copy(data
->mv
));
5991 data
->res
= isl_union_pw_multi_aff_add_pw_multi_aff(data
->res
, pma
);
5998 /* Scale the elements of "upma" by the corresponding elements of "mv",
5999 * for those entries that match the space of "mv".
6001 __isl_give isl_union_pw_multi_aff
*isl_union_pw_multi_aff_scale_multi_val(
6002 __isl_take isl_union_pw_multi_aff
*upma
, __isl_take isl_multi_val
*mv
)
6004 struct isl_union_pw_multi_aff_scale_multi_val_data data
;
6006 upma
= isl_union_pw_multi_aff_align_params(upma
,
6007 isl_multi_val_get_space(mv
));
6008 mv
= isl_multi_val_align_params(mv
,
6009 isl_union_pw_multi_aff_get_space(upma
));
6014 data
.res
= isl_union_pw_multi_aff_alloc(isl_space_copy(upma
->space
),
6016 if (isl_hash_table_foreach(upma
->space
->ctx
, &upma
->table
,
6017 &union_pw_multi_aff_scale_multi_val_entry
, &data
) < 0)
6020 isl_multi_val_free(mv
);
6021 isl_union_pw_multi_aff_free(upma
);
6024 isl_multi_val_free(mv
);
6025 isl_union_pw_multi_aff_free(upma
);
6029 /* Construct and return a piecewise multi affine expression
6030 * in the given space with value zero in each of the output dimensions and
6031 * a universe domain.
6033 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_zero(__isl_take isl_space
*space
)
6035 return isl_pw_multi_aff_from_multi_aff(isl_multi_aff_zero(space
));
6038 /* Construct and return a piecewise multi affine expression
6039 * that is equal to the given piecewise affine expression.
6041 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_from_pw_aff(
6042 __isl_take isl_pw_aff
*pa
)
6046 isl_pw_multi_aff
*pma
;
6051 space
= isl_pw_aff_get_space(pa
);
6052 pma
= isl_pw_multi_aff_alloc_size(space
, pa
->n
);
6054 for (i
= 0; i
< pa
->n
; ++i
) {
6058 set
= isl_set_copy(pa
->p
[i
].set
);
6059 ma
= isl_multi_aff_from_aff(isl_aff_copy(pa
->p
[i
].aff
));
6060 pma
= isl_pw_multi_aff_add_piece(pma
, set
, ma
);
6063 isl_pw_aff_free(pa
);
6067 /* Construct a set or map mapping the shared (parameter) domain
6068 * of the piecewise affine expressions to the range of "mpa"
6069 * with each dimension in the range equated to the
6070 * corresponding piecewise affine expression.
6072 static __isl_give isl_map
*map_from_multi_pw_aff(
6073 __isl_take isl_multi_pw_aff
*mpa
)
6082 if (isl_space_dim(mpa
->space
, isl_dim_out
) != mpa
->n
)
6083 isl_die(isl_multi_pw_aff_get_ctx(mpa
), isl_error_internal
,
6084 "invalid space", goto error
);
6086 space
= isl_multi_pw_aff_get_domain_space(mpa
);
6087 map
= isl_map_universe(isl_space_from_domain(space
));
6089 for (i
= 0; i
< mpa
->n
; ++i
) {
6093 pa
= isl_pw_aff_copy(mpa
->p
[i
]);
6094 map_i
= map_from_pw_aff(pa
);
6096 map
= isl_map_flat_range_product(map
, map_i
);
6099 map
= isl_map_reset_space(map
, isl_multi_pw_aff_get_space(mpa
));
6101 isl_multi_pw_aff_free(mpa
);
6104 isl_multi_pw_aff_free(mpa
);
6108 /* Construct a map mapping the shared domain
6109 * of the piecewise affine expressions to the range of "mpa"
6110 * with each dimension in the range equated to the
6111 * corresponding piecewise affine expression.
6113 __isl_give isl_map
*isl_map_from_multi_pw_aff(__isl_take isl_multi_pw_aff
*mpa
)
6117 if (isl_space_is_set(mpa
->space
))
6118 isl_die(isl_multi_pw_aff_get_ctx(mpa
), isl_error_internal
,
6119 "space of input is not a map", goto error
);
6121 return map_from_multi_pw_aff(mpa
);
6123 isl_multi_pw_aff_free(mpa
);
6127 /* Construct a set mapping the shared parameter domain
6128 * of the piecewise affine expressions to the space of "mpa"
6129 * with each dimension in the range equated to the
6130 * corresponding piecewise affine expression.
6132 __isl_give isl_set
*isl_set_from_multi_pw_aff(__isl_take isl_multi_pw_aff
*mpa
)
6136 if (!isl_space_is_set(mpa
->space
))
6137 isl_die(isl_multi_pw_aff_get_ctx(mpa
), isl_error_internal
,
6138 "space of input is not a set", goto error
);
6140 return map_from_multi_pw_aff(mpa
);
6142 isl_multi_pw_aff_free(mpa
);
6146 /* Construct and return a piecewise multi affine expression
6147 * that is equal to the given multi piecewise affine expression
6148 * on the shared domain of the piecewise affine expressions.
6150 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_from_multi_pw_aff(
6151 __isl_take isl_multi_pw_aff
*mpa
)
6156 isl_pw_multi_aff
*pma
;
6161 space
= isl_multi_pw_aff_get_space(mpa
);
6164 isl_multi_pw_aff_free(mpa
);
6165 return isl_pw_multi_aff_zero(space
);
6168 pa
= isl_multi_pw_aff_get_pw_aff(mpa
, 0);
6169 pma
= isl_pw_multi_aff_from_pw_aff(pa
);
6171 for (i
= 1; i
< mpa
->n
; ++i
) {
6172 isl_pw_multi_aff
*pma_i
;
6174 pa
= isl_multi_pw_aff_get_pw_aff(mpa
, i
);
6175 pma_i
= isl_pw_multi_aff_from_pw_aff(pa
);
6176 pma
= isl_pw_multi_aff_range_product(pma
, pma_i
);
6179 pma
= isl_pw_multi_aff_reset_space(pma
, space
);
6181 isl_multi_pw_aff_free(mpa
);
6185 /* Construct and return a multi piecewise affine expression
6186 * that is equal to the given multi affine expression.
6188 __isl_give isl_multi_pw_aff
*isl_multi_pw_aff_from_multi_aff(
6189 __isl_take isl_multi_aff
*ma
)
6192 isl_multi_pw_aff
*mpa
;
6197 n
= isl_multi_aff_dim(ma
, isl_dim_out
);
6198 mpa
= isl_multi_pw_aff_alloc(isl_multi_aff_get_space(ma
));
6200 for (i
= 0; i
< n
; ++i
) {
6203 pa
= isl_pw_aff_from_aff(isl_multi_aff_get_aff(ma
, i
));
6204 mpa
= isl_multi_pw_aff_set_pw_aff(mpa
, i
, pa
);
6207 isl_multi_aff_free(ma
);
6211 /* Construct and return a multi piecewise affine expression
6212 * that is equal to the given piecewise multi affine expression.
6214 __isl_give isl_multi_pw_aff
*isl_multi_pw_aff_from_pw_multi_aff(
6215 __isl_take isl_pw_multi_aff
*pma
)
6219 isl_multi_pw_aff
*mpa
;
6224 n
= isl_pw_multi_aff_dim(pma
, isl_dim_out
);
6225 space
= isl_pw_multi_aff_get_space(pma
);
6226 mpa
= isl_multi_pw_aff_alloc(space
);
6228 for (i
= 0; i
< n
; ++i
) {
6231 pa
= isl_pw_multi_aff_get_pw_aff(pma
, i
);
6232 mpa
= isl_multi_pw_aff_set_pw_aff(mpa
, i
, pa
);
6235 isl_pw_multi_aff_free(pma
);
6239 /* Do "pa1" and "pa2" represent the same function?
6241 * We first check if they are obviously equal.
6242 * If not, we convert them to maps and check if those are equal.
6244 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff
*pa1
, __isl_keep isl_pw_aff
*pa2
)
6247 isl_map
*map1
, *map2
;
6252 equal
= isl_pw_aff_plain_is_equal(pa1
, pa2
);
6253 if (equal
< 0 || equal
)
6256 map1
= map_from_pw_aff(isl_pw_aff_copy(pa1
));
6257 map2
= map_from_pw_aff(isl_pw_aff_copy(pa2
));
6258 equal
= isl_map_is_equal(map1
, map2
);
6265 /* Do "mpa1" and "mpa2" represent the same function?
6267 * Note that we cannot convert the entire isl_multi_pw_aff
6268 * to a map because the domains of the piecewise affine expressions
6269 * may not be the same.
6271 int isl_multi_pw_aff_is_equal(__isl_keep isl_multi_pw_aff
*mpa1
,
6272 __isl_keep isl_multi_pw_aff
*mpa2
)
6280 if (!isl_space_match(mpa1
->space
, isl_dim_param
,
6281 mpa2
->space
, isl_dim_param
)) {
6282 if (!isl_space_has_named_params(mpa1
->space
))
6284 if (!isl_space_has_named_params(mpa2
->space
))
6286 mpa1
= isl_multi_pw_aff_copy(mpa1
);
6287 mpa2
= isl_multi_pw_aff_copy(mpa2
);
6288 mpa1
= isl_multi_pw_aff_align_params(mpa1
,
6289 isl_multi_pw_aff_get_space(mpa2
));
6290 mpa2
= isl_multi_pw_aff_align_params(mpa2
,
6291 isl_multi_pw_aff_get_space(mpa1
));
6292 equal
= isl_multi_pw_aff_is_equal(mpa1
, mpa2
);
6293 isl_multi_pw_aff_free(mpa1
);
6294 isl_multi_pw_aff_free(mpa2
);
6298 equal
= isl_space_is_equal(mpa1
->space
, mpa2
->space
);
6299 if (equal
< 0 || !equal
)
6302 for (i
= 0; i
< mpa1
->n
; ++i
) {
6303 equal
= isl_pw_aff_is_equal(mpa1
->p
[i
], mpa2
->p
[i
]);
6304 if (equal
< 0 || !equal
)
6311 /* Coalesce the elements of "mpa".
6313 * Note that such coalescing does not change the meaning of "mpa"
6314 * so there is no need to cow. We do need to be careful not to
6315 * destroy any other copies of "mpa" in case of failure.
6317 __isl_give isl_multi_pw_aff
*isl_multi_pw_aff_coalesce(
6318 __isl_take isl_multi_pw_aff
*mpa
)
6325 for (i
= 0; i
< mpa
->n
; ++i
) {
6326 isl_pw_aff
*pa
= isl_pw_aff_copy(mpa
->p
[i
]);
6327 pa
= isl_pw_aff_coalesce(pa
);
6329 return isl_multi_pw_aff_free(mpa
);
6330 isl_pw_aff_free(mpa
->p
[i
]);
6337 /* Compute the pullback of "mpa" by the function represented by "ma".
6338 * In other words, plug in "ma" in "mpa".
6340 * The parameters of "mpa" and "ma" are assumed to have been aligned.
6342 static __isl_give isl_multi_pw_aff
*isl_multi_pw_aff_pullback_multi_aff_aligned(
6343 __isl_take isl_multi_pw_aff
*mpa
, __isl_take isl_multi_aff
*ma
)
6346 isl_space
*space
= NULL
;
6348 mpa
= isl_multi_pw_aff_cow(mpa
);
6352 space
= isl_space_join(isl_multi_aff_get_space(ma
),
6353 isl_multi_pw_aff_get_space(mpa
));
6357 for (i
= 0; i
< mpa
->n
; ++i
) {
6358 mpa
->p
[i
] = isl_pw_aff_pullback_multi_aff(mpa
->p
[i
],
6359 isl_multi_aff_copy(ma
));
6364 isl_multi_aff_free(ma
);
6365 isl_space_free(mpa
->space
);
6369 isl_space_free(space
);
6370 isl_multi_pw_aff_free(mpa
);
6371 isl_multi_aff_free(ma
);
6375 /* Compute the pullback of "mpa" by the function represented by "ma".
6376 * In other words, plug in "ma" in "mpa".
6378 __isl_give isl_multi_pw_aff
*isl_multi_pw_aff_pullback_multi_aff(
6379 __isl_take isl_multi_pw_aff
*mpa
, __isl_take isl_multi_aff
*ma
)
6383 if (isl_space_match(mpa
->space
, isl_dim_param
,
6384 ma
->space
, isl_dim_param
))
6385 return isl_multi_pw_aff_pullback_multi_aff_aligned(mpa
, ma
);
6386 mpa
= isl_multi_pw_aff_align_params(mpa
, isl_multi_aff_get_space(ma
));
6387 ma
= isl_multi_aff_align_params(ma
, isl_multi_pw_aff_get_space(mpa
));
6388 return isl_multi_pw_aff_pullback_multi_aff_aligned(mpa
, ma
);
6390 isl_multi_pw_aff_free(mpa
);
6391 isl_multi_aff_free(ma
);
6395 /* Compute the pullback of "mpa" by the function represented by "pma".
6396 * In other words, plug in "pma" in "mpa".
6398 * The parameters of "mpa" and "mpa" are assumed to have been aligned.
6400 static __isl_give isl_multi_pw_aff
*
6401 isl_multi_pw_aff_pullback_pw_multi_aff_aligned(
6402 __isl_take isl_multi_pw_aff
*mpa
, __isl_take isl_pw_multi_aff
*pma
)
6405 isl_space
*space
= NULL
;
6407 mpa
= isl_multi_pw_aff_cow(mpa
);
6411 space
= isl_space_join(isl_pw_multi_aff_get_space(pma
),
6412 isl_multi_pw_aff_get_space(mpa
));
6414 for (i
= 0; i
< mpa
->n
; ++i
) {
6415 mpa
->p
[i
] = isl_pw_aff_pullback_pw_multi_aff_aligned(mpa
->p
[i
],
6416 isl_pw_multi_aff_copy(pma
));
6421 isl_pw_multi_aff_free(pma
);
6422 isl_space_free(mpa
->space
);
6426 isl_space_free(space
);
6427 isl_multi_pw_aff_free(mpa
);
6428 isl_pw_multi_aff_free(pma
);
6432 /* Compute the pullback of "mpa" by the function represented by "pma".
6433 * In other words, plug in "pma" in "mpa".
6435 __isl_give isl_multi_pw_aff
*isl_multi_pw_aff_pullback_pw_multi_aff(
6436 __isl_take isl_multi_pw_aff
*mpa
, __isl_take isl_pw_multi_aff
*pma
)
6440 if (isl_space_match(mpa
->space
, isl_dim_param
, pma
->dim
, isl_dim_param
))
6441 return isl_multi_pw_aff_pullback_pw_multi_aff_aligned(mpa
, pma
);
6442 mpa
= isl_multi_pw_aff_align_params(mpa
,
6443 isl_pw_multi_aff_get_space(pma
));
6444 pma
= isl_pw_multi_aff_align_params(pma
,
6445 isl_multi_pw_aff_get_space(mpa
));
6446 return isl_multi_pw_aff_pullback_pw_multi_aff_aligned(mpa
, pma
);
6448 isl_multi_pw_aff_free(mpa
);
6449 isl_pw_multi_aff_free(pma
);
6453 /* Apply "aff" to "mpa". The range of "mpa" needs to be compatible
6454 * with the domain of "aff". The domain of the result is the same
6456 * "mpa" and "aff" are assumed to have been aligned.
6458 * We first extract the parametric constant from "aff", defined
6459 * over the correct domain.
6460 * Then we add the appropriate combinations of the members of "mpa".
6461 * Finally, we add the integer divisions through recursive calls.
6463 static __isl_give isl_pw_aff
*isl_multi_pw_aff_apply_aff_aligned(
6464 __isl_take isl_multi_pw_aff
*mpa
, __isl_take isl_aff
*aff
)
6466 int i
, n_param
, n_in
, n_div
;
6472 n_param
= isl_aff_dim(aff
, isl_dim_param
);
6473 n_in
= isl_aff_dim(aff
, isl_dim_in
);
6474 n_div
= isl_aff_dim(aff
, isl_dim_div
);
6476 space
= isl_space_domain(isl_multi_pw_aff_get_space(mpa
));
6477 tmp
= isl_aff_copy(aff
);
6478 tmp
= isl_aff_drop_dims(tmp
, isl_dim_div
, 0, n_div
);
6479 tmp
= isl_aff_drop_dims(tmp
, isl_dim_in
, 0, n_in
);
6480 tmp
= isl_aff_add_dims(tmp
, isl_dim_in
,
6481 isl_space_dim(space
, isl_dim_set
));
6482 tmp
= isl_aff_reset_domain_space(tmp
, space
);
6483 pa
= isl_pw_aff_from_aff(tmp
);
6485 for (i
= 0; i
< n_in
; ++i
) {
6488 if (!isl_aff_involves_dims(aff
, isl_dim_in
, i
, 1))
6490 v
= isl_aff_get_coefficient_val(aff
, isl_dim_in
, i
);
6491 pa_i
= isl_multi_pw_aff_get_pw_aff(mpa
, i
);
6492 pa_i
= isl_pw_aff_scale_val(pa_i
, v
);
6493 pa
= isl_pw_aff_add(pa
, pa_i
);
6496 for (i
= 0; i
< n_div
; ++i
) {
6500 if (!isl_aff_involves_dims(aff
, isl_dim_div
, i
, 1))
6502 div
= isl_aff_get_div(aff
, i
);
6503 pa_i
= isl_multi_pw_aff_apply_aff_aligned(
6504 isl_multi_pw_aff_copy(mpa
), div
);
6505 pa_i
= isl_pw_aff_floor(pa_i
);
6506 v
= isl_aff_get_coefficient_val(aff
, isl_dim_div
, i
);
6507 pa_i
= isl_pw_aff_scale_val(pa_i
, v
);
6508 pa
= isl_pw_aff_add(pa
, pa_i
);
6511 isl_multi_pw_aff_free(mpa
);
6517 /* Apply "aff" to "mpa". The range of "mpa" needs to be compatible
6518 * with the domain of "aff". The domain of the result is the same
6521 __isl_give isl_pw_aff
*isl_multi_pw_aff_apply_aff(
6522 __isl_take isl_multi_pw_aff
*mpa
, __isl_take isl_aff
*aff
)
6526 if (isl_space_match(aff
->ls
->dim
, isl_dim_param
,
6527 mpa
->space
, isl_dim_param
))
6528 return isl_multi_pw_aff_apply_aff_aligned(mpa
, aff
);
6530 aff
= isl_aff_align_params(aff
, isl_multi_pw_aff_get_space(mpa
));
6531 mpa
= isl_multi_pw_aff_align_params(mpa
, isl_aff_get_space(aff
));
6533 return isl_multi_pw_aff_apply_aff_aligned(mpa
, aff
);
6536 isl_multi_pw_aff_free(mpa
);
6540 /* Apply "pa" to "mpa". The range of "mpa" needs to be compatible
6541 * with the domain of "pa". The domain of the result is the same
6543 * "mpa" and "pa" are assumed to have been aligned.
6545 * We consider each piece in turn. Note that the domains of the
6546 * pieces are assumed to be disjoint and they remain disjoint
6547 * after taking the preimage (over the same function).
6549 static __isl_give isl_pw_aff
*isl_multi_pw_aff_apply_pw_aff_aligned(
6550 __isl_take isl_multi_pw_aff
*mpa
, __isl_take isl_pw_aff
*pa
)
6559 space
= isl_space_join(isl_multi_pw_aff_get_space(mpa
),
6560 isl_pw_aff_get_space(pa
));
6561 res
= isl_pw_aff_empty(space
);
6563 for (i
= 0; i
< pa
->n
; ++i
) {
6567 pa_i
= isl_multi_pw_aff_apply_aff_aligned(
6568 isl_multi_pw_aff_copy(mpa
),
6569 isl_aff_copy(pa
->p
[i
].aff
));
6570 domain
= isl_set_copy(pa
->p
[i
].set
);
6571 domain
= isl_set_preimage_multi_pw_aff(domain
,
6572 isl_multi_pw_aff_copy(mpa
));
6573 pa_i
= isl_pw_aff_intersect_domain(pa_i
, domain
);
6574 res
= isl_pw_aff_add_disjoint(res
, pa_i
);
6577 isl_pw_aff_free(pa
);
6578 isl_multi_pw_aff_free(mpa
);
6581 isl_pw_aff_free(pa
);
6582 isl_multi_pw_aff_free(mpa
);
6586 /* Apply "pa" to "mpa". The range of "mpa" needs to be compatible
6587 * with the domain of "pa". The domain of the result is the same
6590 __isl_give isl_pw_aff
*isl_multi_pw_aff_apply_pw_aff(
6591 __isl_take isl_multi_pw_aff
*mpa
, __isl_take isl_pw_aff
*pa
)
6595 if (isl_space_match(pa
->dim
, isl_dim_param
, mpa
->space
, isl_dim_param
))
6596 return isl_multi_pw_aff_apply_pw_aff_aligned(mpa
, pa
);
6598 pa
= isl_pw_aff_align_params(pa
, isl_multi_pw_aff_get_space(mpa
));
6599 mpa
= isl_multi_pw_aff_align_params(mpa
, isl_pw_aff_get_space(pa
));
6601 return isl_multi_pw_aff_apply_pw_aff_aligned(mpa
, pa
);
6603 isl_pw_aff_free(pa
);
6604 isl_multi_pw_aff_free(mpa
);
6608 /* Compute the pullback of "pa" by the function represented by "mpa".
6609 * In other words, plug in "mpa" in "pa".
6610 * "pa" and "mpa" are assumed to have been aligned.
6612 * The pullback is computed by applying "pa" to "mpa".
6614 static __isl_give isl_pw_aff
*isl_pw_aff_pullback_multi_pw_aff_aligned(
6615 __isl_take isl_pw_aff
*pa
, __isl_take isl_multi_pw_aff
*mpa
)
6617 return isl_multi_pw_aff_apply_pw_aff_aligned(mpa
, pa
);
6620 /* Compute the pullback of "pa" by the function represented by "mpa".
6621 * In other words, plug in "mpa" in "pa".
6623 * The pullback is computed by applying "pa" to "mpa".
6625 __isl_give isl_pw_aff
*isl_pw_aff_pullback_multi_pw_aff(
6626 __isl_take isl_pw_aff
*pa
, __isl_take isl_multi_pw_aff
*mpa
)
6628 return isl_multi_pw_aff_apply_pw_aff(mpa
, pa
);
6631 /* Compute the pullback of "mpa1" by the function represented by "mpa2".
6632 * In other words, plug in "mpa2" in "mpa1".
6634 * The parameters of "mpa1" and "mpa2" are assumed to have been aligned.
6636 * We pullback each member of "mpa1" in turn.
6638 static __isl_give isl_multi_pw_aff
*
6639 isl_multi_pw_aff_pullback_multi_pw_aff_aligned(
6640 __isl_take isl_multi_pw_aff
*mpa1
, __isl_take isl_multi_pw_aff
*mpa2
)
6643 isl_space
*space
= NULL
;
6645 mpa1
= isl_multi_pw_aff_cow(mpa1
);
6649 space
= isl_space_join(isl_multi_pw_aff_get_space(mpa2
),
6650 isl_multi_pw_aff_get_space(mpa1
));
6652 for (i
= 0; i
< mpa1
->n
; ++i
) {
6653 mpa1
->p
[i
] = isl_pw_aff_pullback_multi_pw_aff_aligned(
6654 mpa1
->p
[i
], isl_multi_pw_aff_copy(mpa2
));
6659 mpa1
= isl_multi_pw_aff_reset_space(mpa1
, space
);
6661 isl_multi_pw_aff_free(mpa2
);
6664 isl_space_free(space
);
6665 isl_multi_pw_aff_free(mpa1
);
6666 isl_multi_pw_aff_free(mpa2
);
6670 /* Compute the pullback of "mpa1" by the function represented by "mpa2".
6671 * In other words, plug in "mpa2" in "mpa1".
6673 __isl_give isl_multi_pw_aff
*isl_multi_pw_aff_pullback_multi_pw_aff(
6674 __isl_take isl_multi_pw_aff
*mpa1
, __isl_take isl_multi_pw_aff
*mpa2
)
6676 return isl_multi_pw_aff_align_params_multi_multi_and(mpa1
, mpa2
,
6677 &isl_multi_pw_aff_pullback_multi_pw_aff_aligned
);
6680 /* Compare two isl_affs.
6682 * Return -1 if "aff1" is "smaller" than "aff2", 1 if "aff1" is "greater"
6683 * than "aff2" and 0 if they are equal.
6685 * The order is fairly arbitrary. We do consider expressions that only involve
6686 * earlier dimensions as "smaller".
6688 int isl_aff_plain_cmp(__isl_keep isl_aff
*aff1
, __isl_keep isl_aff
*aff2
)
6701 cmp
= isl_local_space_cmp(aff1
->ls
, aff2
->ls
);
6705 last1
= isl_seq_last_non_zero(aff1
->v
->el
+ 1, aff1
->v
->size
- 1);
6706 last2
= isl_seq_last_non_zero(aff2
->v
->el
+ 1, aff1
->v
->size
- 1);
6708 return last1
- last2
;
6710 return isl_seq_cmp(aff1
->v
->el
, aff2
->v
->el
, aff1
->v
->size
);
6713 /* Compare two isl_pw_affs.
6715 * Return -1 if "pa1" is "smaller" than "pa2", 1 if "pa1" is "greater"
6716 * than "pa2" and 0 if they are equal.
6718 * The order is fairly arbitrary. We do consider expressions that only involve
6719 * earlier dimensions as "smaller".
6721 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff
*pa1
,
6722 __isl_keep isl_pw_aff
*pa2
)
6735 cmp
= isl_space_cmp(pa1
->dim
, pa2
->dim
);
6739 if (pa1
->n
!= pa2
->n
)
6740 return pa1
->n
- pa2
->n
;
6742 for (i
= 0; i
< pa1
->n
; ++i
) {
6743 cmp
= isl_set_plain_cmp(pa1
->p
[i
].set
, pa2
->p
[i
].set
);
6746 cmp
= isl_aff_plain_cmp(pa1
->p
[i
].aff
, pa2
->p
[i
].aff
);
6754 /* Return a piecewise affine expression that is equal to "v" on "domain".
6756 __isl_give isl_pw_aff
*isl_pw_aff_val_on_domain(__isl_take isl_set
*domain
,
6757 __isl_take isl_val
*v
)
6760 isl_local_space
*ls
;
6763 space
= isl_set_get_space(domain
);
6764 ls
= isl_local_space_from_space(space
);
6765 aff
= isl_aff_val_on_domain(ls
, v
);
6767 return isl_pw_aff_alloc(domain
, aff
);
6770 /* Return a multi affine expression that is equal to "mv" on domain
6773 __isl_give isl_multi_aff
*isl_multi_aff_multi_val_on_space(
6774 __isl_take isl_space
*space
, __isl_take isl_multi_val
*mv
)
6778 isl_local_space
*ls
;
6784 n
= isl_multi_val_dim(mv
, isl_dim_set
);
6785 space2
= isl_multi_val_get_space(mv
);
6786 space2
= isl_space_align_params(space2
, isl_space_copy(space
));
6787 space
= isl_space_align_params(space
, isl_space_copy(space2
));
6788 space
= isl_space_map_from_domain_and_range(space
, space2
);
6789 ma
= isl_multi_aff_alloc(isl_space_copy(space
));
6790 ls
= isl_local_space_from_space(isl_space_domain(space
));
6791 for (i
= 0; i
< n
; ++i
) {
6795 v
= isl_multi_val_get_val(mv
, i
);
6796 aff
= isl_aff_val_on_domain(isl_local_space_copy(ls
), v
);
6797 ma
= isl_multi_aff_set_aff(ma
, i
, aff
);
6799 isl_local_space_free(ls
);
6801 isl_multi_val_free(mv
);
6804 isl_space_free(space
);
6805 isl_multi_val_free(mv
);
6809 /* Return a piecewise multi-affine expression
6810 * that is equal to "mv" on "domain".
6812 __isl_give isl_pw_multi_aff
*isl_pw_multi_aff_multi_val_on_domain(
6813 __isl_take isl_set
*domain
, __isl_take isl_multi_val
*mv
)
6818 space
= isl_set_get_space(domain
);
6819 ma
= isl_multi_aff_multi_val_on_space(space
, mv
);
6821 return isl_pw_multi_aff_alloc(domain
, ma
);
6824 /* Internal data structure for isl_union_pw_multi_aff_multi_val_on_domain.
6825 * mv is the value that should be attained on each domain set
6826 * res collects the results
6828 struct isl_union_pw_multi_aff_multi_val_on_domain_data
{
6830 isl_union_pw_multi_aff
*res
;
6833 /* Create an isl_pw_multi_aff equal to data->mv on "domain"
6834 * and add it to data->res.
6836 static int pw_multi_aff_multi_val_on_domain(__isl_take isl_set
*domain
,
6839 struct isl_union_pw_multi_aff_multi_val_on_domain_data
*data
= user
;
6840 isl_pw_multi_aff
*pma
;
6843 mv
= isl_multi_val_copy(data
->mv
);
6844 pma
= isl_pw_multi_aff_multi_val_on_domain(domain
, mv
);
6845 data
->res
= isl_union_pw_multi_aff_add_pw_multi_aff(data
->res
, pma
);
6847 return data
->res
? 0 : -1;
6850 /* Return a union piecewise multi-affine expression
6851 * that is equal to "mv" on "domain".
6853 __isl_give isl_union_pw_multi_aff
*isl_union_pw_multi_aff_multi_val_on_domain(
6854 __isl_take isl_union_set
*domain
, __isl_take isl_multi_val
*mv
)
6856 struct isl_union_pw_multi_aff_multi_val_on_domain_data data
;
6859 space
= isl_union_set_get_space(domain
);
6860 data
.res
= isl_union_pw_multi_aff_empty(space
);
6862 if (isl_union_set_foreach_set(domain
,
6863 &pw_multi_aff_multi_val_on_domain
, &data
) < 0)
6864 data
.res
= isl_union_pw_multi_aff_free(data
.res
);
6865 isl_union_set_free(domain
);
6866 isl_multi_val_free(mv
);
6870 /* Compute the pullback of data->pma by the function represented by "pma2",
6871 * provided the spaces match, and add the results to data->res.
6873 static int pullback_entry(void **entry
, void *user
)
6875 struct isl_union_pw_multi_aff_bin_data
*data
= user
;
6876 isl_pw_multi_aff
*pma2
= *entry
;
6878 if (!isl_space_tuple_is_equal(data
->pma
->dim
, isl_dim_in
,
6879 pma2
->dim
, isl_dim_out
))
6882 pma2
= isl_pw_multi_aff_pullback_pw_multi_aff(
6883 isl_pw_multi_aff_copy(data
->pma
),
6884 isl_pw_multi_aff_copy(pma2
));
6886 data
->res
= isl_union_pw_multi_aff_add_pw_multi_aff(data
->res
, pma2
);
6893 /* Compute the pullback of "upma1" by the function represented by "upma2".
6895 __isl_give isl_union_pw_multi_aff
*
6896 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
6897 __isl_take isl_union_pw_multi_aff
*upma1
,
6898 __isl_take isl_union_pw_multi_aff
*upma2
)
6900 return bin_op(upma1
, upma2
, &pullback_entry
);
6903 /* Replace the entry of isl_union_pw_aff to which "entry" points
6906 static int floor_entry(void **entry
, void *user
)
6908 isl_pw_aff
**pa
= (isl_pw_aff
**) entry
;
6910 *pa
= isl_pw_aff_floor(*pa
);
6917 /* Given f, return floor(f).
6919 __isl_give isl_union_pw_aff
*isl_union_pw_aff_floor(
6920 __isl_take isl_union_pw_aff
*upa
)
6924 upa
= isl_union_pw_aff_cow(upa
);
6928 ctx
= isl_union_pw_aff_get_ctx(upa
);
6929 if (isl_hash_table_foreach(ctx
, &upa
->table
, &floor_entry
, NULL
) < 0)
6930 upa
= isl_union_pw_aff_free(upa
);