2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
5 * Use of this software is governed by the GNU LGPLv2.1 license
7 * Written by Sven Verdoolaege, K.U.Leuven, Departement
8 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
9 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
10 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
20 #include "isl_stream.h"
21 #include "isl_map_private.h"
23 #include "isl_polynomial_private.h"
24 #include <isl_union_map.h>
29 struct variable
*next
;
38 static struct vars
*vars_new(struct isl_ctx
*ctx
)
41 v
= isl_alloc_type(ctx
, struct vars
);
50 static void variable_free(struct variable
*var
)
53 struct variable
*next
= var
->next
;
60 static void vars_free(struct vars
*v
)
68 static void vars_drop(struct vars
*v
, int n
)
79 struct variable
*next
= var
->next
;
87 static struct variable
*variable_new(struct vars
*v
, const char *name
, int len
,
91 var
= isl_alloc_type(v
->ctx
, struct variable
);
94 var
->name
= strdup(name
);
95 var
->name
[len
] = '\0';
104 static int vars_pos(struct vars
*v
, const char *s
, int len
)
111 for (q
= v
->v
; q
; q
= q
->next
) {
112 if (strncmp(q
->name
, s
, len
) == 0 && q
->name
[len
] == '\0')
119 v
->v
= variable_new(v
, s
, len
, v
->n
);
127 static __isl_give isl_dim
*set_name(__isl_take isl_dim
*dim
,
128 enum isl_dim_type type
, unsigned pos
, char *name
)
137 prime
= strchr(name
, '\'');
140 dim
= isl_dim_set_name(dim
, type
, pos
, name
);
147 static int accept_cst_factor(struct isl_stream
*s
, isl_int
*f
)
149 struct isl_token
*tok
;
151 tok
= isl_stream_next_token(s
);
152 if (!tok
|| tok
->type
!= ISL_TOKEN_VALUE
) {
153 isl_stream_error(s
, tok
, "expecting constant value");
157 isl_int_mul(*f
, *f
, tok
->u
.v
);
161 if (isl_stream_eat_if_available(s
, '*'))
162 return accept_cst_factor(s
, f
);
170 static struct isl_vec
*accept_affine(struct isl_stream
*s
, struct vars
*v
);
172 static __isl_give isl_vec
*accept_affine_factor(struct isl_stream
*s
,
175 struct isl_token
*tok
= NULL
;
178 tok
= isl_stream_next_token(s
);
180 isl_stream_error(s
, NULL
, "unexpected EOF");
183 if (tok
->type
== ISL_TOKEN_IDENT
) {
185 int pos
= vars_pos(v
, tok
->u
.s
, -1);
189 isl_stream_error(s
, tok
, "unknown identifier");
193 aff
= isl_vec_alloc(v
->ctx
, 1 + v
->n
);
196 isl_seq_clr(aff
->el
, aff
->size
);
197 isl_int_set_si(aff
->el
[1 + pos
], 1);
199 } else if (tok
->type
== ISL_TOKEN_VALUE
) {
200 if (isl_stream_eat_if_available(s
, '*')) {
201 aff
= accept_affine_factor(s
, v
);
202 aff
= isl_vec_scale(aff
, tok
->u
.v
);
204 aff
= isl_vec_alloc(v
->ctx
, 1 + v
->n
);
207 isl_seq_clr(aff
->el
, aff
->size
);
208 isl_int_set(aff
->el
[0], tok
->u
.v
);
211 } else if (tok
->type
== '(') {
214 aff
= accept_affine(s
, v
);
217 if (isl_stream_eat(s
, ')'))
220 isl_stream_error(s
, tok
, "expecting factor");
223 if (isl_stream_eat_if_available(s
, '*')) {
226 isl_int_set_si(f
, 1);
227 if (accept_cst_factor(s
, &f
) < 0) {
231 aff
= isl_vec_scale(aff
, f
);
242 static struct isl_vec
*accept_affine(struct isl_stream
*s
, struct vars
*v
)
244 struct isl_token
*tok
= NULL
;
248 aff
= isl_vec_alloc(v
->ctx
, 1 + v
->n
);
251 isl_seq_clr(aff
->el
, aff
->size
);
254 tok
= isl_stream_next_token(s
);
256 isl_stream_error(s
, NULL
, "unexpected EOF");
259 if (tok
->type
== '-') {
264 if (tok
->type
== '(' || tok
->type
== ISL_TOKEN_IDENT
) {
266 isl_stream_push_token(s
, tok
);
268 aff2
= accept_affine_factor(s
, v
);
270 aff2
= isl_vec_scale(aff2
, s
->ctx
->negone
);
271 aff
= isl_vec_add(aff
, aff2
);
275 } else if (tok
->type
== ISL_TOKEN_VALUE
) {
277 isl_int_neg(tok
->u
.v
, tok
->u
.v
);
278 if (isl_stream_eat_if_available(s
, '*') ||
279 isl_stream_next_token_is(s
, ISL_TOKEN_IDENT
)) {
281 aff2
= accept_affine_factor(s
, v
);
282 aff2
= isl_vec_scale(aff2
, tok
->u
.v
);
283 aff
= isl_vec_add(aff
, aff2
);
287 isl_int_add(aff
->el
[0], aff
->el
[0], tok
->u
.v
);
293 tok
= isl_stream_next_token(s
);
294 if (tok
&& tok
->type
== '-') {
297 } else if (tok
&& tok
->type
== '+') {
300 } else if (tok
&& tok
->type
== ISL_TOKEN_VALUE
&&
301 isl_int_is_neg(tok
->u
.v
)) {
302 isl_stream_push_token(s
, tok
);
305 isl_stream_push_token(s
, tok
);
317 static __isl_give isl_mat
*read_var_def(struct isl_stream
*s
,
318 __isl_take isl_mat
*eq
, enum isl_dim_type type
, struct vars
*v
)
322 vec
= accept_affine(s
, v
);
325 v
->v
= variable_new(v
, "", 0, v
->n
);
329 eq
= isl_mat_add_rows(eq
, 1);
331 isl_seq_cpy(eq
->row
[eq
->n_row
- 1], vec
->el
, vec
->size
);
332 isl_int_set_si(eq
->row
[eq
->n_row
- 1][vec
->size
], -1);
342 static __isl_give isl_dim
*read_var_list(struct isl_stream
*s
,
343 __isl_take isl_dim
*dim
, enum isl_dim_type type
, struct vars
*v
,
344 __isl_keep isl_mat
**eq
)
347 struct isl_token
*tok
;
349 while ((tok
= isl_stream_next_token(s
)) != NULL
) {
352 if (tok
->type
== ISL_TOKEN_IDENT
) {
354 int p
= vars_pos(v
, tok
->u
.s
, -1);
361 dim
= isl_dim_add(dim
, type
, 1);
363 *eq
= isl_mat_add_zero_cols(*eq
, 1);
364 dim
= set_name(dim
, type
, i
, v
->v
->name
);
366 } else if (tok
->type
== ISL_TOKEN_IDENT
||
367 tok
->type
== ISL_TOKEN_VALUE
) {
368 if (type
== isl_dim_param
) {
369 isl_stream_error(s
, tok
,
370 "expecting unique identifier");
373 isl_stream_push_token(s
, tok
);
375 dim
= isl_dim_add(dim
, type
, 1);
376 *eq
= isl_mat_add_zero_cols(*eq
, 1);
377 *eq
= read_var_def(s
, *eq
, type
, v
);
381 tok
= isl_stream_next_token(s
);
382 if (!tok
|| tok
->type
!= ',')
389 isl_stream_push_token(s
, tok
);
398 static __isl_give isl_mat
*accept_affine_list(struct isl_stream
*s
,
403 struct isl_token
*tok
= NULL
;
405 vec
= accept_affine(s
, v
);
406 mat
= isl_mat_from_row_vec(vec
);
411 tok
= isl_stream_next_token(s
);
413 isl_stream_error(s
, NULL
, "unexpected EOF");
416 if (tok
->type
!= ',') {
417 isl_stream_push_token(s
, tok
);
422 vec
= accept_affine(s
, v
);
423 mat
= isl_mat_vec_concat(mat
, vec
);
434 static struct isl_basic_map
*add_div_definition(struct isl_stream
*s
,
435 struct vars
*v
, struct isl_basic_map
*bmap
, int k
)
437 struct isl_token
*tok
;
441 if (isl_stream_eat(s
, '['))
444 tok
= isl_stream_next_token(s
);
447 if (tok
->type
== '(') {
451 isl_stream_push_token(s
, tok
);
453 aff
= accept_affine(s
, v
);
457 isl_seq_cpy(bmap
->div
[k
] + 1, aff
->el
, aff
->size
);
461 if (seen_paren
&& isl_stream_eat(s
, ')'))
463 if (isl_stream_eat(s
, '/'))
466 tok
= isl_stream_next_token(s
);
469 if (tok
->type
!= ISL_TOKEN_VALUE
) {
470 isl_stream_error(s
, tok
, "expected denominator");
471 isl_stream_push_token(s
, tok
);
474 isl_int_set(bmap
->div
[k
][0], tok
->u
.v
);
477 if (isl_stream_eat(s
, ']'))
480 if (isl_basic_map_add_div_constraints(bmap
, k
) < 0)
485 isl_basic_map_free(bmap
);
489 static struct isl_basic_map
*read_defined_var_list(struct isl_stream
*s
,
490 struct vars
*v
, struct isl_basic_map
*bmap
)
492 struct isl_token
*tok
;
494 while ((tok
= isl_stream_next_token(s
)) != NULL
) {
498 unsigned total
= isl_basic_map_total_dim(bmap
);
500 if (tok
->type
!= ISL_TOKEN_IDENT
)
503 p
= vars_pos(v
, tok
->u
.s
, -1);
507 isl_stream_error(s
, tok
, "expecting unique identifier");
511 bmap
= isl_basic_map_cow(bmap
);
512 bmap
= isl_basic_map_extend_dim(bmap
, isl_dim_copy(bmap
->dim
),
515 if ((k
= isl_basic_map_alloc_div(bmap
)) < 0)
517 isl_seq_clr(bmap
->div
[k
], 1 + 1 + total
);
520 tok
= isl_stream_next_token(s
);
521 if (tok
&& tok
->type
== '=') {
523 bmap
= add_div_definition(s
, v
, bmap
, k
);
524 tok
= isl_stream_next_token(s
);
527 if (!tok
|| tok
->type
!= ',')
533 isl_stream_push_token(s
, tok
);
538 isl_basic_map_free(bmap
);
542 static __isl_give isl_dim
*read_tuple(struct isl_stream
*s
,
543 __isl_take isl_dim
*dim
, enum isl_dim_type type
, struct vars
*v
,
544 __isl_keep isl_mat
**eq
)
546 struct isl_token
*tok
;
549 tok
= isl_stream_next_token(s
);
550 if (tok
&& tok
->type
== ISL_TOKEN_IDENT
) {
551 name
= strdup(tok
->u
.s
);
555 tok
= isl_stream_next_token(s
);
557 if (!tok
|| tok
->type
!= '[') {
558 isl_stream_error(s
, tok
, "expecting '['");
562 dim
= read_var_list(s
, dim
, type
, v
, eq
);
563 tok
= isl_stream_next_token(s
);
564 if (!tok
|| tok
->type
!= ']') {
565 isl_stream_error(s
, tok
, "expecting ']'");
571 dim
= isl_dim_set_tuple_name(dim
, type
, name
);
583 static struct isl_basic_map
*add_constraints(struct isl_stream
*s
,
584 struct vars
*v
, struct isl_basic_map
*bmap
);
586 static struct isl_basic_map
*add_exists(struct isl_stream
*s
,
587 struct vars
*v
, struct isl_basic_map
*bmap
)
589 struct isl_token
*tok
;
596 tok
= isl_stream_next_token(s
);
599 if (tok
->type
== '(') {
603 isl_stream_push_token(s
, tok
);
605 bmap
= read_defined_var_list(s
, v
, bmap
);
609 if (isl_stream_eat(s
, ':'))
611 bmap
= add_constraints(s
, v
, bmap
);
612 if (seen_paren
&& isl_stream_eat(s
, ')'))
616 isl_basic_map_free(bmap
);
620 static __isl_give isl_basic_map
*construct_constraint(
621 __isl_take isl_basic_map
*bmap
, enum isl_token_type type
,
622 isl_int
*left
, isl_int
*right
)
630 len
= 1 + isl_basic_map_total_dim(bmap
);
633 k
= isl_basic_map_alloc_inequality(bmap
);
636 if (type
== ISL_TOKEN_LE
)
637 isl_seq_combine(bmap
->ineq
[k
], ctx
->negone
, left
,
640 else if (type
== ISL_TOKEN_GE
)
641 isl_seq_combine(bmap
->ineq
[k
], ctx
->one
, left
,
644 else if (type
== ISL_TOKEN_LT
) {
645 isl_seq_combine(bmap
->ineq
[k
], ctx
->negone
, left
,
648 isl_int_sub_ui(bmap
->ineq
[k
][0], bmap
->ineq
[k
][0], 1);
649 } else if (type
== ISL_TOKEN_GT
) {
650 isl_seq_combine(bmap
->ineq
[k
], ctx
->one
, left
,
653 isl_int_sub_ui(bmap
->ineq
[k
][0], bmap
->ineq
[k
][0], 1);
655 isl_seq_combine(bmap
->ineq
[k
], ctx
->one
, left
,
658 isl_basic_map_inequality_to_equality(bmap
, k
);
663 isl_basic_map_free(bmap
);
667 static int is_comparator(struct isl_token
*tok
)
684 static struct isl_basic_map
*add_constraint(struct isl_stream
*s
,
685 struct vars
*v
, struct isl_basic_map
*bmap
)
688 unsigned total
= isl_basic_map_total_dim(bmap
);
689 struct isl_token
*tok
= NULL
;
690 struct isl_mat
*aff1
= NULL
, *aff2
= NULL
;
692 tok
= isl_stream_next_token(s
);
695 if (tok
->type
== ISL_TOKEN_EXISTS
) {
697 return add_exists(s
, v
, bmap
);
699 isl_stream_push_token(s
, tok
);
702 bmap
= isl_basic_map_cow(bmap
);
704 aff1
= accept_affine_list(s
, v
);
707 tok
= isl_stream_next_token(s
);
708 if (!is_comparator(tok
)) {
709 isl_stream_error(s
, tok
, "missing operator");
711 isl_stream_push_token(s
, tok
);
715 isl_assert(aff1
->ctx
, aff1
->n_col
== 1 + total
, goto error
);
717 aff2
= accept_affine_list(s
, v
);
720 isl_assert(aff2
->ctx
, aff2
->n_col
== 1 + total
, goto error
);
722 bmap
= isl_basic_map_extend_constraints(bmap
, 0,
723 aff1
->n_row
* aff2
->n_row
);
724 for (i
= 0; i
< aff1
->n_row
; ++i
)
725 for (j
= 0; j
< aff2
->n_row
; ++j
)
726 bmap
= construct_constraint(bmap
, tok
->type
,
727 aff1
->row
[i
], aff2
->row
[j
]);
732 tok
= isl_stream_next_token(s
);
733 if (!is_comparator(tok
)) {
735 isl_stream_push_token(s
, tok
);
747 isl_basic_map_free(bmap
);
751 static struct isl_basic_map
*add_constraints(struct isl_stream
*s
,
752 struct vars
*v
, struct isl_basic_map
*bmap
)
754 struct isl_token
*tok
;
757 bmap
= add_constraint(s
, v
, bmap
);
760 tok
= isl_stream_next_token(s
);
762 isl_stream_error(s
, NULL
, "unexpected EOF");
765 if (tok
->type
!= ISL_TOKEN_AND
)
769 isl_stream_push_token(s
, tok
);
775 isl_basic_map_free(bmap
);
779 static struct isl_basic_map
*read_disjunct(struct isl_stream
*s
,
780 struct vars
*v
, __isl_take isl_dim
*dim
)
783 struct isl_token
*tok
;
784 struct isl_basic_map
*bmap
;
786 bmap
= isl_basic_map_alloc_dim(dim
, 0, 0, 0);
790 tok
= isl_stream_next_token(s
);
793 if (tok
->type
== '(') {
797 isl_stream_push_token(s
, tok
);
799 bmap
= add_constraints(s
, v
, bmap
);
800 bmap
= isl_basic_map_simplify(bmap
);
801 bmap
= isl_basic_map_finalize(bmap
);
803 if (seen_paren
&& isl_stream_eat(s
, ')'))
808 isl_basic_map_free(bmap
);
812 static struct isl_map
*read_disjuncts(struct isl_stream
*s
,
813 struct vars
*v
, __isl_take isl_dim
*dim
)
815 struct isl_token
*tok
;
818 tok
= isl_stream_next_token(s
);
820 isl_stream_error(s
, NULL
, "unexpected EOF");
823 if (tok
->type
== '}') {
824 isl_stream_push_token(s
, tok
);
825 return isl_map_universe(dim
);
827 isl_stream_push_token(s
, tok
);
829 map
= isl_map_empty(isl_dim_copy(dim
));
831 struct isl_basic_map
*bmap
;
834 bmap
= read_disjunct(s
, v
, isl_dim_copy(dim
));
835 map
= isl_map_union(map
, isl_map_from_basic_map(bmap
));
837 vars_drop(v
, v
->n
- n
);
839 tok
= isl_stream_next_token(s
);
840 if (!tok
|| tok
->type
!= ISL_TOKEN_OR
)
845 isl_stream_push_token(s
, tok
);
854 static int polylib_pos_to_isl_pos(__isl_keep isl_basic_map
*bmap
, int pos
)
856 if (pos
< isl_basic_map_dim(bmap
, isl_dim_out
))
857 return 1 + isl_basic_map_dim(bmap
, isl_dim_param
) +
858 isl_basic_map_dim(bmap
, isl_dim_in
) + pos
;
859 pos
-= isl_basic_map_dim(bmap
, isl_dim_out
);
861 if (pos
< isl_basic_map_dim(bmap
, isl_dim_in
))
862 return 1 + isl_basic_map_dim(bmap
, isl_dim_param
) + pos
;
863 pos
-= isl_basic_map_dim(bmap
, isl_dim_in
);
865 if (pos
< isl_basic_map_dim(bmap
, isl_dim_div
))
866 return 1 + isl_basic_map_dim(bmap
, isl_dim_param
) +
867 isl_basic_map_dim(bmap
, isl_dim_in
) +
868 isl_basic_map_dim(bmap
, isl_dim_out
) + pos
;
869 pos
-= isl_basic_map_dim(bmap
, isl_dim_div
);
871 if (pos
< isl_basic_map_dim(bmap
, isl_dim_param
))
877 static __isl_give isl_basic_map
*basic_map_read_polylib_constraint(
878 struct isl_stream
*s
, __isl_take isl_basic_map
*bmap
)
881 struct isl_token
*tok
;
891 nparam
= isl_basic_map_dim(bmap
, isl_dim_param
);
892 dim
= isl_basic_map_dim(bmap
, isl_dim_out
);
894 tok
= isl_stream_next_token(s
);
895 if (!tok
|| tok
->type
!= ISL_TOKEN_VALUE
) {
896 isl_stream_error(s
, tok
, "expecting coefficient");
898 isl_stream_push_token(s
, tok
);
901 if (!tok
->on_new_line
) {
902 isl_stream_error(s
, tok
, "coefficient should appear on new line");
903 isl_stream_push_token(s
, tok
);
907 type
= isl_int_get_si(tok
->u
.v
);
910 isl_assert(s
->ctx
, type
== 0 || type
== 1, goto error
);
912 k
= isl_basic_map_alloc_equality(bmap
);
915 k
= isl_basic_map_alloc_inequality(bmap
);
921 for (j
= 0; j
< 1 + isl_basic_map_total_dim(bmap
); ++j
) {
923 tok
= isl_stream_next_token(s
);
924 if (!tok
|| tok
->type
!= ISL_TOKEN_VALUE
) {
925 isl_stream_error(s
, tok
, "expecting coefficient");
927 isl_stream_push_token(s
, tok
);
930 if (tok
->on_new_line
) {
931 isl_stream_error(s
, tok
,
932 "coefficient should not appear on new line");
933 isl_stream_push_token(s
, tok
);
936 pos
= polylib_pos_to_isl_pos(bmap
, j
);
937 isl_int_set(c
[pos
], tok
->u
.v
);
943 isl_basic_map_free(bmap
);
947 static __isl_give isl_basic_map
*basic_map_read_polylib(struct isl_stream
*s
,
951 struct isl_token
*tok
;
952 struct isl_token
*tok2
;
955 unsigned in
= 0, out
, local
= 0;
956 struct isl_basic_map
*bmap
= NULL
;
961 tok
= isl_stream_next_token(s
);
963 isl_stream_error(s
, NULL
, "unexpected EOF");
966 tok2
= isl_stream_next_token(s
);
969 isl_stream_error(s
, NULL
, "unexpected EOF");
972 n_row
= isl_int_get_si(tok
->u
.v
);
973 n_col
= isl_int_get_si(tok2
->u
.v
);
974 on_new_line
= tok2
->on_new_line
;
975 isl_token_free(tok2
);
977 isl_assert(s
->ctx
, !on_new_line
, return NULL
);
978 isl_assert(s
->ctx
, n_row
>= 0, return NULL
);
979 isl_assert(s
->ctx
, n_col
>= 2 + nparam
, return NULL
);
980 tok
= isl_stream_next_token_on_same_line(s
);
982 if (tok
->type
!= ISL_TOKEN_VALUE
) {
983 isl_stream_error(s
, tok
,
984 "expecting number of output dimensions");
985 isl_stream_push_token(s
, tok
);
988 out
= isl_int_get_si(tok
->u
.v
);
991 tok
= isl_stream_next_token_on_same_line(s
);
992 if (!tok
|| tok
->type
!= ISL_TOKEN_VALUE
) {
993 isl_stream_error(s
, tok
,
994 "expecting number of input dimensions");
996 isl_stream_push_token(s
, tok
);
999 in
= isl_int_get_si(tok
->u
.v
);
1000 isl_token_free(tok
);
1002 tok
= isl_stream_next_token_on_same_line(s
);
1003 if (!tok
|| tok
->type
!= ISL_TOKEN_VALUE
) {
1004 isl_stream_error(s
, tok
,
1005 "expecting number of existentials");
1007 isl_stream_push_token(s
, tok
);
1010 local
= isl_int_get_si(tok
->u
.v
);
1011 isl_token_free(tok
);
1013 tok
= isl_stream_next_token_on_same_line(s
);
1014 if (!tok
|| tok
->type
!= ISL_TOKEN_VALUE
) {
1015 isl_stream_error(s
, tok
,
1016 "expecting number of parameters");
1018 isl_stream_push_token(s
, tok
);
1021 nparam
= isl_int_get_si(tok
->u
.v
);
1022 isl_token_free(tok
);
1023 if (n_col
!= 1 + out
+ in
+ local
+ nparam
+ 1) {
1024 isl_stream_error(s
, NULL
,
1025 "dimensions don't match");
1029 out
= n_col
- 2 - nparam
;
1030 bmap
= isl_basic_map_alloc(s
->ctx
, nparam
, in
, out
, local
, n_row
, n_row
);
1034 for (i
= 0; i
< local
; ++i
) {
1035 int k
= isl_basic_map_alloc_div(bmap
);
1040 for (i
= 0; i
< n_row
; ++i
)
1041 bmap
= basic_map_read_polylib_constraint(s
, bmap
);
1043 tok
= isl_stream_next_token_on_same_line(s
);
1045 isl_stream_error(s
, tok
, "unexpected extra token on line");
1046 isl_stream_push_token(s
, tok
);
1050 bmap
= isl_basic_map_simplify(bmap
);
1051 bmap
= isl_basic_map_finalize(bmap
);
1054 isl_basic_map_free(bmap
);
1058 static struct isl_map
*map_read_polylib(struct isl_stream
*s
, int nparam
)
1060 struct isl_token
*tok
;
1061 struct isl_token
*tok2
;
1063 struct isl_map
*map
;
1065 tok
= isl_stream_next_token(s
);
1067 isl_stream_error(s
, NULL
, "unexpected EOF");
1070 tok2
= isl_stream_next_token_on_same_line(s
);
1072 isl_stream_push_token(s
, tok2
);
1073 isl_stream_push_token(s
, tok
);
1074 return isl_map_from_basic_map(basic_map_read_polylib(s
, nparam
));
1076 n
= isl_int_get_si(tok
->u
.v
);
1077 isl_token_free(tok
);
1079 isl_assert(s
->ctx
, n
>= 1, return NULL
);
1081 map
= isl_map_from_basic_map(basic_map_read_polylib(s
, nparam
));
1083 for (i
= 1; i
< n
; ++i
)
1084 map
= isl_map_union(map
,
1085 isl_map_from_basic_map(basic_map_read_polylib(s
, nparam
)));
1090 static int optional_power(struct isl_stream
*s
)
1093 struct isl_token
*tok
;
1095 tok
= isl_stream_next_token(s
);
1098 if (tok
->type
!= '^') {
1099 isl_stream_push_token(s
, tok
);
1102 isl_token_free(tok
);
1103 tok
= isl_stream_next_token(s
);
1104 if (!tok
|| tok
->type
!= ISL_TOKEN_VALUE
) {
1105 isl_stream_error(s
, tok
, "expecting exponent");
1107 isl_stream_push_token(s
, tok
);
1110 pow
= isl_int_get_si(tok
->u
.v
);
1111 isl_token_free(tok
);
1115 static __isl_give isl_div
*read_div(struct isl_stream
*s
,
1116 __isl_keep isl_basic_map
*bmap
, struct vars
*v
)
1118 unsigned total
= isl_basic_map_total_dim(bmap
);
1121 bmap
= isl_basic_map_copy(bmap
);
1122 bmap
= isl_basic_map_cow(bmap
);
1123 bmap
= isl_basic_map_extend_dim(bmap
, isl_dim_copy(bmap
->dim
),
1126 if ((k
= isl_basic_map_alloc_div(bmap
)) < 0)
1128 isl_seq_clr(bmap
->div
[k
], 1 + 1 + total
);
1129 bmap
= add_div_definition(s
, v
, bmap
, k
);
1131 return isl_basic_map_div(bmap
, k
);
1133 isl_basic_map_free(bmap
);
1137 static __isl_give isl_qpolynomial
*read_term(struct isl_stream
*s
,
1138 __isl_keep isl_basic_map
*bmap
, struct vars
*v
);
1140 static __isl_give isl_qpolynomial
*read_factor(struct isl_stream
*s
,
1141 __isl_keep isl_basic_map
*bmap
, struct vars
*v
)
1143 struct isl_qpolynomial
*qp
;
1144 struct isl_token
*tok
;
1146 tok
= isl_stream_next_token(s
);
1148 isl_stream_error(s
, NULL
, "unexpected EOF");
1151 if (tok
->type
== '(') {
1152 isl_token_free(tok
);
1153 qp
= read_term(s
, bmap
, v
);
1156 if (isl_stream_eat(s
, ')'))
1158 } else if (tok
->type
== ISL_TOKEN_VALUE
) {
1159 struct isl_token
*tok2
;
1160 tok2
= isl_stream_next_token(s
);
1161 if (tok2
&& tok2
->type
== '/') {
1162 isl_token_free(tok2
);
1163 tok2
= isl_stream_next_token(s
);
1164 if (!tok2
|| tok2
->type
!= ISL_TOKEN_VALUE
) {
1165 isl_stream_error(s
, tok2
, "expected denominator");
1166 isl_token_free(tok
);
1167 isl_token_free(tok2
);
1170 qp
= isl_qpolynomial_rat_cst(isl_basic_map_get_dim(bmap
),
1171 tok
->u
.v
, tok2
->u
.v
);
1172 isl_token_free(tok2
);
1174 isl_stream_push_token(s
, tok2
);
1175 qp
= isl_qpolynomial_cst(isl_basic_map_get_dim(bmap
),
1178 isl_token_free(tok
);
1179 } else if (tok
->type
== ISL_TOKEN_INFTY
) {
1180 isl_token_free(tok
);
1181 qp
= isl_qpolynomial_infty(isl_basic_map_get_dim(bmap
));
1182 } else if (tok
->type
== ISL_TOKEN_NAN
) {
1183 isl_token_free(tok
);
1184 qp
= isl_qpolynomial_nan(isl_basic_map_get_dim(bmap
));
1185 } else if (tok
->type
== ISL_TOKEN_IDENT
) {
1187 int pos
= vars_pos(v
, tok
->u
.s
, -1);
1189 isl_token_free(tok
);
1193 isl_stream_error(s
, tok
, "unknown identifier");
1196 pow
= optional_power(s
);
1197 qp
= isl_qpolynomial_pow(isl_basic_map_get_dim(bmap
), pos
, pow
);
1198 } else if (tok
->type
== '[') {
1202 isl_stream_push_token(s
, tok
);
1203 div
= read_div(s
, bmap
, v
);
1204 pow
= optional_power(s
);
1205 qp
= isl_qpolynomial_div_pow(div
, pow
);
1206 } else if (tok
->type
== '-') {
1207 struct isl_qpolynomial
*qp2
;
1209 isl_token_free(tok
);
1210 qp
= isl_qpolynomial_cst(isl_basic_map_get_dim(bmap
),
1212 qp2
= read_factor(s
, bmap
, v
);
1213 qp
= isl_qpolynomial_mul(qp
, qp2
);
1215 isl_stream_error(s
, tok
, "unexpected isl_token");
1216 isl_stream_push_token(s
, tok
);
1220 if (isl_stream_eat_if_available(s
, '*') ||
1221 isl_stream_next_token_is(s
, ISL_TOKEN_IDENT
)) {
1222 struct isl_qpolynomial
*qp2
;
1224 qp2
= read_factor(s
, bmap
, v
);
1225 qp
= isl_qpolynomial_mul(qp
, qp2
);
1230 isl_qpolynomial_free(qp
);
1234 static __isl_give isl_qpolynomial
*read_term(struct isl_stream
*s
,
1235 __isl_keep isl_basic_map
*bmap
, struct vars
*v
)
1237 struct isl_token
*tok
;
1238 struct isl_qpolynomial
*qp
;
1240 qp
= read_factor(s
, bmap
, v
);
1243 tok
= isl_stream_next_token(s
);
1247 if (tok
->type
== '+') {
1248 struct isl_qpolynomial
*qp2
;
1250 isl_token_free(tok
);
1251 qp2
= read_factor(s
, bmap
, v
);
1252 qp
= isl_qpolynomial_add(qp
, qp2
);
1253 } else if (tok
->type
== '-') {
1254 struct isl_qpolynomial
*qp2
;
1256 isl_token_free(tok
);
1257 qp2
= read_factor(s
, bmap
, v
);
1258 qp
= isl_qpolynomial_sub(qp
, qp2
);
1259 } else if (tok
->type
== ISL_TOKEN_VALUE
&&
1260 isl_int_is_neg(tok
->u
.v
)) {
1261 struct isl_qpolynomial
*qp2
;
1263 qp2
= isl_qpolynomial_cst(isl_basic_map_get_dim(bmap
),
1265 isl_token_free(tok
);
1266 qp
= isl_qpolynomial_add(qp
, qp2
);
1268 isl_stream_push_token(s
, tok
);
1276 static __isl_give isl_map
*read_optional_disjuncts(struct isl_stream
*s
,
1277 __isl_take isl_basic_map
*bmap
, struct vars
*v
)
1279 struct isl_token
*tok
;
1280 struct isl_map
*map
;
1282 tok
= isl_stream_next_token(s
);
1284 isl_stream_error(s
, NULL
, "unexpected EOF");
1287 map
= isl_map_from_basic_map(isl_basic_map_copy(bmap
));
1288 if (tok
->type
== ':') {
1289 isl_token_free(tok
);
1290 map
= isl_map_intersect(map
,
1291 read_disjuncts(s
, v
, isl_basic_map_get_dim(bmap
)));
1293 isl_stream_push_token(s
, tok
);
1295 isl_basic_map_free(bmap
);
1299 isl_basic_map_free(bmap
);
1303 static struct isl_obj
obj_read_poly(struct isl_stream
*s
,
1304 __isl_take isl_basic_map
*bmap
, struct vars
*v
, int n
)
1306 struct isl_obj obj
= { isl_obj_pw_qpolynomial
, NULL
};
1307 struct isl_pw_qpolynomial
*pwqp
;
1308 struct isl_qpolynomial
*qp
;
1309 struct isl_map
*map
;
1310 struct isl_set
*set
;
1312 bmap
= isl_basic_map_reverse(bmap
);
1314 qp
= read_term(s
, bmap
, v
);
1315 map
= read_optional_disjuncts(s
, bmap
, v
);
1316 set
= isl_map_range(map
);
1318 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
1320 vars_drop(v
, v
->n
- n
);
1326 static int next_is_tuple(struct isl_stream
*s
)
1328 struct isl_token
*tok
;
1331 tok
= isl_stream_next_token(s
);
1334 if (tok
->type
== '[') {
1335 isl_stream_push_token(s
, tok
);
1338 if (tok
->type
!= ISL_TOKEN_IDENT
) {
1339 isl_stream_push_token(s
, tok
);
1343 is_tuple
= isl_stream_next_token_is(s
, '[');
1345 isl_stream_push_token(s
, tok
);
1350 static __isl_give isl_basic_map
*add_equalities(__isl_take isl_basic_map
*bmap
,
1354 unsigned total
= 1 + isl_basic_map_total_dim(bmap
);
1359 bmap
= isl_basic_map_extend_constraints(bmap
, eq
->n_row
, 0);
1361 for (i
= 0; i
< eq
->n_row
; ++i
) {
1362 k
= isl_basic_map_alloc_equality(bmap
);
1365 isl_seq_cpy(bmap
->eq
[k
], eq
->row
[i
], eq
->n_col
);
1366 isl_seq_clr(bmap
->eq
[k
] + eq
->n_col
, total
- eq
->n_col
);
1373 isl_basic_map_free(bmap
);
1377 static struct isl_obj
obj_read_body(struct isl_stream
*s
,
1378 __isl_take isl_dim
*dim
, struct vars
*v
)
1380 struct isl_map
*map
= NULL
;
1381 struct isl_token
*tok
;
1382 struct isl_obj obj
= { isl_obj_set
, NULL
};
1385 isl_basic_map
*bmap
;
1387 if (!next_is_tuple(s
)) {
1388 bmap
= isl_basic_map_alloc_dim(dim
, 0, 0, 0);
1389 return obj_read_poly(s
, bmap
, v
, n
);
1392 eq
= isl_mat_alloc(s
->ctx
, 0, 1 + n
);
1394 dim
= read_tuple(s
, dim
, isl_dim_in
, v
, &eq
);
1397 tok
= isl_stream_next_token(s
);
1398 if (tok
&& tok
->type
== ISL_TOKEN_TO
) {
1399 obj
.type
= isl_obj_map
;
1400 isl_token_free(tok
);
1401 if (!next_is_tuple(s
)) {
1402 bmap
= isl_basic_map_alloc_dim(dim
, 0, 0, 0);
1403 bmap
= add_equalities(bmap
, eq
);
1404 return obj_read_poly(s
, bmap
, v
, n
);
1406 dim
= read_tuple(s
, dim
, isl_dim_out
, v
, &eq
);
1410 dim
= isl_dim_reverse(dim
);
1412 isl_stream_push_token(s
, tok
);
1415 bmap
= isl_basic_map_alloc_dim(dim
, 0, 0, 0);
1416 bmap
= add_equalities(bmap
, eq
);
1418 map
= read_optional_disjuncts(s
, bmap
, v
);
1420 vars_drop(v
, v
->n
- n
);
1427 obj
.type
= isl_obj_none
;
1431 static struct isl_obj
to_union(isl_ctx
*ctx
, struct isl_obj obj
)
1433 if (obj
.type
== isl_obj_map
) {
1434 obj
.v
= isl_union_map_from_map(obj
.v
);
1435 obj
.type
= isl_obj_union_map
;
1436 } else if (obj
.type
== isl_obj_set
) {
1437 obj
.v
= isl_union_set_from_set(obj
.v
);
1438 obj
.type
= isl_obj_union_set
;
1439 } else if (obj
.type
== isl_obj_pw_qpolynomial
) {
1440 obj
.v
= isl_union_pw_qpolynomial_from_pw_qpolynomial(obj
.v
);
1441 obj
.type
= isl_obj_union_pw_qpolynomial
;
1442 } else if (obj
.type
== isl_obj_pw_qpolynomial_fold
) {
1443 obj
.v
= isl_union_pw_qpolynomial_fold_from_pw_qpolynomial_fold(obj
.v
);
1444 obj
.type
= isl_obj_union_pw_qpolynomial_fold
;
1446 isl_assert(ctx
, 0, goto error
);
1449 obj
.type
->free(obj
.v
);
1450 obj
.type
= isl_obj_none
;
1454 static struct isl_obj
obj_add(struct isl_ctx
*ctx
,
1455 struct isl_obj obj1
, struct isl_obj obj2
)
1457 if (obj1
.type
== isl_obj_set
&& obj2
.type
== isl_obj_union_set
)
1458 obj1
= to_union(ctx
, obj1
);
1459 if (obj1
.type
== isl_obj_union_set
&& obj2
.type
== isl_obj_set
)
1460 obj2
= to_union(ctx
, obj2
);
1461 if (obj1
.type
== isl_obj_map
&& obj2
.type
== isl_obj_union_map
)
1462 obj1
= to_union(ctx
, obj1
);
1463 if (obj1
.type
== isl_obj_union_map
&& obj2
.type
== isl_obj_map
)
1464 obj2
= to_union(ctx
, obj2
);
1465 if (obj1
.type
== isl_obj_pw_qpolynomial
&&
1466 obj2
.type
== isl_obj_union_pw_qpolynomial
)
1467 obj1
= to_union(ctx
, obj1
);
1468 if (obj1
.type
== isl_obj_union_pw_qpolynomial
&&
1469 obj2
.type
== isl_obj_pw_qpolynomial
)
1470 obj2
= to_union(ctx
, obj2
);
1471 if (obj1
.type
== isl_obj_pw_qpolynomial_fold
&&
1472 obj2
.type
== isl_obj_union_pw_qpolynomial_fold
)
1473 obj1
= to_union(ctx
, obj1
);
1474 if (obj1
.type
== isl_obj_union_pw_qpolynomial_fold
&&
1475 obj2
.type
== isl_obj_pw_qpolynomial_fold
)
1476 obj2
= to_union(ctx
, obj2
);
1477 isl_assert(ctx
, obj1
.type
== obj2
.type
, goto error
);
1478 if (obj1
.type
== isl_obj_map
&& !isl_map_has_equal_dim(obj1
.v
, obj2
.v
)) {
1479 obj1
= to_union(ctx
, obj1
);
1480 obj2
= to_union(ctx
, obj2
);
1482 if (obj1
.type
== isl_obj_set
&& !isl_set_has_equal_dim(obj1
.v
, obj2
.v
)) {
1483 obj1
= to_union(ctx
, obj1
);
1484 obj2
= to_union(ctx
, obj2
);
1486 if (obj1
.type
== isl_obj_pw_qpolynomial
&&
1487 !isl_pw_qpolynomial_has_equal_dim(obj1
.v
, obj2
.v
)) {
1488 obj1
= to_union(ctx
, obj1
);
1489 obj2
= to_union(ctx
, obj2
);
1491 if (obj1
.type
== isl_obj_pw_qpolynomial_fold
&&
1492 !isl_pw_qpolynomial_fold_has_equal_dim(obj1
.v
, obj2
.v
)) {
1493 obj1
= to_union(ctx
, obj1
);
1494 obj2
= to_union(ctx
, obj2
);
1496 obj1
.v
= obj1
.type
->add(obj1
.v
, obj2
.v
);
1499 obj1
.type
->free(obj1
.v
);
1500 obj2
.type
->free(obj2
.v
);
1501 obj1
.type
= isl_obj_none
;
1506 static struct isl_obj
obj_read(struct isl_stream
*s
, int nparam
)
1508 isl_dim
*dim
= NULL
;
1509 struct isl_token
*tok
;
1510 struct vars
*v
= NULL
;
1511 struct isl_obj obj
= { isl_obj_set
, NULL
};
1513 tok
= isl_stream_next_token(s
);
1515 isl_stream_error(s
, NULL
, "unexpected EOF");
1518 if (tok
->type
== ISL_TOKEN_VALUE
) {
1519 struct isl_map
*map
;
1520 isl_stream_push_token(s
, tok
);
1521 map
= map_read_polylib(s
, nparam
);
1524 if (isl_map_dim(map
, isl_dim_in
) > 0)
1525 obj
.type
= isl_obj_map
;
1529 v
= vars_new(s
->ctx
);
1531 isl_stream_push_token(s
, tok
);
1534 dim
= isl_dim_alloc(s
->ctx
, 0, 0, 0);
1535 if (tok
->type
== '[') {
1536 isl_stream_push_token(s
, tok
);
1537 dim
= read_tuple(s
, dim
, isl_dim_param
, v
, NULL
);
1541 isl_assert(s
->ctx
, nparam
== v
->n
, goto error
);
1542 tok
= isl_stream_next_token(s
);
1543 if (!tok
|| tok
->type
!= ISL_TOKEN_TO
) {
1544 isl_stream_error(s
, tok
, "expecting '->'");
1546 isl_stream_push_token(s
, tok
);
1549 isl_token_free(tok
);
1550 tok
= isl_stream_next_token(s
);
1551 } else if (nparam
> 0)
1552 dim
= isl_dim_add(dim
, isl_dim_param
, nparam
);
1553 if (!tok
|| tok
->type
!= '{') {
1554 isl_stream_error(s
, tok
, "expecting '{'");
1556 isl_stream_push_token(s
, tok
);
1559 isl_token_free(tok
);
1561 tok
= isl_stream_next_token(s
);
1564 else if (tok
->type
== ISL_TOKEN_IDENT
&& !strcmp(tok
->u
.s
, "Sym")) {
1565 isl_token_free(tok
);
1566 if (isl_stream_eat(s
, '='))
1568 dim
= read_tuple(s
, dim
, isl_dim_param
, v
, NULL
);
1572 isl_assert(s
->ctx
, nparam
== v
->n
, goto error
);
1573 } else if (tok
->type
== '}') {
1574 obj
.type
= isl_obj_union_set
;
1575 obj
.v
= isl_union_set_empty(isl_dim_copy(dim
));
1576 isl_token_free(tok
);
1579 isl_stream_push_token(s
, tok
);
1584 o
= obj_read_body(s
, isl_dim_copy(dim
), v
);
1585 if (o
.type
== isl_obj_none
)
1590 obj
= obj_add(s
->ctx
, obj
, o
);
1591 if (obj
.type
== isl_obj_none
)
1594 tok
= isl_stream_next_token(s
);
1595 if (!tok
|| tok
->type
!= ';')
1597 isl_token_free(tok
);
1600 if (tok
&& tok
->type
== '}') {
1601 isl_token_free(tok
);
1603 isl_stream_error(s
, tok
, "unexpected isl_token");
1605 isl_token_free(tok
);
1615 obj
.type
->free(obj
.v
);
1622 struct isl_obj
isl_stream_read_obj(struct isl_stream
*s
)
1624 return obj_read(s
, -1);
1627 __isl_give isl_map
*isl_stream_read_map(struct isl_stream
*s
, int nparam
)
1630 struct isl_map
*map
;
1632 obj
= obj_read(s
, nparam
);
1634 isl_assert(s
->ctx
, obj
.type
== isl_obj_map
||
1635 obj
.type
== isl_obj_set
, goto error
);
1639 obj
.type
->free(obj
.v
);
1643 __isl_give isl_set
*isl_stream_read_set(struct isl_stream
*s
, int nparam
)
1646 struct isl_set
*set
;
1648 obj
= obj_read(s
, nparam
);
1650 isl_assert(s
->ctx
, obj
.type
== isl_obj_set
, goto error
);
1654 obj
.type
->free(obj
.v
);
1658 static struct isl_basic_map
*basic_map_read(struct isl_stream
*s
, int nparam
)
1661 struct isl_map
*map
;
1662 struct isl_basic_map
*bmap
;
1664 obj
= obj_read(s
, nparam
);
1669 isl_assert(map
->ctx
, map
->n
<= 1, goto error
);
1672 bmap
= isl_basic_map_empty_like_map(map
);
1674 bmap
= isl_basic_map_copy(map
->p
[0]);
1684 __isl_give isl_basic_map
*isl_basic_map_read_from_file(isl_ctx
*ctx
,
1685 FILE *input
, int nparam
)
1687 struct isl_basic_map
*bmap
;
1688 struct isl_stream
*s
= isl_stream_new_file(ctx
, input
);
1691 bmap
= basic_map_read(s
, nparam
);
1696 __isl_give isl_basic_set
*isl_basic_set_read_from_file(isl_ctx
*ctx
,
1697 FILE *input
, int nparam
)
1699 struct isl_basic_map
*bmap
;
1700 bmap
= isl_basic_map_read_from_file(ctx
, input
, nparam
);
1703 isl_assert(ctx
, isl_basic_map_n_in(bmap
) == 0, goto error
);
1704 return (struct isl_basic_set
*)bmap
;
1706 isl_basic_map_free(bmap
);
1710 struct isl_basic_map
*isl_basic_map_read_from_str(struct isl_ctx
*ctx
,
1711 const char *str
, int nparam
)
1713 struct isl_basic_map
*bmap
;
1714 struct isl_stream
*s
= isl_stream_new_str(ctx
, str
);
1717 bmap
= basic_map_read(s
, nparam
);
1722 struct isl_basic_set
*isl_basic_set_read_from_str(struct isl_ctx
*ctx
,
1723 const char *str
, int nparam
)
1725 struct isl_basic_map
*bmap
;
1726 bmap
= isl_basic_map_read_from_str(ctx
, str
, nparam
);
1729 isl_assert(ctx
, isl_basic_map_n_in(bmap
) == 0, goto error
);
1730 return (struct isl_basic_set
*)bmap
;
1732 isl_basic_map_free(bmap
);
1736 __isl_give isl_map
*isl_map_read_from_file(struct isl_ctx
*ctx
,
1737 FILE *input
, int nparam
)
1739 struct isl_map
*map
;
1740 struct isl_stream
*s
= isl_stream_new_file(ctx
, input
);
1743 map
= isl_stream_read_map(s
, nparam
);
1748 __isl_give isl_map
*isl_map_read_from_str(struct isl_ctx
*ctx
,
1749 const char *str
, int nparam
)
1751 struct isl_map
*map
;
1752 struct isl_stream
*s
= isl_stream_new_str(ctx
, str
);
1755 map
= isl_stream_read_map(s
, nparam
);
1760 __isl_give isl_set
*isl_set_read_from_file(struct isl_ctx
*ctx
,
1761 FILE *input
, int nparam
)
1763 struct isl_map
*map
;
1764 map
= isl_map_read_from_file(ctx
, input
, nparam
);
1767 isl_assert(ctx
, isl_map_n_in(map
) == 0, goto error
);
1768 return (struct isl_set
*)map
;
1774 struct isl_set
*isl_set_read_from_str(struct isl_ctx
*ctx
,
1775 const char *str
, int nparam
)
1777 struct isl_map
*map
;
1778 map
= isl_map_read_from_str(ctx
, str
, nparam
);
1781 isl_assert(ctx
, isl_map_n_in(map
) == 0, goto error
);
1782 return (struct isl_set
*)map
;
1788 static char *next_line(FILE *input
, char *line
, unsigned len
)
1793 if (!(p
= fgets(line
, len
, input
)))
1795 while (isspace(*p
) && *p
!= '\n')
1797 } while (*p
== '#' || *p
== '\n');
1802 static struct isl_vec
*isl_vec_read_from_file_polylib(struct isl_ctx
*ctx
,
1805 struct isl_vec
*vec
= NULL
;
1814 isl_assert(ctx
, next_line(input
, line
, sizeof(line
)), return NULL
);
1815 isl_assert(ctx
, sscanf(line
, "%u", &size
) == 1, return NULL
);
1817 vec
= isl_vec_alloc(ctx
, size
);
1819 p
= next_line(input
, line
, sizeof(line
));
1820 isl_assert(ctx
, p
, goto error
);
1822 for (j
= 0; j
< size
; ++j
) {
1823 n
= sscanf(p
, "%s%n", val
, &offset
);
1824 isl_assert(ctx
, n
!= 0, goto error
);
1825 isl_int_read(vec
->el
[j
], val
);
1835 struct isl_vec
*isl_vec_read_from_file(struct isl_ctx
*ctx
,
1836 FILE *input
, unsigned input_format
)
1838 if (input_format
== ISL_FORMAT_POLYLIB
)
1839 return isl_vec_read_from_file_polylib(ctx
, input
);
1841 isl_assert(ctx
, 0, return NULL
);
1844 __isl_give isl_pw_qpolynomial
*isl_stream_read_pw_qpolynomial(
1845 struct isl_stream
*s
)
1848 struct isl_pw_qpolynomial
*pwqp
;
1850 obj
= obj_read(s
, -1);
1852 isl_assert(s
->ctx
, obj
.type
== isl_obj_pw_qpolynomial
,
1857 obj
.type
->free(obj
.v
);