8 #include <NTL/mat_ZZ.h>
12 #include <polylib/polylibgmp.h>
13 #include "ev_operations.h"
28 using std::ostringstream
;
30 #define ALLOC(p) (((long *) (p))[0])
31 #define SIZE(p) (((long *) (p))[1])
32 #define DATA(p) ((mp_limb_t *) (((long *) (p)) + 2))
34 static void value2zz(Value v
, ZZ
& z
)
36 int sa
= v
[0]._mp_size
;
37 int abs_sa
= sa
< 0 ? -sa
: sa
;
39 _ntl_gsetlength(&z
.rep
, abs_sa
);
40 mp_limb_t
* adata
= DATA(z
.rep
);
41 for (int i
= 0; i
< abs_sa
; ++i
)
42 adata
[i
] = v
[0]._mp_d
[i
];
46 static void zz2value(ZZ
& z
, Value
& v
)
54 int abs_sa
= sa
< 0 ? -sa
: sa
;
56 mp_limb_t
* adata
= DATA(z
.rep
);
57 _mpz_realloc(v
, abs_sa
);
58 for (int i
= 0; i
< abs_sa
; ++i
)
59 v
[0]._mp_d
[i
] = adata
[i
];
64 #define ALLOC(t,p) p = (t*)malloc(sizeof(*p))
67 * We just ignore the last column and row
68 * If the final element is not equal to one
69 * then the result will actually be a multiple of the input
71 static void matrix2zz(Matrix
*M
, mat_ZZ
& m
, unsigned nr
, unsigned nc
)
75 for (int i
= 0; i
< nr
; ++i
) {
76 // assert(value_one_p(M->p[i][M->NbColumns - 1]));
77 for (int j
= 0; j
< nc
; ++j
) {
78 value2zz(M
->p
[i
][j
], m
[i
][j
]);
83 static void values2zz(Value
*p
, vec_ZZ
& v
, int len
)
87 for (int i
= 0; i
< len
; ++i
) {
94 static void zz2values(vec_ZZ
& v
, Value
*p
)
96 for (int i
= 0; i
< v
.length(); ++i
)
100 static void rays(mat_ZZ
& r
, Polyhedron
*C
)
102 unsigned dim
= C
->NbRays
- 1; /* don't count zero vertex */
103 assert(C
->NbRays
- 1 == C
->Dimension
);
108 for (i
= 0, c
= 0; i
< dim
; ++i
)
109 if (value_zero_p(C
->Ray
[i
][dim
+1])) {
110 for (int j
= 0; j
< dim
; ++j
) {
111 value2zz(C
->Ray
[i
][j
+1], tmp
);
118 static Matrix
* rays(Polyhedron
*C
)
120 unsigned dim
= C
->NbRays
- 1; /* don't count zero vertex */
121 assert(C
->NbRays
- 1 == C
->Dimension
);
123 Matrix
*M
= Matrix_Alloc(dim
+1, dim
+1);
127 for (i
= 0, c
= 0; i
<= dim
&& c
< dim
; ++i
)
128 if (value_zero_p(C
->Ray
[i
][dim
+1])) {
129 Vector_Copy(C
->Ray
[i
] + 1, M
->p
[c
], dim
);
130 value_set_si(M
->p
[c
++][dim
], 0);
133 value_set_si(M
->p
[dim
][dim
], 1);
138 static Matrix
* rays2(Polyhedron
*C
)
140 unsigned dim
= C
->NbRays
- 1; /* don't count zero vertex */
141 assert(C
->NbRays
- 1 == C
->Dimension
);
143 Matrix
*M
= Matrix_Alloc(dim
, dim
);
147 for (i
= 0, c
= 0; i
<= dim
&& c
< dim
; ++i
)
148 if (value_zero_p(C
->Ray
[i
][dim
+1]))
149 Vector_Copy(C
->Ray
[i
] + 1, M
->p
[c
++], dim
);
156 * Returns the largest absolute value in the vector
158 static ZZ
max(vec_ZZ
& v
)
161 for (int i
= 1; i
< v
.length(); ++i
)
171 Rays
= Matrix_Copy(M
);
174 cone(Polyhedron
*C
) {
175 Cone
= Polyhedron_Copy(C
);
181 matrix2zz(Rays
, A
, Rays
->NbRows
- 1, Rays
->NbColumns
- 1);
182 det
= determinant(A
);
189 Vector
* short_vector(vec_ZZ
& lambda
) {
190 Matrix
*M
= Matrix_Copy(Rays
);
191 Matrix
*inv
= Matrix_Alloc(M
->NbRows
, M
->NbColumns
);
192 int ok
= Matrix_Inverse(M
, inv
);
199 matrix2zz(inv
, B
, inv
->NbRows
- 1, inv
->NbColumns
- 1);
200 long r
= LLL(det2
, B
, U
);
204 for (int i
= 1; i
< B
.NumRows(); ++i
) {
216 Vector
*z
= Vector_Alloc(U
[index
].length()+1);
218 zz2values(U
[index
], z
->p
);
219 value_set_si(z
->p
[U
[index
].length()], 0);
223 Polyhedron
*C
= poly();
225 for (i
= 0; i
< C
->NbConstraints
; ++i
) {
226 Inner_Product(z
->p
, C
->Constraint
[i
]+1, z
->Size
-1, &tmp
);
227 if (value_pos_p(tmp
))
230 if (i
== C
->NbConstraints
) {
231 value_set_si(tmp
, -1);
232 Vector_Scale(z
->p
, z
->p
, tmp
, z
->Size
-1);
239 Polyhedron_Free(Cone
);
245 Matrix
*M
= Matrix_Alloc(Rays
->NbRows
+1, Rays
->NbColumns
+1);
246 for (int i
= 0; i
< Rays
->NbRows
; ++i
) {
247 Vector_Copy(Rays
->p
[i
], M
->p
[i
]+1, Rays
->NbColumns
);
248 value_set_si(M
->p
[i
][0], 1);
250 Vector_Set(M
->p
[Rays
->NbRows
]+1, 0, Rays
->NbColumns
-1);
251 value_set_si(M
->p
[Rays
->NbRows
][0], 1);
252 value_set_si(M
->p
[Rays
->NbRows
][Rays
->NbColumns
], 1);
253 Cone
= Rays2Polyhedron(M
, M
->NbRows
+1);
254 assert(Cone
->NbConstraints
== Cone
->NbRays
);
268 dpoly(int d
, ZZ
& degree
, int offset
= 0) {
269 coeff
.SetLength(d
+1);
271 int min
= d
+ offset
;
272 if (degree
>= 0 && degree
< ZZ(INIT_VAL
, min
))
273 min
= to_int(degree
);
275 ZZ c
= ZZ(INIT_VAL
, 1);
278 for (int i
= 1; i
<= min
; ++i
) {
279 c
*= (degree
-i
+ 1);
284 void operator *= (dpoly
& f
) {
285 assert(coeff
.length() == f
.coeff
.length());
287 coeff
= f
.coeff
[0] * coeff
;
288 for (int i
= 1; i
< coeff
.length(); ++i
)
289 for (int j
= 0; i
+j
< coeff
.length(); ++j
)
290 coeff
[i
+j
] += f
.coeff
[i
] * old
[j
];
292 void div(dpoly
& d
, mpq_t count
, ZZ
& sign
) {
293 int len
= coeff
.length();
296 mpq_t
* c
= new mpq_t
[coeff
.length()];
299 for (int i
= 0; i
< len
; ++i
) {
301 zz2value(coeff
[i
], tmp
);
302 mpq_set_z(c
[i
], tmp
);
304 for (int j
= 1; j
<= i
; ++j
) {
305 zz2value(d
.coeff
[j
], tmp
);
306 mpq_set_z(qtmp
, tmp
);
307 mpq_mul(qtmp
, qtmp
, c
[i
-j
]);
308 mpq_sub(c
[i
], c
[i
], qtmp
);
311 zz2value(d
.coeff
[0], tmp
);
312 mpq_set_z(qtmp
, tmp
);
313 mpq_div(c
[i
], c
[i
], qtmp
);
316 mpq_sub(count
, count
, c
[len
-1]);
318 mpq_add(count
, count
, c
[len
-1]);
322 for (int i
= 0; i
< len
; ++i
)
334 dpoly_n(int d
, ZZ
& degree_0
, ZZ
& degree_1
, int offset
= 0) {
338 zz2value(degree_0
, d0
);
339 zz2value(degree_1
, d1
);
340 coeff
= Matrix_Alloc(d
+1, d
+1+1);
341 value_set_si(coeff
->p
[0][0], 1);
342 value_set_si(coeff
->p
[0][d
+1], 1);
343 for (int i
= 1; i
<= d
; ++i
) {
344 value_multiply(coeff
->p
[i
][0], coeff
->p
[i
-1][0], d0
);
345 Vector_Combine(coeff
->p
[i
-1], coeff
->p
[i
-1]+1, coeff
->p
[i
]+1,
347 value_set_si(coeff
->p
[i
][d
+1], i
);
348 value_multiply(coeff
->p
[i
][d
+1], coeff
->p
[i
][d
+1], coeff
->p
[i
-1][d
+1]);
349 value_decrement(d0
, d0
);
354 void div(dpoly
& d
, Vector
*count
, ZZ
& sign
) {
355 int len
= coeff
->NbRows
;
356 Matrix
* c
= Matrix_Alloc(coeff
->NbRows
, coeff
->NbColumns
);
359 for (int i
= 0; i
< len
; ++i
) {
360 Vector_Copy(coeff
->p
[i
], c
->p
[i
], len
+1);
361 for (int j
= 1; j
<= i
; ++j
) {
362 zz2value(d
.coeff
[j
], tmp
);
363 value_multiply(tmp
, tmp
, c
->p
[i
][len
]);
364 value_oppose(tmp
, tmp
);
365 Vector_Combine(c
->p
[i
], c
->p
[i
-j
], c
->p
[i
],
366 c
->p
[i
-j
][len
], tmp
, len
);
367 value_multiply(c
->p
[i
][len
], c
->p
[i
][len
], c
->p
[i
-j
][len
]);
369 zz2value(d
.coeff
[0], tmp
);
370 value_multiply(c
->p
[i
][len
], c
->p
[i
][len
], tmp
);
373 value_set_si(tmp
, -1);
374 Vector_Scale(c
->p
[len
-1], count
->p
, tmp
, len
);
375 value_assign(count
->p
[len
], c
->p
[len
-1][len
]);
377 Vector_Copy(c
->p
[len
-1], count
->p
, len
+1);
378 Vector_Normalize(count
->p
, len
+1);
384 struct dpoly_r_term
{
390 vector
< dpoly_r_term
* > *c
;
394 void add_term(int i
, int * powers
, ZZ
& coeff
) {
395 for (int k
= 0; k
< c
[i
].size(); ++k
) {
396 if (memcmp(c
[i
][k
]->powers
, powers
, dim
* sizeof(int)) == 0) {
397 c
[i
][k
]->coeff
+= coeff
;
401 dpoly_r_term
*t
= new dpoly_r_term
;
402 t
->powers
= new int[dim
];
403 memcpy(t
->powers
, powers
, dim
* sizeof(int));
407 dpoly_r(int len
, int dim
) {
410 c
= new vector
< dpoly_r_term
* > [len
];
412 dpoly_r(dpoly
& num
, dpoly
& den
, int pos
, int sign
, int dim
) {
413 len
= num
.coeff
.length();
414 c
= new vector
< dpoly_r_term
* > [len
];
418 for (int i
= 0; i
< len
; ++i
) {
419 ZZ coeff
= num
.coeff
[i
];
420 memset(powers
, 0, dim
* sizeof(int));
423 add_term(i
, powers
, coeff
);
425 for (int j
= 1; j
<= i
; ++j
) {
426 for (int k
= 0; k
< c
[i
-j
].size(); ++k
) {
427 memcpy(powers
, c
[i
-j
][k
]->powers
, dim
*sizeof(int));
429 coeff
= -den
.coeff
[j
-1] * c
[i
-j
][k
]->coeff
;
430 add_term(i
, powers
, coeff
);
436 void div(dpoly
& d
, ZZ
& sign
, gen_fun
*gf
, mat_ZZ
& pden
, mat_ZZ
& den
,
438 dpoly_r
rc(len
, dim
);
439 ZZ max_d
= power(d
.coeff
[0], len
+1);
443 for (int i
= 0; i
< len
; ++i
) {
446 for (int k
= 0; k
< c
[i
].size(); ++k
) {
447 coeff
= c
[i
][k
]->coeff
* cur_d
;
448 rc
.add_term(i
, c
[i
][k
]->powers
, coeff
);
451 for (int j
= 1; j
<= i
; ++j
) {
452 for (int k
= 0; k
< rc
.c
[i
-j
].size(); ++k
) {
453 coeff
= - d
.coeff
[j
] * rc
.c
[i
-j
][k
]->coeff
/ d
.coeff
[0];
454 rc
.add_term(i
, rc
.c
[i
-j
][k
]->powers
, coeff
);
459 int common
= pden
.NumRows();
461 vector
< dpoly_r_term
* >& final
= rc
.c
[len
-1];
463 for (int j
= 0; j
< final
.size(); ++j
) {
465 pden
.SetDims(rows
, pden
.NumCols());
466 for (int k
= 0; k
< dim
; ++k
) {
467 int n
= final
[j
]->powers
[k
];
470 int abs_n
= n
< 0 ? -n
: n
;
471 pden
.SetDims(rows
+abs_n
, pden
.NumCols());
472 for (int l
= 0; l
< abs_n
; ++l
) {
474 pden
[rows
+l
] = den
[k
];
476 pden
[rows
+l
] = -den
[k
];
480 gf
->add(final
[j
]->coeff
, max_d
, num_p
, pden
);
484 for (int i
= 0; i
< len
; ++i
) {
487 cout
<< c
[i
].size() << endl
;
488 for (int j
= 0; j
< c
[i
].size(); ++j
) {
489 for (int k
= 0; k
< dim
; ++k
) {
490 cout
<< c
[i
][j
]->powers
[k
] << " ";
492 cout
<< ": " << c
[i
][j
]->coeff
<< endl
;
500 * Barvinok's Decomposition of a simplicial cone
502 * Returns two lists of polyhedra
504 void barvinok_decompose(Polyhedron
*C
, Polyhedron
**ppos
, Polyhedron
**pneg
)
506 Polyhedron
*pos
= *ppos
, *neg
= *pneg
;
507 vector
<cone
*> nonuni
;
508 cone
* c
= new cone(C
);
515 Polyhedron
*p
= Polyhedron_Copy(c
->Cone
);
521 while (!nonuni
.empty()) {
524 Vector
* v
= c
->short_vector(lambda
);
525 for (int i
= 0; i
< c
->Rays
->NbRows
- 1; ++i
) {
528 Matrix
* M
= Matrix_Copy(c
->Rays
);
529 Vector_Copy(v
->p
, M
->p
[i
], v
->Size
);
530 cone
* pc
= new cone(M
);
531 assert (pc
->det
!= 0);
532 if (abs(pc
->det
) > 1) {
533 assert(abs(pc
->det
) < abs(c
->det
));
534 nonuni
.push_back(pc
);
536 Polyhedron
*p
= pc
->poly();
538 if (sign(pc
->det
) == s
) {
557 * Returns a single list of npos "positive" cones followed by nneg
559 * The input cone is freed
561 void decompose(Polyhedron
*cone
, Polyhedron
**parts
, int *npos
, int *nneg
, unsigned MaxRays
)
563 Polyhedron_Polarize(cone
);
564 if (cone
->NbRays
- 1 != cone
->Dimension
) {
565 Polyhedron
*tmp
= cone
;
566 cone
= triangularize_cone(cone
, MaxRays
);
567 Polyhedron_Free(tmp
);
569 Polyhedron
*polpos
= NULL
, *polneg
= NULL
;
570 *npos
= 0; *nneg
= 0;
571 for (Polyhedron
*Polar
= cone
; Polar
; Polar
= Polar
->next
)
572 barvinok_decompose(Polar
, &polpos
, &polneg
);
575 for (Polyhedron
*i
= polpos
; i
; i
= i
->next
) {
576 Polyhedron_Polarize(i
);
580 for (Polyhedron
*i
= polneg
; i
; i
= i
->next
) {
581 Polyhedron_Polarize(i
);
592 const int MAX_TRY
=10;
594 * Searches for a vector that is not orthogonal to any
595 * of the rays in rays.
597 static void nonorthog(mat_ZZ
& rays
, vec_ZZ
& lambda
)
599 int dim
= rays
.NumCols();
601 lambda
.SetLength(dim
);
605 for (int i
= 2; !found
&& i
<= 50*dim
; i
+=4) {
606 for (int j
= 0; j
< MAX_TRY
; ++j
) {
607 for (int k
= 0; k
< dim
; ++k
) {
608 int r
= random_int(i
)+2;
609 int v
= (2*(r
%2)-1) * (r
>> 1);
613 for (; k
< rays
.NumRows(); ++k
)
614 if (lambda
* rays
[k
] == 0)
616 if (k
== rays
.NumRows()) {
625 static void randomvector(Polyhedron
*P
, vec_ZZ
& lambda
, int nvar
)
629 unsigned int dim
= P
->Dimension
;
632 for (int i
= 0; i
< P
->NbRays
; ++i
) {
633 for (int j
= 1; j
<= dim
; ++j
) {
634 value_absolute(tmp
, P
->Ray
[i
][j
]);
635 int t
= VALUE_TO_LONG(tmp
);
640 for (int i
= 0; i
< P
->NbConstraints
; ++i
) {
641 for (int j
= 1; j
<= dim
; ++j
) {
642 value_absolute(tmp
, P
->Constraint
[i
][j
]);
643 int t
= VALUE_TO_LONG(tmp
);
650 lambda
.SetLength(nvar
);
651 for (int k
= 0; k
< nvar
; ++k
) {
652 int r
= random_int(8*max
*dim
)+2;
653 int v
= (2*(r
%2)-1) * (4*max
*dim
+ (r
>> 1));
658 static void add_rays(mat_ZZ
& rays
, Polyhedron
*i
, int *r
, int nvar
= -1,
661 unsigned dim
= i
->Dimension
;
664 for (int k
= 0; k
< i
->NbRays
; ++k
) {
665 if (!value_zero_p(i
->Ray
[k
][dim
+1]))
667 if (!all
&& nvar
!= dim
&& First_Non_Zero(i
->Ray
[k
]+1, nvar
) == -1)
669 values2zz(i
->Ray
[k
]+1, rays
[(*r
)++], nvar
);
673 void lattice_point(Value
* values
, Polyhedron
*i
, vec_ZZ
& vertex
)
675 unsigned dim
= i
->Dimension
;
676 if(!value_one_p(values
[dim
])) {
677 Matrix
* Rays
= rays(i
);
678 Matrix
*inv
= Matrix_Alloc(Rays
->NbRows
, Rays
->NbColumns
);
679 int ok
= Matrix_Inverse(Rays
, inv
);
683 Vector
*lambda
= Vector_Alloc(dim
+1);
684 Vector_Matrix_Product(values
, inv
, lambda
->p
);
686 for (int j
= 0; j
< dim
; ++j
)
687 mpz_cdiv_q(lambda
->p
[j
], lambda
->p
[j
], lambda
->p
[dim
]);
688 value_set_si(lambda
->p
[dim
], 1);
689 Vector
*A
= Vector_Alloc(dim
+1);
690 Vector_Matrix_Product(lambda
->p
, Rays
, A
->p
);
693 values2zz(A
->p
, vertex
, dim
);
696 values2zz(values
, vertex
, dim
);
699 static evalue
*term(int param
, ZZ
& c
, Value
*den
= NULL
)
701 evalue
*EP
= new evalue();
703 value_set_si(EP
->d
,0);
704 EP
->x
.p
= new_enode(polynomial
, 2, param
+ 1);
705 evalue_set_si(&EP
->x
.p
->arr
[0], 0, 1);
706 value_init(EP
->x
.p
->arr
[1].x
.n
);
708 value_set_si(EP
->x
.p
->arr
[1].d
, 1);
710 value_assign(EP
->x
.p
->arr
[1].d
, *den
);
711 zz2value(c
, EP
->x
.p
->arr
[1].x
.n
);
715 static void vertex_period(
716 Polyhedron
*i
, vec_ZZ
& lambda
, Matrix
*T
,
717 Value lcm
, int p
, Vector
*val
,
718 evalue
*E
, evalue
* ev
,
721 unsigned nparam
= T
->NbRows
- 1;
722 unsigned dim
= i
->Dimension
;
729 Vector
* values
= Vector_Alloc(dim
+ 1);
730 Vector_Matrix_Product(val
->p
, T
, values
->p
);
731 value_assign(values
->p
[dim
], lcm
);
732 lattice_point(values
->p
, i
, vertex
);
733 num
= vertex
* lambda
;
738 zz2value(num
, ev
->x
.n
);
739 value_assign(ev
->d
, lcm
);
746 values2zz(T
->p
[p
], vertex
, dim
);
747 nump
= vertex
* lambda
;
748 if (First_Non_Zero(val
->p
, p
) == -1) {
749 value_assign(tmp
, lcm
);
750 evalue
*ET
= term(p
, nump
, &tmp
);
752 free_evalue_refs(ET
);
756 value_assign(tmp
, lcm
);
757 if (First_Non_Zero(T
->p
[p
], dim
) != -1)
758 Vector_Gcd(T
->p
[p
], dim
, &tmp
);
760 if (value_lt(tmp
, lcm
)) {
763 value_division(tmp
, lcm
, tmp
);
764 value_set_si(ev
->d
, 0);
765 ev
->x
.p
= new_enode(periodic
, VALUE_TO_INT(tmp
), p
+1);
766 value2zz(tmp
, count
);
768 value_decrement(tmp
, tmp
);
770 ZZ new_offset
= offset
- count
* nump
;
771 value_assign(val
->p
[p
], tmp
);
772 vertex_period(i
, lambda
, T
, lcm
, p
+1, val
, E
,
773 &ev
->x
.p
->arr
[VALUE_TO_INT(tmp
)], new_offset
);
774 } while (value_pos_p(tmp
));
776 vertex_period(i
, lambda
, T
, lcm
, p
+1, val
, E
, ev
, offset
);
780 static void mask_r(Matrix
*f
, int nr
, Vector
*lcm
, int p
, Vector
*val
, evalue
*ev
)
782 unsigned nparam
= lcm
->Size
;
785 Vector
* prod
= Vector_Alloc(f
->NbRows
);
786 Matrix_Vector_Product(f
, val
->p
, prod
->p
);
788 for (int i
= 0; i
< nr
; ++i
) {
789 value_modulus(prod
->p
[i
], prod
->p
[i
], f
->p
[i
][nparam
+1]);
790 isint
&= value_zero_p(prod
->p
[i
]);
792 value_set_si(ev
->d
, 1);
794 value_set_si(ev
->x
.n
, isint
);
801 if (value_one_p(lcm
->p
[p
]))
802 mask_r(f
, nr
, lcm
, p
+1, val
, ev
);
804 value_assign(tmp
, lcm
->p
[p
]);
805 value_set_si(ev
->d
, 0);
806 ev
->x
.p
= new_enode(periodic
, VALUE_TO_INT(tmp
), p
+1);
808 value_decrement(tmp
, tmp
);
809 value_assign(val
->p
[p
], tmp
);
810 mask_r(f
, nr
, lcm
, p
+1, val
, &ev
->x
.p
->arr
[VALUE_TO_INT(tmp
)]);
811 } while (value_pos_p(tmp
));
816 static evalue
*multi_monom(vec_ZZ
& p
)
818 evalue
*X
= new evalue();
821 unsigned nparam
= p
.length()-1;
822 zz2value(p
[nparam
], X
->x
.n
);
823 value_set_si(X
->d
, 1);
824 for (int i
= 0; i
< nparam
; ++i
) {
827 evalue
*T
= term(i
, p
[i
]);
836 * Check whether mapping polyhedron P on the affine combination
837 * num yields a range that has a fixed quotient on integer
839 * If zero is true, then we are only interested in the quotient
840 * for the cases where the remainder is zero.
841 * Returns NULL if false and a newly allocated value if true.
843 static Value
*fixed_quotient(Polyhedron
*P
, vec_ZZ
& num
, Value d
, bool zero
)
846 int len
= num
.length();
847 Matrix
*T
= Matrix_Alloc(2, len
);
848 zz2values(num
, T
->p
[0]);
849 value_set_si(T
->p
[1][len
-1], 1);
850 Polyhedron
*I
= Polyhedron_Image(P
, T
, P
->NbConstraints
);
854 for (i
= 0; i
< I
->NbRays
; ++i
)
855 if (value_zero_p(I
->Ray
[i
][2])) {
863 int bounded
= line_minmax(I
, &min
, &max
);
867 mpz_cdiv_q(min
, min
, d
);
869 mpz_fdiv_q(min
, min
, d
);
870 mpz_fdiv_q(max
, max
, d
);
872 if (value_eq(min
, max
)) {
875 value_assign(*ret
, min
);
883 * Normalize linear expression coef modulo m
884 * Removes common factor and reduces coefficients
885 * Returns index of first non-zero coefficient or len
887 static int normal_mod(Value
*coef
, int len
, Value
*m
)
892 Vector_Gcd(coef
, len
, &gcd
);
894 Vector_AntiScale(coef
, coef
, gcd
, len
);
896 value_division(*m
, *m
, gcd
);
903 for (j
= 0; j
< len
; ++j
)
904 mpz_fdiv_r(coef
[j
], coef
[j
], *m
);
905 for (j
= 0; j
< len
; ++j
)
906 if (value_notzero_p(coef
[j
]))
913 static void mask(Matrix
*f
, evalue
*factor
)
915 int nr
= f
->NbRows
, nc
= f
->NbColumns
;
918 for (n
= 0; n
< nr
&& value_notzero_p(f
->p
[n
][nc
-1]); ++n
)
919 if (value_notone_p(f
->p
[n
][nc
-1]) &&
920 value_notmone_p(f
->p
[n
][nc
-1]))
934 value_set_si(EV
.x
.n
, 1);
936 for (n
= 0; n
< nr
; ++n
) {
937 value_assign(m
, f
->p
[n
][nc
-1]);
938 if (value_one_p(m
) || value_mone_p(m
))
941 int j
= normal_mod(f
->p
[n
], nc
-1, &m
);
943 free_evalue_refs(factor
);
944 value_init(factor
->d
);
945 evalue_set_si(factor
, 0, 1);
949 values2zz(f
->p
[n
], row
, nc
-1);
952 if (j
< (nc
-1)-1 && row
[j
] > g
/2) {
953 for (int k
= j
; k
< (nc
-1); ++k
)
959 value_set_si(EP
.d
, 0);
960 EP
.x
.p
= new_enode(relation
, 2, 0);
961 value_clear(EP
.x
.p
->arr
[1].d
);
962 EP
.x
.p
->arr
[1] = *factor
;
963 evalue
*ev
= &EP
.x
.p
->arr
[0];
964 value_set_si(ev
->d
, 0);
965 ev
->x
.p
= new_enode(fractional
, 3, -1);
966 evalue_set_si(&ev
->x
.p
->arr
[1], 0, 1);
967 evalue_set_si(&ev
->x
.p
->arr
[2], 1, 1);
968 evalue
*E
= multi_monom(row
);
969 value_assign(EV
.d
, m
);
971 value_clear(ev
->x
.p
->arr
[0].d
);
972 ev
->x
.p
->arr
[0] = *E
;
978 free_evalue_refs(&EV
);
984 static void mask(Matrix
*f
, evalue
*factor
)
986 int nr
= f
->NbRows
, nc
= f
->NbColumns
;
989 for (n
= 0; n
< nr
&& value_notzero_p(f
->p
[n
][nc
-1]); ++n
)
990 if (value_notone_p(f
->p
[n
][nc
-1]) &&
991 value_notmone_p(f
->p
[n
][nc
-1]))
999 unsigned np
= nc
- 2;
1000 Vector
*lcm
= Vector_Alloc(np
);
1001 Vector
*val
= Vector_Alloc(nc
);
1002 Vector_Set(val
->p
, 0, nc
);
1003 value_set_si(val
->p
[np
], 1);
1004 Vector_Set(lcm
->p
, 1, np
);
1005 for (n
= 0; n
< nr
; ++n
) {
1006 if (value_one_p(f
->p
[n
][nc
-1]) ||
1007 value_mone_p(f
->p
[n
][nc
-1]))
1009 for (int j
= 0; j
< np
; ++j
)
1010 if (value_notzero_p(f
->p
[n
][j
])) {
1011 Gcd(f
->p
[n
][j
], f
->p
[n
][nc
-1], &tmp
);
1012 value_division(tmp
, f
->p
[n
][nc
-1], tmp
);
1013 value_lcm(tmp
, lcm
->p
[j
], &lcm
->p
[j
]);
1018 mask_r(f
, nr
, lcm
, 0, val
, &EP
);
1023 free_evalue_refs(&EP
);
1034 static bool mod_needed(Polyhedron
*PD
, vec_ZZ
& num
, Value d
, evalue
*E
)
1036 Value
*q
= fixed_quotient(PD
, num
, d
, false);
1041 value_oppose(*q
, *q
);
1044 value_set_si(EV
.d
, 1);
1046 value_multiply(EV
.x
.n
, *q
, d
);
1048 free_evalue_refs(&EV
);
1054 static void ceil_mod(Value
*coef
, int len
, Value d
, ZZ
& f
, evalue
*EP
, Polyhedron
*PD
)
1058 value_set_si(m
, -1);
1060 Vector_Scale(coef
, coef
, m
, len
);
1063 int j
= normal_mod(coef
, len
, &m
);
1071 values2zz(coef
, num
, len
);
1078 evalue_set_si(&tmp
, 0, 1);
1082 while (j
< len
-1 && (num
[j
] == g
/2 || num
[j
] == 0))
1084 if ((j
< len
-1 && num
[j
] > g
/2) || (j
== len
-1 && num
[j
] >= (g
+1)/2)) {
1085 for (int k
= j
; k
< len
-1; ++k
)
1087 num
[k
] = g
- num
[k
];
1088 num
[len
-1] = g
- 1 - num
[len
-1];
1089 value_assign(tmp
.d
, m
);
1091 zz2value(t
, tmp
.x
.n
);
1097 ZZ t
= num
[len
-1] * f
;
1098 zz2value(t
, tmp
.x
.n
);
1099 value_assign(tmp
.d
, m
);
1102 evalue
*E
= multi_monom(num
);
1106 if (PD
&& !mod_needed(PD
, num
, m
, E
)) {
1108 zz2value(f
, EV
.x
.n
);
1109 value_assign(EV
.d
, m
);
1114 value_set_si(EV
.x
.n
, 1);
1115 value_assign(EV
.d
, m
);
1117 value_clear(EV
.x
.n
);
1118 value_set_si(EV
.d
, 0);
1119 EV
.x
.p
= new_enode(fractional
, 3, -1);
1120 evalue_copy(&EV
.x
.p
->arr
[0], E
);
1121 evalue_set_si(&EV
.x
.p
->arr
[1], 0, 1);
1122 value_init(EV
.x
.p
->arr
[2].x
.n
);
1123 zz2value(f
, EV
.x
.p
->arr
[2].x
.n
);
1124 value_set_si(EV
.x
.p
->arr
[2].d
, 1);
1129 free_evalue_refs(&EV
);
1130 free_evalue_refs(E
);
1134 free_evalue_refs(&tmp
);
1140 evalue
* bv_ceil3(Value
*coef
, int len
, Value d
, Polyhedron
*P
)
1142 Vector
*val
= Vector_Alloc(len
);
1146 value_set_si(t
, -1);
1147 Vector_Scale(coef
, val
->p
, t
, len
);
1148 value_absolute(t
, d
);
1151 values2zz(val
->p
, num
, len
);
1152 evalue
*EP
= multi_monom(num
);
1156 value_init(tmp
.x
.n
);
1157 value_set_si(tmp
.x
.n
, 1);
1158 value_assign(tmp
.d
, t
);
1164 ceil_mod(val
->p
, len
, t
, one
, EP
, P
);
1167 /* copy EP to malloc'ed evalue */
1173 free_evalue_refs(&tmp
);
1180 evalue
* lattice_point(
1181 Polyhedron
*i
, vec_ZZ
& lambda
, Matrix
*W
, Value lcm
, Polyhedron
*PD
)
1183 unsigned nparam
= W
->NbColumns
- 1;
1185 Matrix
* Rays
= rays2(i
);
1186 Matrix
*T
= Transpose(Rays
);
1187 Matrix
*T2
= Matrix_Copy(T
);
1188 Matrix
*inv
= Matrix_Alloc(T2
->NbRows
, T2
->NbColumns
);
1189 int ok
= Matrix_Inverse(T2
, inv
);
1194 matrix2zz(W
, vertex
, W
->NbRows
, W
->NbColumns
);
1197 num
= lambda
* vertex
;
1199 evalue
*EP
= multi_monom(num
);
1203 value_init(tmp
.x
.n
);
1204 value_set_si(tmp
.x
.n
, 1);
1205 value_assign(tmp
.d
, lcm
);
1209 Matrix
*L
= Matrix_Alloc(inv
->NbRows
, W
->NbColumns
);
1210 Matrix_Product(inv
, W
, L
);
1213 matrix2zz(T
, RT
, T
->NbRows
, T
->NbColumns
);
1216 vec_ZZ p
= lambda
* RT
;
1218 for (int i
= 0; i
< L
->NbRows
; ++i
) {
1219 ceil_mod(L
->p
[i
], nparam
+1, lcm
, p
[i
], EP
, PD
);
1225 free_evalue_refs(&tmp
);
1229 evalue
* lattice_point(
1230 Polyhedron
*i
, vec_ZZ
& lambda
, Matrix
*W
, Value lcm
, Polyhedron
*PD
)
1232 Matrix
*T
= Transpose(W
);
1233 unsigned nparam
= T
->NbRows
- 1;
1235 evalue
*EP
= new evalue();
1237 evalue_set_si(EP
, 0, 1);
1240 Vector
*val
= Vector_Alloc(nparam
+1);
1241 value_set_si(val
->p
[nparam
], 1);
1242 ZZ
offset(INIT_VAL
, 0);
1244 vertex_period(i
, lambda
, T
, lcm
, 0, val
, EP
, &ev
, offset
);
1247 free_evalue_refs(&ev
);
1258 Param_Vertices
* V
, Polyhedron
*i
, vec_ZZ
& lambda
, term_info
* term
,
1261 unsigned nparam
= V
->Vertex
->NbColumns
- 2;
1262 unsigned dim
= i
->Dimension
;
1264 vertex
.SetDims(V
->Vertex
->NbRows
, nparam
+1);
1268 value_set_si(lcm
, 1);
1269 for (int j
= 0; j
< V
->Vertex
->NbRows
; ++j
) {
1270 value_lcm(lcm
, V
->Vertex
->p
[j
][nparam
+1], &lcm
);
1272 if (value_notone_p(lcm
)) {
1273 Matrix
* mv
= Matrix_Alloc(dim
, nparam
+1);
1274 for (int j
= 0 ; j
< dim
; ++j
) {
1275 value_division(tmp
, lcm
, V
->Vertex
->p
[j
][nparam
+1]);
1276 Vector_Scale(V
->Vertex
->p
[j
], mv
->p
[j
], tmp
, nparam
+1);
1279 term
->E
= lattice_point(i
, lambda
, mv
, lcm
, PD
);
1287 for (int i
= 0; i
< V
->Vertex
->NbRows
; ++i
) {
1288 assert(value_one_p(V
->Vertex
->p
[i
][nparam
+1])); // for now
1289 values2zz(V
->Vertex
->p
[i
], vertex
[i
], nparam
+1);
1293 num
= lambda
* vertex
;
1297 for (int j
= 0; j
< nparam
; ++j
)
1303 term
->E
= multi_monom(num
);
1307 term
->constant
= num
[nparam
];
1310 term
->coeff
= num
[p
];
1317 void normalize(Polyhedron
*i
, vec_ZZ
& lambda
, ZZ
& sign
, ZZ
& num
, vec_ZZ
& den
)
1319 unsigned dim
= i
->Dimension
;
1323 rays
.SetDims(dim
, dim
);
1324 add_rays(rays
, i
, &r
);
1325 den
= rays
* lambda
;
1328 for (int j
= 0; j
< den
.length(); ++j
) {
1332 den
[j
] = abs(den
[j
]);
1340 typedef Polyhedron
* Polyhedron_p
;
1342 void barvinok_count(Polyhedron
*P
, Value
* result
, unsigned NbMaxCons
)
1344 Polyhedron
** vcone
;
1354 value_set_si(*result
, 0);
1358 for (; r
< P
->NbRays
; ++r
)
1359 if (value_zero_p(P
->Ray
[r
][P
->Dimension
+1]))
1361 if (P
->NbBid
!=0 || r
< P
->NbRays
) {
1362 value_set_si(*result
, -1);
1366 P
= remove_equalities(P
);
1369 value_set_si(*result
, 0);
1375 value_set_si(factor
, 1);
1376 Q
= Polyhedron_Reduce(P
, &factor
);
1383 if (P
->Dimension
== 0) {
1384 value_assign(*result
, factor
);
1387 value_clear(factor
);
1394 //nonorthog(rays, lambda);
1395 randomvector(P
, lambda
, dim
);
1396 //cout << "lambda: " << lambda << endl;
1399 rays
.SetDims(dim
, dim
);
1409 for (int j
= 0; j
< P
->NbRays
; ++j
) {
1412 Polyhedron
*C
= supporting_cone(P
, j
);
1413 decompose(C
, &vcone
, &npos
, &nneg
, NbMaxCons
);
1414 ncone
+= npos
+ nneg
;
1418 for (i
= vcone
, l
= 0; i
; i
= i
->next
, ++l
) {
1420 assert(i
->NbRays
-1 == dim
);
1421 add_rays(rays
, i
, &r
);
1422 for (int k
= 0; k
< dim
; ++k
) {
1423 assert(lambda
* rays
[k
] != 0);
1426 sign
= (l
< npos
) ? 1 : -1;
1428 lattice_point(P
->Ray
[j
]+1, i
, vertex
);
1429 num
= vertex
* lambda
;
1430 normalize(i
, lambda
, sign
, num
, den
);
1433 dpoly
n(dim
, den
[0], 1);
1434 for (int k
= 1; k
< dim
; ++k
) {
1435 dpoly
fact(dim
, den
[k
], 1);
1438 d
.div(n
, count
, sign
);
1443 assert(value_one_p(&count
[0]._mp_den
));
1444 value_multiply(*result
, &count
[0]._mp_num
, factor
);
1449 value_clear(factor
);
1452 static void uni_polynom(int param
, Vector
*c
, evalue
*EP
)
1454 unsigned dim
= c
->Size
-2;
1456 value_set_si(EP
->d
,0);
1457 EP
->x
.p
= new_enode(polynomial
, dim
+1, param
+1);
1458 for (int j
= 0; j
<= dim
; ++j
)
1459 evalue_set(&EP
->x
.p
->arr
[j
], c
->p
[j
], c
->p
[dim
+1]);
1462 static void multi_polynom(Vector
*c
, evalue
* X
, evalue
*EP
)
1464 unsigned dim
= c
->Size
-2;
1468 evalue_set(&EC
, c
->p
[dim
], c
->p
[dim
+1]);
1471 evalue_set(EP
, c
->p
[dim
], c
->p
[dim
+1]);
1473 for (int i
= dim
-1; i
>= 0; --i
) {
1475 value_assign(EC
.x
.n
, c
->p
[i
]);
1478 free_evalue_refs(&EC
);
1481 Polyhedron
*unfringe (Polyhedron
*P
, unsigned MaxRays
)
1483 int len
= P
->Dimension
+2;
1484 Polyhedron
*T
, *R
= P
;
1487 Vector
*row
= Vector_Alloc(len
);
1488 value_set_si(row
->p
[0], 1);
1490 R
= DomainConstraintSimplify(Polyhedron_Copy(P
), MaxRays
);
1492 Matrix
*M
= Matrix_Alloc(2, len
-1);
1493 value_set_si(M
->p
[1][len
-2], 1);
1494 for (int v
= 0; v
< P
->Dimension
; ++v
) {
1495 value_set_si(M
->p
[0][v
], 1);
1496 Polyhedron
*I
= Polyhedron_Image(P
, M
, 2+1);
1497 value_set_si(M
->p
[0][v
], 0);
1498 for (int r
= 0; r
< I
->NbConstraints
; ++r
) {
1499 if (value_zero_p(I
->Constraint
[r
][0]))
1501 if (value_zero_p(I
->Constraint
[r
][1]))
1503 if (value_one_p(I
->Constraint
[r
][1]))
1505 if (value_mone_p(I
->Constraint
[r
][1]))
1507 value_absolute(g
, I
->Constraint
[r
][1]);
1508 Vector_Set(row
->p
+1, 0, len
-2);
1509 value_division(row
->p
[1+v
], I
->Constraint
[r
][1], g
);
1510 mpz_fdiv_q(row
->p
[len
-1], I
->Constraint
[r
][2], g
);
1512 R
= AddConstraints(row
->p
, 1, R
, MaxRays
);
1524 static Polyhedron
*reduce_domain(Polyhedron
*D
, Matrix
*CT
, Polyhedron
*CEq
,
1525 Polyhedron
**fVD
, int nd
, unsigned MaxRays
)
1530 Dt
= CT
? DomainPreimage(D
, CT
, MaxRays
) : D
;
1531 Polyhedron
*rVD
= DomainIntersection(Dt
, CEq
, MaxRays
);
1533 /* if rVD is empty or too small in geometric dimension */
1534 if(!rVD
|| emptyQ(rVD
) ||
1535 (rVD
->Dimension
-rVD
->NbEq
< Dt
->Dimension
-Dt
->NbEq
-CEq
->NbEq
)) {
1540 return 0; /* empty validity domain */
1546 fVD
[nd
] = Domain_Copy(rVD
);
1547 for (int i
= 0 ; i
< nd
; ++i
) {
1548 Polyhedron
*I
= DomainIntersection(fVD
[nd
], fVD
[i
], MaxRays
);
1553 Polyhedron
*F
= DomainSimplify(I
, fVD
[nd
], MaxRays
);
1555 Polyhedron
*T
= rVD
;
1556 rVD
= DomainDifference(rVD
, F
, MaxRays
);
1563 rVD
= DomainConstraintSimplify(rVD
, MaxRays
);
1565 Domain_Free(fVD
[nd
]);
1572 barvinok_count(rVD
, &c
, MaxRays
);
1573 if (value_zero_p(c
)) {
1582 static bool Polyhedron_is_infinite(Polyhedron
*P
, unsigned nparam
)
1585 for (r
= 0; r
< P
->NbRays
; ++r
)
1586 if (value_zero_p(P
->Ray
[r
][0]) ||
1587 value_zero_p(P
->Ray
[r
][P
->Dimension
+1])) {
1589 for (i
= P
->Dimension
- nparam
; i
< P
->Dimension
; ++i
)
1590 if (value_notzero_p(P
->Ray
[r
][i
+1]))
1592 if (i
>= P
->Dimension
)
1595 return r
< P
->NbRays
;
1598 /* Check whether all rays point in the positive directions
1599 * for the parameters
1601 static bool Polyhedron_has_positive_rays(Polyhedron
*P
, unsigned nparam
)
1604 for (r
= 0; r
< P
->NbRays
; ++r
)
1605 if (value_zero_p(P
->Ray
[r
][P
->Dimension
+1])) {
1607 for (i
= P
->Dimension
- nparam
; i
< P
->Dimension
; ++i
)
1608 if (value_neg_p(P
->Ray
[r
][i
+1]))
1614 evalue
* barvinok_enumerate_ev(Polyhedron
*P
, Polyhedron
* C
, unsigned MaxRays
)
1616 //P = unfringe(P, MaxRays);
1617 Polyhedron
*CEq
= NULL
, *rVD
, *pVD
, *CA
;
1619 Param_Polyhedron
*PP
= NULL
;
1620 Param_Domain
*D
, *next
;
1623 unsigned nparam
= C
->Dimension
;
1625 ALLOC(evalue
, eres
);
1626 value_init(eres
->d
);
1627 value_set_si(eres
->d
, 0);
1630 value_init(factor
.d
);
1631 evalue_set_si(&factor
, 1, 1);
1633 CA
= align_context(C
, P
->Dimension
, MaxRays
);
1634 P
= DomainIntersection(P
, CA
, MaxRays
);
1635 Polyhedron_Free(CA
);
1637 if (C
->Dimension
== 0 || emptyQ(P
)) {
1639 eres
->x
.p
= new_enode(partition
, 2, C
->Dimension
);
1640 EVALUE_SET_DOMAIN(eres
->x
.p
->arr
[0],
1641 DomainConstraintSimplify(CEq
? CEq
: Polyhedron_Copy(C
), MaxRays
));
1642 value_set_si(eres
->x
.p
->arr
[1].d
, 1);
1643 value_init(eres
->x
.p
->arr
[1].x
.n
);
1645 value_set_si(eres
->x
.p
->arr
[1].x
.n
, 0);
1647 barvinok_count(P
, &eres
->x
.p
->arr
[1].x
.n
, MaxRays
);
1649 emul(&factor
, eres
);
1650 reduce_evalue(eres
);
1651 free_evalue_refs(&factor
);
1656 Param_Polyhedron_Free(PP
);
1660 if (Polyhedron_is_infinite(P
, nparam
))
1665 P
= remove_equalities_p(P
, P
->Dimension
-nparam
, &f
);
1669 if (P
->Dimension
== nparam
) {
1671 P
= Universe_Polyhedron(0);
1675 Polyhedron
*Q
= ParamPolyhedron_Reduce(P
, P
->Dimension
-nparam
, &factor
);
1678 if (Q
->Dimension
== nparam
) {
1680 P
= Universe_Polyhedron(0);
1685 Polyhedron
*oldP
= P
;
1686 PP
= Polyhedron2Param_SimplifiedDomain(&P
,C
,MaxRays
,&CEq
,&CT
);
1688 Polyhedron_Free(oldP
);
1690 if (isIdentity(CT
)) {
1694 assert(CT
->NbRows
!= CT
->NbColumns
);
1695 if (CT
->NbRows
== 1) // no more parameters
1697 nparam
= CT
->NbRows
- 1;
1700 unsigned dim
= P
->Dimension
- nparam
;
1701 Polyhedron
** vcone
= new Polyhedron_p
[PP
->nbV
];
1702 int * npos
= new int[PP
->nbV
];
1703 int * nneg
= new int[PP
->nbV
];
1707 for (i
= 0, V
= PP
->V
; V
; ++i
, V
= V
->next
) {
1708 Polyhedron
*C
= supporting_cone_p(P
, V
);
1709 decompose(C
, &vcone
[i
], &npos
[i
], &nneg
[i
], MaxRays
);
1712 Vector
*c
= Vector_Alloc(dim
+2);
1715 for (nd
= 0, D
=PP
->D
; D
; ++nd
, D
=D
->next
);
1716 struct section
{ Polyhedron
*D
; evalue E
; };
1717 section
*s
= new section
[nd
];
1718 Polyhedron
**fVD
= new Polyhedron_p
[nd
];
1720 for(nd
= 0, D
=PP
->D
; D
; D
=next
) {
1723 Polyhedron
*rVD
= reduce_domain(D
->Domain
, CT
, CEq
,
1728 pVD
= CT
? DomainImage(rVD
,CT
,MaxRays
) : rVD
;
1731 FORALL_PVertex_in_ParamPolyhedron(V
,D
,PP
) // _i is internal counter
1732 ncone
+= npos
[_i
] + nneg
[_i
];
1733 END_FORALL_PVertex_in_ParamPolyhedron
;
1736 rays
.SetDims(ncone
* dim
, dim
);
1738 FORALL_PVertex_in_ParamPolyhedron(V
,D
,PP
) // _i is internal counter
1739 for (Polyhedron
*i
= vcone
[_i
]; i
; i
= i
->next
) {
1740 assert(i
->NbRays
-1 == dim
);
1741 add_rays(rays
, i
, &r
);
1743 END_FORALL_PVertex_in_ParamPolyhedron
;
1745 nonorthog(rays
, lambda
);
1751 value_init(s
[nd
].E
.d
);
1752 evalue_set_si(&s
[nd
].E
, 0, 1);
1755 FORALL_PVertex_in_ParamPolyhedron(V
,D
,PP
)
1757 for (Polyhedron
*i
= vcone
[_i
]; i
; i
= i
->next
) {
1758 sign
= f
< npos
[_i
] ? 1 : -1;
1759 lattice_point(V
, i
, lambda
, &num
, pVD
);
1760 normalize(i
, lambda
, sign
, num
.constant
, den
);
1762 dpoly
n(dim
, den
[0], 1);
1763 for (int k
= 1; k
< dim
; ++k
) {
1764 dpoly
fact(dim
, den
[k
], 1);
1767 if (num
.E
!= NULL
) {
1768 ZZ
one(INIT_VAL
, 1);
1769 dpoly_n
d(dim
, num
.constant
, one
);
1772 multi_polynom(c
, num
.E
, &EV
);
1773 eadd(&EV
, &s
[nd
].E
);
1774 free_evalue_refs(&EV
);
1775 free_evalue_refs(num
.E
);
1777 } else if (num
.pos
!= -1) {
1778 dpoly_n
d(dim
, num
.constant
, num
.coeff
);
1781 uni_polynom(num
.pos
, c
, &EV
);
1782 eadd(&EV
, &s
[nd
].E
);
1783 free_evalue_refs(&EV
);
1785 mpq_set_si(count
, 0, 1);
1786 dpoly
d(dim
, num
.constant
);
1787 d
.div(n
, count
, sign
);
1790 evalue_set(&EV
, &count
[0]._mp_num
, &count
[0]._mp_den
);
1791 eadd(&EV
, &s
[nd
].E
);
1792 free_evalue_refs(&EV
);
1796 END_FORALL_PVertex_in_ParamPolyhedron
;
1801 addeliminatedparams_evalue(&s
[nd
].E
, CT
);
1809 evalue_set_si(eres
, 0, 1);
1811 eres
->x
.p
= new_enode(partition
, 2*nd
, C
->Dimension
);
1812 for (int j
= 0; j
< nd
; ++j
) {
1813 EVALUE_SET_DOMAIN(eres
->x
.p
->arr
[2*j
], s
[j
].D
);
1814 value_clear(eres
->x
.p
->arr
[2*j
+1].d
);
1815 eres
->x
.p
->arr
[2*j
+1] = s
[j
].E
;
1816 Domain_Free(fVD
[j
]);
1824 for (int j
= 0; j
< PP
->nbV
; ++j
)
1825 Domain_Free(vcone
[j
]);
1831 Polyhedron_Free(CEq
);
1836 Enumeration
* barvinok_enumerate(Polyhedron
*P
, Polyhedron
* C
, unsigned MaxRays
)
1838 evalue
*EP
= barvinok_enumerate_ev(P
, C
, MaxRays
);
1840 return partition2enumeration(EP
);
1843 static void SwapColumns(Value
**V
, int n
, int i
, int j
)
1845 for (int r
= 0; r
< n
; ++r
)
1846 value_swap(V
[r
][i
], V
[r
][j
]);
1849 static void SwapColumns(Polyhedron
*P
, int i
, int j
)
1851 SwapColumns(P
->Constraint
, P
->NbConstraints
, i
, j
);
1852 SwapColumns(P
->Ray
, P
->NbRays
, i
, j
);
1855 static void negative_test_constraint(Value
*l
, Value
*u
, Value
*c
, int pos
,
1858 value_oppose(*v
, u
[pos
+1]);
1859 Vector_Combine(l
+1, u
+1, c
+1, *v
, l
[pos
+1], len
-1);
1860 value_multiply(*v
, *v
, l
[pos
+1]);
1861 value_substract(c
[len
-1], c
[len
-1], *v
);
1862 value_set_si(*v
, -1);
1863 Vector_Scale(c
+1, c
+1, *v
, len
-1);
1864 value_decrement(c
[len
-1], c
[len
-1]);
1865 ConstraintSimplify(c
, c
, len
, v
);
1868 static void oppose_constraint(Value
*c
, int len
, Value
*v
)
1870 value_set_si(*v
, -1);
1871 Vector_Scale(c
+1, c
+1, *v
, len
-1);
1872 value_decrement(c
[len
-1], c
[len
-1]);
1875 static bool SplitOnConstraint(Polyhedron
*P
, int i
, int l
, int u
,
1876 int nvar
, int len
, int exist
, int MaxRays
,
1877 Vector
*row
, Value
& f
, bool independent
,
1878 Polyhedron
**pos
, Polyhedron
**neg
)
1880 negative_test_constraint(P
->Constraint
[l
], P
->Constraint
[u
],
1881 row
->p
, nvar
+i
, len
, &f
);
1882 *neg
= AddConstraints(row
->p
, 1, P
, MaxRays
);
1884 /* We found an independent, but useless constraint
1885 * Maybe we should detect this earlier and not
1886 * mark the variable as INDEPENDENT
1888 if (emptyQ((*neg
))) {
1889 Polyhedron_Free(*neg
);
1893 oppose_constraint(row
->p
, len
, &f
);
1894 *pos
= AddConstraints(row
->p
, 1, P
, MaxRays
);
1896 if (emptyQ((*pos
))) {
1897 Polyhedron_Free(*neg
);
1898 Polyhedron_Free(*pos
);
1906 * unimodularly transform P such that constraint r is transformed
1907 * into a constraint that involves only a single (the first)
1908 * existential variable
1911 static Polyhedron
*rotate_along(Polyhedron
*P
, int r
, int nvar
, int exist
,
1917 Vector
*row
= Vector_Alloc(exist
);
1918 Vector_Copy(P
->Constraint
[r
]+1+nvar
, row
->p
, exist
);
1919 Vector_Gcd(row
->p
, exist
, &g
);
1920 if (value_notone_p(g
))
1921 Vector_AntiScale(row
->p
, row
->p
, g
, exist
);
1924 Matrix
*M
= unimodular_complete(row
);
1925 Matrix
*M2
= Matrix_Alloc(P
->Dimension
+1, P
->Dimension
+1);
1926 for (r
= 0; r
< nvar
; ++r
)
1927 value_set_si(M2
->p
[r
][r
], 1);
1928 for ( ; r
< nvar
+exist
; ++r
)
1929 Vector_Copy(M
->p
[r
-nvar
], M2
->p
[r
]+nvar
, exist
);
1930 for ( ; r
< P
->Dimension
+1; ++r
)
1931 value_set_si(M2
->p
[r
][r
], 1);
1932 Polyhedron
*T
= Polyhedron_Image(P
, M2
, MaxRays
);
1941 static bool SplitOnVar(Polyhedron
*P
, int i
,
1942 int nvar
, int len
, int exist
, int MaxRays
,
1943 Vector
*row
, Value
& f
, bool independent
,
1944 Polyhedron
**pos
, Polyhedron
**neg
)
1948 for (int l
= P
->NbEq
; l
< P
->NbConstraints
; ++l
) {
1949 if (value_negz_p(P
->Constraint
[l
][nvar
+i
+1]))
1953 for (j
= 0; j
< exist
; ++j
)
1954 if (j
!= i
&& value_notzero_p(P
->Constraint
[l
][nvar
+j
+1]))
1960 for (int u
= P
->NbEq
; u
< P
->NbConstraints
; ++u
) {
1961 if (value_posz_p(P
->Constraint
[u
][nvar
+i
+1]))
1965 for (j
= 0; j
< exist
; ++j
)
1966 if (j
!= i
&& value_notzero_p(P
->Constraint
[u
][nvar
+j
+1]))
1972 if (SplitOnConstraint(P
, i
, l
, u
,
1973 nvar
, len
, exist
, MaxRays
,
1974 row
, f
, independent
,
1978 SwapColumns(*neg
, nvar
+1, nvar
+1+i
);
1988 static bool double_bound_pair(Polyhedron
*P
, int nvar
, int exist
,
1989 int i
, int l1
, int l2
,
1990 Polyhedron
**pos
, Polyhedron
**neg
)
1994 Vector
*row
= Vector_Alloc(P
->Dimension
+2);
1995 value_set_si(row
->p
[0], 1);
1996 value_oppose(f
, P
->Constraint
[l1
][nvar
+i
+1]);
1997 Vector_Combine(P
->Constraint
[l1
]+1, P
->Constraint
[l2
]+1,
1999 P
->Constraint
[l2
][nvar
+i
+1], f
,
2001 ConstraintSimplify(row
->p
, row
->p
, P
->Dimension
+2, &f
);
2002 *pos
= AddConstraints(row
->p
, 1, P
, 0);
2003 value_set_si(f
, -1);
2004 Vector_Scale(row
->p
+1, row
->p
+1, f
, P
->Dimension
+1);
2005 value_decrement(row
->p
[P
->Dimension
+1], row
->p
[P
->Dimension
+1]);
2006 *neg
= AddConstraints(row
->p
, 1, P
, 0);
2010 return !emptyQ((*pos
)) && !emptyQ((*neg
));
2013 static bool double_bound(Polyhedron
*P
, int nvar
, int exist
,
2014 Polyhedron
**pos
, Polyhedron
**neg
)
2016 for (int i
= 0; i
< exist
; ++i
) {
2018 for (l1
= P
->NbEq
; l1
< P
->NbConstraints
; ++l1
) {
2019 if (value_negz_p(P
->Constraint
[l1
][nvar
+i
+1]))
2021 for (l2
= l1
+ 1; l2
< P
->NbConstraints
; ++l2
) {
2022 if (value_negz_p(P
->Constraint
[l2
][nvar
+i
+1]))
2024 if (double_bound_pair(P
, nvar
, exist
, i
, l1
, l2
, pos
, neg
))
2028 for (l1
= P
->NbEq
; l1
< P
->NbConstraints
; ++l1
) {
2029 if (value_posz_p(P
->Constraint
[l1
][nvar
+i
+1]))
2031 if (l1
< P
->NbConstraints
)
2032 for (l2
= l1
+ 1; l2
< P
->NbConstraints
; ++l2
) {
2033 if (value_posz_p(P
->Constraint
[l2
][nvar
+i
+1]))
2035 if (double_bound_pair(P
, nvar
, exist
, i
, l1
, l2
, pos
, neg
))
2047 INDEPENDENT
= 1 << 2
2050 static evalue
* enumerate_or(Polyhedron
*D
,
2051 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2054 fprintf(stderr
, "\nER: Or\n");
2055 #endif /* DEBUG_ER */
2057 Polyhedron
*N
= D
->next
;
2060 barvinok_enumerate_e(D
, exist
, nparam
, MaxRays
);
2063 for (D
= N
; D
; D
= N
) {
2068 barvinok_enumerate_e(D
, exist
, nparam
, MaxRays
);
2071 free_evalue_refs(EN
);
2081 static evalue
* enumerate_sum(Polyhedron
*P
,
2082 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2084 int nvar
= P
->Dimension
- exist
- nparam
;
2085 int toswap
= nvar
< exist
? nvar
: exist
;
2086 for (int i
= 0; i
< toswap
; ++i
)
2087 SwapColumns(P
, 1 + i
, nvar
+exist
- i
);
2091 fprintf(stderr
, "\nER: Sum\n");
2092 #endif /* DEBUG_ER */
2094 evalue
*EP
= barvinok_enumerate_e(P
, exist
, nparam
, MaxRays
);
2096 for (int i
= 0; i
< /* nvar */ nparam
; ++i
) {
2097 Matrix
*C
= Matrix_Alloc(1, 1 + nparam
+ 1);
2098 value_set_si(C
->p
[0][0], 1);
2100 value_init(split
.d
);
2101 value_set_si(split
.d
, 0);
2102 split
.x
.p
= new_enode(partition
, 4, nparam
);
2103 value_set_si(C
->p
[0][1+i
], 1);
2104 Matrix
*C2
= Matrix_Copy(C
);
2105 EVALUE_SET_DOMAIN(split
.x
.p
->arr
[0],
2106 Constraints2Polyhedron(C2
, MaxRays
));
2108 evalue_set_si(&split
.x
.p
->arr
[1], 1, 1);
2109 value_set_si(C
->p
[0][1+i
], -1);
2110 value_set_si(C
->p
[0][1+nparam
], -1);
2111 EVALUE_SET_DOMAIN(split
.x
.p
->arr
[2],
2112 Constraints2Polyhedron(C
, MaxRays
));
2113 evalue_set_si(&split
.x
.p
->arr
[3], 1, 1);
2115 free_evalue_refs(&split
);
2119 evalue_range_reduction(EP
);
2121 evalue_frac2floor(EP
);
2123 evalue
*sum
= esum(EP
, nvar
);
2125 free_evalue_refs(EP
);
2129 evalue_range_reduction(EP
);
2134 static evalue
* split_sure(Polyhedron
*P
, Polyhedron
*S
,
2135 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2137 int nvar
= P
->Dimension
- exist
- nparam
;
2139 Matrix
*M
= Matrix_Alloc(exist
, S
->Dimension
+2);
2140 for (int i
= 0; i
< exist
; ++i
)
2141 value_set_si(M
->p
[i
][nvar
+i
+1], 1);
2143 S
= DomainAddRays(S
, M
, MaxRays
);
2145 Polyhedron
*F
= DomainAddRays(P
, M
, MaxRays
);
2146 Polyhedron
*D
= DomainDifference(F
, S
, MaxRays
);
2148 D
= Disjoint_Domain(D
, 0, MaxRays
);
2153 M
= Matrix_Alloc(P
->Dimension
+1-exist
, P
->Dimension
+1);
2154 for (int j
= 0; j
< nvar
; ++j
)
2155 value_set_si(M
->p
[j
][j
], 1);
2156 for (int j
= 0; j
< nparam
+1; ++j
)
2157 value_set_si(M
->p
[nvar
+j
][nvar
+exist
+j
], 1);
2158 Polyhedron
*T
= Polyhedron_Image(S
, M
, MaxRays
);
2159 evalue
*EP
= barvinok_enumerate_e(T
, 0, nparam
, MaxRays
);
2164 for (Polyhedron
*Q
= D
; Q
; Q
= Q
->next
) {
2165 Polyhedron
*N
= Q
->next
;
2167 T
= DomainIntersection(P
, Q
, MaxRays
);
2168 evalue
*E
= barvinok_enumerate_e(T
, exist
, nparam
, MaxRays
);
2170 free_evalue_refs(E
);
2179 static evalue
* enumerate_sure(Polyhedron
*P
,
2180 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2184 int nvar
= P
->Dimension
- exist
- nparam
;
2190 for (i
= 0; i
< exist
; ++i
) {
2191 Matrix
*M
= Matrix_Alloc(S
->NbConstraints
, S
->Dimension
+2);
2193 value_set_si(lcm
, 1);
2194 for (int j
= 0; j
< S
->NbConstraints
; ++j
) {
2195 if (value_negz_p(S
->Constraint
[j
][1+nvar
+i
]))
2197 if (value_one_p(S
->Constraint
[j
][1+nvar
+i
]))
2199 value_lcm(lcm
, S
->Constraint
[j
][1+nvar
+i
], &lcm
);
2202 for (int j
= 0; j
< S
->NbConstraints
; ++j
) {
2203 if (value_negz_p(S
->Constraint
[j
][1+nvar
+i
]))
2205 if (value_one_p(S
->Constraint
[j
][1+nvar
+i
]))
2207 value_division(f
, lcm
, S
->Constraint
[j
][1+nvar
+i
]);
2208 Vector_Scale(S
->Constraint
[j
], M
->p
[c
], f
, S
->Dimension
+2);
2209 value_substract(M
->p
[c
][S
->Dimension
+1],
2210 M
->p
[c
][S
->Dimension
+1],
2212 value_increment(M
->p
[c
][S
->Dimension
+1],
2213 M
->p
[c
][S
->Dimension
+1]);
2217 S
= AddConstraints(M
->p
[0], c
, S
, MaxRays
);
2232 fprintf(stderr
, "\nER: Sure\n");
2233 #endif /* DEBUG_ER */
2235 return split_sure(P
, S
, exist
, nparam
, MaxRays
);
2238 static evalue
* enumerate_sure2(Polyhedron
*P
,
2239 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2241 int nvar
= P
->Dimension
- exist
- nparam
;
2243 for (r
= 0; r
< P
->NbRays
; ++r
)
2244 if (value_one_p(P
->Ray
[r
][0]) &&
2245 value_one_p(P
->Ray
[r
][P
->Dimension
+1]))
2251 Matrix
*M
= Matrix_Alloc(nvar
+ 1 + nparam
, P
->Dimension
+2);
2252 for (int i
= 0; i
< nvar
; ++i
)
2253 value_set_si(M
->p
[i
][1+i
], 1);
2254 for (int i
= 0; i
< nparam
; ++i
)
2255 value_set_si(M
->p
[i
+nvar
][1+nvar
+exist
+i
], 1);
2256 Vector_Copy(P
->Ray
[r
]+1+nvar
, M
->p
[nvar
+nparam
]+1+nvar
, exist
);
2257 value_set_si(M
->p
[nvar
+nparam
][0], 1);
2258 value_set_si(M
->p
[nvar
+nparam
][P
->Dimension
+1], 1);
2259 Polyhedron
* F
= Rays2Polyhedron(M
, MaxRays
);
2262 Polyhedron
*I
= DomainIntersection(F
, P
, MaxRays
);
2266 fprintf(stderr
, "\nER: Sure2\n");
2267 #endif /* DEBUG_ER */
2269 return split_sure(P
, I
, exist
, nparam
, MaxRays
);
2272 static evalue
* enumerate_cyclic(Polyhedron
*P
,
2273 unsigned exist
, unsigned nparam
,
2274 evalue
* EP
, int r
, int p
, unsigned MaxRays
)
2276 int nvar
= P
->Dimension
- exist
- nparam
;
2278 /* If EP in its fractional maps only contains references
2279 * to the remainder parameter with appropriate coefficients
2280 * then we could in principle avoid adding existentially
2281 * quantified variables to the validity domains.
2282 * We'd have to replace the remainder by m { p/m }
2283 * and multiply with an appropriate factor that is one
2284 * only in the appropriate range.
2285 * This last multiplication can be avoided if EP
2286 * has a single validity domain with no (further)
2287 * constraints on the remainder parameter
2290 Matrix
*CT
= Matrix_Alloc(nparam
+1, nparam
+3);
2291 Matrix
*M
= Matrix_Alloc(1, 1+nparam
+3);
2292 for (int j
= 0; j
< nparam
; ++j
)
2294 value_set_si(CT
->p
[j
][j
], 1);
2295 value_set_si(CT
->p
[p
][nparam
+1], 1);
2296 value_set_si(CT
->p
[nparam
][nparam
+2], 1);
2297 value_set_si(M
->p
[0][1+p
], -1);
2298 value_absolute(M
->p
[0][1+nparam
], P
->Ray
[0][1+nvar
+exist
+p
]);
2299 value_set_si(M
->p
[0][1+nparam
+1], 1);
2300 Polyhedron
*CEq
= Constraints2Polyhedron(M
, 1);
2302 addeliminatedparams_enum(EP
, CT
, CEq
, MaxRays
, nparam
);
2303 Polyhedron_Free(CEq
);
2309 static void enumerate_vd_add_ray(evalue
*EP
, Matrix
*Rays
, unsigned MaxRays
)
2311 if (value_notzero_p(EP
->d
))
2314 assert(EP
->x
.p
->type
== partition
);
2315 assert(EP
->x
.p
->pos
== EVALUE_DOMAIN(EP
->x
.p
->arr
[0])->Dimension
);
2316 for (int i
= 0; i
< EP
->x
.p
->size
/2; ++i
) {
2317 Polyhedron
*D
= EVALUE_DOMAIN(EP
->x
.p
->arr
[2*i
]);
2318 Polyhedron
*N
= DomainAddRays(D
, Rays
, MaxRays
);
2319 EVALUE_SET_DOMAIN(EP
->x
.p
->arr
[2*i
], N
);
2324 static evalue
* enumerate_line(Polyhedron
*P
,
2325 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2331 fprintf(stderr
, "\nER: Line\n");
2332 #endif /* DEBUG_ER */
2334 int nvar
= P
->Dimension
- exist
- nparam
;
2336 for (i
= 0; i
< nparam
; ++i
)
2337 if (value_notzero_p(P
->Ray
[0][1+nvar
+exist
+i
]))
2340 for (j
= i
+1; j
< nparam
; ++j
)
2341 if (value_notzero_p(P
->Ray
[0][1+nvar
+exist
+i
]))
2343 assert(j
>= nparam
); // for now
2345 Matrix
*M
= Matrix_Alloc(2, P
->Dimension
+2);
2346 value_set_si(M
->p
[0][0], 1);
2347 value_set_si(M
->p
[0][1+nvar
+exist
+i
], 1);
2348 value_set_si(M
->p
[1][0], 1);
2349 value_set_si(M
->p
[1][1+nvar
+exist
+i
], -1);
2350 value_absolute(M
->p
[1][1+P
->Dimension
], P
->Ray
[0][1+nvar
+exist
+i
]);
2351 value_decrement(M
->p
[1][1+P
->Dimension
], M
->p
[1][1+P
->Dimension
]);
2352 Polyhedron
*S
= AddConstraints(M
->p
[0], 2, P
, MaxRays
);
2353 evalue
*EP
= barvinok_enumerate_e(S
, exist
, nparam
, MaxRays
);
2357 return enumerate_cyclic(P
, exist
, nparam
, EP
, 0, i
, MaxRays
);
2360 static int single_param_pos(Polyhedron
*P
, unsigned exist
, unsigned nparam
,
2363 int nvar
= P
->Dimension
- exist
- nparam
;
2364 if (First_Non_Zero(P
->Ray
[r
]+1, nvar
) != -1)
2366 int i
= First_Non_Zero(P
->Ray
[r
]+1+nvar
+exist
, nparam
);
2369 if (First_Non_Zero(P
->Ray
[r
]+1+nvar
+exist
+1, nparam
-i
-1) != -1)
2374 static evalue
* enumerate_remove_ray(Polyhedron
*P
, int r
,
2375 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2378 fprintf(stderr
, "\nER: RedundantRay\n");
2379 #endif /* DEBUG_ER */
2383 value_set_si(one
, 1);
2384 int len
= P
->NbRays
-1;
2385 Matrix
*M
= Matrix_Alloc(2 * len
, P
->Dimension
+2);
2386 Vector_Copy(P
->Ray
[0], M
->p
[0], r
* (P
->Dimension
+2));
2387 Vector_Copy(P
->Ray
[r
+1], M
->p
[r
], (len
-r
) * (P
->Dimension
+2));
2388 for (int j
= 0; j
< P
->NbRays
; ++j
) {
2391 Vector_Combine(P
->Ray
[j
], P
->Ray
[r
], M
->p
[len
+j
-(j
>r
)],
2392 one
, P
->Ray
[j
][P
->Dimension
+1], P
->Dimension
+2);
2395 P
= Rays2Polyhedron(M
, MaxRays
);
2397 evalue
*EP
= barvinok_enumerate_e(P
, exist
, nparam
, MaxRays
);
2404 static evalue
* enumerate_redundant_ray(Polyhedron
*P
,
2405 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2407 assert(P
->NbBid
== 0);
2408 int nvar
= P
->Dimension
- exist
- nparam
;
2412 for (int r
= 0; r
< P
->NbRays
; ++r
) {
2413 if (value_notzero_p(P
->Ray
[r
][P
->Dimension
+1]))
2415 int i1
= single_param_pos(P
, exist
, nparam
, r
);
2418 for (int r2
= r
+1; r2
< P
->NbRays
; ++r2
) {
2419 if (value_notzero_p(P
->Ray
[r2
][P
->Dimension
+1]))
2421 int i2
= single_param_pos(P
, exist
, nparam
, r2
);
2427 value_division(m
, P
->Ray
[r
][1+nvar
+exist
+i1
],
2428 P
->Ray
[r2
][1+nvar
+exist
+i1
]);
2429 value_multiply(m
, m
, P
->Ray
[r2
][1+nvar
+exist
+i1
]);
2430 /* r2 divides r => r redundant */
2431 if (value_eq(m
, P
->Ray
[r
][1+nvar
+exist
+i1
])) {
2433 return enumerate_remove_ray(P
, r
, exist
, nparam
, MaxRays
);
2436 value_division(m
, P
->Ray
[r2
][1+nvar
+exist
+i1
],
2437 P
->Ray
[r
][1+nvar
+exist
+i1
]);
2438 value_multiply(m
, m
, P
->Ray
[r
][1+nvar
+exist
+i1
]);
2439 /* r divides r2 => r2 redundant */
2440 if (value_eq(m
, P
->Ray
[r2
][1+nvar
+exist
+i1
])) {
2442 return enumerate_remove_ray(P
, r2
, exist
, nparam
, MaxRays
);
2450 static Polyhedron
*upper_bound(Polyhedron
*P
,
2451 int pos
, Value
*max
, Polyhedron
**R
)
2460 for (Polyhedron
*Q
= P
; Q
; Q
= N
) {
2462 for (r
= 0; r
< P
->NbRays
; ++r
) {
2463 if (value_zero_p(P
->Ray
[r
][P
->Dimension
+1]) &&
2464 value_pos_p(P
->Ray
[r
][1+pos
]))
2467 if (r
< P
->NbRays
) {
2475 for (r
= 0; r
< P
->NbRays
; ++r
) {
2476 if (value_zero_p(P
->Ray
[r
][P
->Dimension
+1]))
2478 mpz_fdiv_q(v
, P
->Ray
[r
][1+pos
], P
->Ray
[r
][1+P
->Dimension
]);
2479 if ((!Q
->next
&& r
== 0) || value_gt(v
, *max
))
2480 value_assign(*max
, v
);
2487 static evalue
* enumerate_ray(Polyhedron
*P
,
2488 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2490 assert(P
->NbBid
== 0);
2491 int nvar
= P
->Dimension
- exist
- nparam
;
2494 for (r
= 0; r
< P
->NbRays
; ++r
)
2495 if (value_zero_p(P
->Ray
[r
][P
->Dimension
+1]))
2501 for (r2
= r
+1; r2
< P
->NbRays
; ++r2
)
2502 if (value_zero_p(P
->Ray
[r2
][P
->Dimension
+1]))
2504 if (r2
< P
->NbRays
) {
2506 return enumerate_sum(P
, exist
, nparam
, MaxRays
);
2510 fprintf(stderr
, "\nER: Ray\n");
2511 #endif /* DEBUG_ER */
2517 value_set_si(one
, 1);
2518 int i
= single_param_pos(P
, exist
, nparam
, r
);
2519 assert(i
!= -1); // for now;
2521 Matrix
*M
= Matrix_Alloc(P
->NbRays
, P
->Dimension
+2);
2522 for (int j
= 0; j
< P
->NbRays
; ++j
) {
2523 Vector_Combine(P
->Ray
[j
], P
->Ray
[r
], M
->p
[j
],
2524 one
, P
->Ray
[j
][P
->Dimension
+1], P
->Dimension
+2);
2526 Polyhedron
*S
= Rays2Polyhedron(M
, MaxRays
);
2528 Polyhedron
*D
= DomainDifference(P
, S
, MaxRays
);
2530 // Polyhedron_Print(stderr, P_VALUE_FMT, D);
2531 assert(value_pos_p(P
->Ray
[r
][1+nvar
+exist
+i
])); // for now
2533 D
= upper_bound(D
, nvar
+exist
+i
, &m
, &R
);
2537 M
= Matrix_Alloc(2, P
->Dimension
+2);
2538 value_set_si(M
->p
[0][0], 1);
2539 value_set_si(M
->p
[1][0], 1);
2540 value_set_si(M
->p
[0][1+nvar
+exist
+i
], -1);
2541 value_set_si(M
->p
[1][1+nvar
+exist
+i
], 1);
2542 value_assign(M
->p
[0][1+P
->Dimension
], m
);
2543 value_oppose(M
->p
[1][1+P
->Dimension
], m
);
2544 value_addto(M
->p
[1][1+P
->Dimension
], M
->p
[1][1+P
->Dimension
],
2545 P
->Ray
[r
][1+nvar
+exist
+i
]);
2546 value_decrement(M
->p
[1][1+P
->Dimension
], M
->p
[1][1+P
->Dimension
]);
2547 // Matrix_Print(stderr, P_VALUE_FMT, M);
2548 D
= AddConstraints(M
->p
[0], 2, P
, MaxRays
);
2549 // Polyhedron_Print(stderr, P_VALUE_FMT, D);
2550 value_substract(M
->p
[0][1+P
->Dimension
], M
->p
[0][1+P
->Dimension
],
2551 P
->Ray
[r
][1+nvar
+exist
+i
]);
2552 // Matrix_Print(stderr, P_VALUE_FMT, M);
2553 S
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
2554 // Polyhedron_Print(stderr, P_VALUE_FMT, S);
2557 evalue
*EP
= barvinok_enumerate_e(D
, exist
, nparam
, MaxRays
);
2562 if (value_notone_p(P
->Ray
[r
][1+nvar
+exist
+i
]))
2563 EP
= enumerate_cyclic(P
, exist
, nparam
, EP
, r
, i
, MaxRays
);
2565 M
= Matrix_Alloc(1, nparam
+2);
2566 value_set_si(M
->p
[0][0], 1);
2567 value_set_si(M
->p
[0][1+i
], 1);
2568 enumerate_vd_add_ray(EP
, M
, MaxRays
);
2573 evalue
*E
= barvinok_enumerate_e(S
, exist
, nparam
, MaxRays
);
2575 free_evalue_refs(E
);
2582 evalue
*ER
= enumerate_or(R
, exist
, nparam
, MaxRays
);
2584 free_evalue_refs(ER
);
2591 static evalue
* new_zero_ep()
2596 evalue_set_si(EP
, 0, 1);
2600 static evalue
* enumerate_vd(Polyhedron
**PA
,
2601 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2603 Polyhedron
*P
= *PA
;
2604 int nvar
= P
->Dimension
- exist
- nparam
;
2605 Param_Polyhedron
*PP
= NULL
;
2606 Polyhedron
*C
= Universe_Polyhedron(nparam
);
2610 PP
= Polyhedron2Param_SimplifiedDomain(&PR
,C
,MaxRays
,&CEq
,&CT
);
2614 Param_Domain
*D
, *last
;
2617 for (nd
= 0, D
=PP
->D
; D
; D
=D
->next
, ++nd
)
2620 Polyhedron
**VD
= new Polyhedron_p
[nd
];
2621 Polyhedron
**fVD
= new Polyhedron_p
[nd
];
2622 for(nd
= 0, D
=PP
->D
; D
; D
=D
->next
) {
2623 Polyhedron
*rVD
= reduce_domain(D
->Domain
, CT
, CEq
,
2637 /* This doesn't seem to have any effect */
2639 Polyhedron
*CA
= align_context(VD
[0], P
->Dimension
, MaxRays
);
2641 P
= DomainIntersection(P
, CA
, MaxRays
);
2644 Polyhedron_Free(CA
);
2649 if (!EP
&& CT
->NbColumns
!= CT
->NbRows
) {
2650 Polyhedron
*CEqr
= DomainImage(CEq
, CT
, MaxRays
);
2651 Polyhedron
*CA
= align_context(CEqr
, PR
->Dimension
, MaxRays
);
2652 Polyhedron
*I
= DomainIntersection(PR
, CA
, MaxRays
);
2653 Polyhedron_Free(CEqr
);
2654 Polyhedron_Free(CA
);
2656 fprintf(stderr
, "\nER: Eliminate\n");
2657 #endif /* DEBUG_ER */
2658 nparam
-= CT
->NbColumns
- CT
->NbRows
;
2659 EP
= barvinok_enumerate_e(I
, exist
, nparam
, MaxRays
);
2660 nparam
+= CT
->NbColumns
- CT
->NbRows
;
2661 addeliminatedparams_enum(EP
, CT
, CEq
, MaxRays
, nparam
);
2665 Polyhedron_Free(PR
);
2668 if (!EP
&& nd
> 1) {
2670 fprintf(stderr
, "\nER: VD\n");
2671 #endif /* DEBUG_ER */
2672 for (int i
= 0; i
< nd
; ++i
) {
2673 Polyhedron
*CA
= align_context(VD
[i
], P
->Dimension
, MaxRays
);
2674 Polyhedron
*I
= DomainIntersection(P
, CA
, MaxRays
);
2677 EP
= barvinok_enumerate_e(I
, exist
, nparam
, MaxRays
);
2679 evalue
*E
= barvinok_enumerate_e(I
, exist
, nparam
, MaxRays
);
2681 free_evalue_refs(E
);
2685 Polyhedron_Free(CA
);
2689 for (int i
= 0; i
< nd
; ++i
) {
2690 Polyhedron_Free(VD
[i
]);
2691 Polyhedron_Free(fVD
[i
]);
2697 if (!EP
&& nvar
== 0) {
2700 Param_Vertices
*V
, *V2
;
2701 Matrix
* M
= Matrix_Alloc(1, P
->Dimension
+2);
2703 FORALL_PVertex_in_ParamPolyhedron(V
, last
, PP
) {
2705 FORALL_PVertex_in_ParamPolyhedron(V2
, last
, PP
) {
2712 for (int i
= 0; i
< exist
; ++i
) {
2713 value_oppose(f
, V
->Vertex
->p
[i
][nparam
+1]);
2714 Vector_Combine(V
->Vertex
->p
[i
],
2716 M
->p
[0] + 1 + nvar
+ exist
,
2717 V2
->Vertex
->p
[i
][nparam
+1],
2721 for (j
= 0; j
< nparam
; ++j
)
2722 if (value_notzero_p(M
->p
[0][1+nvar
+exist
+j
]))
2726 ConstraintSimplify(M
->p
[0], M
->p
[0],
2727 P
->Dimension
+2, &f
);
2728 value_set_si(M
->p
[0][0], 0);
2729 Polyhedron
*para
= AddConstraints(M
->p
[0], 1, P
,
2732 Polyhedron_Free(para
);
2735 Polyhedron
*pos
, *neg
;
2736 value_set_si(M
->p
[0][0], 1);
2737 value_decrement(M
->p
[0][P
->Dimension
+1],
2738 M
->p
[0][P
->Dimension
+1]);
2739 neg
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
2740 value_set_si(f
, -1);
2741 Vector_Scale(M
->p
[0]+1, M
->p
[0]+1, f
,
2743 value_decrement(M
->p
[0][P
->Dimension
+1],
2744 M
->p
[0][P
->Dimension
+1]);
2745 value_decrement(M
->p
[0][P
->Dimension
+1],
2746 M
->p
[0][P
->Dimension
+1]);
2747 pos
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
2748 if (emptyQ(neg
) && emptyQ(pos
)) {
2749 Polyhedron_Free(para
);
2750 Polyhedron_Free(pos
);
2751 Polyhedron_Free(neg
);
2755 fprintf(stderr
, "\nER: Order\n");
2756 #endif /* DEBUG_ER */
2757 EP
= barvinok_enumerate_e(para
, exist
, nparam
, MaxRays
);
2760 E
= barvinok_enumerate_e(pos
, exist
, nparam
, MaxRays
);
2762 free_evalue_refs(E
);
2766 E
= barvinok_enumerate_e(neg
, exist
, nparam
, MaxRays
);
2768 free_evalue_refs(E
);
2771 Polyhedron_Free(para
);
2772 Polyhedron_Free(pos
);
2773 Polyhedron_Free(neg
);
2778 } END_FORALL_PVertex_in_ParamPolyhedron
;
2781 } END_FORALL_PVertex_in_ParamPolyhedron
;
2784 /* Search for vertex coordinate to split on */
2785 /* First look for one independent of the parameters */
2786 FORALL_PVertex_in_ParamPolyhedron(V
, last
, PP
) {
2787 for (int i
= 0; i
< exist
; ++i
) {
2789 for (j
= 0; j
< nparam
; ++j
)
2790 if (value_notzero_p(V
->Vertex
->p
[i
][j
]))
2794 value_set_si(M
->p
[0][0], 1);
2795 Vector_Set(M
->p
[0]+1, 0, nvar
+exist
);
2796 Vector_Copy(V
->Vertex
->p
[i
],
2797 M
->p
[0] + 1 + nvar
+ exist
, nparam
+1);
2798 value_oppose(M
->p
[0][1+nvar
+i
],
2799 V
->Vertex
->p
[i
][nparam
+1]);
2801 Polyhedron
*pos
, *neg
;
2802 value_set_si(M
->p
[0][0], 1);
2803 value_decrement(M
->p
[0][P
->Dimension
+1],
2804 M
->p
[0][P
->Dimension
+1]);
2805 neg
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
2806 value_set_si(f
, -1);
2807 Vector_Scale(M
->p
[0]+1, M
->p
[0]+1, f
,
2809 value_decrement(M
->p
[0][P
->Dimension
+1],
2810 M
->p
[0][P
->Dimension
+1]);
2811 value_decrement(M
->p
[0][P
->Dimension
+1],
2812 M
->p
[0][P
->Dimension
+1]);
2813 pos
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
2814 if (emptyQ(neg
) || emptyQ(pos
)) {
2815 Polyhedron_Free(pos
);
2816 Polyhedron_Free(neg
);
2819 Polyhedron_Free(pos
);
2820 value_increment(M
->p
[0][P
->Dimension
+1],
2821 M
->p
[0][P
->Dimension
+1]);
2822 pos
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
2824 fprintf(stderr
, "\nER: Vertex\n");
2825 #endif /* DEBUG_ER */
2827 EP
= enumerate_or(pos
, exist
, nparam
, MaxRays
);
2832 } END_FORALL_PVertex_in_ParamPolyhedron
;
2836 /* Search for vertex coordinate to split on */
2837 /* Now look for one that depends on the parameters */
2838 FORALL_PVertex_in_ParamPolyhedron(V
, last
, PP
) {
2839 for (int i
= 0; i
< exist
; ++i
) {
2840 value_set_si(M
->p
[0][0], 1);
2841 Vector_Set(M
->p
[0]+1, 0, nvar
+exist
);
2842 Vector_Copy(V
->Vertex
->p
[i
],
2843 M
->p
[0] + 1 + nvar
+ exist
, nparam
+1);
2844 value_oppose(M
->p
[0][1+nvar
+i
],
2845 V
->Vertex
->p
[i
][nparam
+1]);
2847 Polyhedron
*pos
, *neg
;
2848 value_set_si(M
->p
[0][0], 1);
2849 value_decrement(M
->p
[0][P
->Dimension
+1],
2850 M
->p
[0][P
->Dimension
+1]);
2851 neg
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
2852 value_set_si(f
, -1);
2853 Vector_Scale(M
->p
[0]+1, M
->p
[0]+1, f
,
2855 value_decrement(M
->p
[0][P
->Dimension
+1],
2856 M
->p
[0][P
->Dimension
+1]);
2857 value_decrement(M
->p
[0][P
->Dimension
+1],
2858 M
->p
[0][P
->Dimension
+1]);
2859 pos
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
2860 if (emptyQ(neg
) || emptyQ(pos
)) {
2861 Polyhedron_Free(pos
);
2862 Polyhedron_Free(neg
);
2865 Polyhedron_Free(pos
);
2866 value_increment(M
->p
[0][P
->Dimension
+1],
2867 M
->p
[0][P
->Dimension
+1]);
2868 pos
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
2870 fprintf(stderr
, "\nER: ParamVertex\n");
2871 #endif /* DEBUG_ER */
2873 EP
= enumerate_or(pos
, exist
, nparam
, MaxRays
);
2878 } END_FORALL_PVertex_in_ParamPolyhedron
;
2886 Polyhedron_Free(CEq
);
2890 Param_Polyhedron_Free(PP
);
2897 evalue
*barvinok_enumerate_pip(Polyhedron
*P
,
2898 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2903 evalue
*barvinok_enumerate_pip(Polyhedron
*P
,
2904 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2906 int nvar
= P
->Dimension
- exist
- nparam
;
2907 evalue
*EP
= new_zero_ep();
2908 Polyhedron
*Q
, *N
, *T
= 0;
2914 fprintf(stderr
, "\nER: PIP\n");
2915 #endif /* DEBUG_ER */
2917 for (int i
= 0; i
< P
->Dimension
; ++i
) {
2920 bool posray
= false;
2921 bool negray
= false;
2922 value_set_si(min
, 0);
2923 for (int j
= 0; j
< P
->NbRays
; ++j
) {
2924 if (value_pos_p(P
->Ray
[j
][1+i
])) {
2926 if (value_zero_p(P
->Ray
[j
][1+P
->Dimension
]))
2928 } else if (value_neg_p(P
->Ray
[j
][1+i
])) {
2930 if (value_zero_p(P
->Ray
[j
][1+P
->Dimension
]))
2934 P
->Ray
[j
][1+i
], P
->Ray
[j
][1+P
->Dimension
]);
2935 if (value_lt(tmp
, min
))
2936 value_assign(min
, tmp
);
2941 assert(!(posray
&& negray
));
2942 assert(!negray
); // for now
2943 Polyhedron
*O
= T
? T
: P
;
2944 /* shift by a safe amount */
2945 Matrix
*M
= Matrix_Alloc(O
->NbRays
, O
->Dimension
+2);
2946 Vector_Copy(O
->Ray
[0], M
->p
[0], O
->NbRays
* (O
->Dimension
+2));
2947 for (int j
= 0; j
< P
->NbRays
; ++j
) {
2948 if (value_notzero_p(M
->p
[j
][1+P
->Dimension
])) {
2949 value_multiply(tmp
, min
, M
->p
[j
][1+P
->Dimension
]);
2950 value_substract(M
->p
[j
][1+i
], M
->p
[j
][1+i
], tmp
);
2955 T
= Rays2Polyhedron(M
, MaxRays
);
2958 /* negating a parameter requires that we substitute in the
2959 * sign again afterwards.
2962 assert(i
< nvar
+exist
);
2964 T
= Polyhedron_Copy(P
);
2965 for (int j
= 0; j
< T
->NbRays
; ++j
)
2966 value_oppose(T
->Ray
[j
][1+i
], T
->Ray
[j
][1+i
]);
2967 for (int j
= 0; j
< T
->NbConstraints
; ++j
)
2968 value_oppose(T
->Constraint
[j
][1+i
], T
->Constraint
[j
][1+i
]);
2974 Polyhedron
*D
= pip_lexmin(T
? T
: P
, exist
, nparam
);
2975 for (Q
= D
; Q
; Q
= N
) {
2979 exist
= Q
->Dimension
- nvar
- nparam
;
2980 E
= barvinok_enumerate_e(Q
, exist
, nparam
, MaxRays
);
2983 free_evalue_refs(E
);
2995 static bool is_single(Value
*row
, int pos
, int len
)
2997 return First_Non_Zero(row
, pos
) == -1 &&
2998 First_Non_Zero(row
+pos
+1, len
-pos
-1) == -1;
3001 static evalue
* barvinok_enumerate_e_r(Polyhedron
*P
,
3002 unsigned exist
, unsigned nparam
, unsigned MaxRays
);
3005 static int er_level
= 0;
3007 evalue
* barvinok_enumerate_e(Polyhedron
*P
,
3008 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
3010 fprintf(stderr
, "\nER: level %i\n", er_level
);
3011 int nvar
= P
->Dimension
- exist
- nparam
;
3012 fprintf(stderr
, "%d %d %d\n", nvar
, exist
, nparam
);
3014 Polyhedron_Print(stderr
, P_VALUE_FMT
, P
);
3016 P
= DomainConstraintSimplify(Polyhedron_Copy(P
), MaxRays
);
3017 evalue
*EP
= barvinok_enumerate_e_r(P
, exist
, nparam
, MaxRays
);
3023 evalue
* barvinok_enumerate_e(Polyhedron
*P
,
3024 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
3026 P
= DomainConstraintSimplify(Polyhedron_Copy(P
), MaxRays
);
3027 evalue
*EP
= barvinok_enumerate_e_r(P
, exist
, nparam
, MaxRays
);
3033 static evalue
* barvinok_enumerate_e_r(Polyhedron
*P
,
3034 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
3037 Polyhedron
*U
= Universe_Polyhedron(nparam
);
3038 evalue
*EP
= barvinok_enumerate_ev(P
, U
, MaxRays
);
3039 //char *param_name[] = {"P", "Q", "R", "S", "T" };
3040 //print_evalue(stdout, EP, param_name);
3045 int nvar
= P
->Dimension
- exist
- nparam
;
3046 int len
= P
->Dimension
+ 2;
3049 return new_zero_ep();
3051 if (nvar
== 0 && nparam
== 0) {
3052 evalue
*EP
= new_zero_ep();
3053 barvinok_count(P
, &EP
->x
.n
, MaxRays
);
3054 if (value_pos_p(EP
->x
.n
))
3055 value_set_si(EP
->x
.n
, 1);
3060 for (r
= 0; r
< P
->NbRays
; ++r
)
3061 if (value_zero_p(P
->Ray
[r
][0]) ||
3062 value_zero_p(P
->Ray
[r
][P
->Dimension
+1])) {
3064 for (i
= 0; i
< nvar
; ++i
)
3065 if (value_notzero_p(P
->Ray
[r
][i
+1]))
3069 for (i
= nvar
+ exist
; i
< nvar
+ exist
+ nparam
; ++i
)
3070 if (value_notzero_p(P
->Ray
[r
][i
+1]))
3072 if (i
>= nvar
+ exist
+ nparam
)
3075 if (r
< P
->NbRays
) {
3076 evalue
*EP
= new_zero_ep();
3077 value_set_si(EP
->x
.n
, -1);
3082 for (r
= 0; r
< P
->NbEq
; ++r
)
3083 if ((first
= First_Non_Zero(P
->Constraint
[r
]+1+nvar
, exist
)) != -1)
3086 if (First_Non_Zero(P
->Constraint
[r
]+1+nvar
+first
+1,
3087 exist
-first
-1) != -1) {
3088 Polyhedron
*T
= rotate_along(P
, r
, nvar
, exist
, MaxRays
);
3090 fprintf(stderr
, "\nER: Equality\n");
3091 #endif /* DEBUG_ER */
3092 evalue
*EP
= barvinok_enumerate_e(T
, exist
-1, nparam
, MaxRays
);
3097 fprintf(stderr
, "\nER: Fixed\n");
3098 #endif /* DEBUG_ER */
3100 return barvinok_enumerate_e(P
, exist
-1, nparam
, MaxRays
);
3102 Polyhedron
*T
= Polyhedron_Copy(P
);
3103 SwapColumns(T
, nvar
+1, nvar
+1+first
);
3104 evalue
*EP
= barvinok_enumerate_e(T
, exist
-1, nparam
, MaxRays
);
3111 Vector
*row
= Vector_Alloc(len
);
3112 value_set_si(row
->p
[0], 1);
3117 enum constraint
* info
= new constraint
[exist
];
3118 for (int i
= 0; i
< exist
; ++i
) {
3120 for (int l
= P
->NbEq
; l
< P
->NbConstraints
; ++l
) {
3121 if (value_negz_p(P
->Constraint
[l
][nvar
+i
+1]))
3123 bool l_parallel
= is_single(P
->Constraint
[l
]+nvar
+1, i
, exist
);
3124 for (int u
= P
->NbEq
; u
< P
->NbConstraints
; ++u
) {
3125 if (value_posz_p(P
->Constraint
[u
][nvar
+i
+1]))
3127 bool lu_parallel
= l_parallel
||
3128 is_single(P
->Constraint
[u
]+nvar
+1, i
, exist
);
3129 value_oppose(f
, P
->Constraint
[u
][nvar
+i
+1]);
3130 Vector_Combine(P
->Constraint
[l
]+1, P
->Constraint
[u
]+1, row
->p
+1,
3131 f
, P
->Constraint
[l
][nvar
+i
+1], len
-1);
3132 if (!(info
[i
] & INDEPENDENT
)) {
3134 for (j
= 0; j
< exist
; ++j
)
3135 if (j
!= i
&& value_notzero_p(row
->p
[nvar
+j
+1]))
3138 //printf("independent: i: %d, l: %d, u: %d\n", i, l, u);
3139 info
[i
] = (constraint
)(info
[i
] | INDEPENDENT
);
3142 if (info
[i
] & ALL_POS
) {
3143 value_addto(row
->p
[len
-1], row
->p
[len
-1],
3144 P
->Constraint
[l
][nvar
+i
+1]);
3145 value_addto(row
->p
[len
-1], row
->p
[len
-1], f
);
3146 value_multiply(f
, f
, P
->Constraint
[l
][nvar
+i
+1]);
3147 value_substract(row
->p
[len
-1], row
->p
[len
-1], f
);
3148 value_decrement(row
->p
[len
-1], row
->p
[len
-1]);
3149 ConstraintSimplify(row
->p
, row
->p
, len
, &f
);
3150 value_set_si(f
, -1);
3151 Vector_Scale(row
->p
+1, row
->p
+1, f
, len
-1);
3152 value_decrement(row
->p
[len
-1], row
->p
[len
-1]);
3153 Polyhedron
*T
= AddConstraints(row
->p
, 1, P
, MaxRays
);
3155 //printf("not all_pos: i: %d, l: %d, u: %d\n", i, l, u);
3156 info
[i
] = (constraint
)(info
[i
] ^ ALL_POS
);
3158 //puts("pos remainder");
3159 //Polyhedron_Print(stdout, P_VALUE_FMT, T);
3162 if (!(info
[i
] & ONE_NEG
)) {
3164 negative_test_constraint(P
->Constraint
[l
],
3166 row
->p
, nvar
+i
, len
, &f
);
3167 oppose_constraint(row
->p
, len
, &f
);
3168 Polyhedron
*T
= AddConstraints(row
->p
, 1, P
, MaxRays
);
3170 //printf("one_neg i: %d, l: %d, u: %d\n", i, l, u);
3171 info
[i
] = (constraint
)(info
[i
] | ONE_NEG
);
3173 //puts("neg remainder");
3174 //Polyhedron_Print(stdout, P_VALUE_FMT, T);
3178 if (!(info
[i
] & ALL_POS
) && (info
[i
] & ONE_NEG
))
3182 if (info
[i
] & ALL_POS
)
3189 for (int i = 0; i < exist; ++i)
3190 printf("%i: %i\n", i, info[i]);
3192 for (int i
= 0; i
< exist
; ++i
)
3193 if (info
[i
] & ALL_POS
) {
3195 fprintf(stderr
, "\nER: Positive\n");
3196 #endif /* DEBUG_ER */
3198 // Maybe we should chew off some of the fat here
3199 Matrix
*M
= Matrix_Alloc(P
->Dimension
, P
->Dimension
+1);
3200 for (int j
= 0; j
< P
->Dimension
; ++j
)
3201 value_set_si(M
->p
[j
][j
+ (j
>= i
+nvar
)], 1);
3202 Polyhedron
*T
= Polyhedron_Image(P
, M
, MaxRays
);
3204 evalue
*EP
= barvinok_enumerate_e(T
, exist
-1, nparam
, MaxRays
);
3211 for (int i
= 0; i
< exist
; ++i
)
3212 if (info
[i
] & ONE_NEG
) {
3214 fprintf(stderr
, "\nER: Negative\n");
3215 #endif /* DEBUG_ER */
3220 return barvinok_enumerate_e(P
, exist
-1, nparam
, MaxRays
);
3222 Polyhedron
*T
= Polyhedron_Copy(P
);
3223 SwapColumns(T
, nvar
+1, nvar
+1+i
);
3224 evalue
*EP
= barvinok_enumerate_e(T
, exist
-1, nparam
, MaxRays
);
3229 for (int i
= 0; i
< exist
; ++i
)
3230 if (info
[i
] & INDEPENDENT
) {
3231 Polyhedron
*pos
, *neg
;
3233 /* Find constraint again and split off negative part */
3235 if (SplitOnVar(P
, i
, nvar
, len
, exist
, MaxRays
,
3236 row
, f
, true, &pos
, &neg
)) {
3238 fprintf(stderr
, "\nER: Split\n");
3239 #endif /* DEBUG_ER */
3242 barvinok_enumerate_e(neg
, exist
-1, nparam
, MaxRays
);
3244 barvinok_enumerate_e(pos
, exist
, nparam
, MaxRays
);
3246 free_evalue_refs(E
);
3248 Polyhedron_Free(neg
);
3249 Polyhedron_Free(pos
);
3263 EP
= enumerate_line(P
, exist
, nparam
, MaxRays
);
3267 EP
= barvinok_enumerate_pip(P
, exist
, nparam
, MaxRays
);
3271 EP
= enumerate_redundant_ray(P
, exist
, nparam
, MaxRays
);
3275 EP
= enumerate_sure(P
, exist
, nparam
, MaxRays
);
3279 EP
= enumerate_ray(P
, exist
, nparam
, MaxRays
);
3283 EP
= enumerate_sure2(P
, exist
, nparam
, MaxRays
);
3287 F
= unfringe(P
, MaxRays
);
3288 if (!PolyhedronIncludes(F
, P
)) {
3290 fprintf(stderr
, "\nER: Fringed\n");
3291 #endif /* DEBUG_ER */
3292 EP
= barvinok_enumerate_e(F
, exist
, nparam
, MaxRays
);
3299 EP
= enumerate_vd(&P
, exist
, nparam
, MaxRays
);
3304 EP
= enumerate_sum(P
, exist
, nparam
, MaxRays
);
3311 Polyhedron
*pos
, *neg
;
3312 for (i
= 0; i
< exist
; ++i
)
3313 if (SplitOnVar(P
, i
, nvar
, len
, exist
, MaxRays
,
3314 row
, f
, false, &pos
, &neg
))
3320 EP
= enumerate_or(pos
, exist
, nparam
, MaxRays
);
3332 static void normalize(Polyhedron
*i
, vec_ZZ
& lambda
, ZZ
& sign
,
3333 ZZ
& num_s
, vec_ZZ
& num_p
, vec_ZZ
& den_s
, vec_ZZ
& den_p
,
3336 unsigned dim
= i
->Dimension
;
3337 unsigned nparam
= num_p
.length();
3338 unsigned nvar
= dim
- nparam
;
3342 rays
.SetDims(dim
, nvar
);
3343 add_rays(rays
, i
, &r
, nvar
, true);
3344 den_s
= rays
* lambda
;
3348 for (int j
= 0; j
< den_s
.length(); ++j
) {
3349 values2zz(i
->Ray
[j
]+1+nvar
, f
[j
], nparam
);
3350 if (den_s
[j
] == 0) {
3354 if (First_Non_Zero(i
->Ray
[j
]+1+nvar
, nparam
) != -1) {
3365 den_s
[j
] = abs(den_s
[j
]);
3374 gen_fun
* barvinok_series(Polyhedron
*P
, Polyhedron
* C
, unsigned MaxRays
)
3376 Polyhedron
** vcone
;
3378 unsigned nparam
= C
->Dimension
;
3382 sign
.SetLength(ncone
);
3384 CA
= align_context(C
, P
->Dimension
, MaxRays
);
3385 P
= DomainIntersection(P
, CA
, MaxRays
);
3386 Polyhedron_Free(CA
);
3388 assert(!Polyhedron_is_infinite(P
, nparam
));
3389 assert(P
->NbBid
== 0);
3390 assert(Polyhedron_has_positive_rays(P
, nparam
));
3391 assert(P
->NbEq
== 0);
3394 nvar
= dim
- nparam
;
3395 vcone
= new Polyhedron_p
[P
->NbRays
];
3397 for (int j
= 0; j
< P
->NbRays
; ++j
) {
3398 if (!value_pos_p(P
->Ray
[j
][dim
+1]))
3402 Polyhedron
*C
= supporting_cone(P
, j
);
3403 decompose(C
, &vcone
[j
], &npos
, &nneg
, MaxRays
);
3404 ncone
+= npos
+ nneg
;
3405 sign
.SetLength(ncone
);
3406 for (int k
= 0; k
< npos
; ++k
)
3407 sign
[ncone
-nneg
-k
-1] = 1;
3408 for (int k
= 0; k
< nneg
; ++k
)
3409 sign
[ncone
-k
-1] = -1;
3413 rays
.SetDims(ncone
* dim
, nvar
);
3415 for (int j
= 0; j
< P
->NbRays
; ++j
) {
3416 if (!value_pos_p(P
->Ray
[j
][dim
+1]))
3419 for (Polyhedron
*i
= vcone
[j
]; i
; i
= i
->next
) {
3420 add_rays(rays
, i
, &r
, nvar
);
3423 rays
.SetDims(r
, nvar
);
3425 nonorthog(rays
, lambda
);
3426 //randomvector(P, lambda, nvar);
3429 cout << "rays: " << rays;
3430 cout << "lambda: " << lambda;
3436 num_p
.SetLength(nparam
);
3439 den_s
.SetLength(dim
);
3441 den_p
.SetLength(dim
);
3443 den
.SetDims(dim
, nparam
);
3449 gen_fun
* gf
= new gen_fun
;
3451 for (int j
= 0; j
< P
->NbRays
; ++j
) {
3452 if (!value_pos_p(P
->Ray
[j
][dim
+1]))
3455 for (Polyhedron
*i
= vcone
[j
]; i
; i
= i
->next
, ++f
) {
3456 lattice_point(P
->Ray
[j
]+1, i
, vertex
);
3459 for ( ; k
< nvar
; ++k
)
3460 num_s
+= vertex
[k
] * lambda
[k
];
3461 for ( ; k
< dim
; ++k
)
3462 num_p
[k
-nvar
] = vertex
[k
];
3463 normalize(i
, lambda
, sign
[f
], num_s
, num_p
,
3468 for (int k
= 0; k
< dim
; ++k
) {
3471 else if (den_s
[k
] == 0)
3474 if (no_param
== 0) {
3475 for (int k
= 0; k
< dim
; ++k
)
3478 gf
->add(sign
[f
], one
, num_p
, den
);
3479 } else if (no_param
+ only_param
== dim
) {
3482 pden
.SetDims(only_param
, nparam
);
3484 for (k
= 0, l
= 0; k
< dim
; ++k
)
3488 for (k
= 0; k
< dim
; ++k
)
3492 dpoly
n(no_param
, num_s
);
3493 dpoly
d(no_param
, den_s
[k
], 1);
3494 for ( ; k
< dim
; ++k
)
3495 if (den_s
[k
] != 0) {
3496 dpoly
fact(no_param
, den_s
[k
], 1);
3500 mpq_set_si(count
, 0, 1);
3501 n
.div(d
, count
, sign
[f
]);
3504 value2zz(mpq_numref(count
), qn
);
3505 value2zz(mpq_denref(count
), qd
);
3507 gf
->add(qn
, qd
, num_p
, pden
);
3512 pden
.SetDims(only_param
, nparam
);
3514 for (k
= 0, l
= 0; k
< dim
; ++k
)
3518 for (k
= 0; k
< dim
; ++k
)
3522 dpoly
n(no_param
, num_s
);
3523 dpoly
d(no_param
, den_s
[k
], 1);
3524 for ( ; k
< dim
; ++k
)
3525 if (den_p
[k
] == 0) {
3526 dpoly
fact(no_param
, den_s
[k
], 1);
3530 for (k
= 0; k
< dim
; ++k
) {
3531 if (den_s
[k
] == 0 || den_p
[k
] == 0)
3534 dpoly
pd(no_param
-1, den_s
[k
], 1);
3535 int s
= den_p
[k
] < 0 ? -1 : 1;
3538 r
= new dpoly_r(n
, pd
, k
, s
, dim
);
3540 assert(0); // for now
3543 r
->div(d
, sign
[f
], gf
, pden
, den
, num_p
);
3547 cout << "sign: " << sign[f];
3548 cout << "num_s: " << num_s;
3549 cout << "num_p: " << num_p;
3550 cout << "den_s: " << den_s;
3551 cout << "den_p: " << den_p;
3552 cout << "den: " << den;
3553 cout << "only_param: " << only_param;
3554 cout << "no_param: " << no_param;