2 * Copyright 2010 INRIA Saclay
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
7 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
11 #include <isl_map_private.h>
12 #include <isl_morph.h>
14 #include <isl_mat_private.h>
15 #include <isl_space_private.h>
16 #include <isl_equalities.h>
18 __isl_give isl_morph
*isl_morph_alloc(
19 __isl_take isl_basic_set
*dom
, __isl_take isl_basic_set
*ran
,
20 __isl_take isl_mat
*map
, __isl_take isl_mat
*inv
)
24 if (!dom
|| !ran
|| !map
|| !inv
)
27 morph
= isl_alloc_type(dom
->ctx
, struct isl_morph
);
39 isl_basic_set_free(dom
);
40 isl_basic_set_free(ran
);
46 __isl_give isl_morph
*isl_morph_copy(__isl_keep isl_morph
*morph
)
55 __isl_give isl_morph
*isl_morph_dup(__isl_keep isl_morph
*morph
)
60 return isl_morph_alloc(isl_basic_set_copy(morph
->dom
),
61 isl_basic_set_copy(morph
->ran
),
62 isl_mat_copy(morph
->map
), isl_mat_copy(morph
->inv
));
65 __isl_give isl_morph
*isl_morph_cow(__isl_take isl_morph
*morph
)
73 return isl_morph_dup(morph
);
76 void isl_morph_free(__isl_take isl_morph
*morph
)
84 isl_basic_set_free(morph
->dom
);
85 isl_basic_set_free(morph
->ran
);
86 isl_mat_free(morph
->map
);
87 isl_mat_free(morph
->inv
);
91 __isl_give isl_space
*isl_morph_get_ran_space(__isl_keep isl_morph
*morph
)
96 return isl_space_copy(morph
->ran
->dim
);
99 unsigned isl_morph_dom_dim(__isl_keep isl_morph
*morph
, enum isl_dim_type type
)
104 return isl_basic_set_dim(morph
->dom
, type
);
107 unsigned isl_morph_ran_dim(__isl_keep isl_morph
*morph
, enum isl_dim_type type
)
112 return isl_basic_set_dim(morph
->ran
, type
);
115 __isl_give isl_morph
*isl_morph_remove_dom_dims(__isl_take isl_morph
*morph
,
116 enum isl_dim_type type
, unsigned first
, unsigned n
)
123 morph
= isl_morph_cow(morph
);
127 dom_offset
= 1 + isl_space_offset(morph
->dom
->dim
, type
);
129 morph
->dom
= isl_basic_set_remove_dims(morph
->dom
, type
, first
, n
);
131 morph
->map
= isl_mat_drop_cols(morph
->map
, dom_offset
+ first
, n
);
133 morph
->inv
= isl_mat_drop_rows(morph
->inv
, dom_offset
+ first
, n
);
135 if (morph
->dom
&& morph
->ran
&& morph
->map
&& morph
->inv
)
138 isl_morph_free(morph
);
142 __isl_give isl_morph
*isl_morph_remove_ran_dims(__isl_take isl_morph
*morph
,
143 enum isl_dim_type type
, unsigned first
, unsigned n
)
150 morph
= isl_morph_cow(morph
);
154 ran_offset
= 1 + isl_space_offset(morph
->ran
->dim
, type
);
156 morph
->ran
= isl_basic_set_remove_dims(morph
->ran
, type
, first
, n
);
158 morph
->map
= isl_mat_drop_rows(morph
->map
, ran_offset
+ first
, n
);
160 morph
->inv
= isl_mat_drop_cols(morph
->inv
, ran_offset
+ first
, n
);
162 if (morph
->dom
&& morph
->ran
&& morph
->map
&& morph
->inv
)
165 isl_morph_free(morph
);
169 /* Project domain of morph onto its parameter domain.
171 __isl_give isl_morph
*isl_morph_dom_params(__isl_take isl_morph
*morph
)
177 n
= isl_basic_set_dim(morph
->dom
, isl_dim_set
);
178 morph
= isl_morph_remove_dom_dims(morph
, isl_dim_set
, 0, n
);
181 morph
->dom
= isl_basic_set_params(morph
->dom
);
185 isl_morph_free(morph
);
189 /* Project range of morph onto its parameter domain.
191 __isl_give isl_morph
*isl_morph_ran_params(__isl_take isl_morph
*morph
)
197 n
= isl_basic_set_dim(morph
->ran
, isl_dim_set
);
198 morph
= isl_morph_remove_ran_dims(morph
, isl_dim_set
, 0, n
);
201 morph
->ran
= isl_basic_set_params(morph
->ran
);
205 isl_morph_free(morph
);
209 void isl_morph_print_internal(__isl_take isl_morph
*morph
, FILE *out
)
214 isl_basic_set_print(morph
->dom
, out
, 0, "", "", ISL_FORMAT_ISL
);
215 isl_basic_set_print(morph
->ran
, out
, 0, "", "", ISL_FORMAT_ISL
);
216 isl_mat_print_internal(morph
->map
, out
, 4);
217 isl_mat_print_internal(morph
->inv
, out
, 4);
220 __isl_give isl_morph
*isl_morph_identity(__isl_keep isl_basic_set
*bset
)
223 isl_basic_set
*universe
;
229 total
= isl_basic_set_total_dim(bset
);
230 id
= isl_mat_identity(bset
->ctx
, 1 + total
);
231 universe
= isl_basic_set_universe(isl_space_copy(bset
->dim
));
233 return isl_morph_alloc(universe
, isl_basic_set_copy(universe
),
234 id
, isl_mat_copy(id
));
237 /* Create a(n identity) morphism between empty sets of the same dimension
240 __isl_give isl_morph
*isl_morph_empty(__isl_keep isl_basic_set
*bset
)
243 isl_basic_set
*empty
;
249 total
= isl_basic_set_total_dim(bset
);
250 id
= isl_mat_identity(bset
->ctx
, 1 + total
);
251 empty
= isl_basic_set_empty(isl_space_copy(bset
->dim
));
253 return isl_morph_alloc(empty
, isl_basic_set_copy(empty
),
254 id
, isl_mat_copy(id
));
257 /* Given a matrix that maps a (possibly) parametric domain to
258 * a parametric domain, add in rows that map the "nparam" parameters onto
261 static __isl_give isl_mat
*insert_parameter_rows(__isl_take isl_mat
*mat
,
271 mat
= isl_mat_insert_rows(mat
, 1, nparam
);
275 for (i
= 0; i
< nparam
; ++i
) {
276 isl_seq_clr(mat
->row
[1 + i
], mat
->n_col
);
277 isl_int_set(mat
->row
[1 + i
][1 + i
], mat
->row
[0][0]);
283 /* Construct a basic set described by the "n" equalities of "bset" starting
286 static __isl_give isl_basic_set
*copy_equalities(__isl_keep isl_basic_set
*bset
,
287 unsigned first
, unsigned n
)
293 isl_assert(bset
->ctx
, bset
->n_div
== 0, return NULL
);
295 total
= isl_basic_set_total_dim(bset
);
296 eq
= isl_basic_set_alloc_space(isl_space_copy(bset
->dim
), 0, n
, 0);
299 for (i
= 0; i
< n
; ++i
) {
300 k
= isl_basic_set_alloc_equality(eq
);
303 isl_seq_cpy(eq
->eq
[k
], bset
->eq
[first
+ k
], 1 + total
);
308 isl_basic_set_free(eq
);
312 /* Given a basic set, exploit the equalties in the a basic set to construct
313 * a morphishm that maps the basic set to a lower-dimensional space.
314 * Specifically, the morphism reduces the number of dimensions of type "type".
316 * This function is a slight generalization of isl_mat_variable_compression
317 * in that it allows the input to be parametric and that it allows for the
318 * compression of either parameters or set variables.
320 * We first select the equalities of interest, that is those that involve
321 * variables of type "type" and no later variables.
322 * Denote those equalities as
326 * where C(p) depends on the parameters if type == isl_dim_set and
327 * is a constant if type == isl_dim_param.
329 * First compute the (left) Hermite normal form of M,
331 * M [U1 U2] = M U = H = [H1 0]
333 * M = H Q = [H1 0] [Q1]
336 * with U, Q unimodular, Q = U^{-1} (and H lower triangular).
337 * Define the transformed variables as
339 * x = [U1 U2] [ x1' ] = [U1 U2] [Q1] x
342 * The equalities then become
344 * -C(p) + H1 x1' = 0 or x1' = H1^{-1} C(p) = C'(p)
346 * If the denominator of the constant term does not divide the
347 * the common denominator of the parametric terms, then every
348 * integer point is mapped to a non-integer point and then the original set has no
349 * integer solutions (since the x' are a unimodular transformation
350 * of the x). In this case, an empty morphism is returned.
351 * Otherwise, the transformation is given by
353 * x = U1 H1^{-1} C(p) + U2 x2'
355 * The inverse transformation is simply
359 * Both matrices are extended to map the full original space to the full
362 __isl_give isl_morph
*isl_basic_set_variable_compression(
363 __isl_keep isl_basic_set
*bset
, enum isl_dim_type type
)
371 isl_mat
*H
, *U
, *Q
, *C
= NULL
, *H1
, *U1
, *U2
;
372 isl_basic_set
*dom
, *ran
;
377 if (isl_basic_set_plain_is_empty(bset
))
378 return isl_morph_empty(bset
);
380 isl_assert(bset
->ctx
, bset
->n_div
== 0, return NULL
);
382 otype
= 1 + isl_space_offset(bset
->dim
, type
);
383 ntype
= isl_basic_set_dim(bset
, type
);
384 orest
= otype
+ ntype
;
385 nrest
= isl_basic_set_total_dim(bset
) - (orest
- 1);
387 for (f_eq
= 0; f_eq
< bset
->n_eq
; ++f_eq
)
388 if (isl_seq_first_non_zero(bset
->eq
[f_eq
] + orest
, nrest
) == -1)
390 for (n_eq
= 0; f_eq
+ n_eq
< bset
->n_eq
; ++n_eq
)
391 if (isl_seq_first_non_zero(bset
->eq
[f_eq
+ n_eq
] + otype
, ntype
) == -1)
394 return isl_morph_identity(bset
);
396 H
= isl_mat_sub_alloc6(bset
->ctx
, bset
->eq
, f_eq
, n_eq
, otype
, ntype
);
397 H
= isl_mat_left_hermite(H
, 0, &U
, &Q
);
400 Q
= isl_mat_drop_rows(Q
, 0, n_eq
);
401 Q
= isl_mat_diagonal(isl_mat_identity(bset
->ctx
, otype
), Q
);
402 Q
= isl_mat_diagonal(Q
, isl_mat_identity(bset
->ctx
, nrest
));
403 C
= isl_mat_alloc(bset
->ctx
, 1 + n_eq
, otype
);
406 isl_int_set_si(C
->row
[0][0], 1);
407 isl_seq_clr(C
->row
[0] + 1, otype
- 1);
408 isl_mat_sub_neg(C
->ctx
, C
->row
+ 1, bset
->eq
+ f_eq
, n_eq
, 0, 0, otype
);
409 H1
= isl_mat_sub_alloc(H
, 0, H
->n_row
, 0, H
->n_row
);
410 H1
= isl_mat_lin_to_aff(H1
);
411 C
= isl_mat_inverse_product(H1
, C
);
416 if (!isl_int_is_one(C
->row
[0][0])) {
421 for (i
= 0; i
< n_eq
; ++i
) {
422 isl_seq_gcd(C
->row
[1 + i
] + 1, otype
- 1, &g
);
423 isl_int_gcd(g
, g
, C
->row
[0][0]);
424 if (!isl_int_is_divisible_by(C
->row
[1 + i
][0], g
))
433 return isl_morph_empty(bset
);
436 C
= isl_mat_normalize(C
);
439 U1
= isl_mat_sub_alloc(U
, 0, U
->n_row
, 0, n_eq
);
440 U1
= isl_mat_lin_to_aff(U1
);
441 U2
= isl_mat_sub_alloc(U
, 0, U
->n_row
, n_eq
, U
->n_row
- n_eq
);
442 U2
= isl_mat_lin_to_aff(U2
);
445 C
= isl_mat_product(U1
, C
);
446 C
= isl_mat_aff_direct_sum(C
, U2
);
447 C
= insert_parameter_rows(C
, otype
- 1);
448 C
= isl_mat_diagonal(C
, isl_mat_identity(bset
->ctx
, nrest
));
450 dim
= isl_space_copy(bset
->dim
);
451 dim
= isl_space_drop_dims(dim
, type
, 0, ntype
);
452 dim
= isl_space_add_dims(dim
, type
, ntype
- n_eq
);
453 ran
= isl_basic_set_universe(dim
);
454 dom
= copy_equalities(bset
, f_eq
, n_eq
);
456 return isl_morph_alloc(dom
, ran
, Q
, C
);
465 /* Construct a parameter compression for "bset".
466 * We basically just call isl_mat_parameter_compression with the right input
467 * and then extend the resulting matrix to include the variables.
469 * Let the equalities be given as
473 * and let [H 0] be the Hermite Normal Form of A, then
477 * needs to be integer, so we impose that each row is divisible by
480 __isl_give isl_morph
*isl_basic_set_parameter_compression(
481 __isl_keep isl_basic_set
*bset
)
489 isl_basic_set
*dom
, *ran
;
494 if (isl_basic_set_plain_is_empty(bset
))
495 return isl_morph_empty(bset
);
497 return isl_morph_identity(bset
);
499 isl_assert(bset
->ctx
, bset
->n_div
== 0, return NULL
);
502 nparam
= isl_basic_set_dim(bset
, isl_dim_param
);
503 nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
505 isl_assert(bset
->ctx
, n_eq
<= nvar
, return NULL
);
507 d
= isl_vec_alloc(bset
->ctx
, n_eq
);
508 B
= isl_mat_sub_alloc6(bset
->ctx
, bset
->eq
, 0, n_eq
, 0, 1 + nparam
);
509 H
= isl_mat_sub_alloc6(bset
->ctx
, bset
->eq
, 0, n_eq
, 1 + nparam
, nvar
);
510 H
= isl_mat_left_hermite(H
, 0, NULL
, NULL
);
511 H
= isl_mat_drop_cols(H
, n_eq
, nvar
- n_eq
);
512 H
= isl_mat_lin_to_aff(H
);
513 H
= isl_mat_right_inverse(H
);
516 isl_seq_set(d
->el
, H
->row
[0][0], d
->size
);
517 H
= isl_mat_drop_rows(H
, 0, 1);
518 H
= isl_mat_drop_cols(H
, 0, 1);
519 B
= isl_mat_product(H
, B
);
520 inv
= isl_mat_parameter_compression(B
, d
);
521 inv
= isl_mat_diagonal(inv
, isl_mat_identity(bset
->ctx
, nvar
));
522 map
= isl_mat_right_inverse(isl_mat_copy(inv
));
524 dom
= isl_basic_set_universe(isl_space_copy(bset
->dim
));
525 ran
= isl_basic_set_universe(isl_space_copy(bset
->dim
));
527 return isl_morph_alloc(dom
, ran
, map
, inv
);
535 /* Add stride constraints to "bset" based on the inverse mapping
536 * that was plugged in. In particular, if morph maps x' to x,
537 * the the constraints of the original input
541 * have been rewritten to
545 * However, this substitution may loose information on the integrality of x',
546 * so we need to impose that
550 * is integral. If inv = B/d, this means that we need to impose that
556 * exists alpha in Z^m: B x = d alpha
559 static __isl_give isl_basic_set
*add_strides(__isl_take isl_basic_set
*bset
,
560 __isl_keep isl_morph
*morph
)
565 if (isl_int_is_one(morph
->inv
->row
[0][0]))
570 for (i
= 0; 1 + i
< morph
->inv
->n_row
; ++i
) {
571 isl_seq_gcd(morph
->inv
->row
[1 + i
], morph
->inv
->n_col
, &gcd
);
572 if (isl_int_is_divisible_by(gcd
, morph
->inv
->row
[0][0]))
574 div
= isl_basic_set_alloc_div(bset
);
577 k
= isl_basic_set_alloc_equality(bset
);
580 isl_seq_cpy(bset
->eq
[k
], morph
->inv
->row
[1 + i
],
582 isl_seq_clr(bset
->eq
[k
] + morph
->inv
->n_col
, bset
->n_div
);
583 isl_int_set(bset
->eq
[k
][morph
->inv
->n_col
+ div
],
584 morph
->inv
->row
[0][0]);
592 isl_basic_set_free(bset
);
596 /* Apply the morphism to the basic set.
597 * We basically just compute the preimage of "bset" under the inverse mapping
598 * in morph, add in stride constraints and intersect with the range
601 __isl_give isl_basic_set
*isl_morph_basic_set(__isl_take isl_morph
*morph
,
602 __isl_take isl_basic_set
*bset
)
604 isl_basic_set
*res
= NULL
;
612 isl_assert(bset
->ctx
, isl_space_is_equal(bset
->dim
, morph
->dom
->dim
),
615 max_stride
= morph
->inv
->n_row
- 1;
616 if (isl_int_is_one(morph
->inv
->row
[0][0]))
618 res
= isl_basic_set_alloc_space(isl_space_copy(morph
->ran
->dim
),
619 bset
->n_div
+ max_stride
, bset
->n_eq
+ max_stride
, bset
->n_ineq
);
621 for (i
= 0; i
< bset
->n_div
; ++i
)
622 if (isl_basic_set_alloc_div(res
) < 0)
625 mat
= isl_mat_sub_alloc6(bset
->ctx
, bset
->eq
, 0, bset
->n_eq
,
626 0, morph
->inv
->n_row
);
627 mat
= isl_mat_product(mat
, isl_mat_copy(morph
->inv
));
630 for (i
= 0; i
< bset
->n_eq
; ++i
) {
631 k
= isl_basic_set_alloc_equality(res
);
634 isl_seq_cpy(res
->eq
[k
], mat
->row
[i
], mat
->n_col
);
635 isl_seq_scale(res
->eq
[k
] + mat
->n_col
, bset
->eq
[i
] + mat
->n_col
,
636 morph
->inv
->row
[0][0], bset
->n_div
);
640 mat
= isl_mat_sub_alloc6(bset
->ctx
, bset
->ineq
, 0, bset
->n_ineq
,
641 0, morph
->inv
->n_row
);
642 mat
= isl_mat_product(mat
, isl_mat_copy(morph
->inv
));
645 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
646 k
= isl_basic_set_alloc_inequality(res
);
649 isl_seq_cpy(res
->ineq
[k
], mat
->row
[i
], mat
->n_col
);
650 isl_seq_scale(res
->ineq
[k
] + mat
->n_col
,
651 bset
->ineq
[i
] + mat
->n_col
,
652 morph
->inv
->row
[0][0], bset
->n_div
);
656 mat
= isl_mat_sub_alloc6(bset
->ctx
, bset
->div
, 0, bset
->n_div
,
657 1, morph
->inv
->n_row
);
658 mat
= isl_mat_product(mat
, isl_mat_copy(morph
->inv
));
661 for (i
= 0; i
< bset
->n_div
; ++i
) {
662 isl_int_mul(res
->div
[i
][0],
663 morph
->inv
->row
[0][0], bset
->div
[i
][0]);
664 isl_seq_cpy(res
->div
[i
] + 1, mat
->row
[i
], mat
->n_col
);
665 isl_seq_scale(res
->div
[i
] + 1 + mat
->n_col
,
666 bset
->div
[i
] + 1 + mat
->n_col
,
667 morph
->inv
->row
[0][0], bset
->n_div
);
671 res
= add_strides(res
, morph
);
673 if (isl_basic_set_is_rational(bset
))
674 res
= isl_basic_set_set_rational(res
);
676 res
= isl_basic_set_simplify(res
);
677 res
= isl_basic_set_finalize(res
);
679 res
= isl_basic_set_intersect(res
, isl_basic_set_copy(morph
->ran
));
681 isl_morph_free(morph
);
682 isl_basic_set_free(bset
);
686 isl_morph_free(morph
);
687 isl_basic_set_free(bset
);
688 isl_basic_set_free(res
);
692 /* Apply the morphism to the set.
694 __isl_give isl_set
*isl_morph_set(__isl_take isl_morph
*morph
,
695 __isl_take isl_set
*set
)
702 isl_assert(set
->ctx
, isl_space_is_equal(set
->dim
, morph
->dom
->dim
), goto error
);
704 set
= isl_set_cow(set
);
708 isl_space_free(set
->dim
);
709 set
->dim
= isl_space_copy(morph
->ran
->dim
);
713 for (i
= 0; i
< set
->n
; ++i
) {
714 set
->p
[i
] = isl_morph_basic_set(isl_morph_copy(morph
), set
->p
[i
]);
719 isl_morph_free(morph
);
721 ISL_F_CLR(set
, ISL_SET_NORMALIZED
);
726 isl_morph_free(morph
);
730 /* Construct a morphism that first does morph2 and then morph1.
732 __isl_give isl_morph
*isl_morph_compose(__isl_take isl_morph
*morph1
,
733 __isl_take isl_morph
*morph2
)
736 isl_basic_set
*dom
, *ran
;
738 if (!morph1
|| !morph2
)
741 map
= isl_mat_product(isl_mat_copy(morph1
->map
), isl_mat_copy(morph2
->map
));
742 inv
= isl_mat_product(isl_mat_copy(morph2
->inv
), isl_mat_copy(morph1
->inv
));
743 dom
= isl_morph_basic_set(isl_morph_inverse(isl_morph_copy(morph2
)),
744 isl_basic_set_copy(morph1
->dom
));
745 dom
= isl_basic_set_intersect(dom
, isl_basic_set_copy(morph2
->dom
));
746 ran
= isl_morph_basic_set(isl_morph_copy(morph1
),
747 isl_basic_set_copy(morph2
->ran
));
748 ran
= isl_basic_set_intersect(ran
, isl_basic_set_copy(morph1
->ran
));
750 isl_morph_free(morph1
);
751 isl_morph_free(morph2
);
753 return isl_morph_alloc(dom
, ran
, map
, inv
);
755 isl_morph_free(morph1
);
756 isl_morph_free(morph2
);
760 __isl_give isl_morph
*isl_morph_inverse(__isl_take isl_morph
*morph
)
765 morph
= isl_morph_cow(morph
);
770 morph
->dom
= morph
->ran
;
774 morph
->map
= morph
->inv
;
780 __isl_give isl_morph
*isl_basic_set_full_compression(
781 __isl_keep isl_basic_set
*bset
)
783 isl_morph
*morph
, *morph2
;
785 bset
= isl_basic_set_copy(bset
);
787 morph
= isl_basic_set_variable_compression(bset
, isl_dim_param
);
788 bset
= isl_morph_basic_set(isl_morph_copy(morph
), bset
);
790 morph2
= isl_basic_set_parameter_compression(bset
);
791 bset
= isl_morph_basic_set(isl_morph_copy(morph2
), bset
);
793 morph
= isl_morph_compose(morph2
, morph
);
795 morph2
= isl_basic_set_variable_compression(bset
, isl_dim_set
);
796 isl_basic_set_free(bset
);
798 morph
= isl_morph_compose(morph2
, morph
);
803 __isl_give isl_vec
*isl_morph_vec(__isl_take isl_morph
*morph
,
804 __isl_take isl_vec
*vec
)
809 vec
= isl_mat_vec_product(isl_mat_copy(morph
->map
), vec
);
811 isl_morph_free(morph
);
814 isl_morph_free(morph
);