6 #define partition STL_PARTITION
10 #include <NTL/vec_ZZ.h>
11 #include <NTL/mat_ZZ.h>
12 #include <isl_set_polylib.h>
13 #include <barvinok/barvinok.h>
14 #include <barvinok/evalue.h>
15 #include <barvinok/options.h>
16 #include <barvinok/util.h>
17 #include "conversion.h"
18 #include "decomposer.h"
19 #include "lattice_point.h"
20 #include "reduce_domain.h"
23 #include "evalue_util.h"
24 #include "remove_equalities.h"
28 #include "param_util.h"
30 #undef CS /* for Solaris 10 */
41 #define ALLOC(type) (type*)malloc(sizeof(type))
42 #define ALLOCN(type,n) (type*)malloc((n) * sizeof(type))
44 static int type_offset(enode
*p
)
46 return p
->type
== fractional
? 1 :
47 p
->type
== flooring
? 1 : 0;
50 void compute_evalue(evalue
*e
, Value
*val
, Value
*res
)
52 double d
= compute_evalue(e
, val
);
57 value_set_double(*res
, d
);
60 struct indicator_term
{
62 int pos
; /* number of rational vertex */
63 int n
; /* number of cone associated to given rational vertex */
67 indicator_term(unsigned dim
, int pos
) {
69 vertex
= new evalue
* [dim
];
74 indicator_term(unsigned dim
, int pos
, int n
) {
75 den
.SetDims(dim
, dim
);
76 vertex
= new evalue
* [dim
];
80 indicator_term(const indicator_term
& src
) {
85 unsigned dim
= den
.NumCols();
86 vertex
= new evalue
* [dim
];
87 for (int i
= 0; i
< dim
; ++i
) {
88 vertex
[i
] = ALLOC(evalue
);
89 value_init(vertex
[i
]->d
);
90 evalue_copy(vertex
[i
], src
.vertex
[i
]);
93 void swap(indicator_term
*other
) {
95 tmp
= sign
; sign
= other
->sign
; other
->sign
= tmp
;
96 tmp
= pos
; pos
= other
->pos
; other
->pos
= tmp
;
97 tmp
= n
; n
= other
->n
; other
->n
= tmp
;
98 mat_ZZ tmp_den
= den
; den
= other
->den
; other
->den
= tmp_den
;
99 unsigned dim
= den
.NumCols();
100 for (int i
= 0; i
< dim
; ++i
) {
101 evalue
*tmp
= vertex
[i
];
102 vertex
[i
] = other
->vertex
[i
];
103 other
->vertex
[i
] = tmp
;
107 unsigned dim
= den
.NumCols();
108 for (int i
= 0; i
< dim
; ++i
)
109 evalue_free(vertex
[i
]);
112 void print(ostream
& os
, char **p
) const;
113 void substitute(Matrix
*T
);
115 void substitute(evalue
*fract
, evalue
*val
);
116 void substitute(int pos
, evalue
*val
);
117 void reduce_in_domain(Polyhedron
*D
);
118 bool is_opposite(const indicator_term
*neg
) const;
119 vec_ZZ
eval(Value
*val
) const {
121 unsigned dim
= den
.NumCols();
125 for (int i
= 0; i
< dim
; ++i
) {
126 compute_evalue(vertex
[i
], val
, &tmp
);
134 static int evalue_rational_cmp(const evalue
*e1
, const evalue
*e2
)
142 assert(value_notzero_p(e1
->d
));
143 assert(value_notzero_p(e2
->d
));
144 value_multiply(m
, e1
->x
.n
, e2
->d
);
145 value_multiply(m2
, e2
->x
.n
, e1
->d
);
148 else if (value_gt(m
, m2
))
158 static int evalue_cmp(const evalue
*e1
, const evalue
*e2
)
160 if (value_notzero_p(e1
->d
)) {
161 if (value_zero_p(e2
->d
))
163 return evalue_rational_cmp(e1
, e2
);
165 if (value_notzero_p(e2
->d
))
167 if (e1
->x
.p
->type
!= e2
->x
.p
->type
)
168 return e1
->x
.p
->type
- e2
->x
.p
->type
;
169 if (e1
->x
.p
->size
!= e2
->x
.p
->size
)
170 return e1
->x
.p
->size
- e2
->x
.p
->size
;
171 if (e1
->x
.p
->pos
!= e2
->x
.p
->pos
)
172 return e1
->x
.p
->pos
- e2
->x
.p
->pos
;
173 assert(e1
->x
.p
->type
== polynomial
||
174 e1
->x
.p
->type
== fractional
||
175 e1
->x
.p
->type
== flooring
);
176 for (int i
= 0; i
< e1
->x
.p
->size
; ++i
) {
177 int s
= evalue_cmp(&e1
->x
.p
->arr
[i
], &e2
->x
.p
->arr
[i
]);
184 void evalue_length(evalue
*e
, int len
[2])
189 while (value_zero_p(e
->d
)) {
190 assert(e
->x
.p
->type
== polynomial
||
191 e
->x
.p
->type
== fractional
||
192 e
->x
.p
->type
== flooring
);
193 if (e
->x
.p
->type
== polynomial
)
197 int offset
= type_offset(e
->x
.p
);
198 assert(e
->x
.p
->size
== offset
+2);
199 e
= &e
->x
.p
->arr
[offset
];
203 static bool it_smaller(const indicator_term
* it1
, const indicator_term
* it2
)
207 int len1
[2], len2
[2];
208 unsigned dim
= it1
->den
.NumCols();
209 for (int i
= 0; i
< dim
; ++i
) {
210 evalue_length(it1
->vertex
[i
], len1
);
211 evalue_length(it2
->vertex
[i
], len2
);
212 if (len1
[0] != len2
[0])
213 return len1
[0] < len2
[0];
214 if (len1
[1] != len2
[1])
215 return len1
[1] < len2
[1];
217 if (it1
->pos
!= it2
->pos
)
218 return it1
->pos
< it2
->pos
;
219 if (it1
->n
!= it2
->n
)
220 return it1
->n
< it2
->n
;
221 int s
= lex_cmp(it1
->den
, it2
->den
);
224 for (int i
= 0; i
< dim
; ++i
) {
225 s
= evalue_cmp(it1
->vertex
[i
], it2
->vertex
[i
]);
229 assert(it1
->sign
!= 0);
230 assert(it2
->sign
!= 0);
231 if (it1
->sign
!= it2
->sign
)
232 return it1
->sign
> 0;
237 static const int requires_resort
;
238 bool operator()(const indicator_term
* it1
, const indicator_term
* it2
) const {
239 return it_smaller(it1
, it2
);
242 const int smaller_it::requires_resort
= 1;
244 struct smaller_it_p
{
245 static const int requires_resort
;
246 bool operator()(const indicator_term
* it1
, const indicator_term
* it2
) const {
250 const int smaller_it_p::requires_resort
= 0;
252 /* Returns true if this and neg are opposite using the knowledge
253 * that they have the same numerator.
254 * In particular, we check that the signs are different and that
255 * the denominator is the same.
257 bool indicator_term::is_opposite(const indicator_term
*neg
) const
259 if (sign
+ neg
->sign
!= 0)
266 void indicator_term::reduce_in_domain(Polyhedron
*D
)
268 for (int k
= 0; k
< den
.NumCols(); ++k
) {
269 reduce_evalue_in_domain(vertex
[k
], D
);
270 if (evalue_range_reduction_in_domain(vertex
[k
], D
))
271 reduce_evalue(vertex
[k
]);
275 void indicator_term::print(ostream
& os
, char **p
) const
277 unsigned dim
= den
.NumCols();
278 unsigned factors
= den
.NumRows();
286 for (int i
= 0; i
< dim
; ++i
) {
289 evalue_print(os
, vertex
[i
], p
);
292 for (int i
= 0; i
< factors
; ++i
) {
293 os
<< " + t" << i
<< "*[";
294 for (int j
= 0; j
< dim
; ++j
) {
301 os
<< " ((" << pos
<< ", " << n
<< ", " << (void*)this << "))";
304 /* Perform the substitution specified by T on the variables.
305 * T has dimension (newdim+nparam+1) x (olddim + nparam + 1).
306 * The substitution is performed as in gen_fun::substitute
308 void indicator_term::substitute(Matrix
*T
)
310 unsigned dim
= den
.NumCols();
311 unsigned nparam
= T
->NbColumns
- dim
- 1;
312 unsigned newdim
= T
->NbRows
- nparam
- 1;
315 matrix2zz(T
, trans
, newdim
, dim
);
316 trans
= transpose(trans
);
318 newvertex
= new evalue
* [newdim
];
321 v
.SetLength(nparam
+1);
324 value_init(factor
.d
);
325 value_set_si(factor
.d
, 1);
326 value_init(factor
.x
.n
);
327 for (int i
= 0; i
< newdim
; ++i
) {
328 values2zz(T
->p
[i
]+dim
, v
, nparam
+1);
329 newvertex
[i
] = multi_monom(v
);
331 for (int j
= 0; j
< dim
; ++j
) {
332 if (value_zero_p(T
->p
[i
][j
]))
336 evalue_copy(&term
, vertex
[j
]);
337 value_assign(factor
.x
.n
, T
->p
[i
][j
]);
338 emul(&factor
, &term
);
339 eadd(&term
, newvertex
[i
]);
340 free_evalue_refs(&term
);
343 free_evalue_refs(&factor
);
344 for (int i
= 0; i
< dim
; ++i
)
345 evalue_free(vertex
[i
]);
350 static void evalue_add_constant(evalue
*e
, ZZ v
)
355 /* go down to constant term */
356 while (value_zero_p(e
->d
))
357 e
= &e
->x
.p
->arr
[type_offset(e
->x
.p
)];
360 value_multiply(tmp
, tmp
, e
->d
);
361 value_addto(e
->x
.n
, e
->x
.n
, tmp
);
366 /* Make all powers in denominator lexico-positive */
367 void indicator_term::normalize()
370 extra_vertex
.SetLength(den
.NumCols());
371 for (int r
= 0; r
< den
.NumRows(); ++r
) {
372 for (int k
= 0; k
< den
.NumCols(); ++k
) {
379 extra_vertex
+= den
[r
];
383 for (int k
= 0; k
< extra_vertex
.length(); ++k
)
384 if (extra_vertex
[k
] != 0)
385 evalue_add_constant(vertex
[k
], extra_vertex
[k
]);
388 static void substitute(evalue
*e
, evalue
*fract
, evalue
*val
)
392 for (t
= e
; value_zero_p(t
->d
); t
= &t
->x
.p
->arr
[type_offset(t
->x
.p
)]) {
393 if (t
->x
.p
->type
== fractional
&& eequal(&t
->x
.p
->arr
[0], fract
))
396 if (value_notzero_p(t
->d
))
399 free_evalue_refs(&t
->x
.p
->arr
[0]);
400 evalue
*term
= &t
->x
.p
->arr
[2];
407 free_evalue_refs(term
);
413 void indicator_term::substitute(evalue
*fract
, evalue
*val
)
415 unsigned dim
= den
.NumCols();
416 for (int i
= 0; i
< dim
; ++i
) {
417 ::substitute(vertex
[i
], fract
, val
);
421 static void substitute(evalue
*e
, int pos
, evalue
*val
)
425 for (t
= e
; value_zero_p(t
->d
); t
= &t
->x
.p
->arr
[type_offset(t
->x
.p
)]) {
426 if (t
->x
.p
->type
== polynomial
&& t
->x
.p
->pos
== pos
)
429 if (value_notzero_p(t
->d
))
432 evalue
*term
= &t
->x
.p
->arr
[1];
439 free_evalue_refs(term
);
445 void indicator_term::substitute(int pos
, evalue
*val
)
447 unsigned dim
= den
.NumCols();
448 for (int i
= 0; i
< dim
; ++i
) {
449 ::substitute(vertex
[i
], pos
, val
);
453 struct indicator_constructor
: public signed_cone_consumer
,
454 public vertex_decomposer
{
456 vector
<indicator_term
*> *terms
;
457 Matrix
*T
; /* Transformation to original space */
462 indicator_constructor(Polyhedron
*P
, unsigned dim
, Param_Polyhedron
*PP
,
464 vertex_decomposer(PP
, *this), T(T
), nbV(PP
->nbV
) {
465 vertex
.SetLength(dim
);
466 terms
= new vector
<indicator_term
*>[PP
->nbV
];
468 ~indicator_constructor() {
469 for (int i
= 0; i
< nbV
; ++i
)
470 for (int j
= 0; j
< terms
[i
].size(); ++j
)
474 void print(ostream
& os
, char **p
);
476 virtual void handle(const signed_cone
& sc
, barvinok_options
*options
);
477 void decompose_at_vertex(Param_Vertices
*V
, int _i
,
478 barvinok_options
*options
) {
481 vertex_decomposer::decompose_at_vertex(V
, _i
, options
);
485 void indicator_constructor::handle(const signed_cone
& sc
, barvinok_options
*options
)
488 unsigned dim
= vertex
.length();
490 assert(sc
.rays
.NumRows() == dim
);
492 indicator_term
*term
= new indicator_term(dim
, pos
, n
++);
493 term
->sign
= sc
.sign
;
494 terms
[vert
].push_back(term
);
496 lattice_point(V
, sc
.rays
, vertex
, term
->vertex
, options
);
499 for (int r
= 0; r
< dim
; ++r
) {
500 for (int j
= 0; j
< dim
; ++j
) {
501 if (term
->den
[r
][j
] == 0)
503 if (term
->den
[r
][j
] > 0)
505 term
->sign
= -term
->sign
;
506 term
->den
[r
] = -term
->den
[r
];
507 vertex
+= term
->den
[r
];
512 for (int i
= 0; i
< dim
; ++i
) {
513 if (!term
->vertex
[i
]) {
514 term
->vertex
[i
] = ALLOC(evalue
);
515 value_init(term
->vertex
[i
]->d
);
516 value_init(term
->vertex
[i
]->x
.n
);
517 zz2value(vertex
[i
], term
->vertex
[i
]->x
.n
);
518 value_set_si(term
->vertex
[i
]->d
, 1);
523 evalue_add_constant(term
->vertex
[i
], vertex
[i
]);
531 lex_order_rows(term
->den
);
534 void indicator_constructor::print(ostream
& os
, char **p
)
536 for (int i
= 0; i
< PP
->nbV
; ++i
)
537 for (int j
= 0; j
< terms
[i
].size(); ++j
) {
538 os
<< "i: " << i
<< ", j: " << j
<< endl
;
539 terms
[i
][j
]->print(os
, p
);
544 struct order_cache_el
{
546 order_cache_el
copy() const {
548 for (int i
= 0; i
< e
.size(); ++i
) {
549 evalue
*c
= new evalue
;
551 evalue_copy(c
, e
[i
]);
557 for (int i
= 0; i
< e
.size(); ++i
) {
558 free_evalue_refs(e
[i
]);
565 evalue_set_si(&mone
, -1, 1);
566 for (int i
= 0; i
< e
.size(); ++i
)
568 free_evalue_refs(&mone
);
570 void print(ostream
& os
, char **p
);
573 void order_cache_el::print(ostream
& os
, char **p
)
576 for (int i
= 0; i
< e
.size(); ++i
) {
579 evalue_print(os
, e
[i
], p
);
585 vector
<order_cache_el
> lt
;
586 vector
<order_cache_el
> le
;
587 vector
<order_cache_el
> unknown
;
589 void clear_transients() {
590 for (int i
= 0; i
< le
.size(); ++i
)
592 for (int i
= 0; i
< unknown
.size(); ++i
)
599 for (int i
= 0; i
< lt
.size(); ++i
)
603 void add(order_cache_el
& cache_el
, order_sign sign
);
604 order_sign
check_lt(vector
<order_cache_el
>* list
,
605 const indicator_term
*a
, const indicator_term
*b
,
606 order_cache_el
& cache_el
);
607 order_sign
check_lt(const indicator_term
*a
, const indicator_term
*b
,
608 order_cache_el
& cache_el
);
609 order_sign
check_direct(const indicator_term
*a
, const indicator_term
*b
,
610 order_cache_el
& cache_el
);
611 order_sign
check(const indicator_term
*a
, const indicator_term
*b
,
612 order_cache_el
& cache_el
);
613 void copy(const order_cache
& cache
);
614 void print(ostream
& os
, char **p
);
617 void order_cache::copy(const order_cache
& cache
)
619 for (int i
= 0; i
< cache
.lt
.size(); ++i
) {
620 order_cache_el n
= cache
.lt
[i
].copy();
625 void order_cache::add(order_cache_el
& cache_el
, order_sign sign
)
627 if (sign
== order_lt
) {
628 lt
.push_back(cache_el
);
629 } else if (sign
== order_gt
) {
631 lt
.push_back(cache_el
);
632 } else if (sign
== order_le
) {
633 le
.push_back(cache_el
);
634 } else if (sign
== order_ge
) {
636 le
.push_back(cache_el
);
637 } else if (sign
== order_unknown
) {
638 unknown
.push_back(cache_el
);
640 assert(sign
== order_eq
);
647 static evalue
*ediff(const evalue
*a
, const evalue
*b
)
651 evalue_set_si(&mone
, -1, 1);
652 evalue
*diff
= new evalue
;
654 evalue_copy(diff
, b
);
658 free_evalue_refs(&mone
);
662 static bool evalue_first_difference(const evalue
*e1
, const evalue
*e2
,
663 const evalue
**d1
, const evalue
**d2
)
668 if (value_ne(e1
->d
, e2
->d
))
671 if (value_notzero_p(e1
->d
)) {
672 if (value_eq(e1
->x
.n
, e2
->x
.n
))
676 if (e1
->x
.p
->type
!= e2
->x
.p
->type
)
678 if (e1
->x
.p
->size
!= e2
->x
.p
->size
)
680 if (e1
->x
.p
->pos
!= e2
->x
.p
->pos
)
683 assert(e1
->x
.p
->type
== polynomial
||
684 e1
->x
.p
->type
== fractional
||
685 e1
->x
.p
->type
== flooring
);
686 int offset
= type_offset(e1
->x
.p
);
687 assert(e1
->x
.p
->size
== offset
+2);
688 for (int i
= 0; i
< e1
->x
.p
->size
; ++i
)
689 if (i
!= type_offset(e1
->x
.p
) &&
690 !eequal(&e1
->x
.p
->arr
[i
], &e2
->x
.p
->arr
[i
]))
693 return evalue_first_difference(&e1
->x
.p
->arr
[offset
],
694 &e2
->x
.p
->arr
[offset
], d1
, d2
);
697 static order_sign
evalue_diff_constant_sign(const evalue
*e1
, const evalue
*e2
)
699 if (!evalue_first_difference(e1
, e2
, &e1
, &e2
))
701 if (value_zero_p(e1
->d
) || value_zero_p(e2
->d
))
702 return order_undefined
;
703 int s
= evalue_rational_cmp(e1
, e2
);
712 order_sign
order_cache::check_lt(vector
<order_cache_el
>* list
,
713 const indicator_term
*a
, const indicator_term
*b
,
714 order_cache_el
& cache_el
)
716 order_sign sign
= order_undefined
;
717 for (int i
= 0; i
< list
->size(); ++i
) {
719 for (j
= cache_el
.e
.size(); j
< (*list
)[i
].e
.size(); ++j
)
720 cache_el
.e
.push_back(ediff(a
->vertex
[j
], b
->vertex
[j
]));
721 for (j
= 0; j
< (*list
)[i
].e
.size(); ++j
) {
722 order_sign diff_sign
;
723 diff_sign
= evalue_diff_constant_sign((*list
)[i
].e
[j
], cache_el
.e
[j
]);
724 if (diff_sign
== order_gt
) {
727 } else if (diff_sign
== order_lt
)
729 else if (diff_sign
== order_undefined
)
732 assert(diff_sign
== order_eq
);
734 if (j
== (*list
)[i
].e
.size())
735 sign
= list
== <
? order_lt
: order_le
;
736 if (sign
!= order_undefined
)
742 order_sign
order_cache::check_direct(const indicator_term
*a
,
743 const indicator_term
*b
,
744 order_cache_el
& cache_el
)
746 order_sign sign
= check_lt(<
, a
, b
, cache_el
);
747 if (sign
!= order_undefined
)
749 sign
= check_lt(&le
, a
, b
, cache_el
);
750 if (sign
!= order_undefined
)
753 for (int i
= 0; i
< unknown
.size(); ++i
) {
755 for (j
= cache_el
.e
.size(); j
< unknown
[i
].e
.size(); ++j
)
756 cache_el
.e
.push_back(ediff(a
->vertex
[j
], b
->vertex
[j
]));
757 for (j
= 0; j
< unknown
[i
].e
.size(); ++j
) {
758 if (!eequal(unknown
[i
].e
[j
], cache_el
.e
[j
]))
761 if (j
== unknown
[i
].e
.size()) {
762 sign
= order_unknown
;
769 order_sign
order_cache::check(const indicator_term
*a
, const indicator_term
*b
,
770 order_cache_el
& cache_el
)
772 order_sign sign
= check_direct(a
, b
, cache_el
);
773 if (sign
!= order_undefined
)
775 int size
= cache_el
.e
.size();
777 sign
= check_direct(a
, b
, cache_el
);
779 assert(cache_el
.e
.size() == size
);
780 if (sign
== order_undefined
)
782 if (sign
== order_lt
)
784 else if (sign
== order_le
)
787 assert(sign
== order_unknown
);
793 struct partial_order
{
796 typedef std::set
<const indicator_term
*, smaller_it
> head_type
;
798 typedef map
<const indicator_term
*, int, smaller_it
> pred_type
;
800 typedef map
<const indicator_term
*, vector
<const indicator_term
* >, smaller_it
> order_type
;
809 partial_order(indicator
*ind
) : ind(ind
) {}
810 void copy(const partial_order
& order
,
811 map
< const indicator_term
*, indicator_term
* > old2new
);
813 order_type::iterator i
;
814 pred_type::iterator j
;
815 head_type::iterator k
;
817 if (head
.key_comp().requires_resort
) {
819 for (k
= head
.begin(); k
!= head
.end(); ++k
)
825 if (pred
.key_comp().requires_resort
) {
827 for (j
= pred
.begin(); j
!= pred
.end(); ++j
)
828 new_pred
[(*j
).first
] = (*j
).second
;
833 if (lt
.key_comp().requires_resort
) {
835 for (i
= lt
.begin(); i
!= lt
.end(); ++i
)
836 m
[(*i
).first
] = (*i
).second
;
841 if (le
.key_comp().requires_resort
) {
843 for (i
= le
.begin(); i
!= le
.end(); ++i
)
844 m
[(*i
).first
] = (*i
).second
;
849 if (eq
.key_comp().requires_resort
) {
851 for (i
= eq
.begin(); i
!= eq
.end(); ++i
)
852 m
[(*i
).first
] = (*i
).second
;
857 if (pending
.key_comp().requires_resort
) {
859 for (i
= pending
.begin(); i
!= pending
.end(); ++i
)
860 m
[(*i
).first
] = (*i
).second
;
866 order_sign
compare(const indicator_term
*a
, const indicator_term
*b
);
867 void set_equal(const indicator_term
*a
, const indicator_term
*b
);
868 void unset_le(const indicator_term
*a
, const indicator_term
*b
);
869 void dec_pred(const indicator_term
*it
) {
870 if (--pred
[it
] == 0) {
875 void inc_pred(const indicator_term
*it
) {
876 if (head
.find(it
) != head
.end())
881 bool compared(const indicator_term
* a
, const indicator_term
* b
);
882 void add(const indicator_term
* it
, std::set
<const indicator_term
*> *filter
);
883 void remove(const indicator_term
* it
);
885 void print(ostream
& os
, char **p
);
887 /* replace references to orig to references to replacement */
888 void replace(const indicator_term
* orig
, indicator_term
* replacement
);
889 void sanity_check() const;
892 /* We actually replace the contents of orig by that of replacement,
893 * but we have to be careful since replacing the content changes
894 * the order of orig in the maps.
896 void partial_order::replace(const indicator_term
* orig
, indicator_term
* replacement
)
898 head_type::iterator k
;
900 bool is_head
= k
!= head
.end();
905 orig_pred
= pred
[orig
];
908 vector
<const indicator_term
* > orig_lt
;
909 vector
<const indicator_term
* > orig_le
;
910 vector
<const indicator_term
* > orig_eq
;
911 vector
<const indicator_term
* > orig_pending
;
912 order_type::iterator i
;
913 bool in_lt
= ((i
= lt
.find(orig
)) != lt
.end());
915 orig_lt
= (*i
).second
;
918 bool in_le
= ((i
= le
.find(orig
)) != le
.end());
920 orig_le
= (*i
).second
;
923 bool in_eq
= ((i
= eq
.find(orig
)) != eq
.end());
925 orig_eq
= (*i
).second
;
928 bool in_pending
= ((i
= pending
.find(orig
)) != pending
.end());
930 orig_pending
= (*i
).second
;
933 indicator_term
*old
= const_cast<indicator_term
*>(orig
);
934 old
->swap(replacement
);
938 pred
[old
] = orig_pred
;
946 pending
[old
] = orig_pending
;
949 void partial_order::unset_le(const indicator_term
*a
, const indicator_term
*b
)
951 vector
<const indicator_term
*>::iterator i
;
952 i
= std::find(le
[a
].begin(), le
[a
].end(), b
);
954 if (le
[a
].size() == 0)
957 i
= std::find(pending
[a
].begin(), pending
[a
].end(), b
);
958 if (i
!= pending
[a
].end())
962 void partial_order::set_equal(const indicator_term
*a
, const indicator_term
*b
)
964 if (eq
[a
].size() == 0)
966 if (eq
[b
].size() == 0)
971 if (pred
.key_comp()(b
, a
)) {
972 const indicator_term
*c
= a
;
977 const indicator_term
*base
= a
;
979 order_type::iterator i
;
981 for (int j
= 0; j
< eq
[b
].size(); ++j
) {
982 eq
[base
].push_back(eq
[b
][j
]);
983 eq
[eq
[b
][j
]][0] = base
;
989 for (int j
= 0; j
< lt
[b
].size(); ++j
) {
990 if (std::find(eq
[base
].begin(), eq
[base
].end(), lt
[b
][j
]) != eq
[base
].end())
992 else if (std::find(lt
[base
].begin(), lt
[base
].end(), lt
[b
][j
])
996 lt
[base
].push_back(lt
[b
][j
]);
1002 if (i
!= le
.end()) {
1003 for (int j
= 0; j
< le
[b
].size(); ++j
) {
1004 if (std::find(eq
[base
].begin(), eq
[base
].end(), le
[b
][j
]) != eq
[base
].end())
1006 else if (std::find(le
[base
].begin(), le
[base
].end(), le
[b
][j
])
1010 le
[base
].push_back(le
[b
][j
]);
1015 i
= pending
.find(base
);
1016 if (i
!= pending
.end()) {
1017 vector
<const indicator_term
* > old
= pending
[base
];
1018 pending
[base
].clear();
1019 for (int j
= 0; j
< old
.size(); ++j
) {
1020 if (std::find(eq
[base
].begin(), eq
[base
].end(), old
[j
]) == eq
[base
].end())
1021 pending
[base
].push_back(old
[j
]);
1025 i
= pending
.find(b
);
1026 if (i
!= pending
.end()) {
1027 for (int j
= 0; j
< pending
[b
].size(); ++j
) {
1028 if (std::find(eq
[base
].begin(), eq
[base
].end(), pending
[b
][j
]) == eq
[base
].end())
1029 pending
[base
].push_back(pending
[b
][j
]);
1035 void partial_order::copy(const partial_order
& order
,
1036 map
< const indicator_term
*, indicator_term
* > old2new
)
1038 cache
.copy(order
.cache
);
1040 order_type::const_iterator i
;
1041 pred_type::const_iterator j
;
1042 head_type::const_iterator k
;
1044 for (k
= order
.head
.begin(); k
!= order
.head
.end(); ++k
)
1045 head
.insert(old2new
[*k
]);
1047 for (j
= order
.pred
.begin(); j
!= order
.pred
.end(); ++j
)
1048 pred
[old2new
[(*j
).first
]] = (*j
).second
;
1050 for (i
= order
.lt
.begin(); i
!= order
.lt
.end(); ++i
) {
1051 for (int j
= 0; j
< (*i
).second
.size(); ++j
)
1052 lt
[old2new
[(*i
).first
]].push_back(old2new
[(*i
).second
[j
]]);
1054 for (i
= order
.le
.begin(); i
!= order
.le
.end(); ++i
) {
1055 for (int j
= 0; j
< (*i
).second
.size(); ++j
)
1056 le
[old2new
[(*i
).first
]].push_back(old2new
[(*i
).second
[j
]]);
1058 for (i
= order
.eq
.begin(); i
!= order
.eq
.end(); ++i
) {
1059 for (int j
= 0; j
< (*i
).second
.size(); ++j
)
1060 eq
[old2new
[(*i
).first
]].push_back(old2new
[(*i
).second
[j
]]);
1062 for (i
= order
.pending
.begin(); i
!= order
.pending
.end(); ++i
) {
1063 for (int j
= 0; j
< (*i
).second
.size(); ++j
)
1064 pending
[old2new
[(*i
).first
]].push_back(old2new
[(*i
).second
[j
]]);
1070 vector
<evalue
*> max
;
1072 void print(ostream
& os
, char **p
, barvinok_options
*options
) const;
1073 void substitute(Matrix
*T
, barvinok_options
*options
);
1074 Vector
*eval(Value
*val
, unsigned MaxRays
) const;
1077 for (int i
= 0; i
< max
.size(); ++i
) {
1078 free_evalue_refs(max
[i
]);
1086 * Project on first dim dimensions
1088 Polyhedron
* Polyhedron_Project_Initial(Polyhedron
*P
, int dim
)
1094 if (P
->Dimension
== dim
)
1095 return Polyhedron_Copy(P
);
1097 T
= Matrix_Alloc(dim
+1, P
->Dimension
+1);
1098 for (i
= 0; i
< dim
; ++i
)
1099 value_set_si(T
->p
[i
][i
], 1);
1100 value_set_si(T
->p
[dim
][P
->Dimension
], 1);
1101 I
= Polyhedron_Image(P
, T
, P
->NbConstraints
);
1107 vector
<indicator_term
*> term
;
1108 indicator_constructor
& ic
;
1109 partial_order order
;
1113 lexmin_options
*options
;
1114 vector
<evalue
*> substitutions
;
1116 indicator(indicator_constructor
& ic
, Param_Domain
*PD
, EDomain
*D
,
1117 lexmin_options
*options
) :
1118 ic(ic
), PD(PD
), D(D
), order(this), options(options
), P(NULL
) {}
1119 indicator(const indicator
& ind
, EDomain
*D
) :
1120 ic(ind
.ic
), PD(ind
.PD
), D(NULL
), order(this), options(ind
.options
),
1121 P(Polyhedron_Copy(ind
.P
)) {
1122 map
< const indicator_term
*, indicator_term
* > old2new
;
1123 for (int i
= 0; i
< ind
.term
.size(); ++i
) {
1124 indicator_term
*it
= new indicator_term(*ind
.term
[i
]);
1125 old2new
[ind
.term
[i
]] = it
;
1128 order
.copy(ind
.order
, old2new
);
1132 for (int i
= 0; i
< term
.size(); ++i
)
1140 void set_domain(EDomain
*D
) {
1141 order
.cache
.clear_transients();
1145 int nparam
= ic
.PP
->Constraints
->NbColumns
-2 - ic
.vertex
.length();
1146 if (options
->reduce
) {
1147 Polyhedron
*Q
= Polyhedron_Project_Initial(D
->D
, nparam
);
1148 Q
= DomainConstraintSimplify(Q
, options
->verify
->barvinok
->MaxRays
);
1149 if (!P
|| !PolyhedronIncludes(Q
, P
))
1150 reduce_in_domain(Q
);
1158 void add(const indicator_term
* it
);
1159 void remove(const indicator_term
* it
);
1160 void remove_initial_rational_vertices();
1161 void expand_rational_vertex(const indicator_term
*initial
);
1163 void print(ostream
& os
, char **p
);
1165 void peel(int i
, int j
);
1166 void combine(const indicator_term
*a
, const indicator_term
*b
);
1167 void add_substitution(evalue
*equation
);
1168 void perform_pending_substitutions();
1169 void reduce_in_domain(Polyhedron
*D
);
1170 bool handle_equal_numerators(const indicator_term
*base
);
1172 max_term
* create_max_term(const indicator_term
*it
);
1174 void substitute(evalue
*equation
);
1177 void partial_order::sanity_check() const
1179 order_type::const_iterator i
;
1180 order_type::const_iterator prev
;
1181 order_type::const_iterator l
;
1182 pred_type::const_iterator k
, prev_k
;
1184 for (k
= pred
.begin(); k
!= pred
.end(); prev_k
= k
, ++k
)
1185 if (k
!= pred
.begin())
1186 assert(pred
.key_comp()((*prev_k
).first
, (*k
).first
));
1187 for (i
= lt
.begin(); i
!= lt
.end(); prev
= i
, ++i
) {
1190 i_v
= (*i
).first
->eval(ind
->D
->sample
->p
);
1191 if (i
!= lt
.begin())
1192 assert(lt
.key_comp()((*prev
).first
, (*i
).first
));
1193 l
= eq
.find((*i
).first
);
1195 assert((*l
).second
.size() > 1);
1196 assert(head
.find((*i
).first
) != head
.end() ||
1197 pred
.find((*i
).first
) != pred
.end());
1198 for (int j
= 0; j
< (*i
).second
.size(); ++j
) {
1199 k
= pred
.find((*i
).second
[j
]);
1200 assert(k
!= pred
.end());
1201 assert((*k
).second
!= 0);
1202 if ((*i
).first
->sign
!= 0 &&
1203 (*i
).second
[j
]->sign
!= 0 && ind
->D
->sample
) {
1204 vec_ZZ j_v
= (*i
).second
[j
]->eval(ind
->D
->sample
->p
);
1205 assert(lex_cmp(i_v
, j_v
) < 0);
1209 for (i
= le
.begin(); i
!= le
.end(); ++i
) {
1210 assert((*i
).second
.size() > 0);
1211 assert(head
.find((*i
).first
) != head
.end() ||
1212 pred
.find((*i
).first
) != pred
.end());
1213 for (int j
= 0; j
< (*i
).second
.size(); ++j
) {
1214 k
= pred
.find((*i
).second
[j
]);
1215 assert(k
!= pred
.end());
1216 assert((*k
).second
!= 0);
1219 for (i
= eq
.begin(); i
!= eq
.end(); ++i
) {
1220 assert(head
.find((*i
).first
) != head
.end() ||
1221 pred
.find((*i
).first
) != pred
.end());
1222 assert((*i
).second
.size() >= 1);
1224 for (i
= pending
.begin(); i
!= pending
.end(); ++i
) {
1225 assert(head
.find((*i
).first
) != head
.end() ||
1226 pred
.find((*i
).first
) != pred
.end());
1227 for (int j
= 0; j
< (*i
).second
.size(); ++j
)
1228 assert(head
.find((*i
).second
[j
]) != head
.end() ||
1229 pred
.find((*i
).second
[j
]) != pred
.end());
1233 max_term
* indicator::create_max_term(const indicator_term
*it
)
1235 int dim
= it
->den
.NumCols();
1236 max_term
*maximum
= new max_term
;
1237 maximum
->domain
= new EDomain(D
);
1238 for (int j
= 0; j
< dim
; ++j
) {
1239 evalue
*E
= new evalue
;
1241 evalue_copy(E
, it
->vertex
[j
]);
1242 if (evalue_frac2floor_in_domain(E
, D
->D
))
1244 maximum
->max
.push_back(E
);
1249 static order_sign
evalue_sign(evalue
*diff
, EDomain
*D
, barvinok_options
*options
)
1251 order_sign sign
= order_eq
;
1254 evalue_set_si(&mone
, -1, 1);
1255 int len
= 1 + D
->D
->Dimension
+ 1;
1256 Vector
*c
= Vector_Alloc(len
);
1257 Matrix
*T
= Matrix_Alloc(2, len
-1);
1259 int fract
= evalue2constraint(D
, diff
, c
->p
, len
);
1260 Vector_Copy(c
->p
+1, T
->p
[0], len
-1);
1261 value_assign(T
->p
[1][len
-2], c
->p
[0]);
1263 order_sign upper_sign
= polyhedron_affine_sign(D
->D
, T
, options
);
1264 if (upper_sign
== order_lt
|| !fract
)
1268 evalue2constraint(D
, diff
, c
->p
, len
);
1270 Vector_Copy(c
->p
+1, T
->p
[0], len
-1);
1271 value_assign(T
->p
[1][len
-2], c
->p
[0]);
1273 order_sign neg_lower_sign
= polyhedron_affine_sign(D
->D
, T
, options
);
1275 if (neg_lower_sign
== order_lt
)
1277 else if (neg_lower_sign
== order_eq
|| neg_lower_sign
== order_le
) {
1278 if (upper_sign
== order_eq
|| upper_sign
== order_le
)
1283 if (upper_sign
== order_lt
|| upper_sign
== order_le
||
1284 upper_sign
== order_eq
)
1287 sign
= order_unknown
;
1293 free_evalue_refs(&mone
);
1298 /* An auxiliary class that keeps a reference to an evalue
1299 * and frees it when it goes out of scope.
1301 struct temp_evalue
{
1303 temp_evalue() : E(NULL
) {}
1304 temp_evalue(evalue
*e
) : E(e
) {}
1305 operator evalue
* () const { return E
; }
1306 evalue
*operator=(evalue
*e
) {
1308 free_evalue_refs(E
);
1316 free_evalue_refs(E
);
1322 static void substitute(vector
<indicator_term
*>& term
, evalue
*equation
)
1324 evalue
*fract
= NULL
;
1325 evalue
*val
= new evalue
;
1327 evalue_copy(val
, equation
);
1330 value_init(factor
.d
);
1331 value_init(factor
.x
.n
);
1334 for (e
= val
; value_zero_p(e
->d
) && e
->x
.p
->type
!= fractional
;
1335 e
= &e
->x
.p
->arr
[type_offset(e
->x
.p
)])
1338 if (value_zero_p(e
->d
) && e
->x
.p
->type
== fractional
)
1339 fract
= &e
->x
.p
->arr
[0];
1341 for (e
= val
; value_zero_p(e
->d
) && e
->x
.p
->type
!= polynomial
;
1342 e
= &e
->x
.p
->arr
[type_offset(e
->x
.p
)])
1344 assert(value_zero_p(e
->d
) && e
->x
.p
->type
== polynomial
);
1347 int offset
= type_offset(e
->x
.p
);
1349 assert(value_notzero_p(e
->x
.p
->arr
[offset
+1].d
));
1350 assert(value_notzero_p(e
->x
.p
->arr
[offset
+1].x
.n
));
1351 if (value_neg_p(e
->x
.p
->arr
[offset
+1].x
.n
)) {
1352 value_oppose(factor
.d
, e
->x
.p
->arr
[offset
+1].x
.n
);
1353 value_assign(factor
.x
.n
, e
->x
.p
->arr
[offset
+1].d
);
1355 value_assign(factor
.d
, e
->x
.p
->arr
[offset
+1].x
.n
);
1356 value_oppose(factor
.x
.n
, e
->x
.p
->arr
[offset
+1].d
);
1359 free_evalue_refs(&e
->x
.p
->arr
[offset
+1]);
1362 *e
= e
->x
.p
->arr
[offset
];
1367 for (int i
= 0; i
< term
.size(); ++i
)
1368 term
[i
]->substitute(fract
, val
);
1370 free_evalue_refs(&p
->arr
[0]);
1372 for (int i
= 0; i
< term
.size(); ++i
)
1373 term
[i
]->substitute(p
->pos
, val
);
1376 free_evalue_refs(&factor
);
1377 free_evalue_refs(val
);
1383 order_sign
partial_order::compare(const indicator_term
*a
, const indicator_term
*b
)
1385 unsigned dim
= a
->den
.NumCols();
1386 order_sign sign
= order_eq
;
1387 bool rational
= a
->sign
== 0 || b
->sign
== 0;
1389 order_sign cached_sign
= order_eq
;
1390 for (int k
= 0; k
< dim
; ++k
) {
1391 cached_sign
= evalue_diff_constant_sign(a
->vertex
[k
], b
->vertex
[k
]);
1392 if (cached_sign
!= order_eq
)
1395 if (cached_sign
!= order_undefined
)
1398 order_cache_el cache_el
;
1399 cached_sign
= order_undefined
;
1401 cached_sign
= cache
.check(a
, b
, cache_el
);
1402 if (cached_sign
!= order_undefined
) {
1409 vector
<indicator_term
*> term
;
1411 for (int k
= 0; k
< dim
; ++k
) {
1412 /* compute a->vertex[k] - b->vertex[k] */
1414 if (cache_el
.e
.size() <= k
) {
1415 diff
= ediff(a
->vertex
[k
], b
->vertex
[k
]);
1416 cache_el
.e
.push_back(diff
);
1418 diff
= cache_el
.e
[k
];
1421 tdiff
= diff
= ediff(term
[0]->vertex
[k
], term
[1]->vertex
[k
]);
1422 order_sign diff_sign
;
1423 if (eequal(a
->vertex
[k
], b
->vertex
[k
]))
1424 diff_sign
= order_eq
;
1426 diff_sign
= evalue_sign(diff
, ind
->D
,
1427 ind
->options
->verify
->barvinok
);
1429 if (diff_sign
== order_undefined
) {
1430 assert(sign
== order_le
|| sign
== order_ge
);
1431 if (sign
== order_le
)
1437 if (diff_sign
== order_lt
) {
1438 if (sign
== order_eq
|| sign
== order_le
)
1441 sign
= order_unknown
;
1444 if (diff_sign
== order_gt
) {
1445 if (sign
== order_eq
|| sign
== order_ge
)
1448 sign
= order_unknown
;
1451 if (diff_sign
== order_eq
) {
1452 if (term
.size() == 0 && !rational
&& !EVALUE_IS_ZERO(*diff
))
1453 ind
->add_substitution(diff
);
1456 if ((diff_sign
== order_unknown
) ||
1457 ((diff_sign
== order_lt
|| diff_sign
== order_le
) && sign
== order_ge
) ||
1458 ((diff_sign
== order_gt
|| diff_sign
== order_ge
) && sign
== order_le
)) {
1459 sign
= order_unknown
;
1466 term
.push_back(new indicator_term(*a
));
1467 term
.push_back(new indicator_term(*b
));
1469 substitute(term
, diff
);
1473 cache
.add(cache_el
, sign
);
1485 bool partial_order::compared(const indicator_term
* a
, const indicator_term
* b
)
1487 order_type::iterator j
;
1490 if (j
!= lt
.end() && std::find(lt
[a
].begin(), lt
[a
].end(), b
) != lt
[a
].end())
1494 if (j
!= le
.end() && std::find(le
[a
].begin(), le
[a
].end(), b
) != le
[a
].end())
1500 void partial_order::add(const indicator_term
* it
,
1501 std::set
<const indicator_term
*> *filter
)
1503 if (eq
.find(it
) != eq
.end() && eq
[it
].size() == 1)
1506 head_type
head_copy(head
);
1511 head_type::iterator i
;
1512 for (i
= head_copy
.begin(); i
!= head_copy
.end(); ++i
) {
1515 if (eq
.find(*i
) != eq
.end() && eq
[*i
].size() == 1)
1518 if (filter
->find(*i
) == filter
->end())
1520 if (compared(*i
, it
))
1523 order_sign sign
= compare(it
, *i
);
1524 if (sign
== order_lt
) {
1525 lt
[it
].push_back(*i
);
1527 } else if (sign
== order_le
) {
1528 le
[it
].push_back(*i
);
1530 } else if (sign
== order_eq
) {
1533 } else if (sign
== order_gt
) {
1534 pending
[*i
].push_back(it
);
1535 lt
[*i
].push_back(it
);
1537 } else if (sign
== order_ge
) {
1538 pending
[*i
].push_back(it
);
1539 le
[*i
].push_back(it
);
1545 void partial_order::remove(const indicator_term
* it
)
1547 std::set
<const indicator_term
*> filter
;
1548 order_type::iterator i
;
1550 assert(head
.find(it
) != head
.end());
1553 if (i
!= eq
.end()) {
1554 assert(eq
[it
].size() >= 1);
1555 const indicator_term
*base
;
1556 if (eq
[it
].size() == 1) {
1560 vector
<const indicator_term
* >::iterator j
;
1561 j
= std::find(eq
[base
].begin(), eq
[base
].end(), it
);
1562 assert(j
!= eq
[base
].end());
1565 /* "it" may no longer be the smallest, since the order
1566 * structure may have been copied from another one.
1568 std::sort(eq
[it
].begin()+1, eq
[it
].end(), pred
.key_comp());
1569 assert(eq
[it
][0] == it
);
1570 eq
[it
].erase(eq
[it
].begin());
1575 for (int j
= 1; j
< eq
[base
].size(); ++j
)
1576 eq
[eq
[base
][j
]][0] = base
;
1579 if (i
!= lt
.end()) {
1585 if (i
!= le
.end()) {
1590 i
= pending
.find(it
);
1591 if (i
!= pending
.end()) {
1592 pending
[base
] = pending
[it
];
1597 if (eq
[base
].size() == 1)
1606 if (i
!= lt
.end()) {
1607 for (int j
= 0; j
< lt
[it
].size(); ++j
) {
1608 filter
.insert(lt
[it
][j
]);
1609 dec_pred(lt
[it
][j
]);
1615 if (i
!= le
.end()) {
1616 for (int j
= 0; j
< le
[it
].size(); ++j
) {
1617 filter
.insert(le
[it
][j
]);
1618 dec_pred(le
[it
][j
]);
1625 i
= pending
.find(it
);
1626 if (i
!= pending
.end()) {
1627 vector
<const indicator_term
*> it_pending
= pending
[it
];
1629 for (int j
= 0; j
< it_pending
.size(); ++j
) {
1630 filter
.erase(it_pending
[j
]);
1631 add(it_pending
[j
], &filter
);
1636 void partial_order::print(ostream
& os
, char **p
)
1638 order_type::iterator i
;
1639 pred_type::iterator j
;
1640 head_type::iterator k
;
1641 for (k
= head
.begin(); k
!= head
.end(); ++k
) {
1645 for (j
= pred
.begin(); j
!= pred
.end(); ++j
) {
1646 (*j
).first
->print(os
, p
);
1647 os
<< ": " << (*j
).second
<< endl
;
1649 for (i
= lt
.begin(); i
!= lt
.end(); ++i
) {
1650 (*i
).first
->print(os
, p
);
1651 assert(head
.find((*i
).first
) != head
.end() ||
1652 pred
.find((*i
).first
) != pred
.end());
1653 if (pred
.find((*i
).first
) != pred
.end())
1654 os
<< "(" << pred
[(*i
).first
] << ")";
1656 for (int j
= 0; j
< (*i
).second
.size(); ++j
) {
1659 (*i
).second
[j
]->print(os
, p
);
1660 assert(pred
.find((*i
).second
[j
]) != pred
.end());
1661 os
<< "(" << pred
[(*i
).second
[j
]] << ")";
1665 for (i
= le
.begin(); i
!= le
.end(); ++i
) {
1666 (*i
).first
->print(os
, p
);
1667 assert(head
.find((*i
).first
) != head
.end() ||
1668 pred
.find((*i
).first
) != pred
.end());
1669 if (pred
.find((*i
).first
) != pred
.end())
1670 os
<< "(" << pred
[(*i
).first
] << ")";
1672 for (int j
= 0; j
< (*i
).second
.size(); ++j
) {
1675 (*i
).second
[j
]->print(os
, p
);
1676 assert(pred
.find((*i
).second
[j
]) != pred
.end());
1677 os
<< "(" << pred
[(*i
).second
[j
]] << ")";
1681 for (i
= eq
.begin(); i
!= eq
.end(); ++i
) {
1682 if ((*i
).second
.size() <= 1)
1684 (*i
).first
->print(os
, p
);
1685 assert(head
.find((*i
).first
) != head
.end() ||
1686 pred
.find((*i
).first
) != pred
.end());
1687 if (pred
.find((*i
).first
) != pred
.end())
1688 os
<< "(" << pred
[(*i
).first
] << ")";
1689 for (int j
= 1; j
< (*i
).second
.size(); ++j
) {
1692 (*i
).second
[j
]->print(os
, p
);
1693 assert(head
.find((*i
).second
[j
]) != head
.end() ||
1694 pred
.find((*i
).second
[j
]) != pred
.end());
1695 if (pred
.find((*i
).second
[j
]) != pred
.end())
1696 os
<< "(" << pred
[(*i
).second
[j
]] << ")";
1700 for (i
= pending
.begin(); i
!= pending
.end(); ++i
) {
1701 os
<< "pending on ";
1702 (*i
).first
->print(os
, p
);
1703 assert(head
.find((*i
).first
) != head
.end() ||
1704 pred
.find((*i
).first
) != pred
.end());
1705 if (pred
.find((*i
).first
) != pred
.end())
1706 os
<< "(" << pred
[(*i
).first
] << ")";
1708 for (int j
= 0; j
< (*i
).second
.size(); ++j
) {
1711 (*i
).second
[j
]->print(os
, p
);
1712 assert(pred
.find((*i
).second
[j
]) != pred
.end());
1713 os
<< "(" << pred
[(*i
).second
[j
]] << ")";
1719 void indicator::add(const indicator_term
* it
)
1721 indicator_term
*nt
= new indicator_term(*it
);
1722 if (options
->reduce
)
1723 nt
->reduce_in_domain(P
? P
: D
->D
);
1725 order
.add(nt
, NULL
);
1726 assert(term
.size() == order
.head
.size() + order
.pred
.size());
1729 void indicator::remove(const indicator_term
* it
)
1731 vector
<indicator_term
*>::iterator i
;
1732 i
= std::find(term
.begin(), term
.end(), it
);
1733 assert(i
!= term
.end());
1736 assert(term
.size() == order
.head
.size() + order
.pred
.size());
1740 void indicator::expand_rational_vertex(const indicator_term
*initial
)
1742 int pos
= initial
->pos
;
1744 if (ic
.terms
[pos
].size() == 0) {
1746 FORALL_PVertex_in_ParamPolyhedron(V
, PD
, ic
.PP
) // _i is internal counter
1748 ic
.decompose_at_vertex(V
, pos
, options
->verify
->barvinok
);
1751 END_FORALL_PVertex_in_ParamPolyhedron
;
1753 for (int j
= 0; j
< ic
.terms
[pos
].size(); ++j
)
1754 add(ic
.terms
[pos
][j
]);
1757 void indicator::remove_initial_rational_vertices()
1760 const indicator_term
*initial
= NULL
;
1761 partial_order::head_type::iterator i
;
1762 for (i
= order
.head
.begin(); i
!= order
.head
.end(); ++i
) {
1763 if ((*i
)->sign
!= 0)
1765 if (order
.eq
.find(*i
) != order
.eq
.end() && order
.eq
[*i
].size() <= 1)
1772 expand_rational_vertex(initial
);
1776 void indicator::reduce_in_domain(Polyhedron
*D
)
1778 for (int i
= 0; i
< term
.size(); ++i
)
1779 term
[i
]->reduce_in_domain(D
);
1782 void indicator::print(ostream
& os
, char **p
)
1784 assert(term
.size() == order
.head
.size() + order
.pred
.size());
1785 for (int i
= 0; i
< term
.size(); ++i
) {
1786 term
[i
]->print(os
, p
);
1788 os
<< ": " << term
[i
]->eval(D
->sample
->p
);
1795 /* Remove pairs of opposite terms */
1796 void indicator::simplify()
1798 for (int i
= 0; i
< term
.size(); ++i
) {
1799 for (int j
= i
+1; j
< term
.size(); ++j
) {
1800 if (term
[i
]->sign
+ term
[j
]->sign
!= 0)
1802 if (term
[i
]->den
!= term
[j
]->den
)
1805 for (k
= 0; k
< term
[i
]->den
.NumCols(); ++k
)
1806 if (!eequal(term
[i
]->vertex
[k
], term
[j
]->vertex
[k
]))
1808 if (k
< term
[i
]->den
.NumCols())
1812 term
.erase(term
.begin()+j
);
1813 term
.erase(term
.begin()+i
);
1820 void indicator::peel(int i
, int j
)
1828 int dim
= term
[i
]->den
.NumCols();
1833 int n_common
= 0, n_i
= 0, n_j
= 0;
1835 common
.SetDims(min(term
[i
]->den
.NumRows(), term
[j
]->den
.NumRows()), dim
);
1836 rest_i
.SetDims(term
[i
]->den
.NumRows(), dim
);
1837 rest_j
.SetDims(term
[j
]->den
.NumRows(), dim
);
1840 for (k
= 0, l
= 0; k
< term
[i
]->den
.NumRows() && l
< term
[j
]->den
.NumRows(); ) {
1841 int s
= lex_cmp(term
[i
]->den
[k
], term
[j
]->den
[l
]);
1843 common
[n_common
++] = term
[i
]->den
[k
];
1847 rest_i
[n_i
++] = term
[i
]->den
[k
++];
1849 rest_j
[n_j
++] = term
[j
]->den
[l
++];
1851 while (k
< term
[i
]->den
.NumRows())
1852 rest_i
[n_i
++] = term
[i
]->den
[k
++];
1853 while (l
< term
[j
]->den
.NumRows())
1854 rest_j
[n_j
++] = term
[j
]->den
[l
++];
1855 common
.SetDims(n_common
, dim
);
1856 rest_i
.SetDims(n_i
, dim
);
1857 rest_j
.SetDims(n_j
, dim
);
1859 for (k
= 0; k
<= n_i
; ++k
) {
1860 indicator_term
*it
= new indicator_term(*term
[i
]);
1861 it
->den
.SetDims(n_common
+ k
, dim
);
1862 for (l
= 0; l
< n_common
; ++l
)
1863 it
->den
[l
] = common
[l
];
1864 for (l
= 0; l
< k
; ++l
)
1865 it
->den
[n_common
+l
] = rest_i
[l
];
1866 lex_order_rows(it
->den
);
1868 for (l
= 0; l
< dim
; ++l
)
1869 evalue_add_constant(it
->vertex
[l
], rest_i
[k
-1][l
]);
1873 for (k
= 0; k
<= n_j
; ++k
) {
1874 indicator_term
*it
= new indicator_term(*term
[j
]);
1875 it
->den
.SetDims(n_common
+ k
, dim
);
1876 for (l
= 0; l
< n_common
; ++l
)
1877 it
->den
[l
] = common
[l
];
1878 for (l
= 0; l
< k
; ++l
)
1879 it
->den
[n_common
+l
] = rest_j
[l
];
1880 lex_order_rows(it
->den
);
1882 for (l
= 0; l
< dim
; ++l
)
1883 evalue_add_constant(it
->vertex
[l
], rest_j
[k
-1][l
]);
1886 term
.erase(term
.begin()+j
);
1887 term
.erase(term
.begin()+i
);
1890 void indicator::combine(const indicator_term
*a
, const indicator_term
*b
)
1892 int dim
= a
->den
.NumCols();
1895 mat_ZZ rest_i
; /* factors in a, but not in b */
1896 mat_ZZ rest_j
; /* factors in b, but not in a */
1897 int n_common
= 0, n_i
= 0, n_j
= 0;
1899 common
.SetDims(min(a
->den
.NumRows(), b
->den
.NumRows()), dim
);
1900 rest_i
.SetDims(a
->den
.NumRows(), dim
);
1901 rest_j
.SetDims(b
->den
.NumRows(), dim
);
1904 for (k
= 0, l
= 0; k
< a
->den
.NumRows() && l
< b
->den
.NumRows(); ) {
1905 int s
= lex_cmp(a
->den
[k
], b
->den
[l
]);
1907 common
[n_common
++] = a
->den
[k
];
1911 rest_i
[n_i
++] = a
->den
[k
++];
1913 rest_j
[n_j
++] = b
->den
[l
++];
1915 while (k
< a
->den
.NumRows())
1916 rest_i
[n_i
++] = a
->den
[k
++];
1917 while (l
< b
->den
.NumRows())
1918 rest_j
[n_j
++] = b
->den
[l
++];
1919 common
.SetDims(n_common
, dim
);
1920 rest_i
.SetDims(n_i
, dim
);
1921 rest_j
.SetDims(n_j
, dim
);
1923 assert(order
.eq
[a
].size() > 1);
1924 indicator_term
*prev
;
1927 for (int k
= n_i
-1; k
>= 0; --k
) {
1928 indicator_term
*it
= new indicator_term(*b
);
1929 it
->den
.SetDims(n_common
+ n_j
+ n_i
-k
, dim
);
1930 for (int l
= k
; l
< n_i
; ++l
)
1931 it
->den
[n_common
+n_j
+l
-k
] = rest_i
[l
];
1932 lex_order_rows(it
->den
);
1933 for (int m
= 0; m
< dim
; ++m
)
1934 evalue_add_constant(it
->vertex
[m
], rest_i
[k
][m
]);
1935 it
->sign
= -it
->sign
;
1937 order
.pending
[it
].push_back(prev
);
1938 order
.lt
[it
].push_back(prev
);
1939 order
.inc_pred(prev
);
1942 order
.head
.insert(it
);
1946 indicator_term
*it
= new indicator_term(*b
);
1947 it
->den
.SetDims(n_common
+ n_i
+ n_j
, dim
);
1948 for (l
= 0; l
< n_i
; ++l
)
1949 it
->den
[n_common
+n_j
+l
] = rest_i
[l
];
1950 lex_order_rows(it
->den
);
1952 order
.pending
[a
].push_back(prev
);
1953 order
.lt
[a
].push_back(prev
);
1954 order
.inc_pred(prev
);
1955 order
.replace(b
, it
);
1960 for (int k
= n_j
-1; k
>= 0; --k
) {
1961 indicator_term
*it
= new indicator_term(*a
);
1962 it
->den
.SetDims(n_common
+ n_i
+ n_j
-k
, dim
);
1963 for (int l
= k
; l
< n_j
; ++l
)
1964 it
->den
[n_common
+n_i
+l
-k
] = rest_j
[l
];
1965 lex_order_rows(it
->den
);
1966 for (int m
= 0; m
< dim
; ++m
)
1967 evalue_add_constant(it
->vertex
[m
], rest_j
[k
][m
]);
1968 it
->sign
= -it
->sign
;
1970 order
.pending
[it
].push_back(prev
);
1971 order
.lt
[it
].push_back(prev
);
1972 order
.inc_pred(prev
);
1975 order
.head
.insert(it
);
1979 indicator_term
*it
= new indicator_term(*a
);
1980 it
->den
.SetDims(n_common
+ n_i
+ n_j
, dim
);
1981 for (l
= 0; l
< n_j
; ++l
)
1982 it
->den
[n_common
+n_i
+l
] = rest_j
[l
];
1983 lex_order_rows(it
->den
);
1985 order
.pending
[a
].push_back(prev
);
1986 order
.lt
[a
].push_back(prev
);
1987 order
.inc_pred(prev
);
1988 order
.replace(a
, it
);
1992 assert(term
.size() == order
.head
.size() + order
.pred
.size());
1995 bool indicator::handle_equal_numerators(const indicator_term
*base
)
1997 for (int i
= 0; i
< order
.eq
[base
].size(); ++i
) {
1998 for (int j
= i
+1; j
< order
.eq
[base
].size(); ++j
) {
1999 if (order
.eq
[base
][i
]->is_opposite(order
.eq
[base
][j
])) {
2000 remove(order
.eq
[base
][j
]);
2001 remove(i
? order
.eq
[base
][i
] : base
);
2006 for (int j
= 1; j
< order
.eq
[base
].size(); ++j
)
2007 if (order
.eq
[base
][j
]->sign
!= base
->sign
) {
2008 combine(base
, order
.eq
[base
][j
]);
2014 void indicator::substitute(evalue
*equation
)
2016 ::substitute(term
, equation
);
2019 void indicator::add_substitution(evalue
*equation
)
2021 for (int i
= 0; i
< substitutions
.size(); ++i
)
2022 if (eequal(substitutions
[i
], equation
))
2024 evalue
*copy
= new evalue();
2025 value_init(copy
->d
);
2026 evalue_copy(copy
, equation
);
2027 substitutions
.push_back(copy
);
2030 void indicator::perform_pending_substitutions()
2032 if (substitutions
.size() == 0)
2035 for (int i
= 0; i
< substitutions
.size(); ++i
) {
2036 substitute(substitutions
[i
]);
2037 free_evalue_refs(substitutions
[i
]);
2038 delete substitutions
[i
];
2040 substitutions
.clear();
2044 static void print_varlist(ostream
& os
, int n
, char **names
)
2048 for (i
= 0; i
< n
; ++i
) {
2056 void max_term::print(ostream
& os
, char **p
, barvinok_options
*options
) const
2059 print_varlist(os
, domain
->dimension(), p
);
2062 for (int i
= 0; i
< max
.size(); ++i
) {
2065 evalue_print(os
, max
[i
], p
);
2069 domain
->print_constraints(os
, p
, options
);
2073 /* T maps the compressed parameters to the original parameters,
2074 * while this max_term is based on the compressed parameters
2075 * and we want get the original parameters back.
2077 void max_term::substitute(Matrix
*T
, barvinok_options
*options
)
2079 assert(domain
->dimension() == T
->NbColumns
-1);
2081 Matrix
*inv
= left_inverse(T
, &Eq
);
2084 value_init(denom
.d
);
2085 value_init(denom
.x
.n
);
2086 value_set_si(denom
.x
.n
, 1);
2087 value_assign(denom
.d
, inv
->p
[inv
->NbRows
-1][inv
->NbColumns
-1]);
2090 v
.SetLength(inv
->NbColumns
);
2091 evalue
**subs
= new evalue
*[inv
->NbRows
-1];
2092 for (int i
= 0; i
< inv
->NbRows
-1; ++i
) {
2093 values2zz(inv
->p
[i
], v
, v
.length());
2094 subs
[i
] = multi_monom(v
);
2095 emul(&denom
, subs
[i
]);
2097 free_evalue_refs(&denom
);
2099 domain
->substitute(subs
, inv
, Eq
, options
->MaxRays
);
2102 for (int i
= 0; i
< max
.size(); ++i
) {
2103 evalue_substitute(max
[i
], subs
);
2104 reduce_evalue(max
[i
]);
2107 for (int i
= 0; i
< inv
->NbRows
-1; ++i
) {
2108 free_evalue_refs(subs
[i
]);
2115 Vector
*max_term::eval(Value
*val
, unsigned MaxRays
) const
2117 if (!domain
->contains(val
, domain
->dimension()))
2119 Vector
*res
= Vector_Alloc(max
.size());
2120 for (int i
= 0; i
< max
.size(); ++i
) {
2121 compute_evalue(max
[i
], val
, &res
->p
[i
]);
2128 enum sign
{ le
, ge
, lge
} sign
;
2130 split (evalue
*c
, enum sign s
) : constraint(c
), sign(s
) {}
2133 static void split_on(const split
& sp
, EDomain
*D
,
2134 EDomain
**Dlt
, EDomain
**Deq
, EDomain
**Dgt
,
2135 lexmin_options
*options
)
2141 ge_constraint
*ge
= D
->compute_ge_constraint(sp
.constraint
);
2142 if (sp
.sign
== split::lge
|| sp
.sign
== split::ge
)
2143 ED
[2] = EDomain::new_from_ge_constraint(ge
, 1, options
->verify
->barvinok
);
2146 if (sp
.sign
== split::lge
|| sp
.sign
== split::le
)
2147 ED
[0] = EDomain::new_from_ge_constraint(ge
, -1, options
->verify
->barvinok
);
2151 assert(sp
.sign
== split::lge
|| sp
.sign
== split::ge
|| sp
.sign
== split::le
);
2152 ED
[1] = EDomain::new_from_ge_constraint(ge
, 0, options
->verify
->barvinok
);
2156 for (int i
= 0; i
< 3; ++i
) {
2159 if (D
->sample
&& ED
[i
]->contains(D
->sample
->p
, D
->sample
->Size
-1)) {
2160 ED
[i
]->sample
= Vector_Alloc(D
->sample
->Size
);
2161 Vector_Copy(D
->sample
->p
, ED
[i
]->sample
->p
, D
->sample
->Size
);
2162 } else if (emptyQ2(ED
[i
]->D
) ||
2163 (options
->emptiness_check
!= BV_LEXMIN_EMPTINESS_CHECK_NONE
&&
2164 !(ED
[i
]->not_empty(options
)))) {
2174 ostream
& operator<< (ostream
& os
, const vector
<int> & v
)
2177 for (int i
= 0; i
< v
.size(); ++i
) {
2186 void construct_rational_vertices(Param_Polyhedron
*PP
, Matrix
*T
, unsigned dim
,
2187 int nparam
, vector
<indicator_term
*>& vertices
)
2196 v
.SetLength(nparam
+1);
2199 value_init(factor
.d
);
2200 value_init(factor
.x
.n
);
2201 value_set_si(factor
.x
.n
, 1);
2202 value_set_si(factor
.d
, 1);
2204 for (i
= 0, PV
= PP
->V
; PV
; ++i
, PV
= PV
->next
) {
2205 indicator_term
*term
= new indicator_term(dim
, i
);
2206 vertices
.push_back(term
);
2207 Matrix
*M
= Matrix_Alloc(PV
->Vertex
->NbRows
+nparam
+1, nparam
+1);
2208 value_set_si(lcm
, 1);
2209 for (int j
= 0; j
< PV
->Vertex
->NbRows
; ++j
)
2210 value_lcm(lcm
, lcm
, PV
->Vertex
->p
[j
][nparam
+1]);
2211 value_assign(M
->p
[M
->NbRows
-1][M
->NbColumns
-1], lcm
);
2212 for (int j
= 0; j
< PV
->Vertex
->NbRows
; ++j
) {
2213 value_division(tmp
, lcm
, PV
->Vertex
->p
[j
][nparam
+1]);
2214 Vector_Scale(PV
->Vertex
->p
[j
], M
->p
[j
], tmp
, nparam
+1);
2216 for (int j
= 0; j
< nparam
; ++j
)
2217 value_assign(M
->p
[PV
->Vertex
->NbRows
+j
][j
], lcm
);
2219 Matrix
*M2
= Matrix_Alloc(T
->NbRows
, M
->NbColumns
);
2220 Matrix_Product(T
, M
, M2
);
2224 for (int j
= 0; j
< dim
; ++j
) {
2225 values2zz(M
->p
[j
], v
, nparam
+1);
2226 term
->vertex
[j
] = multi_monom(v
);
2227 value_assign(factor
.d
, lcm
);
2228 emul(&factor
, term
->vertex
[j
]);
2232 assert(i
== PP
->nbV
);
2233 free_evalue_refs(&factor
);
2238 static vector
<max_term
*> lexmin(indicator
& ind
, unsigned nparam
,
2241 vector
<max_term
*> maxima
;
2242 partial_order::head_type::iterator i
;
2243 vector
<int> best_score
;
2244 vector
<int> second_score
;
2245 vector
<int> neg_score
;
2248 ind
.perform_pending_substitutions();
2249 const indicator_term
*best
= NULL
, *second
= NULL
, *neg
= NULL
,
2250 *neg_eq
= NULL
, *neg_le
= NULL
;
2251 for (i
= ind
.order
.head
.begin(); i
!= ind
.order
.head
.end(); ++i
) {
2253 const indicator_term
*term
= *i
;
2254 if (term
->sign
== 0) {
2255 ind
.expand_rational_vertex(term
);
2259 if (ind
.order
.eq
.find(term
) != ind
.order
.eq
.end()) {
2261 if (ind
.order
.eq
[term
].size() <= 1)
2263 for (j
= 1; j
< ind
.order
.eq
[term
].size(); ++j
)
2264 if (ind
.order
.pred
.find(ind
.order
.eq
[term
][j
]) !=
2265 ind
.order
.pred
.end())
2267 if (j
< ind
.order
.eq
[term
].size())
2269 score
.push_back(ind
.order
.eq
[term
].size());
2272 if (ind
.order
.le
.find(term
) != ind
.order
.le
.end())
2273 score
.push_back(ind
.order
.le
[term
].size());
2276 if (ind
.order
.lt
.find(term
) != ind
.order
.lt
.end())
2277 score
.push_back(-ind
.order
.lt
[term
].size());
2281 if (term
->sign
> 0) {
2282 if (!best
|| score
< best_score
) {
2284 second_score
= best_score
;
2287 } else if (!second
|| score
< second_score
) {
2289 second_score
= score
;
2292 if (!neg_eq
&& ind
.order
.eq
.find(term
) != ind
.order
.eq
.end()) {
2293 for (int j
= 1; j
< ind
.order
.eq
[term
].size(); ++j
)
2294 if (ind
.order
.eq
[term
][j
]->sign
!= term
->sign
) {
2299 if (!neg_le
&& ind
.order
.le
.find(term
) != ind
.order
.le
.end())
2301 if (!neg
|| score
< neg_score
) {
2307 if (i
!= ind
.order
.head
.end())
2310 if (!best
&& neg_eq
) {
2311 assert(ind
.order
.eq
[neg_eq
].size() != 0);
2312 bool handled
= ind
.handle_equal_numerators(neg_eq
);
2317 if (!best
&& neg_le
) {
2318 /* The smallest term is negative and <= some positive term */
2324 /* apparently there can be negative initial term on empty domains */
2325 if (ind
.options
->emptiness_check
!= BV_LEXMIN_EMPTINESS_CHECK_NONE
&&
2326 ind
.options
->verify
->barvinok
->lp_solver
== BV_LP_POLYLIB
)
2331 if (!second
&& !neg
) {
2332 const indicator_term
*rat
= NULL
;
2334 if (ind
.order
.le
.find(best
) == ind
.order
.le
.end()) {
2335 if (ind
.order
.eq
.find(best
) != ind
.order
.eq
.end()) {
2336 bool handled
= ind
.handle_equal_numerators(best
);
2337 if (ind
.options
->emptiness_check
!=
2338 BV_LEXMIN_EMPTINESS_CHECK_NONE
&&
2339 ind
.options
->verify
->barvinok
->lp_solver
== BV_LP_POLYLIB
)
2341 /* If !handled then the leading coefficient is bigger than one;
2342 * must be an empty domain
2349 maxima
.push_back(ind
.create_max_term(best
));
2352 for (int j
= 0; j
< ind
.order
.le
[best
].size(); ++j
) {
2353 if (ind
.order
.le
[best
][j
]->sign
== 0) {
2354 if (!rat
&& ind
.order
.pred
[ind
.order
.le
[best
][j
]] == 1)
2355 rat
= ind
.order
.le
[best
][j
];
2356 } else if (ind
.order
.le
[best
][j
]->sign
> 0) {
2357 second
= ind
.order
.le
[best
][j
];
2360 neg
= ind
.order
.le
[best
][j
];
2363 if (!second
&& !neg
) {
2365 ind
.order
.unset_le(best
, rat
);
2366 ind
.expand_rational_vertex(rat
);
2373 ind
.order
.unset_le(best
, second
);
2379 unsigned dim
= best
->den
.NumCols();
2382 for (int k
= 0; k
< dim
; ++k
) {
2383 diff
= ediff(best
->vertex
[k
], second
->vertex
[k
]);
2384 sign
= evalue_sign(diff
, ind
.D
, ind
.options
->verify
->barvinok
);
2386 /* neg can never be smaller than best, unless it may still cancel.
2387 * This can happen if positive terms have been determined to
2388 * be equal or less than or equal to some negative term.
2390 if (second
== neg
&& !neg_eq
&& !neg_le
) {
2391 if (sign
== order_ge
)
2393 if (sign
== order_unknown
)
2397 if (sign
!= order_eq
)
2399 if (!EVALUE_IS_ZERO(*diff
)) {
2400 ind
.add_substitution(diff
);
2401 ind
.perform_pending_substitutions();
2404 if (sign
== order_eq
) {
2405 ind
.order
.set_equal(best
, second
);
2408 if (sign
== order_lt
) {
2409 ind
.order
.lt
[best
].push_back(second
);
2410 ind
.order
.inc_pred(second
);
2413 if (sign
== order_gt
) {
2414 ind
.order
.lt
[second
].push_back(best
);
2415 ind
.order
.inc_pred(best
);
2419 split
sp(diff
, sign
== order_le
? split::le
:
2420 sign
== order_ge
? split::ge
: split::lge
);
2422 EDomain
*Dlt
, *Deq
, *Dgt
;
2423 split_on(sp
, ind
.D
, &Dlt
, &Deq
, &Dgt
, ind
.options
);
2424 if (ind
.options
->emptiness_check
!= BV_LEXMIN_EMPTINESS_CHECK_NONE
)
2425 assert(Dlt
|| Deq
|| Dgt
);
2426 else if (!(Dlt
|| Deq
|| Dgt
))
2427 /* Must have been empty all along */
2430 if (Deq
&& (Dlt
|| Dgt
)) {
2431 int locsize
= loc
.size();
2433 indicator
indeq(ind
, Deq
);
2435 indeq
.add_substitution(diff
);
2436 indeq
.perform_pending_substitutions();
2437 vector
<max_term
*> maxeq
= lexmin(indeq
, nparam
, loc
);
2438 maxima
.insert(maxima
.end(), maxeq
.begin(), maxeq
.end());
2439 loc
.resize(locsize
);
2442 int locsize
= loc
.size();
2444 indicator
indgt(ind
, Dgt
);
2446 /* we don't know the new location of these terms in indgt */
2448 indgt.order.lt[second].push_back(best);
2449 indgt.order.inc_pred(best);
2451 vector
<max_term
*> maxgt
= lexmin(indgt
, nparam
, loc
);
2452 maxima
.insert(maxima
.end(), maxgt
.begin(), maxgt
.end());
2453 loc
.resize(locsize
);
2458 ind
.set_domain(Deq
);
2459 ind
.add_substitution(diff
);
2460 ind
.perform_pending_substitutions();
2464 ind
.set_domain(Dlt
);
2465 ind
.order
.lt
[best
].push_back(second
);
2466 ind
.order
.inc_pred(second
);
2470 ind
.set_domain(Dgt
);
2471 ind
.order
.lt
[second
].push_back(best
);
2472 ind
.order
.inc_pred(best
);
2479 static void lexmin_base(Polyhedron
*P
, Polyhedron
*C
,
2480 Matrix
*CP
, Matrix
*T
,
2481 vector
<max_term
*>& all_max
,
2482 lexmin_options
*options
)
2484 unsigned nparam
= C
->Dimension
;
2485 Param_Polyhedron
*PP
= NULL
;
2487 PP
= Polyhedron2Param_Polyhedron(P
, C
, options
->verify
->barvinok
);
2489 unsigned dim
= P
->Dimension
- nparam
;
2493 indicator_constructor
ic(P
, dim
, PP
, T
);
2495 vector
<indicator_term
*> all_vertices
;
2496 construct_rational_vertices(PP
, T
, T
? T
->NbRows
-nparam
-1 : dim
,
2497 nparam
, all_vertices
);
2499 Polyhedron
*TC
= true_context(P
, C
, options
->verify
->barvinok
->MaxRays
);
2500 FORALL_REDUCED_DOMAIN(PP
, TC
, nd
, options
->verify
->barvinok
, i
, D
, rVD
)
2503 EDomain
*epVD
= new EDomain(rVD
);
2504 indicator
ind(ic
, D
, epVD
, options
);
2506 FORALL_PVertex_in_ParamPolyhedron(V
,D
,PP
) // _i is internal counter
2507 ind
.add(all_vertices
[_i
]);
2508 END_FORALL_PVertex_in_ParamPolyhedron
;
2510 ind
.remove_initial_rational_vertices();
2513 vector
<max_term
*> maxima
= lexmin(ind
, nparam
, loc
);
2515 for (int j
= 0; j
< maxima
.size(); ++j
)
2516 maxima
[j
]->substitute(CP
, options
->verify
->barvinok
);
2517 all_max
.insert(all_max
.end(), maxima
.begin(), maxima
.end());
2520 END_FORALL_REDUCED_DOMAIN
2521 Polyhedron_Free(TC
);
2522 for (int i
= 0; i
< all_vertices
.size(); ++i
)
2523 delete all_vertices
[i
];
2524 Param_Polyhedron_Free(PP
);
2527 static vector
<max_term
*> lexmin(Polyhedron
*P
, Polyhedron
*C
,
2528 lexmin_options
*options
)
2530 unsigned nparam
= C
->Dimension
;
2531 Matrix
*T
= NULL
, *CP
= NULL
;
2532 Polyhedron
*Porig
= P
;
2533 Polyhedron
*Corig
= C
;
2534 vector
<max_term
*> all_max
;
2539 POL_ENSURE_VERTICES(P
);
2544 assert(P
->NbBid
== 0);
2547 remove_all_equalities(&P
, &C
, &CP
, &T
, nparam
,
2548 options
->verify
->barvinok
->MaxRays
);
2550 lexmin_base(P
, C
, CP
, T
, all_max
, options
);
2563 static void verify_results(Polyhedron
*A
, Polyhedron
*C
,
2564 vector
<max_term
*>& maxima
,
2565 struct verify_options
*options
);
2567 /* Turn the set dimensions of "context" into parameters and return
2568 * the corresponding parameter domain.
2570 static struct isl_basic_set
*to_parameter_domain(struct isl_basic_set
*context
)
2572 context
= isl_basic_set_move_dims(context
, isl_dim_param
, 0,
2573 isl_dim_set
, 0, isl_basic_set_dim(context
, isl_dim_set
));
2574 context
= isl_basic_set_params(context
);
2578 int main(int argc
, char **argv
)
2581 isl_basic_set
*context
, *bset
;
2586 int urs_unknowns
= 0;
2587 int print_solution
= 1;
2588 struct lexmin_options
*options
= lexmin_options_new_with_defaults();
2590 options
->verify
->barvinok
->lookup_table
= 0;
2592 argc
= lexmin_options_parse(options
, argc
, argv
, ISL_ARG_ALL
);
2593 ctx
= isl_ctx_alloc_with_options(&lexmin_options_args
, options
);
2595 context
= isl_basic_set_read_from_file(ctx
, stdin
);
2597 n
= fscanf(stdin
, "%d", &neg_one
);
2599 assert(neg_one
== -1);
2600 bset
= isl_basic_set_read_from_file(ctx
, stdin
);
2602 while (fgets(s
, sizeof(s
), stdin
)) {
2603 if (strncasecmp(s
, "Maximize", 8) == 0) {
2604 fprintf(stderr
, "Maximize option not supported\n");
2607 if (strncasecmp(s
, "Rational", 8) == 0) {
2608 fprintf(stderr
, "Rational option not supported\n");
2611 if (strncasecmp(s
, "Urs_parms", 9) == 0)
2613 if (strncasecmp(s
, "Urs_unknowns", 12) == 0)
2617 context
= isl_basic_set_intersect(context
,
2618 isl_basic_set_positive_orthant(isl_basic_set_get_space(context
)));
2619 context
= to_parameter_domain(context
);
2620 nparam
= isl_basic_set_dim(context
, isl_dim_param
);
2621 if (nparam
!= isl_basic_set_dim(bset
, isl_dim_param
)) {
2622 int dim
= isl_basic_set_dim(bset
, isl_dim_set
);
2623 bset
= isl_basic_set_move_dims(bset
, isl_dim_param
, 0,
2624 isl_dim_set
, dim
- nparam
, nparam
);
2627 bset
= isl_basic_set_intersect(bset
,
2628 isl_basic_set_positive_orthant(isl_basic_set_get_space(bset
)));
2630 if (options
->verify
->verify
)
2633 A
= isl_basic_set_to_polylib(bset
);
2634 verify_options_set_range(options
->verify
, A
->Dimension
);
2635 C
= isl_basic_set_to_polylib(context
);
2636 vector
<max_term
*> maxima
= lexmin(A
, C
, options
);
2637 if (print_solution
) {
2639 param_names
= util_generate_names(C
->Dimension
, "p");
2640 for (int i
= 0; i
< maxima
.size(); ++i
)
2641 maxima
[i
]->print(cout
, param_names
,
2642 options
->verify
->barvinok
);
2643 util_free_names(C
->Dimension
, param_names
);
2646 if (options
->verify
->verify
)
2647 verify_results(A
, C
, maxima
, options
->verify
);
2649 for (int i
= 0; i
< maxima
.size(); ++i
)
2655 isl_basic_set_free(bset
);
2656 isl_basic_set_free(context
);
2662 static bool lexmin(int pos
, Polyhedron
*P
, Value
*context
)
2671 value_init(LB
); value_init(UB
); value_init(k
);
2674 lu_flags
= lower_upper_bounds(pos
,P
,context
,&LB
,&UB
);
2675 assert(!(lu_flags
& LB_INFINITY
));
2677 value_set_si(context
[pos
],0);
2678 if (!lu_flags
&& value_lt(UB
,LB
)) {
2679 value_clear(LB
); value_clear(UB
); value_clear(k
);
2683 value_assign(context
[pos
], LB
);
2684 value_clear(LB
); value_clear(UB
); value_clear(k
);
2687 for (value_assign(k
,LB
); lu_flags
|| value_le(k
,UB
); value_increment(k
,k
)) {
2688 value_assign(context
[pos
],k
);
2689 if ((found
= lexmin(pos
+1, P
->next
, context
)))
2693 value_set_si(context
[pos
],0);
2694 value_clear(LB
); value_clear(UB
); value_clear(k
);
2698 static void print_list(FILE *out
, Value
*z
, const char* brackets
, int len
)
2700 fprintf(out
, "%c", brackets
[0]);
2701 value_print(out
, VALUE_FMT
,z
[0]);
2702 for (int k
= 1; k
< len
; ++k
) {
2704 value_print(out
, VALUE_FMT
,z
[k
]);
2706 fprintf(out
, "%c", brackets
[1]);
2709 static int check_poly_lexmin(const struct check_poly_data
*data
,
2710 int nparam
, Value
*z
,
2711 const struct verify_options
*options
);
2713 struct check_poly_lexmin_data
: public check_poly_data
{
2715 vector
<max_term
*>& maxima
;
2717 check_poly_lexmin_data(Polyhedron
*S
, Value
*z
,
2718 vector
<max_term
*>& maxima
) : S(S
), maxima(maxima
) {
2720 this->check
= &check_poly_lexmin
;
2724 static int check_poly_lexmin(const struct check_poly_data
*data
,
2725 int nparam
, Value
*z
,
2726 const struct verify_options
*options
)
2728 const check_poly_lexmin_data
*lexmin_data
;
2729 lexmin_data
= static_cast<const check_poly_lexmin_data
*>(data
);
2730 Polyhedron
*S
= lexmin_data
->S
;
2731 vector
<max_term
*>& maxima
= lexmin_data
->maxima
;
2733 bool found
= lexmin(1, S
, lexmin_data
->z
);
2735 if (options
->print_all
) {
2737 print_list(stdout
, z
, "()", nparam
);
2740 print_list(stdout
, lexmin_data
->z
+1, "[]", S
->Dimension
-nparam
);
2745 for (int i
= 0; i
< maxima
.size(); ++i
)
2746 if ((min
= maxima
[i
]->eval(z
, options
->barvinok
->MaxRays
)))
2749 int ok
= !(found
^ !!min
);
2751 for (int i
= 0; i
< S
->Dimension
-nparam
; ++i
)
2752 if (value_ne(lexmin_data
->z
[1+i
], min
->p
[i
])) {
2759 fprintf(stderr
, "Error !\n");
2760 fprintf(stderr
, "lexmin");
2761 print_list(stderr
, z
, "()", nparam
);
2762 fprintf(stderr
, " should be ");
2764 print_list(stderr
, lexmin_data
->z
+1, "[]", S
->Dimension
-nparam
);
2765 fprintf(stderr
, " while digging gives ");
2767 print_list(stderr
, min
->p
, "[]", S
->Dimension
-nparam
);
2768 fprintf(stderr
, ".\n");
2770 } else if (options
->print_all
)
2775 for (k
= 1; k
<= S
->Dimension
-nparam
; ++k
)
2776 value_set_si(lexmin_data
->z
[k
], 0);
2781 void verify_results(Polyhedron
*A
, Polyhedron
*C
, vector
<max_term
*>& maxima
,
2782 struct verify_options
*options
)
2785 unsigned nparam
= C
->Dimension
;
2786 unsigned MaxRays
= options
->barvinok
->MaxRays
;
2789 CS
= check_poly_context_scan(A
, &C
, nparam
, options
);
2791 p
= Vector_Alloc(A
->Dimension
+2);
2792 value_set_si(p
->p
[A
->Dimension
+1], 1);
2794 S
= Polyhedron_Scan(A
, C
, MaxRays
& POL_NO_DUAL
? 0 : MaxRays
);
2796 check_poly_init(C
, options
);
2799 if (!(CS
&& emptyQ2(CS
))) {
2800 check_poly_lexmin_data
data(S
, p
->p
, maxima
);
2801 check_poly(CS
, &data
, nparam
, 0, p
->p
+S
->Dimension
-nparam
+1, options
);
2806 if (!options
->print_all
)