1 #include "isl_sample.h"
2 #include "isl_sample_piplib.h"
6 #include "isl_map_private.h"
7 #include "isl_equalities.h"
9 #include "isl_basis_reduction.h"
11 static struct isl_vec
*empty_sample(struct isl_basic_set
*bset
)
15 vec
= isl_vec_alloc(bset
->ctx
, 0);
16 isl_basic_set_free(bset
);
20 /* Construct a zero sample of the same dimension as bset.
21 * As a special case, if bset is zero-dimensional, this
22 * function creates a zero-dimensional sample point.
24 static struct isl_vec
*zero_sample(struct isl_basic_set
*bset
)
27 struct isl_vec
*sample
;
29 dim
= isl_basic_set_total_dim(bset
);
30 sample
= isl_vec_alloc(bset
->ctx
, 1 + dim
);
32 isl_int_set_si(sample
->el
[0], 1);
33 isl_seq_clr(sample
->el
+ 1, dim
);
35 isl_basic_set_free(bset
);
39 static struct isl_vec
*interval_sample(struct isl_basic_set
*bset
)
43 struct isl_vec
*sample
;
45 bset
= isl_basic_set_simplify(bset
);
48 if (isl_basic_set_fast_is_empty(bset
))
49 return empty_sample(bset
);
50 if (bset
->n_eq
== 0 && bset
->n_ineq
== 0)
51 return zero_sample(bset
);
53 sample
= isl_vec_alloc(bset
->ctx
, 2);
54 isl_int_set_si(sample
->block
.data
[0], 1);
57 isl_assert(bset
->ctx
, bset
->n_eq
== 1, goto error
);
58 isl_assert(bset
->ctx
, bset
->n_ineq
== 0, goto error
);
59 if (isl_int_is_one(bset
->eq
[0][1]))
60 isl_int_neg(sample
->el
[1], bset
->eq
[0][0]);
62 isl_assert(bset
->ctx
, isl_int_is_negone(bset
->eq
[0][1]),
64 isl_int_set(sample
->el
[1], bset
->eq
[0][0]);
66 isl_basic_set_free(bset
);
71 if (isl_int_is_one(bset
->ineq
[0][1]))
72 isl_int_neg(sample
->block
.data
[1], bset
->ineq
[0][0]);
74 isl_int_set(sample
->block
.data
[1], bset
->ineq
[0][0]);
75 for (i
= 1; i
< bset
->n_ineq
; ++i
) {
76 isl_seq_inner_product(sample
->block
.data
,
77 bset
->ineq
[i
], 2, &t
);
78 if (isl_int_is_neg(t
))
82 if (i
< bset
->n_ineq
) {
84 return empty_sample(bset
);
87 isl_basic_set_free(bset
);
90 isl_basic_set_free(bset
);
95 static struct isl_mat
*independent_bounds(struct isl_basic_set
*bset
)
98 struct isl_mat
*dirs
= NULL
;
99 struct isl_mat
*bounds
= NULL
;
105 dim
= isl_basic_set_n_dim(bset
);
106 bounds
= isl_mat_alloc(bset
->ctx
, 1+dim
, 1+dim
);
110 isl_int_set_si(bounds
->row
[0][0], 1);
111 isl_seq_clr(bounds
->row
[0]+1, dim
);
114 if (bset
->n_ineq
== 0)
117 dirs
= isl_mat_alloc(bset
->ctx
, dim
, dim
);
119 isl_mat_free(bounds
);
122 isl_seq_cpy(dirs
->row
[0], bset
->ineq
[0]+1, dirs
->n_col
);
123 isl_seq_cpy(bounds
->row
[1], bset
->ineq
[0], bounds
->n_col
);
124 for (j
= 1, n
= 1; n
< dim
&& j
< bset
->n_ineq
; ++j
) {
127 isl_seq_cpy(dirs
->row
[n
], bset
->ineq
[j
]+1, dirs
->n_col
);
129 pos
= isl_seq_first_non_zero(dirs
->row
[n
], dirs
->n_col
);
132 for (i
= 0; i
< n
; ++i
) {
134 pos_i
= isl_seq_first_non_zero(dirs
->row
[i
], dirs
->n_col
);
139 isl_seq_elim(dirs
->row
[n
], dirs
->row
[i
], pos
,
141 pos
= isl_seq_first_non_zero(dirs
->row
[n
], dirs
->n_col
);
149 isl_int
*t
= dirs
->row
[n
];
150 for (k
= n
; k
> i
; --k
)
151 dirs
->row
[k
] = dirs
->row
[k
-1];
155 isl_seq_cpy(bounds
->row
[n
], bset
->ineq
[j
], bounds
->n_col
);
162 static void swap_inequality(struct isl_basic_set
*bset
, int a
, int b
)
164 isl_int
*t
= bset
->ineq
[a
];
165 bset
->ineq
[a
] = bset
->ineq
[b
];
169 /* Skew into positive orthant and project out lineality space.
171 * We perform a unimodular transformation that turns a selected
172 * maximal set of linearly independent bounds into constraints
173 * on the first dimensions that impose that these first dimensions
174 * are non-negative. In particular, the constraint matrix is lower
175 * triangular with positive entries on the diagonal and negative
177 * If "bset" has a lineality space then these constraints (and therefore
178 * all constraints in bset) only involve the first dimensions.
179 * The remaining dimensions then do not appear in any constraints and
180 * we can select any value for them, say zero. We therefore project
181 * out this final dimensions and plug in the value zero later. This
182 * is accomplished by simply dropping the final columns of
183 * the unimodular transformation.
185 static struct isl_basic_set
*isl_basic_set_skew_to_positive_orthant(
186 struct isl_basic_set
*bset
, struct isl_mat
**T
)
188 struct isl_mat
*U
= NULL
;
189 struct isl_mat
*bounds
= NULL
;
191 unsigned old_dim
, new_dim
;
197 isl_assert(bset
->ctx
, isl_basic_set_n_param(bset
) == 0, goto error
);
198 isl_assert(bset
->ctx
, bset
->n_div
== 0, goto error
);
199 isl_assert(bset
->ctx
, bset
->n_eq
== 0, goto error
);
201 old_dim
= isl_basic_set_n_dim(bset
);
202 /* Try to move (multiples of) unit rows up. */
203 for (i
= 0, j
= 0; i
< bset
->n_ineq
; ++i
) {
204 int pos
= isl_seq_first_non_zero(bset
->ineq
[i
]+1, old_dim
);
207 if (isl_seq_first_non_zero(bset
->ineq
[i
]+1+pos
+1,
211 swap_inequality(bset
, i
, j
);
214 bounds
= independent_bounds(bset
);
217 new_dim
= bounds
->n_row
- 1;
218 bounds
= isl_mat_left_hermite(bounds
, 1, &U
, NULL
);
221 U
= isl_mat_drop_cols(U
, 1 + new_dim
, old_dim
- new_dim
);
222 bset
= isl_basic_set_preimage(bset
, isl_mat_copy(U
));
226 isl_mat_free(bounds
);
229 isl_mat_free(bounds
);
231 isl_basic_set_free(bset
);
235 /* Find a sample integer point, if any, in bset, which is known
236 * to have equalities. If bset contains no integer points, then
237 * return a zero-length vector.
238 * We simply remove the known equalities, compute a sample
239 * in the resulting bset, using the specified recurse function,
240 * and then transform the sample back to the original space.
242 static struct isl_vec
*sample_eq(struct isl_basic_set
*bset
,
243 struct isl_vec
*(*recurse
)(struct isl_basic_set
*))
246 struct isl_vec
*sample
;
251 bset
= isl_basic_set_remove_equalities(bset
, &T
, NULL
);
252 sample
= recurse(bset
);
253 if (!sample
|| sample
->size
== 0)
256 sample
= isl_mat_vec_product(T
, sample
);
260 /* Return a matrix containing the equalities of the tableau
261 * in constraint form. The tableau is assumed to have
262 * an associated bset that has been kept up-to-date.
264 static struct isl_mat
*tab_equalities(struct isl_tab
*tab
)
269 struct isl_basic_set
*bset
;
274 isl_assert(tab
->mat
->ctx
, tab
->bset
, return NULL
);
277 n_eq
= tab
->n_var
- tab
->n_col
+ tab
->n_dead
;
278 if (tab
->empty
|| n_eq
== 0)
279 return isl_mat_alloc(tab
->mat
->ctx
, 0, tab
->n_var
);
280 if (n_eq
== tab
->n_var
)
281 return isl_mat_identity(tab
->mat
->ctx
, tab
->n_var
);
283 eq
= isl_mat_alloc(tab
->mat
->ctx
, n_eq
, tab
->n_var
);
286 for (i
= 0, j
= 0; i
< tab
->n_con
; ++i
) {
287 if (tab
->con
[i
].is_row
)
289 if (tab
->con
[i
].index
>= 0 && tab
->con
[i
].index
>= tab
->n_dead
)
292 isl_seq_cpy(eq
->row
[j
], bset
->eq
[i
] + 1, tab
->n_var
);
294 isl_seq_cpy(eq
->row
[j
],
295 bset
->ineq
[i
- bset
->n_eq
] + 1, tab
->n_var
);
298 isl_assert(bset
->ctx
, j
== n_eq
, goto error
);
305 /* Compute and return an initial basis for the bounded tableau "tab".
307 * If the tableau is either full-dimensional or zero-dimensional,
308 * the we simply return an identity matrix.
309 * Otherwise, we construct a basis whose first directions correspond
312 static struct isl_mat
*initial_basis(struct isl_tab
*tab
)
318 n_eq
= tab
->n_var
- tab
->n_col
+ tab
->n_dead
;
319 if (tab
->empty
|| n_eq
== 0 || n_eq
== tab
->n_var
)
320 return isl_mat_identity(tab
->mat
->ctx
, 1 + tab
->n_var
);
322 eq
= tab_equalities(tab
);
323 eq
= isl_mat_left_hermite(eq
, 0, NULL
, &Q
);
328 Q
= isl_mat_lin_to_aff(Q
);
332 /* Given a tableau representing a set, find and return
333 * an integer point in the set, if there is any.
335 * We perform a depth first search
336 * for an integer point, by scanning all possible values in the range
337 * attained by a basis vector, where an initial basis may have been set
338 * by the calling function. Otherwise an initial basis that exploits
339 * the equalities in the tableau is created.
340 * tab->n_zero is currently ignored and is clobbered by this function.
342 * The tableau is allowed to have unbounded direction, but then
343 * the calling function needs to set an initial basis, with the
344 * unbounded directions last and with tab->n_unbounded set
345 * to the number of unbounded directions.
346 * Furthermore, the calling functions needs to add shifted copies
347 * of all constraints involving unbounded directions to ensure
348 * that any feasible rational value in these directions can be rounded
349 * up to yield a feasible integer value.
350 * In particular, let B define the given basis x' = B x
351 * and let T be the inverse of B, i.e., X = T x'.
352 * Let a x + c >= 0 be a constraint of the set represented by the tableau,
353 * or a T x' + c >= 0 in terms of the given basis. Assume that
354 * the bounded directions have an integer value, then we can safely
355 * round up the values for the unbounded directions if we make sure
356 * that x' not only satisfies the original constraint, but also
357 * the constraint "a T x' + c + s >= 0" with s the sum of all
358 * negative values in the last n_unbounded entries of "a T".
359 * The calling function therefore needs to add the constraint
360 * a x + c + s >= 0. The current function then scans the first
361 * directions for an integer value and once those have been found,
362 * it can compute "T ceil(B x)" to yield an integer point in the set.
363 * Note that during the search, the first rows of B may be changed
364 * by a basis reduction, but the last n_unbounded rows of B remain
365 * unaltered and are also not mixed into the first rows.
367 * The search is implemented iteratively. "level" identifies the current
368 * basis vector. "init" is true if we want the first value at the current
369 * level and false if we want the next value.
371 * The initial basis is the identity matrix. If the range in some direction
372 * contains more than one integer value, we perform basis reduction based
373 * on the value of ctx->gbr
374 * - ISL_GBR_NEVER: never perform basis reduction
375 * - ISL_GBR_ONCE: only perform basis reduction the first
376 * time such a range is encountered
377 * - ISL_GBR_ALWAYS: always perform basis reduction when
378 * such a range is encountered
380 * When ctx->gbr is set to ISL_GBR_ALWAYS, then we allow the basis
381 * reduction computation to return early. That is, as soon as it
382 * finds a reasonable first direction.
384 struct isl_vec
*isl_tab_sample(struct isl_tab
*tab
)
389 struct isl_vec
*sample
;
392 enum isl_lp_result res
;
396 struct isl_tab_undo
**snap
;
401 return isl_vec_alloc(tab
->mat
->ctx
, 0);
404 tab
->basis
= initial_basis(tab
);
407 isl_assert(tab
->mat
->ctx
, tab
->basis
->n_row
== tab
->n_var
+ 1,
409 isl_assert(tab
->mat
->ctx
, tab
->basis
->n_col
== tab
->n_var
+ 1,
416 if (tab
->n_unbounded
== tab
->n_var
) {
417 sample
= isl_tab_get_sample_value(tab
);
418 sample
= isl_mat_vec_product(isl_mat_copy(tab
->basis
), sample
);
419 sample
= isl_vec_ceil(sample
);
420 sample
= isl_mat_vec_inverse_product(isl_mat_copy(tab
->basis
),
425 if (isl_tab_extend_cons(tab
, dim
+ 1) < 0)
428 min
= isl_vec_alloc(ctx
, dim
);
429 max
= isl_vec_alloc(ctx
, dim
);
430 snap
= isl_alloc_array(ctx
, struct isl_tab_undo
*, dim
);
432 if (!min
|| !max
|| !snap
)
442 res
= isl_tab_min(tab
, tab
->basis
->row
[1 + level
],
443 ctx
->one
, &min
->el
[level
], NULL
, 0);
444 if (res
== isl_lp_empty
)
446 isl_assert(ctx
, res
!= isl_lp_unbounded
, goto error
);
447 if (res
== isl_lp_error
)
449 if (!empty
&& isl_tab_sample_is_integer(tab
))
451 isl_seq_neg(tab
->basis
->row
[1 + level
] + 1,
452 tab
->basis
->row
[1 + level
] + 1, dim
);
453 res
= isl_tab_min(tab
, tab
->basis
->row
[1 + level
],
454 ctx
->one
, &max
->el
[level
], NULL
, 0);
455 isl_seq_neg(tab
->basis
->row
[1 + level
] + 1,
456 tab
->basis
->row
[1 + level
] + 1, dim
);
457 isl_int_neg(max
->el
[level
], max
->el
[level
]);
458 if (res
== isl_lp_empty
)
460 isl_assert(ctx
, res
!= isl_lp_unbounded
, goto error
);
461 if (res
== isl_lp_error
)
463 if (!empty
&& isl_tab_sample_is_integer(tab
))
465 if (!empty
&& !reduced
&& ctx
->gbr
!= ISL_GBR_NEVER
&&
466 isl_int_lt(min
->el
[level
], max
->el
[level
])) {
467 unsigned gbr_only_first
;
468 if (ctx
->gbr
== ISL_GBR_ONCE
)
469 ctx
->gbr
= ISL_GBR_NEVER
;
471 gbr_only_first
= ctx
->gbr_only_first
;
472 ctx
->gbr_only_first
=
473 ctx
->gbr
== ISL_GBR_ALWAYS
;
474 tab
= isl_tab_compute_reduced_basis(tab
);
475 ctx
->gbr_only_first
= gbr_only_first
;
476 if (!tab
|| !tab
->basis
)
482 snap
[level
] = isl_tab_snap(tab
);
484 isl_int_add_ui(min
->el
[level
], min
->el
[level
], 1);
486 if (empty
|| isl_int_gt(min
->el
[level
], max
->el
[level
])) {
490 isl_tab_rollback(tab
, snap
[level
]);
493 isl_int_neg(tab
->basis
->row
[1 + level
][0], min
->el
[level
]);
494 tab
= isl_tab_add_valid_eq(tab
, tab
->basis
->row
[1 + level
]);
495 isl_int_set_si(tab
->basis
->row
[1 + level
][0], 0);
496 if (level
+ tab
->n_unbounded
< dim
- 1) {
505 sample
= isl_tab_get_sample_value(tab
);
508 if (tab
->n_unbounded
&& !isl_int_is_one(sample
->el
[0])) {
509 sample
= isl_mat_vec_product(isl_mat_copy(tab
->basis
),
511 sample
= isl_vec_ceil(sample
);
512 sample
= isl_mat_vec_inverse_product(
513 isl_mat_copy(tab
->basis
), sample
);
516 sample
= isl_vec_alloc(ctx
, 0);
531 /* Given a basic set that is known to be bounded, find and return
532 * an integer point in the basic set, if there is any.
534 * After handling some trivial cases, we construct a tableau
535 * and then use isl_tab_sample to find a sample, passing it
536 * the identity matrix as initial basis.
538 static struct isl_vec
*sample_bounded(struct isl_basic_set
*bset
)
542 struct isl_vec
*sample
;
543 struct isl_tab
*tab
= NULL
;
548 if (isl_basic_set_fast_is_empty(bset
))
549 return empty_sample(bset
);
551 dim
= isl_basic_set_total_dim(bset
);
553 return zero_sample(bset
);
555 return interval_sample(bset
);
557 return sample_eq(bset
, sample_bounded
);
561 tab
= isl_tab_from_basic_set(bset
);
562 if (!ISL_F_ISSET(bset
, ISL_BASIC_SET_NO_IMPLICIT
))
563 tab
= isl_tab_detect_implicit_equalities(tab
);
567 tab
->bset
= isl_basic_set_copy(bset
);
569 sample
= isl_tab_sample(tab
);
573 if (sample
->size
> 0) {
574 isl_vec_free(bset
->sample
);
575 bset
->sample
= isl_vec_copy(sample
);
578 isl_basic_set_free(bset
);
582 isl_basic_set_free(bset
);
587 /* Given a basic set "bset" and a value "sample" for the first coordinates
588 * of bset, plug in these values and drop the corresponding coordinates.
590 * We do this by computing the preimage of the transformation
596 * where [1 s] is the sample value and I is the identity matrix of the
597 * appropriate dimension.
599 static struct isl_basic_set
*plug_in(struct isl_basic_set
*bset
,
600 struct isl_vec
*sample
)
606 if (!bset
|| !sample
)
609 total
= isl_basic_set_total_dim(bset
);
610 T
= isl_mat_alloc(bset
->ctx
, 1 + total
, 1 + total
- (sample
->size
- 1));
614 for (i
= 0; i
< sample
->size
; ++i
) {
615 isl_int_set(T
->row
[i
][0], sample
->el
[i
]);
616 isl_seq_clr(T
->row
[i
] + 1, T
->n_col
- 1);
618 for (i
= 0; i
< T
->n_col
- 1; ++i
) {
619 isl_seq_clr(T
->row
[sample
->size
+ i
], T
->n_col
);
620 isl_int_set_si(T
->row
[sample
->size
+ i
][1 + i
], 1);
622 isl_vec_free(sample
);
624 bset
= isl_basic_set_preimage(bset
, T
);
627 isl_basic_set_free(bset
);
628 isl_vec_free(sample
);
632 /* Given a basic set "bset", return any (possibly non-integer) point
635 static struct isl_vec
*rational_sample(struct isl_basic_set
*bset
)
638 struct isl_vec
*sample
;
643 tab
= isl_tab_from_basic_set(bset
);
644 sample
= isl_tab_get_sample_value(tab
);
647 isl_basic_set_free(bset
);
652 /* Given a linear cone "cone" and a rational point "vec",
653 * construct a polyhedron with shifted copies of the constraints in "cone",
654 * i.e., a polyhedron with "cone" as its recession cone, such that each
655 * point x in this polyhedron is such that the unit box positioned at x
656 * lies entirely inside the affine cone 'vec + cone'.
657 * Any rational point in this polyhedron may therefore be rounded up
658 * to yield an integer point that lies inside said affine cone.
660 * Denote the constraints of cone by "<a_i, x> >= 0" and the rational
661 * point "vec" by v/d.
662 * Let b_i = <a_i, v>. Then the affine cone 'vec + cone' is given
663 * by <a_i, x> - b/d >= 0.
664 * The polyhedron <a_i, x> - ceil{b/d} >= 0 is a subset of this affine cone.
665 * We prefer this polyhedron over the actual affine cone because it doesn't
666 * require a scaling of the constraints.
667 * If each of the vertices of the unit cube positioned at x lies inside
668 * this polyhedron, then the whole unit cube at x lies inside the affine cone.
669 * We therefore impose that x' = x + \sum e_i, for any selection of unit
670 * vectors lies inside the polyhedron, i.e.,
672 * <a_i, x'> - ceil{b/d} = <a_i, x> + sum a_i - ceil{b/d} >= 0
674 * The most stringent of these constraints is the one that selects
675 * all negative a_i, so the polyhedron we are looking for has constraints
677 * <a_i, x> + sum_{a_i < 0} a_i - ceil{b/d} >= 0
679 * Note that if cone were known to have only non-negative rays
680 * (which can be accomplished by a unimodular transformation),
681 * then we would only have to check the points x' = x + e_i
682 * and we only have to add the smallest negative a_i (if any)
683 * instead of the sum of all negative a_i.
685 static struct isl_basic_set
*shift_cone(struct isl_basic_set
*cone
,
691 struct isl_basic_set
*shift
= NULL
;
696 isl_assert(cone
->ctx
, cone
->n_eq
== 0, goto error
);
698 total
= isl_basic_set_total_dim(cone
);
700 shift
= isl_basic_set_alloc_dim(isl_basic_set_get_dim(cone
),
703 for (i
= 0; i
< cone
->n_ineq
; ++i
) {
704 k
= isl_basic_set_alloc_inequality(shift
);
707 isl_seq_cpy(shift
->ineq
[k
] + 1, cone
->ineq
[i
] + 1, total
);
708 isl_seq_inner_product(shift
->ineq
[k
] + 1, vec
->el
+ 1, total
,
710 isl_int_cdiv_q(shift
->ineq
[k
][0],
711 shift
->ineq
[k
][0], vec
->el
[0]);
712 isl_int_neg(shift
->ineq
[k
][0], shift
->ineq
[k
][0]);
713 for (j
= 0; j
< total
; ++j
) {
714 if (isl_int_is_nonneg(shift
->ineq
[k
][1 + j
]))
716 isl_int_add(shift
->ineq
[k
][0],
717 shift
->ineq
[k
][0], shift
->ineq
[k
][1 + j
]);
721 isl_basic_set_free(cone
);
724 return isl_basic_set_finalize(shift
);
726 isl_basic_set_free(shift
);
727 isl_basic_set_free(cone
);
732 /* Given a rational point vec in a (transformed) basic set,
733 * such that cone is the recession cone of the original basic set,
734 * "round up" the rational point to an integer point.
736 * We first check if the rational point just happens to be integer.
737 * If not, we transform the cone in the same way as the basic set,
738 * pick a point x in this cone shifted to the rational point such that
739 * the whole unit cube at x is also inside this affine cone.
740 * Then we simply round up the coordinates of x and return the
741 * resulting integer point.
743 static struct isl_vec
*round_up_in_cone(struct isl_vec
*vec
,
744 struct isl_basic_set
*cone
, struct isl_mat
*U
)
748 if (!vec
|| !cone
|| !U
)
751 isl_assert(vec
->ctx
, vec
->size
!= 0, goto error
);
752 if (isl_int_is_one(vec
->el
[0])) {
754 isl_basic_set_free(cone
);
758 total
= isl_basic_set_total_dim(cone
);
759 cone
= isl_basic_set_preimage(cone
, U
);
760 cone
= isl_basic_set_remove_dims(cone
, 0, total
- (vec
->size
- 1));
762 cone
= shift_cone(cone
, vec
);
764 vec
= rational_sample(cone
);
765 vec
= isl_vec_ceil(vec
);
770 isl_basic_set_free(cone
);
774 /* Concatenate two integer vectors, i.e., two vectors with denominator
775 * (stored in element 0) equal to 1.
777 static struct isl_vec
*vec_concat(struct isl_vec
*vec1
, struct isl_vec
*vec2
)
783 isl_assert(vec1
->ctx
, vec1
->size
> 0, goto error
);
784 isl_assert(vec2
->ctx
, vec2
->size
> 0, goto error
);
785 isl_assert(vec1
->ctx
, isl_int_is_one(vec1
->el
[0]), goto error
);
786 isl_assert(vec2
->ctx
, isl_int_is_one(vec2
->el
[0]), goto error
);
788 vec
= isl_vec_alloc(vec1
->ctx
, vec1
->size
+ vec2
->size
- 1);
792 isl_seq_cpy(vec
->el
, vec1
->el
, vec1
->size
);
793 isl_seq_cpy(vec
->el
+ vec1
->size
, vec2
->el
+ 1, vec2
->size
- 1);
805 /* Drop all constraints in bset that involve any of the dimensions
806 * first to first+n-1.
808 static struct isl_basic_set
*drop_constraints_involving
809 (struct isl_basic_set
*bset
, unsigned first
, unsigned n
)
816 bset
= isl_basic_set_cow(bset
);
818 for (i
= bset
->n_ineq
- 1; i
>= 0; --i
) {
819 if (isl_seq_first_non_zero(bset
->ineq
[i
] + 1 + first
, n
) == -1)
821 isl_basic_set_drop_inequality(bset
, i
);
827 /* Give a basic set "bset" with recession cone "cone", compute and
828 * return an integer point in bset, if any.
830 * If the recession cone is full-dimensional, then we know that
831 * bset contains an infinite number of integer points and it is
832 * fairly easy to pick one of them.
833 * If the recession cone is not full-dimensional, then we first
834 * transform bset such that the bounded directions appear as
835 * the first dimensions of the transformed basic set.
836 * We do this by using a unimodular transformation that transforms
837 * the equalities in the recession cone to equalities on the first
840 * The transformed set is then projected onto its bounded dimensions.
841 * Note that to compute this projection, we can simply drop all constraints
842 * involving any of the unbounded dimensions since these constraints
843 * cannot be combined to produce a constraint on the bounded dimensions.
844 * To see this, assume that there is such a combination of constraints
845 * that produces a constraint on the bounded dimensions. This means
846 * that some combination of the unbounded dimensions has both an upper
847 * bound and a lower bound in terms of the bounded dimensions, but then
848 * this combination would be a bounded direction too and would have been
849 * transformed into a bounded dimensions.
851 * We then compute a sample value in the bounded dimensions.
852 * If no such value can be found, then the original set did not contain
853 * any integer points and we are done.
854 * Otherwise, we plug in the value we found in the bounded dimensions,
855 * project out these bounded dimensions and end up with a set with
856 * a full-dimensional recession cone.
857 * A sample point in this set is computed by "rounding up" any
858 * rational point in the set.
860 * The sample points in the bounded and unbounded dimensions are
861 * then combined into a single sample point and transformed back
862 * to the original space.
864 __isl_give isl_vec
*isl_basic_set_sample_with_cone(
865 __isl_take isl_basic_set
*bset
, __isl_take isl_basic_set
*cone
)
869 struct isl_mat
*M
, *U
;
870 struct isl_vec
*sample
;
871 struct isl_vec
*cone_sample
;
873 struct isl_basic_set
*bounded
;
879 total
= isl_basic_set_total_dim(cone
);
880 cone_dim
= total
- cone
->n_eq
;
882 M
= isl_mat_sub_alloc(bset
->ctx
, cone
->eq
, 0, cone
->n_eq
, 1, total
);
883 M
= isl_mat_left_hermite(M
, 0, &U
, NULL
);
888 U
= isl_mat_lin_to_aff(U
);
889 bset
= isl_basic_set_preimage(bset
, isl_mat_copy(U
));
891 bounded
= isl_basic_set_copy(bset
);
892 bounded
= drop_constraints_involving(bounded
, total
- cone_dim
, cone_dim
);
893 bounded
= isl_basic_set_drop_dims(bounded
, total
- cone_dim
, cone_dim
);
894 sample
= sample_bounded(bounded
);
895 if (!sample
|| sample
->size
== 0) {
896 isl_basic_set_free(bset
);
897 isl_basic_set_free(cone
);
901 bset
= plug_in(bset
, isl_vec_copy(sample
));
902 cone_sample
= rational_sample(bset
);
903 cone_sample
= round_up_in_cone(cone_sample
, cone
, isl_mat_copy(U
));
904 sample
= vec_concat(sample
, cone_sample
);
905 sample
= isl_mat_vec_product(U
, sample
);
908 isl_basic_set_free(cone
);
909 isl_basic_set_free(bset
);
913 /* Compute and return a sample point in bset using generalized basis
914 * reduction. We first check if the input set has a non-trivial
915 * recession cone. If so, we perform some extra preprocessing in
916 * sample_with_cone. Otherwise, we directly perform generalized basis
919 static struct isl_vec
*gbr_sample(struct isl_basic_set
*bset
)
922 struct isl_basic_set
*cone
;
924 dim
= isl_basic_set_total_dim(bset
);
926 cone
= isl_basic_set_recession_cone(isl_basic_set_copy(bset
));
928 if (cone
->n_eq
< dim
)
929 return isl_basic_set_sample_with_cone(bset
, cone
);
931 isl_basic_set_free(cone
);
932 return sample_bounded(bset
);
935 static struct isl_vec
*pip_sample(struct isl_basic_set
*bset
)
939 struct isl_vec
*sample
;
941 bset
= isl_basic_set_skew_to_positive_orthant(bset
, &T
);
946 sample
= isl_pip_basic_set_sample(bset
);
948 if (sample
&& sample
->size
!= 0)
949 sample
= isl_mat_vec_product(T
, sample
);
956 static struct isl_vec
*basic_set_sample(struct isl_basic_set
*bset
, int bounded
)
964 if (isl_basic_set_fast_is_empty(bset
))
965 return empty_sample(bset
);
967 dim
= isl_basic_set_n_dim(bset
);
968 isl_assert(ctx
, isl_basic_set_n_param(bset
) == 0, goto error
);
969 isl_assert(ctx
, bset
->n_div
== 0, goto error
);
971 if (bset
->sample
&& bset
->sample
->size
== 1 + dim
) {
972 int contains
= isl_basic_set_contains(bset
, bset
->sample
);
976 struct isl_vec
*sample
= isl_vec_copy(bset
->sample
);
977 isl_basic_set_free(bset
);
981 isl_vec_free(bset
->sample
);
985 return sample_eq(bset
, bounded
? isl_basic_set_sample_bounded
986 : isl_basic_set_sample_vec
);
988 return zero_sample(bset
);
990 return interval_sample(bset
);
992 switch (bset
->ctx
->ilp_solver
) {
994 return pip_sample(bset
);
996 return bounded
? sample_bounded(bset
) : gbr_sample(bset
);
998 isl_assert(bset
->ctx
, 0, );
1000 isl_basic_set_free(bset
);
1004 __isl_give isl_vec
*isl_basic_set_sample_vec(__isl_take isl_basic_set
*bset
)
1006 return basic_set_sample(bset
, 0);
1009 /* Compute an integer sample in "bset", where the caller guarantees
1010 * that "bset" is bounded.
1012 struct isl_vec
*isl_basic_set_sample_bounded(struct isl_basic_set
*bset
)
1014 return basic_set_sample(bset
, 1);
1017 __isl_give isl_basic_set
*isl_basic_set_from_vec(__isl_take isl_vec
*vec
)
1021 struct isl_basic_set
*bset
= NULL
;
1022 struct isl_ctx
*ctx
;
1028 isl_assert(ctx
, vec
->size
!= 0, goto error
);
1030 bset
= isl_basic_set_alloc(ctx
, 0, vec
->size
- 1, 0, vec
->size
- 1, 0);
1033 dim
= isl_basic_set_n_dim(bset
);
1034 for (i
= dim
- 1; i
>= 0; --i
) {
1035 k
= isl_basic_set_alloc_equality(bset
);
1038 isl_seq_clr(bset
->eq
[k
], 1 + dim
);
1039 isl_int_neg(bset
->eq
[k
][0], vec
->el
[1 + i
]);
1040 isl_int_set(bset
->eq
[k
][1 + i
], vec
->el
[0]);
1046 isl_basic_set_free(bset
);
1051 __isl_give isl_basic_map
*isl_basic_map_sample(__isl_take isl_basic_map
*bmap
)
1053 struct isl_basic_set
*bset
;
1054 struct isl_vec
*sample_vec
;
1056 bset
= isl_basic_map_underlying_set(isl_basic_map_copy(bmap
));
1057 sample_vec
= isl_basic_set_sample_vec(bset
);
1060 if (sample_vec
->size
== 0) {
1061 struct isl_basic_map
*sample
;
1062 sample
= isl_basic_map_empty_like(bmap
);
1063 isl_vec_free(sample_vec
);
1064 isl_basic_map_free(bmap
);
1067 bset
= isl_basic_set_from_vec(sample_vec
);
1068 return isl_basic_map_overlying_set(bset
, bmap
);
1070 isl_basic_map_free(bmap
);
1074 __isl_give isl_basic_map
*isl_map_sample(__isl_take isl_map
*map
)
1077 isl_basic_map
*sample
= NULL
;
1082 for (i
= 0; i
< map
->n
; ++i
) {
1083 sample
= isl_basic_map_sample(isl_basic_map_copy(map
->p
[i
]));
1086 if (!ISL_F_ISSET(sample
, ISL_BASIC_MAP_EMPTY
))
1088 isl_basic_map_free(sample
);
1091 sample
= isl_basic_map_empty_like_map(map
);
1099 __isl_give isl_basic_set
*isl_set_sample(__isl_take isl_set
*set
)
1101 return (isl_basic_set
*) isl_map_sample((isl_map
*)set
);