6 #include <NTL/vec_ZZ.h>
7 #include <NTL/mat_ZZ.h>
9 #include <polylib/polylibgmp.h>
11 #include <barvinok/barvinok.h>
12 #include <barvinok/evalue.h>
13 #include <barvinok/options.h>
14 #include <barvinok/util.h>
15 #include "conversion.h"
16 #include "decomposer.h"
17 #include "lattice_point.h"
18 #include "reduce_domain.h"
22 #include "evalue_util.h"
37 /* RANGE : normal range for evalutations (-RANGE -> RANGE) */
40 /* SRANGE : small range for evalutations */
43 /* if dimension >= BIDDIM, use SRANGE */
46 /* VSRANGE : very small range for evalutations */
49 /* if dimension >= VBIDDIM, use VSRANGE */
53 #define getopt_long(a,b,c,d,e) getopt(a,b,c)
56 #define NO_EMPTINESS_CHECK 256
57 struct option lexmin_options
[] = {
58 { "verify", no_argument
, 0, 'T' },
59 { "print-all", no_argument
, 0, 'A' },
60 { "no-emptiness-check", no_argument
, 0, NO_EMPTINESS_CHECK
},
61 { "min", required_argument
, 0, 'm' },
62 { "max", required_argument
, 0, 'M' },
63 { "range", required_argument
, 0, 'r' },
64 { "version", no_argument
, 0, 'V' },
69 #define ALLOCN(type,n) (type*)malloc((n) * sizeof(type))
71 static int type_offset(enode
*p
)
73 return p
->type
== fractional
? 1 :
74 p
->type
== flooring
? 1 : 0;
77 struct indicator_term
{
83 indicator_term(unsigned dim
, int pos
) {
85 vertex
= new evalue
* [dim
];
89 indicator_term(unsigned dim
) {
90 den
.SetDims(dim
, dim
);
91 vertex
= new evalue
* [dim
];
94 indicator_term(const indicator_term
& src
) {
98 unsigned dim
= den
.NumCols();
99 vertex
= new evalue
* [dim
];
100 for (int i
= 0; i
< dim
; ++i
) {
101 vertex
[i
] = new evalue();
102 value_init(vertex
[i
]->d
);
103 evalue_copy(vertex
[i
], src
.vertex
[i
]);
107 unsigned dim
= den
.NumCols();
108 for (int i
= 0; i
< dim
; ++i
) {
109 free_evalue_refs(vertex
[i
]);
114 void print(ostream
& os
, char **p
) const;
115 void substitute(Matrix
*T
);
117 void substitute(evalue
*fract
, evalue
*val
);
118 void substitute(int pos
, evalue
*val
);
119 void reduce_in_domain(Polyhedron
*D
);
120 bool is_opposite(indicator_term
*neg
);
123 bool indicator_term::is_opposite(indicator_term
*neg
)
125 if (sign
+ neg
->sign
!= 0)
129 for (int k
= 0; k
< den
.NumCols(); ++k
)
130 if (!eequal(vertex
[k
], neg
->vertex
[k
]))
135 void indicator_term::reduce_in_domain(Polyhedron
*D
)
137 for (int k
= 0; k
< den
.NumCols(); ++k
) {
138 reduce_evalue_in_domain(vertex
[k
], D
);
139 if (evalue_range_reduction_in_domain(vertex
[k
], D
))
140 reduce_evalue(vertex
[k
]);
144 void indicator_term::print(ostream
& os
, char **p
) const
146 unsigned dim
= den
.NumCols();
147 unsigned factors
= den
.NumRows();
155 for (int i
= 0; i
< dim
; ++i
) {
158 evalue_print(os
, vertex
[i
], p
);
161 for (int i
= 0; i
< factors
; ++i
) {
162 os
<< " + t" << i
<< "*[";
163 for (int j
= 0; j
< dim
; ++j
) {
171 os
<< " (" << pos
<< ")";
174 /* Perform the substitution specified by T on the variables.
175 * T has dimension (newdim+nparam+1) x (olddim + nparam + 1).
176 * The substitution is performed as in gen_fun::substitute
178 void indicator_term::substitute(Matrix
*T
)
180 unsigned dim
= den
.NumCols();
181 unsigned nparam
= T
->NbColumns
- dim
- 1;
182 unsigned newdim
= T
->NbRows
- nparam
- 1;
185 matrix2zz(T
, trans
, newdim
, dim
);
186 trans
= transpose(trans
);
188 newvertex
= new evalue
* [newdim
];
191 v
.SetLength(nparam
+1);
194 value_init(factor
.d
);
195 value_set_si(factor
.d
, 1);
196 value_init(factor
.x
.n
);
197 for (int i
= 0; i
< newdim
; ++i
) {
198 values2zz(T
->p
[i
]+dim
, v
, nparam
+1);
199 newvertex
[i
] = multi_monom(v
);
201 for (int j
= 0; j
< dim
; ++j
) {
202 if (value_zero_p(T
->p
[i
][j
]))
206 evalue_copy(&term
, vertex
[j
]);
207 value_assign(factor
.x
.n
, T
->p
[i
][j
]);
208 emul(&factor
, &term
);
209 eadd(&term
, newvertex
[i
]);
210 free_evalue_refs(&term
);
213 free_evalue_refs(&factor
);
214 for (int i
= 0; i
< dim
; ++i
) {
215 free_evalue_refs(vertex
[i
]);
222 static void evalue_add_constant(evalue
*e
, ZZ v
)
227 /* go down to constant term */
228 while (value_zero_p(e
->d
))
229 e
= &e
->x
.p
->arr
[type_offset(e
->x
.p
)];
232 value_multiply(tmp
, tmp
, e
->d
);
233 value_addto(e
->x
.n
, e
->x
.n
, tmp
);
238 /* Make all powers in denominator lexico-positive */
239 void indicator_term::normalize()
242 extra_vertex
.SetLength(den
.NumCols());
243 for (int r
= 0; r
< den
.NumRows(); ++r
) {
244 for (int k
= 0; k
< den
.NumCols(); ++k
) {
251 extra_vertex
+= den
[r
];
255 for (int k
= 0; k
< extra_vertex
.length(); ++k
)
256 if (extra_vertex
[k
] != 0)
257 evalue_add_constant(vertex
[k
], extra_vertex
[k
]);
260 static void substitute(evalue
*e
, evalue
*fract
, evalue
*val
)
264 for (t
= e
; value_zero_p(t
->d
); t
= &t
->x
.p
->arr
[type_offset(t
->x
.p
)]) {
265 if (t
->x
.p
->type
== fractional
&& eequal(&t
->x
.p
->arr
[0], fract
))
268 if (value_notzero_p(t
->d
))
271 free_evalue_refs(&t
->x
.p
->arr
[0]);
272 evalue
*term
= &t
->x
.p
->arr
[2];
279 free_evalue_refs(term
);
285 void indicator_term::substitute(evalue
*fract
, evalue
*val
)
287 unsigned dim
= den
.NumCols();
288 for (int i
= 0; i
< dim
; ++i
) {
289 ::substitute(vertex
[i
], fract
, val
);
293 static void substitute(evalue
*e
, int pos
, evalue
*val
)
297 for (t
= e
; value_zero_p(t
->d
); t
= &t
->x
.p
->arr
[type_offset(t
->x
.p
)]) {
298 if (t
->x
.p
->type
== polynomial
&& t
->x
.p
->pos
== pos
)
301 if (value_notzero_p(t
->d
))
304 evalue
*term
= &t
->x
.p
->arr
[1];
311 free_evalue_refs(term
);
317 void indicator_term::substitute(int pos
, evalue
*val
)
319 unsigned dim
= den
.NumCols();
320 for (int i
= 0; i
< dim
; ++i
) {
321 ::substitute(vertex
[i
], pos
, val
);
325 struct indicator_constructor
: public polar_decomposer
, public vertex_decomposer
{
327 vector
<indicator_term
*> *terms
;
328 Matrix
*T
; /* Transformation to original space */
329 Param_Polyhedron
*PP
;
331 indicator_constructor(Polyhedron
*P
, unsigned dim
, Param_Polyhedron
*PP
,
333 vertex_decomposer(P
, PP
->nbV
, this), T(T
), PP(PP
) {
334 vertex
.SetLength(dim
);
335 terms
= new vector
<indicator_term
*>[nbV
];
337 ~indicator_constructor() {
338 for (int i
= 0; i
< nbV
; ++i
)
339 for (int j
= 0; j
< terms
[i
].size(); ++j
)
343 void substitute(Matrix
*T
);
345 void print(ostream
& os
, char **p
);
347 virtual void handle_polar(Polyhedron
*P
, int sign
);
350 void indicator_constructor::handle_polar(Polyhedron
*C
, int s
)
352 unsigned dim
= vertex
.length();
354 assert(C
->NbRays
-1 == dim
);
356 indicator_term
*term
= new indicator_term(dim
);
358 terms
[vert
].push_back(term
);
360 lattice_point(V
, C
, vertex
, term
->vertex
);
362 for (int r
= 0; r
< dim
; ++r
) {
363 values2zz(C
->Ray
[r
]+1, term
->den
[r
], dim
);
364 for (int j
= 0; j
< dim
; ++j
) {
365 if (term
->den
[r
][j
] == 0)
367 if (term
->den
[r
][j
] > 0)
369 term
->sign
= -term
->sign
;
370 term
->den
[r
] = -term
->den
[r
];
371 vertex
+= term
->den
[r
];
376 for (int i
= 0; i
< dim
; ++i
) {
377 if (!term
->vertex
[i
]) {
378 term
->vertex
[i
] = new evalue();
379 value_init(term
->vertex
[i
]->d
);
380 value_init(term
->vertex
[i
]->x
.n
);
381 zz2value(vertex
[i
], term
->vertex
[i
]->x
.n
);
382 value_set_si(term
->vertex
[i
]->d
, 1);
387 evalue_add_constant(term
->vertex
[i
], vertex
[i
]);
395 lex_order_rows(term
->den
);
398 void indicator_constructor::print(ostream
& os
, char **p
)
400 for (int i
= 0; i
< nbV
; ++i
)
401 for (int j
= 0; j
< terms
[i
].size(); ++j
) {
402 os
<< "i: " << i
<< ", j: " << j
<< endl
;
403 terms
[i
][j
]->print(os
, p
);
408 void indicator_constructor::normalize()
410 for (int i
= 0; i
< nbV
; ++i
)
411 for (int j
= 0; j
< terms
[i
].size(); ++j
) {
413 vertex
.SetLength(terms
[i
][j
]->den
.NumCols());
414 for (int r
= 0; r
< terms
[i
][j
]->den
.NumRows(); ++r
) {
415 for (int k
= 0; k
< terms
[i
][j
]->den
.NumCols(); ++k
) {
416 if (terms
[i
][j
]->den
[r
][k
] == 0)
418 if (terms
[i
][j
]->den
[r
][k
] > 0)
420 terms
[i
][j
]->sign
= -terms
[i
][j
]->sign
;
421 terms
[i
][j
]->den
[r
] = -terms
[i
][j
]->den
[r
];
422 vertex
+= terms
[i
][j
]->den
[r
];
426 lex_order_rows(terms
[i
][j
]->den
);
427 for (int k
= 0; k
< vertex
.length(); ++k
)
429 evalue_add_constant(terms
[i
][j
]->vertex
[k
], vertex
[k
]);
435 enum order_sign
{ order_lt
, order_le
, order_eq
, order_ge
, order_gt
, order_unknown
};
437 struct partial_order
{
440 map
<indicator_term
*, int > pred
;
441 map
<indicator_term
*, vector
<indicator_term
* > > lt
;
442 map
<indicator_term
*, vector
<indicator_term
* > > le
;
443 map
<indicator_term
*, vector
<indicator_term
* > > eq
;
445 map
<indicator_term
*, vector
<indicator_term
* > > pending
;
447 partial_order(indicator
*ind
) : ind(ind
) {}
448 void copy(const partial_order
& order
,
449 map
< indicator_term
*, indicator_term
* > old2new
);
451 order_sign
compare(indicator_term
*a
, indicator_term
*b
);
452 void set_equal(indicator_term
*a
, indicator_term
*b
);
453 void unset_le(indicator_term
*a
, indicator_term
*b
);
455 bool compared(indicator_term
* a
, indicator_term
* b
);
456 void add(indicator_term
* it
, std::set
<indicator_term
*> *filter
);
457 void remove(indicator_term
* it
);
459 void print(ostream
& os
, char **p
);
462 void partial_order::unset_le(indicator_term
*a
, indicator_term
*b
)
464 vector
<indicator_term
*>::iterator i
;
465 i
= find(le
[a
].begin(), le
[a
].end(), b
);
468 i
= find(pending
[a
].begin(), pending
[a
].end(), b
);
469 if (i
!= pending
[a
].end())
473 void partial_order::set_equal(indicator_term
*a
, indicator_term
*b
)
475 if (eq
[a
].size() == 0)
477 if (eq
[b
].size() == 0)
483 indicator_term
*c
= a
;
488 indicator_term
*base
= a
;
490 map
<indicator_term
*, vector
<indicator_term
* > >::iterator i
;
492 for (int j
= 0; j
< eq
[b
].size(); ++j
) {
493 eq
[base
].push_back(eq
[b
][j
]);
494 eq
[eq
[b
][j
]][0] = base
;
500 for (int j
= 0; j
< lt
[b
].size(); ++j
) {
501 if (find(eq
[base
].begin(), eq
[base
].end(), lt
[b
][j
]) != eq
[base
].end())
503 else if (find(lt
[base
].begin(), lt
[base
].end(), lt
[b
][j
])
507 lt
[base
].push_back(lt
[b
][j
]);
514 for (int j
= 0; j
< le
[b
].size(); ++j
) {
515 if (find(eq
[base
].begin(), eq
[base
].end(), le
[b
][j
]) != eq
[base
].end())
517 else if (find(le
[base
].begin(), le
[base
].end(), le
[b
][j
])
521 le
[base
].push_back(le
[b
][j
]);
526 i
= pending
.find(base
);
527 if (i
!= pending
.end()) {
528 vector
<indicator_term
* > old
= pending
[base
];
529 pending
[base
].clear();
530 for (int j
= 0; j
< old
.size(); ++j
) {
531 if (find(eq
[base
].begin(), eq
[base
].end(), old
[j
]) == eq
[base
].end())
532 pending
[base
].push_back(old
[j
]);
537 if (i
!= pending
.end()) {
538 for (int j
= 0; j
< pending
[b
].size(); ++j
) {
539 if (find(eq
[base
].begin(), eq
[base
].end(), pending
[b
][j
]) == eq
[base
].end())
540 pending
[base
].push_back(pending
[b
][j
]);
546 void partial_order::copy(const partial_order
& order
,
547 map
< indicator_term
*, indicator_term
* > old2new
)
549 map
<indicator_term
*, vector
<indicator_term
* > >::const_iterator i
;
550 map
<indicator_term
*, int >::const_iterator j
;
552 for (j
= order
.pred
.begin(); j
!= order
.pred
.end(); ++j
)
553 pred
[old2new
[(*j
).first
]] = (*j
).second
;
555 for (i
= order
.lt
.begin(); i
!= order
.lt
.end(); ++i
) {
556 for (int j
= 0; j
< (*i
).second
.size(); ++j
)
557 lt
[old2new
[(*i
).first
]].push_back(old2new
[(*i
).second
[j
]]);
559 for (i
= order
.le
.begin(); i
!= order
.le
.end(); ++i
) {
560 for (int j
= 0; j
< (*i
).second
.size(); ++j
)
561 le
[old2new
[(*i
).first
]].push_back(old2new
[(*i
).second
[j
]]);
563 for (i
= order
.eq
.begin(); i
!= order
.eq
.end(); ++i
) {
564 for (int j
= 0; j
< (*i
).second
.size(); ++j
)
565 eq
[old2new
[(*i
).first
]].push_back(old2new
[(*i
).second
[j
]]);
567 for (i
= order
.pending
.begin(); i
!= order
.pending
.end(); ++i
) {
568 for (int j
= 0; j
< (*i
).second
.size(); ++j
)
569 pending
[old2new
[(*i
).first
]].push_back(old2new
[(*i
).second
[j
]]);
573 static void add_coeff(Value
*cons
, int len
, evalue
*coeff
, int pos
)
577 assert(value_notzero_p(coeff
->d
));
581 value_lcm(cons
[0], coeff
->d
, &tmp
);
582 value_division(tmp
, tmp
, cons
[0]);
583 Vector_Scale(cons
, cons
, tmp
, len
);
584 value_division(tmp
, cons
[0], coeff
->d
);
585 value_addmul(cons
[pos
], tmp
, coeff
->x
.n
);
590 static int evalue2constraint_r(EDomain
*D
, evalue
*E
, Value
*cons
, int len
);
592 static void add_fract(evalue
*e
, Value
*cons
, int len
, int pos
)
596 evalue_set_si(&mone
, -1, 1);
598 /* contribution of alpha * fract(X) is
601 assert(e
->x
.p
->size
== 3);
603 value_init(argument
.d
);
604 evalue_copy(&argument
, &e
->x
.p
->arr
[0]);
605 emul(&e
->x
.p
->arr
[2], &argument
);
606 evalue2constraint_r(NULL
, &argument
, cons
, len
);
607 free_evalue_refs(&argument
);
609 /* - alpha * floor(X) */
610 emul(&mone
, &e
->x
.p
->arr
[2]);
611 add_coeff(cons
, len
, &e
->x
.p
->arr
[2], pos
);
612 emul(&mone
, &e
->x
.p
->arr
[2]);
614 free_evalue_refs(&mone
);
617 static int evalue2constraint_r(EDomain
*D
, evalue
*E
, Value
*cons
, int len
)
620 if (value_zero_p(E
->d
) && E
->x
.p
->type
== fractional
) {
622 assert(E
->x
.p
->size
== 3);
623 r
= evalue2constraint_r(D
, &E
->x
.p
->arr
[1], cons
, len
);
624 assert(value_notzero_p(E
->x
.p
->arr
[2].d
));
625 if (D
&& (i
= D
->find_floor(&E
->x
.p
->arr
[0])) >= 0) {
626 add_fract(E
, cons
, len
, 1+D
->D
->Dimension
-D
->floors
.size()+i
);
628 if (value_pos_p(E
->x
.p
->arr
[2].x
.n
)) {
631 value_init(coeff
.x
.n
);
632 value_set_si(coeff
.d
, 1);
633 evalue_denom(&E
->x
.p
->arr
[0], &coeff
.d
);
634 value_decrement(coeff
.x
.n
, coeff
.d
);
635 emul(&E
->x
.p
->arr
[2], &coeff
);
636 add_coeff(cons
, len
, &coeff
, len
-1);
637 free_evalue_refs(&coeff
);
641 } else if (value_zero_p(E
->d
)) {
642 assert(E
->x
.p
->type
== polynomial
);
643 assert(E
->x
.p
->size
== 2);
644 r
= evalue2constraint_r(D
, &E
->x
.p
->arr
[0], cons
, len
) || r
;
645 add_coeff(cons
, len
, &E
->x
.p
->arr
[1], E
->x
.p
->pos
);
647 add_coeff(cons
, len
, E
, len
-1);
652 static int evalue2constraint(EDomain
*D
, evalue
*E
, Value
*cons
, int len
)
654 Vector_Set(cons
, 0, len
);
655 value_set_si(cons
[0], 1);
656 return evalue2constraint_r(D
, E
, cons
, len
);
659 static void interval_minmax(Polyhedron
*I
, int *min
, int *max
)
661 assert(I
->Dimension
== 1);
664 POL_ENSURE_VERTICES(I
);
665 for (int i
= 0; i
< I
->NbRays
; ++i
) {
666 if (value_pos_p(I
->Ray
[i
][1]))
668 else if (value_neg_p(I
->Ray
[i
][1]))
679 static void interval_minmax(Polyhedron
*D
, Matrix
*T
, int *min
, int *max
,
682 Polyhedron
*I
= Polyhedron_Image(D
, T
, MaxRays
);
683 if (MaxRays
& POL_INTEGER
)
684 I
= DomainConstraintSimplify(I
, MaxRays
);
687 I
= Polyhedron_Image(D
, T
, MaxRays
);
689 interval_minmax(I
, min
, max
);
696 vector
<evalue
*> max
;
698 void print(ostream
& os
, char **p
) const;
699 void resolve_existential_vars() const;
700 void substitute(Matrix
*T
, unsigned MaxRays
);
701 Vector
*eval(Value
*val
, unsigned MaxRays
) const;
704 for (int i
= 0; i
< max
.size(); ++i
) {
705 free_evalue_refs(max
[i
]);
708 Polyhedron_Free(domain
);
713 * Project on first dim dimensions
715 Polyhedron
* Polyhedron_Project_Initial(Polyhedron
*P
, int dim
)
721 if (P
->Dimension
== dim
)
722 return Polyhedron_Copy(P
);
724 T
= Matrix_Alloc(dim
+1, P
->Dimension
+1);
725 for (i
= 0; i
< dim
; ++i
)
726 value_set_si(T
->p
[i
][i
], 1);
727 value_set_si(T
->p
[dim
][P
->Dimension
], 1);
728 I
= Polyhedron_Image(P
, T
, P
->NbConstraints
);
734 vector
<indicator_term
*> term
;
735 indicator_constructor
& ic
;
740 barvinok_options
*options
;
742 indicator(indicator_constructor
& ic
, Param_Domain
*PD
, EDomain
*D
,
743 barvinok_options
*options
) :
744 ic(ic
), PD(PD
), D(D
), order(this), options(options
), P(NULL
) {}
745 indicator(const indicator
& ind
, EDomain
*D
) :
746 ic(ind
.ic
), PD(ind
.PD
), D(NULL
), order(this), options(ind
.options
),
747 P(Polyhedron_Copy(ind
.P
)) {
748 map
< indicator_term
*, indicator_term
* > old2new
;
749 for (int i
= 0; i
< ind
.term
.size(); ++i
) {
750 indicator_term
*it
= new indicator_term(*ind
.term
[i
]);
751 old2new
[ind
.term
[i
]] = it
;
754 order
.copy(ind
.order
, old2new
);
758 for (int i
= 0; i
< term
.size(); ++i
)
766 void set_domain(EDomain
*D
) {
770 int nparam
= ic
.P
->Dimension
- ic
.vertex
.length();
771 Polyhedron
*Q
= Polyhedron_Project_Initial(D
->D
, nparam
);
772 Q
= DomainConstraintSimplify(Q
, options
->MaxRays
);
773 if (!P
|| !PolyhedronIncludes(Q
, P
))
780 void add(const indicator_term
* it
);
781 void remove(indicator_term
* it
);
782 void remove_initial_rational_vertices();
783 void expand_rational_vertex(indicator_term
*initial
);
785 void print(ostream
& os
, char **p
);
787 void peel(int i
, int j
);
788 void combine(indicator_term
*a
, indicator_term
*b
);
789 void substitute(evalue
*equation
);
790 void reduce_in_domain(Polyhedron
*D
);
791 bool handle_equal_numerators(indicator_term
*base
);
793 max_term
* create_max_term(indicator_term
*it
);
796 max_term
* indicator::create_max_term(indicator_term
*it
)
798 int dim
= it
->den
.NumCols();
799 int nparam
= ic
.P
->Dimension
- ic
.vertex
.length();
800 max_term
*maximum
= new max_term
;
801 maximum
->dim
= nparam
;
802 maximum
->domain
= Polyhedron_Copy(D
->D
);
803 for (int j
= 0; j
< dim
; ++j
) {
804 evalue
*E
= new evalue
;
806 evalue_copy(E
, it
->vertex
[j
]);
807 if (evalue_frac2floor_in_domain(E
, D
->D
))
809 maximum
->max
.push_back(E
);
814 static Matrix
*add_ge_constraint(EDomain
*ED
, evalue
*constraint
,
815 vector
<evalue
*>& new_floors
)
817 Polyhedron
*D
= ED
->D
;
820 evalue_set_si(&mone
, -1, 1);
822 for (evalue
*e
= constraint
; value_zero_p(e
->d
);
823 e
= &e
->x
.p
->arr
[type_offset(e
->x
.p
)]) {
825 if (e
->x
.p
->type
!= fractional
)
827 for (i
= 0; i
< ED
->floors
.size(); ++i
)
828 if (eequal(&e
->x
.p
->arr
[0], ED
->floors
[i
]))
830 if (i
< ED
->floors
.size())
835 int rows
= D
->NbConstraints
+2*fract
+1;
836 int cols
= 2+D
->Dimension
+fract
;
837 Matrix
*M
= Matrix_Alloc(rows
, cols
);
838 for (int i
= 0; i
< D
->NbConstraints
; ++i
) {
839 Vector_Copy(D
->Constraint
[i
], M
->p
[i
], 1+D
->Dimension
);
840 value_assign(M
->p
[i
][1+D
->Dimension
+fract
],
841 D
->Constraint
[i
][1+D
->Dimension
]);
843 value_set_si(M
->p
[rows
-1][0], 1);
846 for (e
= constraint
; value_zero_p(e
->d
); e
= &e
->x
.p
->arr
[type_offset(e
->x
.p
)]) {
847 if (e
->x
.p
->type
== fractional
) {
850 i
= ED
->find_floor(&e
->x
.p
->arr
[0]);
852 pos
= D
->Dimension
-ED
->floors
.size()+i
;
854 pos
= D
->Dimension
+fract
;
856 add_fract(e
, M
->p
[rows
-1], cols
, 1+pos
);
858 if (pos
< D
->Dimension
)
861 /* constraints for the new floor */
862 int row
= D
->NbConstraints
+2*fract
;
863 value_set_si(M
->p
[row
][0], 1);
864 evalue2constraint_r(NULL
, &e
->x
.p
->arr
[0], M
->p
[row
], cols
);
865 value_oppose(M
->p
[row
][1+D
->Dimension
+fract
], M
->p
[row
][0]);
866 value_set_si(M
->p
[row
][0], 1);
868 Vector_Scale(M
->p
[row
]+1, M
->p
[row
+1]+1, mone
.x
.n
, cols
-1);
869 value_set_si(M
->p
[row
+1][0], 1);
870 value_addto(M
->p
[row
+1][cols
-1], M
->p
[row
+1][cols
-1],
871 M
->p
[row
+1][1+D
->Dimension
+fract
]);
872 value_decrement(M
->p
[row
+1][cols
-1], M
->p
[row
+1][cols
-1]);
874 evalue
*arg
= new evalue
;
876 evalue_copy(arg
, &e
->x
.p
->arr
[0]);
877 new_floors
.push_back(arg
);
881 assert(e
->x
.p
->type
== polynomial
);
882 assert(e
->x
.p
->size
== 2);
883 add_coeff(M
->p
[rows
-1], cols
, &e
->x
.p
->arr
[1], e
->x
.p
->pos
);
886 add_coeff(M
->p
[rows
-1], cols
, e
, cols
-1);
887 value_set_si(M
->p
[rows
-1][0], 1);
888 free_evalue_refs(&mone
);
893 static evalue
*ediff(const evalue
*a
, const evalue
*b
)
897 evalue_set_si(&mone
, -1, 1);
898 evalue
*diff
= new evalue
;
900 evalue_copy(diff
, b
);
904 free_evalue_refs(&mone
);
908 static order_sign
evalue_sign(evalue
*diff
, EDomain
*D
, unsigned MaxRays
)
910 order_sign sign
= order_eq
;
913 evalue_set_si(&mone
, -1, 1);
914 int len
= 1 + D
->D
->Dimension
+ 1;
915 Vector
*c
= Vector_Alloc(len
);
916 Matrix
*T
= Matrix_Alloc(2, len
-1);
918 int fract
= evalue2constraint(D
, diff
, c
->p
, len
);
919 Vector_Copy(c
->p
+1, T
->p
[0], len
-1);
920 value_assign(T
->p
[1][len
-2], c
->p
[0]);
923 interval_minmax(D
->D
, T
, &min
, &max
, MaxRays
);
929 evalue2constraint(D
, diff
, c
->p
, len
);
931 Vector_Copy(c
->p
+1, T
->p
[0], len
-1);
932 value_assign(T
->p
[1][len
-2], c
->p
[0]);
935 interval_minmax(D
->D
, T
, &negmin
, &negmax
, MaxRays
);
940 else if (max
== 0 && min
== 0)
942 else if (min
< 0 && max
> 0)
943 sign
= order_unknown
;
952 free_evalue_refs(&mone
);
957 order_sign
partial_order::compare(indicator_term
*a
, indicator_term
*b
)
959 unsigned dim
= a
->den
.NumCols();
960 order_sign sign
= order_eq
;
962 unsigned MaxRays
= ind
->options
->MaxRays
;
963 if (MaxRays
& POL_INTEGER
&& (a
->sign
== 0 || b
->sign
== 0))
966 for (int k
= 0; k
< dim
; ++k
) {
967 /* compute a->vertex[k] - b->vertex[k] */
968 evalue
*diff
= ediff(a
->vertex
[k
], b
->vertex
[k
]);
969 order_sign diff_sign
= evalue_sign(diff
, D
, MaxRays
);
971 if (diff_sign
== order_lt
) {
972 if (sign
== order_eq
|| sign
== order_le
)
975 sign
= order_unknown
;
976 free_evalue_refs(diff
);
980 if (diff_sign
== order_gt
) {
981 if (sign
== order_eq
|| sign
== order_ge
)
984 sign
= order_unknown
;
985 free_evalue_refs(diff
);
989 if (diff_sign
== order_eq
) {
990 if (D
== ind
->D
&& !EVALUE_IS_ZERO(*diff
))
991 ind
->substitute(diff
);
992 free_evalue_refs(diff
);
996 if ((diff_sign
== order_unknown
) ||
997 ((diff_sign
== order_lt
|| diff_sign
== order_le
) && sign
== order_ge
) ||
998 ((diff_sign
== order_gt
|| diff_sign
== order_ge
) && sign
== order_le
)) {
999 free_evalue_refs(diff
);
1001 sign
= order_unknown
;
1008 vector
<evalue
*> new_floors
;
1009 M
= add_ge_constraint(D
, diff
, new_floors
);
1010 value_set_si(M
->p
[M
->NbRows
-1][0], 0);
1011 Polyhedron
*D2
= Constraints2Polyhedron(M
, MaxRays
);
1012 EDomain
*EDeq
= new EDomain(D2
, D
, new_floors
);
1013 Polyhedron_Free(D2
);
1015 for (int i
= 0; i
< new_floors
.size(); ++i
) {
1016 free_evalue_refs(new_floors
[i
]);
1017 delete new_floors
[i
];
1024 free_evalue_refs(diff
);
1034 bool partial_order::compared(indicator_term
* a
, indicator_term
* b
)
1036 map
<indicator_term
*, vector
<indicator_term
* > >::iterator j
;
1039 if (j
!= lt
.end() && find(lt
[a
].begin(), lt
[a
].end(), b
) != lt
[a
].end())
1043 if (j
!= le
.end() && find(le
[a
].begin(), le
[a
].end(), b
) != le
[a
].end())
1049 void partial_order::add(indicator_term
* it
, std::set
<indicator_term
*> *filter
)
1051 if (eq
.find(it
) != eq
.end() && eq
[it
].size() == 1)
1054 int it_pred
= filter
? pred
[it
] : 0;
1056 map
<indicator_term
*, int >::iterator i
;
1057 for (i
= pred
.begin(); i
!= pred
.end(); ++i
) {
1058 if ((*i
).second
!= 0)
1060 if (eq
.find((*i
).first
) != eq
.end() && eq
[(*i
).first
].size() == 1)
1063 if ((*i
).first
== it
)
1065 if (filter
->find((*i
).first
) == filter
->end())
1067 if (compared((*i
).first
, it
))
1070 order_sign sign
= compare(it
, (*i
).first
);
1071 if (sign
== order_lt
) {
1072 lt
[it
].push_back((*i
).first
);
1074 } else if (sign
== order_le
) {
1075 le
[it
].push_back((*i
).first
);
1077 } else if (sign
== order_eq
) {
1079 set_equal(it
, (*i
).first
);
1081 } else if (sign
== order_gt
) {
1082 pending
[(*i
).first
].push_back(it
);
1083 lt
[(*i
).first
].push_back(it
);
1085 } else if (sign
== order_ge
) {
1086 pending
[(*i
).first
].push_back(it
);
1087 le
[(*i
).first
].push_back(it
);
1094 void partial_order::remove(indicator_term
* it
)
1096 std::set
<indicator_term
*> filter
;
1097 map
<indicator_term
*, vector
<indicator_term
* > >::iterator i
;
1099 assert(pred
[it
] == 0);
1102 if (i
!= eq
.end()) {
1103 assert(eq
[it
].size() >= 1);
1104 indicator_term
*base
;
1105 if (eq
[it
].size() == 1) {
1109 vector
<indicator_term
* >::iterator j
;
1110 j
= find(eq
[base
].begin(), eq
[base
].end(), it
);
1111 assert(j
!= eq
[base
].end());
1114 /* "it" may no longer be the smallest, since the order
1115 * structure may have been copied from another one.
1117 sort(eq
[it
].begin()+1, eq
[it
].end());
1118 assert(eq
[it
][0] == it
);
1119 eq
[it
].erase(eq
[it
].begin());
1124 for (int j
= 1; j
< eq
[base
].size(); ++j
)
1125 eq
[eq
[base
][j
]][0] = base
;
1128 if (i
!= lt
.end()) {
1134 if (i
!= le
.end()) {
1139 i
= pending
.find(it
);
1140 if (i
!= pending
.end()) {
1141 pending
[base
] = pending
[it
];
1146 if (eq
[base
].size() == 1)
1149 map
<indicator_term
*, int >::iterator j
;
1157 if (i
!= lt
.end()) {
1158 for (int j
= 0; j
< lt
[it
].size(); ++j
) {
1159 filter
.insert(lt
[it
][j
]);
1166 if (i
!= le
.end()) {
1167 for (int j
= 0; j
< le
[it
].size(); ++j
) {
1168 filter
.insert(le
[it
][j
]);
1174 map
<indicator_term
*, int >::iterator j
;
1178 i
= pending
.find(it
);
1179 if (i
!= pending
.end()) {
1180 for (int j
= 0; j
< pending
[it
].size(); ++j
) {
1181 filter
.erase(pending
[it
][j
]);
1182 add(pending
[it
][j
], &filter
);
1188 void partial_order::print(ostream
& os
, char **p
)
1190 map
<indicator_term
*, vector
<indicator_term
* > >::iterator i
;
1191 for (i
= lt
.begin(); i
!= lt
.end(); ++i
) {
1192 (*i
).first
->print(os
, p
);
1193 assert(pred
.find((*i
).first
) != pred
.end());
1194 os
<< "(" << pred
[(*i
).first
] << ")";
1196 for (int j
= 0; j
< (*i
).second
.size(); ++j
) {
1199 (*i
).second
[j
]->print(os
, p
);
1200 assert(pred
.find((*i
).second
[j
]) != pred
.end());
1201 os
<< "(" << pred
[(*i
).second
[j
]] << ")";
1205 for (i
= le
.begin(); i
!= le
.end(); ++i
) {
1206 (*i
).first
->print(os
, p
);
1207 assert(pred
.find((*i
).first
) != pred
.end());
1208 os
<< "(" << pred
[(*i
).first
] << ")";
1210 for (int j
= 0; j
< (*i
).second
.size(); ++j
) {
1213 (*i
).second
[j
]->print(os
, p
);
1214 assert(pred
.find((*i
).second
[j
]) != pred
.end());
1215 os
<< "(" << pred
[(*i
).second
[j
]] << ")";
1219 for (i
= eq
.begin(); i
!= eq
.end(); ++i
) {
1220 if ((*i
).second
.size() <= 1)
1222 (*i
).first
->print(os
, p
);
1223 assert(pred
.find((*i
).first
) != pred
.end());
1224 os
<< "(" << pred
[(*i
).first
] << ")";
1225 for (int j
= 1; j
< (*i
).second
.size(); ++j
) {
1228 (*i
).second
[j
]->print(os
, p
);
1229 assert(pred
.find((*i
).second
[j
]) != pred
.end());
1230 os
<< "(" << pred
[(*i
).second
[j
]] << ")";
1234 for (i
= pending
.begin(); i
!= pending
.end(); ++i
) {
1235 os
<< "pending on ";
1236 (*i
).first
->print(os
, p
);
1237 assert(pred
.find((*i
).first
) != pred
.end());
1238 os
<< "(" << pred
[(*i
).first
] << ")";
1240 for (int j
= 0; j
< (*i
).second
.size(); ++j
) {
1243 (*i
).second
[j
]->print(os
, p
);
1244 assert(pred
.find((*i
).second
[j
]) != pred
.end());
1245 os
<< "(" << pred
[(*i
).second
[j
]] << ")";
1251 void indicator::add(const indicator_term
* it
)
1253 indicator_term
*nt
= new indicator_term(*it
);
1254 nt
->reduce_in_domain(P
? P
: D
->D
);
1256 order
.add(nt
, NULL
);
1257 assert(term
.size() == order
.pred
.size());
1260 void indicator::remove(indicator_term
* it
)
1262 vector
<indicator_term
*>::iterator i
;
1263 i
= find(term
.begin(), term
.end(), it
);
1264 assert(i
!= term
.end());
1267 assert(term
.size() == order
.pred
.size());
1271 void indicator::expand_rational_vertex(indicator_term
*initial
)
1273 int pos
= initial
->pos
;
1275 if (ic
.terms
[pos
].size() == 0) {
1277 FORALL_PVertex_in_ParamPolyhedron(V
, PD
, ic
.PP
) // _i is internal counter
1279 ic
.decompose_at_vertex(V
, pos
, options
->MaxRays
);
1282 END_FORALL_PVertex_in_ParamPolyhedron
;
1284 for (int j
= 0; j
< ic
.terms
[pos
].size(); ++j
)
1285 add(ic
.terms
[pos
][j
]);
1288 void indicator::remove_initial_rational_vertices()
1291 indicator_term
*initial
= NULL
;
1292 map
<indicator_term
*, int >::iterator i
;
1293 for (i
= order
.pred
.begin(); i
!= order
.pred
.end(); ++i
) {
1294 if ((*i
).second
!= 0)
1296 if ((*i
).first
->sign
!= 0)
1298 if (order
.eq
.find((*i
).first
) != order
.eq
.end() &&
1299 order
.eq
[(*i
).first
].size() <= 1)
1301 initial
= (*i
).first
;
1306 expand_rational_vertex(initial
);
1310 void indicator::reduce_in_domain(Polyhedron
*D
)
1312 for (int i
= 0; i
< term
.size(); ++i
)
1313 term
[i
]->reduce_in_domain(D
);
1316 void indicator::print(ostream
& os
, char **p
)
1318 assert(term
.size() == order
.pred
.size());
1319 for (int i
= 0; i
< term
.size(); ++i
) {
1320 term
[i
]->print(os
, p
);
1326 /* Remove pairs of opposite terms */
1327 void indicator::simplify()
1329 for (int i
= 0; i
< term
.size(); ++i
) {
1330 for (int j
= i
+1; j
< term
.size(); ++j
) {
1331 if (term
[i
]->sign
+ term
[j
]->sign
!= 0)
1333 if (term
[i
]->den
!= term
[j
]->den
)
1336 for (k
= 0; k
< term
[i
]->den
.NumCols(); ++k
)
1337 if (!eequal(term
[i
]->vertex
[k
], term
[j
]->vertex
[k
]))
1339 if (k
< term
[i
]->den
.NumCols())
1343 term
.erase(term
.begin()+j
);
1344 term
.erase(term
.begin()+i
);
1351 void indicator::peel(int i
, int j
)
1359 int dim
= term
[i
]->den
.NumCols();
1364 int n_common
= 0, n_i
= 0, n_j
= 0;
1366 common
.SetDims(min(term
[i
]->den
.NumRows(), term
[j
]->den
.NumRows()), dim
);
1367 rest_i
.SetDims(term
[i
]->den
.NumRows(), dim
);
1368 rest_j
.SetDims(term
[j
]->den
.NumRows(), dim
);
1371 for (k
= 0, l
= 0; k
< term
[i
]->den
.NumRows() && l
< term
[j
]->den
.NumRows(); ) {
1372 int s
= lex_cmp(term
[i
]->den
[k
], term
[j
]->den
[l
]);
1374 common
[n_common
++] = term
[i
]->den
[k
];
1378 rest_i
[n_i
++] = term
[i
]->den
[k
++];
1380 rest_j
[n_j
++] = term
[j
]->den
[l
++];
1382 while (k
< term
[i
]->den
.NumRows())
1383 rest_i
[n_i
++] = term
[i
]->den
[k
++];
1384 while (l
< term
[j
]->den
.NumRows())
1385 rest_j
[n_j
++] = term
[j
]->den
[l
++];
1386 common
.SetDims(n_common
, dim
);
1387 rest_i
.SetDims(n_i
, dim
);
1388 rest_j
.SetDims(n_j
, dim
);
1390 for (k
= 0; k
<= n_i
; ++k
) {
1391 indicator_term
*it
= new indicator_term(*term
[i
]);
1392 it
->den
.SetDims(n_common
+ k
, dim
);
1393 for (l
= 0; l
< n_common
; ++l
)
1394 it
->den
[l
] = common
[l
];
1395 for (l
= 0; l
< k
; ++l
)
1396 it
->den
[n_common
+l
] = rest_i
[l
];
1397 lex_order_rows(it
->den
);
1399 for (l
= 0; l
< dim
; ++l
)
1400 evalue_add_constant(it
->vertex
[l
], rest_i
[k
-1][l
]);
1404 for (k
= 0; k
<= n_j
; ++k
) {
1405 indicator_term
*it
= new indicator_term(*term
[j
]);
1406 it
->den
.SetDims(n_common
+ k
, dim
);
1407 for (l
= 0; l
< n_common
; ++l
)
1408 it
->den
[l
] = common
[l
];
1409 for (l
= 0; l
< k
; ++l
)
1410 it
->den
[n_common
+l
] = rest_j
[l
];
1411 lex_order_rows(it
->den
);
1413 for (l
= 0; l
< dim
; ++l
)
1414 evalue_add_constant(it
->vertex
[l
], rest_j
[k
-1][l
]);
1417 term
.erase(term
.begin()+j
);
1418 term
.erase(term
.begin()+i
);
1421 void indicator::combine(indicator_term
*a
, indicator_term
*b
)
1423 int dim
= a
->den
.NumCols();
1428 int n_common
= 0, n_i
= 0, n_j
= 0;
1430 common
.SetDims(min(a
->den
.NumRows(), b
->den
.NumRows()), dim
);
1431 rest_i
.SetDims(a
->den
.NumRows(), dim
);
1432 rest_j
.SetDims(b
->den
.NumRows(), dim
);
1435 for (k
= 0, l
= 0; k
< a
->den
.NumRows() && l
< b
->den
.NumRows(); ) {
1436 int s
= lex_cmp(a
->den
[k
], b
->den
[l
]);
1438 common
[n_common
++] = a
->den
[k
];
1442 rest_i
[n_i
++] = a
->den
[k
++];
1444 rest_j
[n_j
++] = b
->den
[l
++];
1446 while (k
< a
->den
.NumRows())
1447 rest_i
[n_i
++] = a
->den
[k
++];
1448 while (l
< b
->den
.NumRows())
1449 rest_j
[n_j
++] = b
->den
[l
++];
1450 common
.SetDims(n_common
, dim
);
1451 rest_i
.SetDims(n_i
, dim
);
1452 rest_j
.SetDims(n_j
, dim
);
1457 for (k
= (1 << n_i
)-1; k
>= 0; --k
) {
1458 indicator_term
*it
= k
? new indicator_term(*b
) : b
;
1459 it
->den
.SetDims(n_common
+ n_i
+ n_j
, dim
);
1460 for (l
= 0; l
< n_common
; ++l
)
1461 it
->den
[l
] = common
[l
];
1462 for (l
= 0; l
< n_i
; ++l
)
1463 it
->den
[n_common
+l
] = rest_i
[l
];
1464 for (l
= 0; l
< n_j
; ++l
)
1465 it
->den
[n_common
+n_i
+l
] = rest_j
[l
];
1466 lex_order_rows(it
->den
);
1468 for (l
= 0; l
< n_i
; ++l
) {
1472 for (int m
= 0; m
< dim
; ++m
)
1473 evalue_add_constant(it
->vertex
[m
], rest_i
[l
][m
]);
1476 it
->sign
= -it
->sign
;
1479 order
.add(it
, NULL
);
1483 for (k
= (1 << n_j
)-1; k
>= 0; --k
) {
1484 indicator_term
*it
= k
? new indicator_term(*a
) : a
;
1485 it
->den
.SetDims(n_common
+ n_i
+ n_j
, dim
);
1486 for (l
= 0; l
< n_common
; ++l
)
1487 it
->den
[l
] = common
[l
];
1488 for (l
= 0; l
< n_i
; ++l
)
1489 it
->den
[n_common
+l
] = rest_i
[l
];
1490 for (l
= 0; l
< n_j
; ++l
)
1491 it
->den
[n_common
+n_i
+l
] = rest_j
[l
];
1492 lex_order_rows(it
->den
);
1494 for (l
= 0; l
< n_j
; ++l
) {
1498 for (int m
= 0; m
< dim
; ++m
)
1499 evalue_add_constant(it
->vertex
[m
], rest_j
[l
][m
]);
1502 it
->sign
= -it
->sign
;
1505 order
.add(it
, NULL
);
1510 bool indicator::handle_equal_numerators(indicator_term
*base
)
1512 for (int i
= 0; i
< order
.eq
[base
].size(); ++i
) {
1513 for (int j
= i
+1; j
< order
.eq
[base
].size(); ++j
) {
1514 if (order
.eq
[base
][i
]->is_opposite(order
.eq
[base
][j
])) {
1515 remove(order
.eq
[base
][j
]);
1516 remove(i
? order
.eq
[base
][i
] : base
);
1521 for (int j
= 1; j
< order
.eq
[base
].size(); ++j
)
1522 if (order
.eq
[base
][j
]->sign
!= base
->sign
) {
1523 combine(base
, order
.eq
[base
][j
]);
1529 void indicator::substitute(evalue
*equation
)
1531 evalue
*fract
= NULL
;
1532 evalue
*val
= new evalue
;
1534 evalue_copy(val
, equation
);
1537 value_init(factor
.d
);
1538 value_init(factor
.x
.n
);
1541 for (e
= val
; value_zero_p(e
->d
) && e
->x
.p
->type
!= fractional
;
1542 e
= &e
->x
.p
->arr
[type_offset(e
->x
.p
)])
1545 if (value_zero_p(e
->d
) && e
->x
.p
->type
== fractional
)
1546 fract
= &e
->x
.p
->arr
[0];
1548 for (e
= val
; value_zero_p(e
->d
) && e
->x
.p
->type
!= polynomial
;
1549 e
= &e
->x
.p
->arr
[type_offset(e
->x
.p
)])
1551 assert(value_zero_p(e
->d
) && e
->x
.p
->type
== polynomial
);
1554 int offset
= type_offset(e
->x
.p
);
1556 assert(value_notzero_p(e
->x
.p
->arr
[offset
+1].d
));
1557 assert(value_notzero_p(e
->x
.p
->arr
[offset
+1].x
.n
));
1558 if (value_neg_p(e
->x
.p
->arr
[offset
+1].x
.n
)) {
1559 value_oppose(factor
.d
, e
->x
.p
->arr
[offset
+1].x
.n
);
1560 value_assign(factor
.x
.n
, e
->x
.p
->arr
[offset
+1].d
);
1562 value_assign(factor
.d
, e
->x
.p
->arr
[offset
+1].x
.n
);
1563 value_oppose(factor
.x
.n
, e
->x
.p
->arr
[offset
+1].d
);
1566 free_evalue_refs(&e
->x
.p
->arr
[offset
+1]);
1569 *e
= e
->x
.p
->arr
[offset
];
1574 for (int i
= 0; i
< term
.size(); ++i
)
1575 term
[i
]->substitute(fract
, val
);
1577 free_evalue_refs(&p
->arr
[0]);
1579 for (int i
= 0; i
< term
.size(); ++i
)
1580 term
[i
]->substitute(p
->pos
, val
);
1583 free_evalue_refs(&factor
);
1584 free_evalue_refs(val
);
1590 static void print_varlist(ostream
& os
, int n
, char **names
)
1594 for (i
= 0; i
< n
; ++i
) {
1602 static void print_term(ostream
& os
, Value v
, int pos
, int dim
,
1603 char **names
, int *first
)
1605 if (value_zero_p(v
)) {
1606 if (first
&& *first
&& pos
>= dim
)
1612 if (!*first
&& value_pos_p(v
))
1617 if (value_mone_p(v
)) {
1619 } else if (!value_one_p(v
))
1620 os
<< VALUE_TO_INT(v
);
1623 os
<< VALUE_TO_INT(v
);
1626 /* We put all possible existentially quantified variables at the back
1627 * and so if any equalities exist between these variables and the
1628 * other variables, then PolyLib will replace all occurrences of some
1629 * of the other variables by some existentially quantified variables.
1630 * We want the output to have as few as possible references to the
1631 * existentially quantified variables, so we undo what PolyLib did here.
1633 void resolve_existential_vars(Polyhedron
*domain
, unsigned dim
)
1635 int last
= domain
->NbEq
- 1;
1636 /* Matrix "view" of domain for ExchangeRows */
1638 M
.NbRows
= domain
->NbConstraints
;
1639 M
.NbColumns
= domain
->Dimension
+2;
1640 M
.p_Init
= domain
->p_Init
;
1641 M
.p
= domain
->Constraint
;
1644 value_set_si(mone
, -1);
1645 for (int e
= domain
->Dimension
-1; e
>= dim
; --e
) {
1647 for (r
= last
; r
>= 0; --r
)
1648 if (value_notzero_p(domain
->Constraint
[r
][1+e
]))
1653 ExchangeRows(&M
, r
, last
);
1655 /* Combine uses the coefficient as a multiplier, so it must
1656 * be positive, since we are modifying an inequality.
1658 if (value_neg_p(domain
->Constraint
[last
][1+e
]))
1659 Vector_Scale(domain
->Constraint
[last
]+1, domain
->Constraint
[last
]+1,
1660 mone
, domain
->Dimension
+1);
1662 for (int c
= 0; c
< domain
->NbConstraints
; ++c
) {
1665 if (value_notzero_p(domain
->Constraint
[c
][1+e
]))
1666 Combine(domain
->Constraint
[c
], domain
->Constraint
[last
],
1667 domain
->Constraint
[c
], 1+e
, domain
->Dimension
+1);
1674 void max_term::resolve_existential_vars() const
1676 ::resolve_existential_vars(domain
, dim
);
1679 void max_term::print(ostream
& os
, char **p
) const
1682 if (dim
< domain
->Dimension
) {
1683 resolve_existential_vars();
1684 names
= new char * [domain
->Dimension
];
1686 for (i
= 0; i
< dim
; ++i
)
1688 for ( ; i
< domain
->Dimension
; ++i
) {
1689 names
[i
] = new char[10];
1690 snprintf(names
[i
], 10, "a%d", i
- dim
);
1697 print_varlist(os
, dim
, p
);
1700 for (int i
= 0; i
< max
.size(); ++i
) {
1703 evalue_print(os
, max
[i
], p
);
1707 if (dim
< domain
->Dimension
) {
1709 print_varlist(os
, domain
->Dimension
-dim
, names
+dim
);
1712 for (int i
= 0; i
< domain
->NbConstraints
; ++i
) {
1714 int v
= First_Non_Zero(domain
->Constraint
[i
]+1, domain
->Dimension
);
1719 if (value_pos_p(domain
->Constraint
[i
][v
+1])) {
1720 print_term(os
, domain
->Constraint
[i
][v
+1], v
, domain
->Dimension
,
1722 if (value_zero_p(domain
->Constraint
[i
][0]))
1726 for (int j
= v
+1; j
<= domain
->Dimension
; ++j
) {
1727 value_oppose(tmp
, domain
->Constraint
[i
][1+j
]);
1728 print_term(os
, tmp
, j
, domain
->Dimension
,
1732 value_oppose(tmp
, domain
->Constraint
[i
][1+v
]);
1733 print_term(os
, tmp
, v
, domain
->Dimension
,
1735 if (value_zero_p(domain
->Constraint
[i
][0]))
1739 for (int j
= v
+1; j
<= domain
->Dimension
; ++j
)
1740 print_term(os
, domain
->Constraint
[i
][1+j
], j
, domain
->Dimension
,
1747 if (dim
< domain
->Dimension
) {
1748 for (int i
= dim
; i
< domain
->Dimension
; ++i
)
1754 static void evalue_substitute(evalue
*e
, evalue
**subs
)
1758 if (value_notzero_p(e
->d
))
1762 for (int i
= 0; i
< p
->size
; ++i
)
1763 evalue_substitute(&p
->arr
[i
], subs
);
1765 if (p
->type
== polynomial
)
1770 value_set_si(v
->d
, 0);
1771 v
->x
.p
= new_enode(p
->type
, 3, -1);
1772 value_clear(v
->x
.p
->arr
[0].d
);
1773 v
->x
.p
->arr
[0] = p
->arr
[0];
1774 evalue_set_si(&v
->x
.p
->arr
[1], 0, 1);
1775 evalue_set_si(&v
->x
.p
->arr
[2], 1, 1);
1778 int offset
= type_offset(p
);
1780 for (int i
= p
->size
-1; i
>= offset
+1; i
--) {
1781 emul(v
, &p
->arr
[i
]);
1782 eadd(&p
->arr
[i
], &p
->arr
[i
-1]);
1783 free_evalue_refs(&(p
->arr
[i
]));
1786 if (p
->type
!= polynomial
) {
1787 free_evalue_refs(v
);
1792 *e
= p
->arr
[offset
];
1796 /* "align" matrix to have nrows by inserting
1797 * the necessary number of rows and an equal number of columns at the end
1798 * right before the constant row/column
1800 static Matrix
*align_matrix_initial(Matrix
*M
, int nrows
)
1803 int newrows
= nrows
- M
->NbRows
;
1804 Matrix
*M2
= Matrix_Alloc(nrows
, newrows
+ M
->NbColumns
);
1805 for (i
= 0; i
< newrows
; ++i
)
1806 value_set_si(M2
->p
[M
->NbRows
-1+i
][M
->NbColumns
-1+i
], 1);
1807 for (i
= 0; i
< M
->NbRows
-1; ++i
) {
1808 Vector_Copy(M
->p
[i
], M2
->p
[i
], M
->NbColumns
-1);
1809 value_assign(M2
->p
[i
][M2
->NbColumns
-1], M
->p
[i
][M
->NbColumns
-1]);
1811 value_assign(M2
->p
[M2
->NbRows
-1][M2
->NbColumns
-1],
1812 M
->p
[M
->NbRows
-1][M
->NbColumns
-1]);
1816 /* T maps the compressed parameters to the original parameters,
1817 * while this max_term is based on the compressed parameters
1818 * and we want get the original parameters back.
1820 void max_term::substitute(Matrix
*T
, unsigned MaxRays
)
1822 int nexist
= domain
->Dimension
- (T
->NbColumns
-1);
1823 Matrix
*M
= align_matrix_initial(T
, T
->NbRows
+nexist
);
1825 Polyhedron
*D
= DomainImage(domain
, M
, MaxRays
);
1826 Polyhedron_Free(domain
);
1830 assert(T
->NbRows
== T
->NbColumns
);
1831 Matrix
*T2
= Matrix_Copy(T
);
1832 Matrix
*inv
= Matrix_Alloc(T
->NbColumns
, T
->NbRows
);
1833 int ok
= Matrix_Inverse(T2
, inv
);
1838 value_init(denom
.d
);
1839 value_init(denom
.x
.n
);
1840 value_set_si(denom
.x
.n
, 1);
1841 value_assign(denom
.d
, inv
->p
[inv
->NbRows
-1][inv
->NbColumns
-1]);
1844 v
.SetLength(inv
->NbColumns
);
1845 evalue
* subs
[inv
->NbRows
-1];
1846 for (int i
= 0; i
< inv
->NbRows
-1; ++i
) {
1847 values2zz(inv
->p
[i
], v
, v
.length());
1848 subs
[i
] = multi_monom(v
);
1849 emul(&denom
, subs
[i
]);
1851 free_evalue_refs(&denom
);
1853 for (int i
= 0; i
< max
.size(); ++i
) {
1854 evalue_substitute(max
[i
], subs
);
1855 reduce_evalue(max
[i
]);
1858 for (int i
= 0; i
< inv
->NbRows
-1; ++i
) {
1859 free_evalue_refs(subs
[i
]);
1865 int Last_Non_Zero(Value
*p
, unsigned len
)
1867 for (int i
= len
-1; i
>= 0; --i
)
1868 if (value_notzero_p(p
[i
]))
1873 static void SwapColumns(Value
**V
, int n
, int i
, int j
)
1875 for (int r
= 0; r
< n
; ++r
)
1876 value_swap(V
[r
][i
], V
[r
][j
]);
1879 static void SwapColumns(Polyhedron
*P
, int i
, int j
)
1881 SwapColumns(P
->Constraint
, P
->NbConstraints
, i
, j
);
1882 SwapColumns(P
->Ray
, P
->NbRays
, i
, j
);
1885 bool in_domain(Polyhedron
*P
, Value
*val
, unsigned dim
, unsigned MaxRays
)
1887 int nexist
= P
->Dimension
- dim
;
1888 int last
[P
->NbConstraints
];
1889 Value tmp
, min
, max
;
1890 Vector
*all_val
= Vector_Alloc(P
->Dimension
+1);
1895 resolve_existential_vars(P
, dim
);
1897 Vector_Copy(val
, all_val
->p
, dim
);
1898 value_set_si(all_val
->p
[P
->Dimension
], 1);
1901 for (int i
= 0; i
< P
->NbConstraints
; ++i
) {
1902 last
[i
] = Last_Non_Zero(P
->Constraint
[i
]+1+dim
, nexist
);
1903 if (last
[i
] == -1) {
1904 Inner_Product(P
->Constraint
[i
]+1, all_val
->p
, P
->Dimension
+1, &tmp
);
1905 if (value_neg_p(tmp
))
1907 if (i
< P
->NbEq
&& value_pos_p(tmp
))
1914 alternate
= nexist
- 1;
1915 for (i
= 0; i
< nexist
; ++i
) {
1916 bool min_set
= false;
1917 bool max_set
= false;
1918 for (int j
= 0; j
< P
->NbConstraints
; ++j
) {
1921 Inner_Product(P
->Constraint
[j
]+1, all_val
->p
, P
->Dimension
+1, &tmp
);
1922 value_oppose(tmp
, tmp
);
1924 if (!mpz_divisible_p(tmp
, P
->Constraint
[j
][1+dim
+i
]))
1926 value_division(tmp
, tmp
, P
->Constraint
[j
][1+dim
+i
]);
1927 if (!max_set
|| value_lt(tmp
, max
)) {
1929 value_assign(max
, tmp
);
1931 if (!min_set
|| value_gt(tmp
, min
)) {
1933 value_assign(min
, tmp
);
1936 if (value_pos_p(P
->Constraint
[j
][1+dim
+i
])) {
1937 mpz_cdiv_q(tmp
, tmp
, P
->Constraint
[j
][1+dim
+i
]);
1938 if (!min_set
|| value_gt(tmp
, min
)) {
1940 value_assign(min
, tmp
);
1943 mpz_fdiv_q(tmp
, tmp
, P
->Constraint
[j
][1+dim
+i
]);
1944 if (!max_set
|| value_lt(tmp
, max
)) {
1946 value_assign(max
, tmp
);
1951 /* Move another existential variable in current position */
1952 if (!max_set
|| !min_set
) {
1953 if (!(alternate
> i
)) {
1954 Matrix
*M
= Matrix_Alloc(dim
+i
, 1+P
->Dimension
+1);
1955 for (int j
= 0; j
< dim
+i
; ++j
) {
1956 value_set_si(M
->p
[j
][1+j
], -1);
1957 value_assign(M
->p
[j
][1+P
->Dimension
], all_val
->p
[j
]);
1959 Polyhedron
*Q
= AddConstraints(M
->p
[0], dim
+i
, P
, MaxRays
);
1961 Q
= DomainConstraintSimplify(Q
, MaxRays
);
1962 Vector
*sample
= Polyhedron_Sample(Q
, MaxRays
);
1965 Vector_Free(sample
);
1969 assert(alternate
> i
);
1970 SwapColumns(P
, 1+dim
+i
, 1+dim
+alternate
);
1971 resolve_existential_vars(P
, dim
);
1972 for (int j
= 0; j
< P
->NbConstraints
; ++j
) {
1973 if (j
>= P
->NbEq
&& last
[j
] < i
)
1975 last
[j
] = Last_Non_Zero(P
->Constraint
[j
]+1+dim
, nexist
);
1977 Inner_Product(P
->Constraint
[j
]+1, all_val
->p
, P
->Dimension
+1,
1979 if (value_neg_p(tmp
))
1981 if (j
< P
->NbEq
&& value_pos_p(tmp
))
1989 assert(max_set
&& min_set
);
1990 if (value_lt(max
, min
))
1992 if (value_ne(max
, min
)) {
1993 Matrix
*M
= Matrix_Alloc(dim
+i
, 1+P
->Dimension
+1);
1994 for (int j
= 0; j
< dim
+i
; ++j
) {
1995 value_set_si(M
->p
[j
][1+j
], -1);
1996 value_assign(M
->p
[j
][1+P
->Dimension
], all_val
->p
[j
]);
1998 Polyhedron
*Q
= AddConstraints(M
->p
[0], dim
+i
, P
, MaxRays
);
2000 Q
= DomainConstraintSimplify(Q
, MaxRays
);
2001 Vector
*sample
= Polyhedron_Sample(Q
, MaxRays
);
2004 Vector_Free(sample
);
2008 assert(value_eq(max
, min
));
2009 value_assign(all_val
->p
[dim
+i
], max
);
2010 alternate
= nexist
- 1;
2017 Vector_Free(all_val
);
2019 return in
|| (P
->next
&& in_domain(P
->next
, val
, dim
, MaxRays
));
2022 void compute_evalue(evalue
*e
, Value
*val
, Value
*res
)
2024 double d
= compute_evalue(e
, val
);
2029 value_set_double(*res
, d
);
2032 Vector
*max_term::eval(Value
*val
, unsigned MaxRays
) const
2034 if (dim
== domain
->Dimension
) {
2035 if (!in_domain(domain
, val
))
2038 if (!in_domain(domain
, val
, dim
, MaxRays
))
2041 Vector
*res
= Vector_Alloc(max
.size());
2042 for (int i
= 0; i
< max
.size(); ++i
) {
2043 compute_evalue(max
[i
], val
, &res
->p
[i
]);
2048 static Matrix
*remove_equalities(Polyhedron
**P
, unsigned nparam
, unsigned MaxRays
);
2050 Vector
*Polyhedron_not_empty(Polyhedron
*P
, unsigned MaxRays
)
2052 Polyhedron
*Porig
= P
;
2053 Vector
*sample
= NULL
;
2055 POL_ENSURE_VERTICES(P
);
2059 for (int i
= 0; i
< P
->NbRays
; ++i
)
2060 if (value_one_p(P
->Ray
[i
][1+P
->Dimension
])) {
2061 sample
= Vector_Alloc(P
->Dimension
+ 1);
2062 Vector_Copy(P
->Ray
[i
]+1, sample
->p
, P
->Dimension
+1);
2066 Matrix
*T
= remove_equalities(&P
, 0, MaxRays
);
2068 sample
= Polyhedron_Sample(P
, MaxRays
);
2071 Vector
*P_sample
= Vector_Alloc(Porig
->Dimension
+ 1);
2072 Matrix_Vector_Product(T
, sample
->p
, P_sample
->p
);
2073 Vector_Free(sample
);
2087 enum sign
{ le
, ge
, lge
} sign
;
2089 split (evalue
*c
, enum sign s
) : constraint(c
), sign(s
) {}
2092 static void split_on(const split
& sp
, EDomain
*D
,
2093 EDomain
**Dlt
, EDomain
**Deq
, EDomain
**Dgt
,
2094 barvinok_options
*options
)
2101 value_set_si(mone
, -1);
2105 vector
<evalue
*> new_floors
;
2106 M
= add_ge_constraint(D
, sp
.constraint
, new_floors
);
2107 if (sp
.sign
== split::lge
|| sp
.sign
== split::ge
) {
2108 M2
= Matrix_Copy(M
);
2109 value_decrement(M2
->p
[M2
->NbRows
-1][M2
->NbColumns
-1],
2110 M2
->p
[M2
->NbRows
-1][M2
->NbColumns
-1]);
2111 D2
= Constraints2Polyhedron(M2
, options
->MaxRays
);
2112 ED
[2] = new EDomain(D2
, D
, new_floors
);
2113 Polyhedron_Free(D2
);
2117 if (sp
.sign
== split::lge
|| sp
.sign
== split::le
) {
2118 M2
= Matrix_Copy(M
);
2119 Vector_Scale(M2
->p
[M2
->NbRows
-1]+1, M2
->p
[M2
->NbRows
-1]+1,
2120 mone
, M2
->NbColumns
-1);
2121 value_decrement(M2
->p
[M2
->NbRows
-1][M2
->NbColumns
-1],
2122 M2
->p
[M2
->NbRows
-1][M2
->NbColumns
-1]);
2123 D2
= Constraints2Polyhedron(M2
, options
->MaxRays
);
2124 ED
[0] = new EDomain(D2
, D
, new_floors
);
2125 Polyhedron_Free(D2
);
2130 assert(sp
.sign
== split::lge
|| sp
.sign
== split::ge
|| sp
.sign
== split::le
);
2131 value_set_si(M
->p
[M
->NbRows
-1][0], 0);
2132 D2
= Constraints2Polyhedron(M
, options
->MaxRays
);
2133 ED
[1] = new EDomain(D2
, D
, new_floors
);
2134 Polyhedron_Free(D2
);
2137 Vector
*sample
= D
->sample
;
2138 if (sample
&& new_floors
.size() > 0) {
2139 assert(sample
->Size
== D
->D
->Dimension
+1);
2140 sample
= Vector_Alloc(D
->D
->Dimension
+new_floors
.size()+1);
2141 Vector_Copy(D
->sample
->p
, sample
->p
, D
->D
->Dimension
);
2142 value_set_si(sample
->p
[D
->D
->Dimension
+new_floors
.size()], 1);
2143 for (int i
= 0; i
< new_floors
.size(); ++i
)
2144 compute_evalue(new_floors
[i
], sample
->p
, sample
->p
+D
->D
->Dimension
+i
);
2147 for (int i
= 0; i
< new_floors
.size(); ++i
) {
2148 free_evalue_refs(new_floors
[i
]);
2149 delete new_floors
[i
];
2152 for (int i
= 0; i
< 3; ++i
) {
2156 in_domain(ED
[i
]->D
, sample
->p
, sample
->Size
-1, options
->MaxRays
)) {
2157 ED
[i
]->sample
= Vector_Alloc(sample
->Size
);
2158 Vector_Copy(sample
->p
, ED
[i
]->sample
->p
, sample
->Size
);
2159 } else if (emptyQ2(ED
[i
]->D
) ||
2160 (options
->emptiness_check
== 1 &&
2161 !(ED
[i
]->sample
= Polyhedron_not_empty(ED
[i
]->D
,
2162 options
->MaxRays
)))) {
2171 if (sample
!= D
->sample
)
2172 Vector_Free(sample
);
2175 ostream
& operator<< (ostream
& os
, const vector
<int> & v
)
2178 for (int i
= 0; i
< v
.size(); ++i
) {
2187 static bool isTranslation(Matrix
*M
)
2190 if (M
->NbRows
!= M
->NbColumns
)
2193 for (i
= 0;i
< M
->NbRows
; i
++)
2194 for (j
= 0; j
< M
->NbColumns
-1; j
++)
2196 if(value_notone_p(M
->p
[i
][j
]))
2199 if(value_notzero_p(M
->p
[i
][j
]))
2202 return value_one_p(M
->p
[M
->NbRows
-1][M
->NbColumns
-1]);
2205 static Matrix
*compress_parameters(Polyhedron
**P
, Polyhedron
**C
,
2206 unsigned nparam
, unsigned MaxRays
)
2210 /* compress_parms doesn't like equalities that only involve parameters */
2211 for (int i
= 0; i
< (*P
)->NbEq
; ++i
)
2212 assert(First_Non_Zero((*P
)->Constraint
[i
]+1, (*P
)->Dimension
-nparam
) != -1);
2214 M
= Matrix_Alloc((*P
)->NbEq
, (*P
)->Dimension
+2);
2215 Vector_Copy((*P
)->Constraint
[0], M
->p
[0], (*P
)->NbEq
* ((*P
)->Dimension
+2));
2216 CP
= compress_parms(M
, nparam
);
2219 if (isTranslation(CP
)) {
2224 T
= align_matrix(CP
, (*P
)->Dimension
+1);
2225 *P
= Polyhedron_Preimage(*P
, T
, MaxRays
);
2228 *C
= Polyhedron_Preimage(*C
, CP
, MaxRays
);
2233 static Matrix
*remove_equalities(Polyhedron
**P
, unsigned nparam
, unsigned MaxRays
)
2235 /* Matrix "view" of equalities */
2237 M
.NbRows
= (*P
)->NbEq
;
2238 M
.NbColumns
= (*P
)->Dimension
+2;
2239 M
.p_Init
= (*P
)->p_Init
;
2240 M
.p
= (*P
)->Constraint
;
2242 Matrix
*T
= compress_variables(&M
, nparam
);
2248 if (isIdentity(T
)) {
2252 *P
= Polyhedron_Preimage(*P
, T
, MaxRays
);
2257 void construct_rational_vertices(Param_Polyhedron
*PP
, Matrix
*T
, unsigned dim
,
2258 int nparam
, vector
<indicator_term
*>& vertices
)
2267 v
.SetLength(nparam
+1);
2270 value_init(factor
.d
);
2271 value_init(factor
.x
.n
);
2272 value_set_si(factor
.x
.n
, 1);
2273 value_set_si(factor
.d
, 1);
2275 for (i
= 0, PV
= PP
->V
; PV
; ++i
, PV
= PV
->next
) {
2276 indicator_term
*term
= new indicator_term(dim
, i
);
2277 vertices
.push_back(term
);
2278 Matrix
*M
= Matrix_Alloc(PV
->Vertex
->NbRows
+nparam
+1, nparam
+1);
2279 value_set_si(lcm
, 1);
2280 for (int j
= 0; j
< PV
->Vertex
->NbRows
; ++j
)
2281 value_lcm(lcm
, PV
->Vertex
->p
[j
][nparam
+1], &lcm
);
2282 value_assign(M
->p
[M
->NbRows
-1][M
->NbColumns
-1], lcm
);
2283 for (int j
= 0; j
< PV
->Vertex
->NbRows
; ++j
) {
2284 value_division(tmp
, lcm
, PV
->Vertex
->p
[j
][nparam
+1]);
2285 Vector_Scale(PV
->Vertex
->p
[j
], M
->p
[j
], tmp
, nparam
+1);
2287 for (int j
= 0; j
< nparam
; ++j
)
2288 value_assign(M
->p
[PV
->Vertex
->NbRows
+j
][j
], lcm
);
2290 Matrix
*M2
= Matrix_Alloc(T
->NbRows
, M
->NbColumns
);
2291 Matrix_Product(T
, M
, M2
);
2295 for (int j
= 0; j
< dim
; ++j
) {
2296 values2zz(M
->p
[j
], v
, nparam
+1);
2297 term
->vertex
[j
] = multi_monom(v
);
2298 value_assign(factor
.d
, lcm
);
2299 emul(&factor
, term
->vertex
[j
]);
2303 assert(i
== PP
->nbV
);
2304 free_evalue_refs(&factor
);
2309 /* An auxiliary class that keeps a reference to an evalue
2310 * and frees it when it goes out of scope.
2312 struct temp_evalue
{
2314 temp_evalue() : E(NULL
) {}
2315 temp_evalue(evalue
*e
) : E(e
) {}
2316 operator evalue
* () const { return E
; }
2317 evalue
*operator=(evalue
*e
) {
2319 free_evalue_refs(E
);
2327 free_evalue_refs(E
);
2333 static vector
<max_term
*> lexmin(indicator
& ind
, unsigned nparam
,
2336 vector
<max_term
*> maxima
;
2337 map
<indicator_term
*, int >::iterator i
;
2338 vector
<int> best_score
;
2339 vector
<int> second_score
;
2340 vector
<int> neg_score
;
2343 indicator_term
*best
= NULL
, *second
= NULL
, *neg
= NULL
,
2344 *neg_eq
= NULL
, *neg_le
= NULL
;
2345 for (i
= ind
.order
.pred
.begin(); i
!= ind
.order
.pred
.end(); ++i
) {
2347 if ((*i
).second
!= 0)
2349 indicator_term
*term
= (*i
).first
;
2350 if (term
->sign
== 0) {
2351 ind
.expand_rational_vertex(term
);
2355 if (ind
.order
.eq
.find(term
) != ind
.order
.eq
.end()) {
2357 if (ind
.order
.eq
[term
].size() <= 1)
2359 for (j
= 1; j
< ind
.order
.eq
[term
].size(); ++j
)
2360 if (ind
.order
.pred
[ind
.order
.eq
[term
][j
]] != 0)
2362 if (j
< ind
.order
.eq
[term
].size())
2364 score
.push_back(ind
.order
.eq
[term
].size());
2367 if (ind
.order
.le
.find(term
) != ind
.order
.le
.end())
2368 score
.push_back(ind
.order
.le
[term
].size());
2371 if (ind
.order
.lt
.find(term
) != ind
.order
.lt
.end())
2372 score
.push_back(-ind
.order
.lt
[term
].size());
2376 if (term
->sign
> 0) {
2377 if (!best
|| score
< best_score
) {
2379 second_score
= best_score
;
2382 } else if (!second
|| score
< second_score
) {
2384 second_score
= score
;
2387 if (!neg_eq
&& ind
.order
.eq
.find(term
) != ind
.order
.eq
.end()) {
2388 for (int j
= 1; j
< ind
.order
.eq
[term
].size(); ++j
)
2389 if (ind
.order
.eq
[term
][j
]->sign
!= term
->sign
) {
2394 if (!neg_le
&& ind
.order
.le
.find(term
) != ind
.order
.le
.end())
2396 if (!neg
|| score
< neg_score
) {
2402 if (i
!= ind
.order
.pred
.end())
2405 if (!best
&& neg_eq
) {
2406 assert(ind
.order
.eq
[neg_eq
].size() != 0);
2407 bool handled
= ind
.handle_equal_numerators(neg_eq
);
2412 if (!best
&& neg_le
) {
2413 /* The smallest term is negative and <= some positive term */
2419 /* apparently there can be negative initial term on empty domains */
2420 if (ind
.options
->emptiness_check
== 1)
2425 if (!second
&& !neg
) {
2426 indicator_term
*rat
= NULL
;
2428 if (ind
.order
.le
[best
].size() == 0) {
2429 if (ind
.order
.eq
[best
].size() != 0) {
2430 bool handled
= ind
.handle_equal_numerators(best
);
2431 if (ind
.options
->emptiness_check
== 1)
2433 /* If !handled then the leading coefficient is bigger than one;
2434 * must be an empty domain
2441 maxima
.push_back(ind
.create_max_term(best
));
2444 for (int j
= 0; j
< ind
.order
.le
[best
].size(); ++j
) {
2445 if (ind
.order
.le
[best
][j
]->sign
== 0) {
2446 if (!rat
&& ind
.order
.pred
[ind
.order
.le
[best
][j
]] == 1)
2447 rat
= ind
.order
.le
[best
][j
];
2448 } else if (ind
.order
.le
[best
][j
]->sign
> 0) {
2449 second
= ind
.order
.le
[best
][j
];
2452 neg
= ind
.order
.le
[best
][j
];
2455 if (!second
&& !neg
) {
2457 ind
.order
.unset_le(best
, rat
);
2458 ind
.expand_rational_vertex(rat
);
2465 ind
.order
.unset_le(best
, second
);
2471 unsigned dim
= best
->den
.NumCols();
2474 for (int k
= 0; k
< dim
; ++k
) {
2475 diff
= ediff(best
->vertex
[k
], second
->vertex
[k
]);
2476 sign
= evalue_sign(diff
, ind
.D
, ind
.options
->MaxRays
);
2478 /* neg can never be smaller than best, unless it may still cancel */
2479 if (second
== neg
&&
2480 ind
.order
.eq
.find(neg
) == ind
.order
.eq
.end() &&
2481 ind
.order
.le
.find(neg
) == ind
.order
.le
.end()) {
2482 if (sign
== order_ge
)
2484 if (sign
== order_unknown
)
2488 if (sign
!= order_eq
)
2490 if (!EVALUE_IS_ZERO(*diff
))
2491 ind
.substitute(diff
);
2493 if (sign
== order_eq
) {
2494 ind
.order
.set_equal(best
, second
);
2497 if (sign
== order_lt
) {
2498 ind
.order
.lt
[best
].push_back(second
);
2499 ind
.order
.pred
[second
]++;
2502 if (sign
== order_gt
) {
2503 ind
.order
.lt
[second
].push_back(best
);
2504 ind
.order
.pred
[best
]++;
2508 split
sp(diff
, sign
== order_le
? split::le
:
2509 sign
== order_ge
? split::ge
: split::lge
);
2511 EDomain
*Dlt
, *Deq
, *Dgt
;
2512 split_on(sp
, ind
.D
, &Dlt
, &Deq
, &Dgt
, ind
.options
);
2513 if (ind
.options
->emptiness_check
== 1)
2514 assert(Dlt
|| Deq
|| Dgt
);
2515 else if (!(Dlt
|| Deq
|| Dgt
))
2516 /* Must have been empty all along */
2519 if (Deq
&& (Dlt
|| Dgt
)) {
2520 int locsize
= loc
.size();
2522 indicator
indeq(ind
, Deq
);
2524 indeq
.substitute(diff
);
2525 vector
<max_term
*> maxeq
= lexmin(indeq
, nparam
, loc
);
2526 maxima
.insert(maxima
.end(), maxeq
.begin(), maxeq
.end());
2527 loc
.resize(locsize
);
2530 int locsize
= loc
.size();
2532 indicator
indgt(ind
, Dgt
);
2534 /* we don't know the new location of these terms in indgt */
2536 indgt.order.lt[second].push_back(best);
2537 indgt.order.pred[best]++;
2539 vector
<max_term
*> maxgt
= lexmin(indgt
, nparam
, loc
);
2540 maxima
.insert(maxima
.end(), maxgt
.begin(), maxgt
.end());
2541 loc
.resize(locsize
);
2546 ind
.substitute(diff
);
2547 ind
.set_domain(Deq
);
2551 ind
.order
.lt
[best
].push_back(second
);
2552 ind
.order
.pred
[second
]++;
2553 ind
.set_domain(Dlt
);
2557 ind
.order
.lt
[second
].push_back(best
);
2558 ind
.order
.pred
[best
]++;
2559 ind
.set_domain(Dgt
);
2566 static vector
<max_term
*> lexmin(Polyhedron
*P
, Polyhedron
*C
,
2567 barvinok_options
*options
)
2569 unsigned nparam
= C
->Dimension
;
2570 Param_Polyhedron
*PP
= NULL
;
2571 Polyhedron
*CEq
= NULL
, *pVD
;
2573 Matrix
*T
= NULL
, *CP
= NULL
;
2574 Param_Domain
*D
, *next
;
2576 Polyhedron
*Porig
= P
;
2577 Polyhedron
*Corig
= C
;
2578 vector
<max_term
*> all_max
;
2580 unsigned P2PSD_MaxRays
;
2585 POL_ENSURE_VERTICES(P
);
2590 assert(P
->NbBid
== 0);
2594 CP
= compress_parameters(&P
, &C
, nparam
, options
->MaxRays
);
2596 T
= remove_equalities(&P
, nparam
, options
->MaxRays
);
2597 if (P
!= Q
&& Q
!= Porig
)
2606 if (options
->MaxRays
& POL_NO_DUAL
)
2609 P2PSD_MaxRays
= options
->MaxRays
;
2612 PP
= Polyhedron2Param_SimplifiedDomain(&P
, C
, P2PSD_MaxRays
, &CEq
, &CT
);
2613 if (P
!= Q
&& Q
!= Porig
)
2617 if (isIdentity(CT
)) {
2621 nparam
= CT
->NbRows
- 1;
2625 unsigned dim
= P
->Dimension
- nparam
;
2628 for (nd
= 0, D
=PP
->D
; D
; ++nd
, D
=D
->next
);
2629 Polyhedron
**fVD
= new Polyhedron
*[nd
];
2631 indicator_constructor
ic(P
, dim
, PP
, T
);
2633 vector
<indicator_term
*> all_vertices
;
2634 construct_rational_vertices(PP
, T
, T
? T
->NbRows
-nparam
-1 : dim
,
2635 nparam
, all_vertices
);
2637 for (nd
= 0, D
=PP
->D
; D
; D
=next
) {
2640 Polyhedron
*rVD
= reduce_domain(D
->Domain
, CT
, CEq
,
2641 fVD
, nd
, options
->MaxRays
);
2645 pVD
= CT
? DomainImage(rVD
,CT
,options
->MaxRays
) : rVD
;
2647 EDomain
*epVD
= new EDomain(pVD
);
2648 indicator
ind(ic
, D
, epVD
, options
);
2650 FORALL_PVertex_in_ParamPolyhedron(V
,D
,PP
) // _i is internal counter
2651 ind
.add(all_vertices
[_i
]);
2652 END_FORALL_PVertex_in_ParamPolyhedron
;
2654 ind
.remove_initial_rational_vertices();
2657 vector
<max_term
*> maxima
= lexmin(ind
, nparam
, loc
);
2659 for (int j
= 0; j
< maxima
.size(); ++j
)
2660 maxima
[j
]->substitute(CP
, options
->MaxRays
);
2661 all_max
.insert(all_max
.end(), maxima
.begin(), maxima
.end());
2668 for (int i
= 0; i
< all_vertices
.size(); ++i
)
2669 delete all_vertices
[i
];
2674 Param_Polyhedron_Free(PP
);
2676 Polyhedron_Free(CEq
);
2677 for (--nd
; nd
>= 0; --nd
) {
2678 Domain_Free(fVD
[nd
]);
2689 static void verify_results(Polyhedron
*A
, Polyhedron
*C
,
2690 vector
<max_term
*>& maxima
, int m
, int M
,
2691 int print_all
, unsigned MaxRays
);
2693 int main(int argc
, char **argv
)
2698 char **iter_names
, **param_names
;
2703 int m
= INT_MAX
, M
= INT_MIN
, r
;
2704 int print_solution
= 1;
2705 struct barvinok_options
*options
;
2707 options
= barvinok_options_new_with_defaults();
2709 while ((c
= getopt_long(argc
, argv
, "TAm:M:r:V", lexmin_options
, &ind
)) != -1) {
2711 case NO_EMPTINESS_CHECK
:
2712 options
->emptiness_check
= 0;
2734 printf(barvinok_version());
2741 C
= Constraints2Polyhedron(MA
, options
->MaxRays
);
2743 fscanf(stdin
, " %d", &bignum
);
2744 assert(bignum
== -1);
2746 A
= Constraints2Polyhedron(MA
, options
->MaxRays
);
2749 if (A
->Dimension
>= VBIGDIM
)
2751 else if (A
->Dimension
>= BIGDIM
)
2760 if (verify
&& m
> M
) {
2761 fprintf(stderr
,"Nothing to do: min > max !\n");
2767 iter_names
= util_generate_names(A
->Dimension
- C
->Dimension
, "i");
2768 param_names
= util_generate_names(C
->Dimension
, "p");
2769 if (print_solution
) {
2770 Polyhedron_Print(stdout
, P_VALUE_FMT
, A
);
2771 Polyhedron_Print(stdout
, P_VALUE_FMT
, C
);
2773 vector
<max_term
*> maxima
= lexmin(A
, C
, options
);
2775 for (int i
= 0; i
< maxima
.size(); ++i
)
2776 maxima
[i
]->print(cout
, param_names
);
2779 verify_results(A
, C
, maxima
, m
, M
, print_all
, options
->MaxRays
);
2781 for (int i
= 0; i
< maxima
.size(); ++i
)
2784 util_free_names(A
->Dimension
- C
->Dimension
, iter_names
);
2785 util_free_names(C
->Dimension
, param_names
);
2794 static bool lexmin(int pos
, Polyhedron
*P
, Value
*context
)
2803 value_init(LB
); value_init(UB
); value_init(k
);
2806 lu_flags
= lower_upper_bounds(pos
,P
,context
,&LB
,&UB
);
2807 assert(!(lu_flags
& LB_INFINITY
));
2809 value_set_si(context
[pos
],0);
2810 if (!lu_flags
&& value_lt(UB
,LB
)) {
2811 value_clear(LB
); value_clear(UB
); value_clear(k
);
2815 value_assign(context
[pos
], LB
);
2816 value_clear(LB
); value_clear(UB
); value_clear(k
);
2819 for (value_assign(k
,LB
); lu_flags
|| value_le(k
,UB
); value_increment(k
,k
)) {
2820 value_assign(context
[pos
],k
);
2821 if ((found
= lexmin(pos
+1, P
->next
, context
)))
2825 value_set_si(context
[pos
],0);
2826 value_clear(LB
); value_clear(UB
); value_clear(k
);
2830 static void print_list(FILE *out
, Value
*z
, char* brackets
, int len
)
2832 fprintf(out
, "%c", brackets
[0]);
2833 value_print(out
, VALUE_FMT
,z
[0]);
2834 for (int k
= 1; k
< len
; ++k
) {
2836 value_print(out
, VALUE_FMT
,z
[k
]);
2838 fprintf(out
, "%c", brackets
[1]);
2841 static int check_poly(Polyhedron
*S
, Polyhedron
*CS
, vector
<max_term
*>& maxima
,
2842 int nparam
, int pos
, Value
*z
, int print_all
, int st
,
2845 if (pos
== nparam
) {
2847 bool found
= lexmin(1, S
, z
);
2851 print_list(stdout
, z
+S
->Dimension
-nparam
+1, "()", nparam
);
2854 print_list(stdout
, z
+1, "[]", S
->Dimension
-nparam
);
2859 for (int i
= 0; i
< maxima
.size(); ++i
)
2860 if ((min
= maxima
[i
]->eval(z
+S
->Dimension
-nparam
+1, MaxRays
)))
2863 int ok
= !(found
^ !!min
);
2865 for (int i
= 0; i
< S
->Dimension
-nparam
; ++i
)
2866 if (value_ne(z
[1+i
], min
->p
[i
])) {
2873 fprintf(stderr
, "Error !\n");
2874 fprintf(stderr
, "lexmin");
2875 print_list(stderr
, z
+S
->Dimension
-nparam
+1, "()", nparam
);
2876 fprintf(stderr
, " should be ");
2878 print_list(stderr
, z
+1, "[]", S
->Dimension
-nparam
);
2879 fprintf(stderr
, " while digging gives ");
2881 print_list(stderr
, min
->p
, "[]", S
->Dimension
-nparam
);
2882 fprintf(stderr
, ".\n");
2884 } else if (print_all
)
2889 for (k
= 1; k
<= S
->Dimension
-nparam
; ++k
)
2890 value_set_si(z
[k
], 0);
2898 !(lower_upper_bounds(1+pos
, CS
, &z
[S
->Dimension
-nparam
], &LB
, &UB
));
2899 for (value_assign(tmp
,LB
); value_le(tmp
,UB
); value_increment(tmp
,tmp
)) {
2901 int k
= VALUE_TO_INT(tmp
);
2902 if (!pos
&& !(k
%st
)) {
2907 value_assign(z
[pos
+S
->Dimension
-nparam
+1],tmp
);
2908 if (!check_poly(S
, CS
->next
, maxima
, nparam
, pos
+1, z
, print_all
, st
,
2916 value_set_si(z
[pos
+S
->Dimension
-nparam
+1],0);
2924 void verify_results(Polyhedron
*A
, Polyhedron
*C
, vector
<max_term
*>& maxima
,
2925 int m
, int M
, int print_all
, unsigned MaxRays
)
2927 Polyhedron
*CC
, *CC2
, *CS
, *S
;
2928 unsigned nparam
= C
->Dimension
;
2933 CC
= Polyhedron_Project(A
, nparam
);
2934 CC2
= DomainIntersection(C
, CC
, MaxRays
);
2938 /* Intersect context with range */
2943 MM
= Matrix_Alloc(2*C
->Dimension
, C
->Dimension
+2);
2944 for (int i
= 0; i
< C
->Dimension
; ++i
) {
2945 value_set_si(MM
->p
[2*i
][0], 1);
2946 value_set_si(MM
->p
[2*i
][1+i
], 1);
2947 value_set_si(MM
->p
[2*i
][1+C
->Dimension
], -m
);
2948 value_set_si(MM
->p
[2*i
+1][0], 1);
2949 value_set_si(MM
->p
[2*i
+1][1+i
], -1);
2950 value_set_si(MM
->p
[2*i
+1][1+C
->Dimension
], M
);
2952 CC2
= AddConstraints(MM
->p
[0], 2*CC
->Dimension
, CC
, MaxRays
);
2953 U
= Universe_Polyhedron(0);
2954 CS
= Polyhedron_Scan(CC2
, U
, MaxRays
& POL_NO_DUAL
? 0 : MaxRays
);
2956 Polyhedron_Free(CC2
);
2961 p
= ALLOCN(Value
, A
->Dimension
+2);
2962 for (i
=0; i
<= A
->Dimension
; i
++) {
2964 value_set_si(p
[i
],0);
2967 value_set_si(p
[i
], 1);
2969 S
= Polyhedron_Scan(A
, C
, MaxRays
& POL_NO_DUAL
? 0 : MaxRays
);
2971 if (!print_all
&& C
->Dimension
> 0) {
2976 for (int i
= m
; i
<= M
; i
+= st
)
2983 if (!(CS
&& emptyQ2(CS
)))
2984 check_poly(S
, CS
, maxima
, nparam
, 0, p
, print_all
, st
, MaxRays
);
2991 for (i
=0; i
<= (A
->Dimension
+1); i
++)
2996 Polyhedron_Free(CC
);