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 void decompose(Polyhedron
*C
);
501 virtual void handle(Polyhedron
*P
, int sign
) = 0;
504 struct polar_decomposer
: public decomposer
{
505 void decompose(Polyhedron
*C
, unsigned MaxRays
);
506 virtual void handle(Polyhedron
*P
, int sign
);
507 virtual void handle_polar(Polyhedron
*P
, int sign
) = 0;
510 void decomposer::decompose(Polyhedron
*C
)
512 vector
<cone
*> nonuni
;
513 cone
* c
= new cone(C
);
524 while (!nonuni
.empty()) {
527 Vector
* v
= c
->short_vector(lambda
);
528 for (int i
= 0; i
< c
->Rays
->NbRows
- 1; ++i
) {
531 Matrix
* M
= Matrix_Copy(c
->Rays
);
532 Vector_Copy(v
->p
, M
->p
[i
], v
->Size
);
533 cone
* pc
= new cone(M
);
534 assert (pc
->det
!= 0);
535 if (abs(pc
->det
) > 1) {
536 assert(abs(pc
->det
) < abs(c
->det
));
537 nonuni
.push_back(pc
);
539 handle(pc
->poly(), sign(pc
->det
) * s
);
549 void polar_decomposer::decompose(Polyhedron
*cone
, unsigned MaxRays
)
551 Polyhedron_Polarize(cone
);
552 if (cone
->NbRays
- 1 != cone
->Dimension
) {
553 Polyhedron
*tmp
= cone
;
554 cone
= triangularize_cone(cone
, MaxRays
);
555 Polyhedron_Free(tmp
);
557 for (Polyhedron
*Polar
= cone
; Polar
; Polar
= Polar
->next
)
558 decomposer::decompose(Polar
);
562 void polar_decomposer::handle(Polyhedron
*P
, int sign
)
564 Polyhedron_Polarize(P
);
565 handle_polar(P
, sign
);
569 * Barvinok's Decomposition of a simplicial cone
571 * Returns two lists of polyhedra
573 void barvinok_decompose(Polyhedron
*C
, Polyhedron
**ppos
, Polyhedron
**pneg
)
575 Polyhedron
*pos
= *ppos
, *neg
= *pneg
;
576 vector
<cone
*> nonuni
;
577 cone
* c
= new cone(C
);
584 Polyhedron
*p
= Polyhedron_Copy(c
->Cone
);
590 while (!nonuni
.empty()) {
593 Vector
* v
= c
->short_vector(lambda
);
594 for (int i
= 0; i
< c
->Rays
->NbRows
- 1; ++i
) {
597 Matrix
* M
= Matrix_Copy(c
->Rays
);
598 Vector_Copy(v
->p
, M
->p
[i
], v
->Size
);
599 cone
* pc
= new cone(M
);
600 assert (pc
->det
!= 0);
601 if (abs(pc
->det
) > 1) {
602 assert(abs(pc
->det
) < abs(c
->det
));
603 nonuni
.push_back(pc
);
605 Polyhedron
*p
= pc
->poly();
607 if (sign(pc
->det
) == s
) {
626 * Returns a single list of npos "positive" cones followed by nneg
628 * The input cone is freed
630 void decompose(Polyhedron
*cone
, Polyhedron
**parts
, int *npos
, int *nneg
, unsigned MaxRays
)
632 Polyhedron_Polarize(cone
);
633 if (cone
->NbRays
- 1 != cone
->Dimension
) {
634 Polyhedron
*tmp
= cone
;
635 cone
= triangularize_cone(cone
, MaxRays
);
636 Polyhedron_Free(tmp
);
638 Polyhedron
*polpos
= NULL
, *polneg
= NULL
;
639 *npos
= 0; *nneg
= 0;
640 for (Polyhedron
*Polar
= cone
; Polar
; Polar
= Polar
->next
)
641 barvinok_decompose(Polar
, &polpos
, &polneg
);
644 for (Polyhedron
*i
= polpos
; i
; i
= i
->next
) {
645 Polyhedron_Polarize(i
);
649 for (Polyhedron
*i
= polneg
; i
; i
= i
->next
) {
650 Polyhedron_Polarize(i
);
661 const int MAX_TRY
=10;
663 * Searches for a vector that is not orthogonal to any
664 * of the rays in rays.
666 static void nonorthog(mat_ZZ
& rays
, vec_ZZ
& lambda
)
668 int dim
= rays
.NumCols();
670 lambda
.SetLength(dim
);
674 for (int i
= 2; !found
&& i
<= 50*dim
; i
+=4) {
675 for (int j
= 0; j
< MAX_TRY
; ++j
) {
676 for (int k
= 0; k
< dim
; ++k
) {
677 int r
= random_int(i
)+2;
678 int v
= (2*(r
%2)-1) * (r
>> 1);
682 for (; k
< rays
.NumRows(); ++k
)
683 if (lambda
* rays
[k
] == 0)
685 if (k
== rays
.NumRows()) {
694 static void randomvector(Polyhedron
*P
, vec_ZZ
& lambda
, int nvar
)
698 unsigned int dim
= P
->Dimension
;
701 for (int i
= 0; i
< P
->NbRays
; ++i
) {
702 for (int j
= 1; j
<= dim
; ++j
) {
703 value_absolute(tmp
, P
->Ray
[i
][j
]);
704 int t
= VALUE_TO_LONG(tmp
);
709 for (int i
= 0; i
< P
->NbConstraints
; ++i
) {
710 for (int j
= 1; j
<= dim
; ++j
) {
711 value_absolute(tmp
, P
->Constraint
[i
][j
]);
712 int t
= VALUE_TO_LONG(tmp
);
719 lambda
.SetLength(nvar
);
720 for (int k
= 0; k
< nvar
; ++k
) {
721 int r
= random_int(8*max
*dim
)+2;
722 int v
= (2*(r
%2)-1) * (4*max
*dim
+ (r
>> 1));
727 static void add_rays(mat_ZZ
& rays
, Polyhedron
*i
, int *r
, int nvar
= -1,
730 unsigned dim
= i
->Dimension
;
733 for (int k
= 0; k
< i
->NbRays
; ++k
) {
734 if (!value_zero_p(i
->Ray
[k
][dim
+1]))
736 if (!all
&& nvar
!= dim
&& First_Non_Zero(i
->Ray
[k
]+1, nvar
) == -1)
738 values2zz(i
->Ray
[k
]+1, rays
[(*r
)++], nvar
);
742 void lattice_point(Value
* values
, Polyhedron
*i
, vec_ZZ
& vertex
)
744 unsigned dim
= i
->Dimension
;
745 if(!value_one_p(values
[dim
])) {
746 Matrix
* Rays
= rays(i
);
747 Matrix
*inv
= Matrix_Alloc(Rays
->NbRows
, Rays
->NbColumns
);
748 int ok
= Matrix_Inverse(Rays
, inv
);
752 Vector
*lambda
= Vector_Alloc(dim
+1);
753 Vector_Matrix_Product(values
, inv
, lambda
->p
);
755 for (int j
= 0; j
< dim
; ++j
)
756 mpz_cdiv_q(lambda
->p
[j
], lambda
->p
[j
], lambda
->p
[dim
]);
757 value_set_si(lambda
->p
[dim
], 1);
758 Vector
*A
= Vector_Alloc(dim
+1);
759 Vector_Matrix_Product(lambda
->p
, Rays
, A
->p
);
762 values2zz(A
->p
, vertex
, dim
);
765 values2zz(values
, vertex
, dim
);
768 static evalue
*term(int param
, ZZ
& c
, Value
*den
= NULL
)
770 evalue
*EP
= new evalue();
772 value_set_si(EP
->d
,0);
773 EP
->x
.p
= new_enode(polynomial
, 2, param
+ 1);
774 evalue_set_si(&EP
->x
.p
->arr
[0], 0, 1);
775 value_init(EP
->x
.p
->arr
[1].x
.n
);
777 value_set_si(EP
->x
.p
->arr
[1].d
, 1);
779 value_assign(EP
->x
.p
->arr
[1].d
, *den
);
780 zz2value(c
, EP
->x
.p
->arr
[1].x
.n
);
784 static void vertex_period(
785 Polyhedron
*i
, vec_ZZ
& lambda
, Matrix
*T
,
786 Value lcm
, int p
, Vector
*val
,
787 evalue
*E
, evalue
* ev
,
790 unsigned nparam
= T
->NbRows
- 1;
791 unsigned dim
= i
->Dimension
;
798 Vector
* values
= Vector_Alloc(dim
+ 1);
799 Vector_Matrix_Product(val
->p
, T
, values
->p
);
800 value_assign(values
->p
[dim
], lcm
);
801 lattice_point(values
->p
, i
, vertex
);
802 num
= vertex
* lambda
;
807 zz2value(num
, ev
->x
.n
);
808 value_assign(ev
->d
, lcm
);
815 values2zz(T
->p
[p
], vertex
, dim
);
816 nump
= vertex
* lambda
;
817 if (First_Non_Zero(val
->p
, p
) == -1) {
818 value_assign(tmp
, lcm
);
819 evalue
*ET
= term(p
, nump
, &tmp
);
821 free_evalue_refs(ET
);
825 value_assign(tmp
, lcm
);
826 if (First_Non_Zero(T
->p
[p
], dim
) != -1)
827 Vector_Gcd(T
->p
[p
], dim
, &tmp
);
829 if (value_lt(tmp
, lcm
)) {
832 value_division(tmp
, lcm
, tmp
);
833 value_set_si(ev
->d
, 0);
834 ev
->x
.p
= new_enode(periodic
, VALUE_TO_INT(tmp
), p
+1);
835 value2zz(tmp
, count
);
837 value_decrement(tmp
, tmp
);
839 ZZ new_offset
= offset
- count
* nump
;
840 value_assign(val
->p
[p
], tmp
);
841 vertex_period(i
, lambda
, T
, lcm
, p
+1, val
, E
,
842 &ev
->x
.p
->arr
[VALUE_TO_INT(tmp
)], new_offset
);
843 } while (value_pos_p(tmp
));
845 vertex_period(i
, lambda
, T
, lcm
, p
+1, val
, E
, ev
, offset
);
849 static void mask_r(Matrix
*f
, int nr
, Vector
*lcm
, int p
, Vector
*val
, evalue
*ev
)
851 unsigned nparam
= lcm
->Size
;
854 Vector
* prod
= Vector_Alloc(f
->NbRows
);
855 Matrix_Vector_Product(f
, val
->p
, prod
->p
);
857 for (int i
= 0; i
< nr
; ++i
) {
858 value_modulus(prod
->p
[i
], prod
->p
[i
], f
->p
[i
][nparam
+1]);
859 isint
&= value_zero_p(prod
->p
[i
]);
861 value_set_si(ev
->d
, 1);
863 value_set_si(ev
->x
.n
, isint
);
870 if (value_one_p(lcm
->p
[p
]))
871 mask_r(f
, nr
, lcm
, p
+1, val
, ev
);
873 value_assign(tmp
, lcm
->p
[p
]);
874 value_set_si(ev
->d
, 0);
875 ev
->x
.p
= new_enode(periodic
, VALUE_TO_INT(tmp
), p
+1);
877 value_decrement(tmp
, tmp
);
878 value_assign(val
->p
[p
], tmp
);
879 mask_r(f
, nr
, lcm
, p
+1, val
, &ev
->x
.p
->arr
[VALUE_TO_INT(tmp
)]);
880 } while (value_pos_p(tmp
));
885 static evalue
*multi_monom(vec_ZZ
& p
)
887 evalue
*X
= new evalue();
890 unsigned nparam
= p
.length()-1;
891 zz2value(p
[nparam
], X
->x
.n
);
892 value_set_si(X
->d
, 1);
893 for (int i
= 0; i
< nparam
; ++i
) {
896 evalue
*T
= term(i
, p
[i
]);
905 * Check whether mapping polyhedron P on the affine combination
906 * num yields a range that has a fixed quotient on integer
908 * If zero is true, then we are only interested in the quotient
909 * for the cases where the remainder is zero.
910 * Returns NULL if false and a newly allocated value if true.
912 static Value
*fixed_quotient(Polyhedron
*P
, vec_ZZ
& num
, Value d
, bool zero
)
915 int len
= num
.length();
916 Matrix
*T
= Matrix_Alloc(2, len
);
917 zz2values(num
, T
->p
[0]);
918 value_set_si(T
->p
[1][len
-1], 1);
919 Polyhedron
*I
= Polyhedron_Image(P
, T
, P
->NbConstraints
);
923 for (i
= 0; i
< I
->NbRays
; ++i
)
924 if (value_zero_p(I
->Ray
[i
][2])) {
932 int bounded
= line_minmax(I
, &min
, &max
);
936 mpz_cdiv_q(min
, min
, d
);
938 mpz_fdiv_q(min
, min
, d
);
939 mpz_fdiv_q(max
, max
, d
);
941 if (value_eq(min
, max
)) {
944 value_assign(*ret
, min
);
952 * Normalize linear expression coef modulo m
953 * Removes common factor and reduces coefficients
954 * Returns index of first non-zero coefficient or len
956 static int normal_mod(Value
*coef
, int len
, Value
*m
)
961 Vector_Gcd(coef
, len
, &gcd
);
963 Vector_AntiScale(coef
, coef
, gcd
, len
);
965 value_division(*m
, *m
, gcd
);
972 for (j
= 0; j
< len
; ++j
)
973 mpz_fdiv_r(coef
[j
], coef
[j
], *m
);
974 for (j
= 0; j
< len
; ++j
)
975 if (value_notzero_p(coef
[j
]))
982 static void mask(Matrix
*f
, evalue
*factor
)
984 int nr
= f
->NbRows
, nc
= f
->NbColumns
;
987 for (n
= 0; n
< nr
&& value_notzero_p(f
->p
[n
][nc
-1]); ++n
)
988 if (value_notone_p(f
->p
[n
][nc
-1]) &&
989 value_notmone_p(f
->p
[n
][nc
-1]))
1003 value_set_si(EV
.x
.n
, 1);
1005 for (n
= 0; n
< nr
; ++n
) {
1006 value_assign(m
, f
->p
[n
][nc
-1]);
1007 if (value_one_p(m
) || value_mone_p(m
))
1010 int j
= normal_mod(f
->p
[n
], nc
-1, &m
);
1012 free_evalue_refs(factor
);
1013 value_init(factor
->d
);
1014 evalue_set_si(factor
, 0, 1);
1018 values2zz(f
->p
[n
], row
, nc
-1);
1021 if (j
< (nc
-1)-1 && row
[j
] > g
/2) {
1022 for (int k
= j
; k
< (nc
-1); ++k
)
1024 row
[k
] = g
- row
[k
];
1028 value_set_si(EP
.d
, 0);
1029 EP
.x
.p
= new_enode(relation
, 2, 0);
1030 value_clear(EP
.x
.p
->arr
[1].d
);
1031 EP
.x
.p
->arr
[1] = *factor
;
1032 evalue
*ev
= &EP
.x
.p
->arr
[0];
1033 value_set_si(ev
->d
, 0);
1034 ev
->x
.p
= new_enode(fractional
, 3, -1);
1035 evalue_set_si(&ev
->x
.p
->arr
[1], 0, 1);
1036 evalue_set_si(&ev
->x
.p
->arr
[2], 1, 1);
1037 evalue
*E
= multi_monom(row
);
1038 value_assign(EV
.d
, m
);
1040 value_clear(ev
->x
.p
->arr
[0].d
);
1041 ev
->x
.p
->arr
[0] = *E
;
1047 free_evalue_refs(&EV
);
1053 static void mask(Matrix
*f
, evalue
*factor
)
1055 int nr
= f
->NbRows
, nc
= f
->NbColumns
;
1058 for (n
= 0; n
< nr
&& value_notzero_p(f
->p
[n
][nc
-1]); ++n
)
1059 if (value_notone_p(f
->p
[n
][nc
-1]) &&
1060 value_notmone_p(f
->p
[n
][nc
-1]))
1068 unsigned np
= nc
- 2;
1069 Vector
*lcm
= Vector_Alloc(np
);
1070 Vector
*val
= Vector_Alloc(nc
);
1071 Vector_Set(val
->p
, 0, nc
);
1072 value_set_si(val
->p
[np
], 1);
1073 Vector_Set(lcm
->p
, 1, np
);
1074 for (n
= 0; n
< nr
; ++n
) {
1075 if (value_one_p(f
->p
[n
][nc
-1]) ||
1076 value_mone_p(f
->p
[n
][nc
-1]))
1078 for (int j
= 0; j
< np
; ++j
)
1079 if (value_notzero_p(f
->p
[n
][j
])) {
1080 Gcd(f
->p
[n
][j
], f
->p
[n
][nc
-1], &tmp
);
1081 value_division(tmp
, f
->p
[n
][nc
-1], tmp
);
1082 value_lcm(tmp
, lcm
->p
[j
], &lcm
->p
[j
]);
1087 mask_r(f
, nr
, lcm
, 0, val
, &EP
);
1092 free_evalue_refs(&EP
);
1103 static bool mod_needed(Polyhedron
*PD
, vec_ZZ
& num
, Value d
, evalue
*E
)
1105 Value
*q
= fixed_quotient(PD
, num
, d
, false);
1110 value_oppose(*q
, *q
);
1113 value_set_si(EV
.d
, 1);
1115 value_multiply(EV
.x
.n
, *q
, d
);
1117 free_evalue_refs(&EV
);
1123 static void ceil_mod(Value
*coef
, int len
, Value d
, ZZ
& f
, evalue
*EP
, Polyhedron
*PD
)
1127 value_set_si(m
, -1);
1129 Vector_Scale(coef
, coef
, m
, len
);
1132 int j
= normal_mod(coef
, len
, &m
);
1140 values2zz(coef
, num
, len
);
1147 evalue_set_si(&tmp
, 0, 1);
1151 while (j
< len
-1 && (num
[j
] == g
/2 || num
[j
] == 0))
1153 if ((j
< len
-1 && num
[j
] > g
/2) || (j
== len
-1 && num
[j
] >= (g
+1)/2)) {
1154 for (int k
= j
; k
< len
-1; ++k
)
1156 num
[k
] = g
- num
[k
];
1157 num
[len
-1] = g
- 1 - num
[len
-1];
1158 value_assign(tmp
.d
, m
);
1160 zz2value(t
, tmp
.x
.n
);
1166 ZZ t
= num
[len
-1] * f
;
1167 zz2value(t
, tmp
.x
.n
);
1168 value_assign(tmp
.d
, m
);
1171 evalue
*E
= multi_monom(num
);
1175 if (PD
&& !mod_needed(PD
, num
, m
, E
)) {
1177 zz2value(f
, EV
.x
.n
);
1178 value_assign(EV
.d
, m
);
1183 value_set_si(EV
.x
.n
, 1);
1184 value_assign(EV
.d
, m
);
1186 value_clear(EV
.x
.n
);
1187 value_set_si(EV
.d
, 0);
1188 EV
.x
.p
= new_enode(fractional
, 3, -1);
1189 evalue_copy(&EV
.x
.p
->arr
[0], E
);
1190 evalue_set_si(&EV
.x
.p
->arr
[1], 0, 1);
1191 value_init(EV
.x
.p
->arr
[2].x
.n
);
1192 zz2value(f
, EV
.x
.p
->arr
[2].x
.n
);
1193 value_set_si(EV
.x
.p
->arr
[2].d
, 1);
1198 free_evalue_refs(&EV
);
1199 free_evalue_refs(E
);
1203 free_evalue_refs(&tmp
);
1209 evalue
* bv_ceil3(Value
*coef
, int len
, Value d
, Polyhedron
*P
)
1211 Vector
*val
= Vector_Alloc(len
);
1215 value_set_si(t
, -1);
1216 Vector_Scale(coef
, val
->p
, t
, len
);
1217 value_absolute(t
, d
);
1220 values2zz(val
->p
, num
, len
);
1221 evalue
*EP
= multi_monom(num
);
1225 value_init(tmp
.x
.n
);
1226 value_set_si(tmp
.x
.n
, 1);
1227 value_assign(tmp
.d
, t
);
1233 ceil_mod(val
->p
, len
, t
, one
, EP
, P
);
1236 /* copy EP to malloc'ed evalue */
1242 free_evalue_refs(&tmp
);
1249 evalue
* lattice_point(
1250 Polyhedron
*i
, vec_ZZ
& lambda
, Matrix
*W
, Value lcm
, Polyhedron
*PD
)
1252 unsigned nparam
= W
->NbColumns
- 1;
1254 Matrix
* Rays
= rays2(i
);
1255 Matrix
*T
= Transpose(Rays
);
1256 Matrix
*T2
= Matrix_Copy(T
);
1257 Matrix
*inv
= Matrix_Alloc(T2
->NbRows
, T2
->NbColumns
);
1258 int ok
= Matrix_Inverse(T2
, inv
);
1263 matrix2zz(W
, vertex
, W
->NbRows
, W
->NbColumns
);
1266 num
= lambda
* vertex
;
1268 evalue
*EP
= multi_monom(num
);
1272 value_init(tmp
.x
.n
);
1273 value_set_si(tmp
.x
.n
, 1);
1274 value_assign(tmp
.d
, lcm
);
1278 Matrix
*L
= Matrix_Alloc(inv
->NbRows
, W
->NbColumns
);
1279 Matrix_Product(inv
, W
, L
);
1282 matrix2zz(T
, RT
, T
->NbRows
, T
->NbColumns
);
1285 vec_ZZ p
= lambda
* RT
;
1287 for (int i
= 0; i
< L
->NbRows
; ++i
) {
1288 ceil_mod(L
->p
[i
], nparam
+1, lcm
, p
[i
], EP
, PD
);
1294 free_evalue_refs(&tmp
);
1298 evalue
* lattice_point(
1299 Polyhedron
*i
, vec_ZZ
& lambda
, Matrix
*W
, Value lcm
, Polyhedron
*PD
)
1301 Matrix
*T
= Transpose(W
);
1302 unsigned nparam
= T
->NbRows
- 1;
1304 evalue
*EP
= new evalue();
1306 evalue_set_si(EP
, 0, 1);
1309 Vector
*val
= Vector_Alloc(nparam
+1);
1310 value_set_si(val
->p
[nparam
], 1);
1311 ZZ
offset(INIT_VAL
, 0);
1313 vertex_period(i
, lambda
, T
, lcm
, 0, val
, EP
, &ev
, offset
);
1316 free_evalue_refs(&ev
);
1327 Param_Vertices
* V
, Polyhedron
*i
, vec_ZZ
& lambda
, term_info
* term
,
1330 unsigned nparam
= V
->Vertex
->NbColumns
- 2;
1331 unsigned dim
= i
->Dimension
;
1333 vertex
.SetDims(V
->Vertex
->NbRows
, nparam
+1);
1337 value_set_si(lcm
, 1);
1338 for (int j
= 0; j
< V
->Vertex
->NbRows
; ++j
) {
1339 value_lcm(lcm
, V
->Vertex
->p
[j
][nparam
+1], &lcm
);
1341 if (value_notone_p(lcm
)) {
1342 Matrix
* mv
= Matrix_Alloc(dim
, nparam
+1);
1343 for (int j
= 0 ; j
< dim
; ++j
) {
1344 value_division(tmp
, lcm
, V
->Vertex
->p
[j
][nparam
+1]);
1345 Vector_Scale(V
->Vertex
->p
[j
], mv
->p
[j
], tmp
, nparam
+1);
1348 term
->E
= lattice_point(i
, lambda
, mv
, lcm
, PD
);
1356 for (int i
= 0; i
< V
->Vertex
->NbRows
; ++i
) {
1357 assert(value_one_p(V
->Vertex
->p
[i
][nparam
+1])); // for now
1358 values2zz(V
->Vertex
->p
[i
], vertex
[i
], nparam
+1);
1362 num
= lambda
* vertex
;
1366 for (int j
= 0; j
< nparam
; ++j
)
1372 term
->E
= multi_monom(num
);
1376 term
->constant
= num
[nparam
];
1379 term
->coeff
= num
[p
];
1386 void normalize(Polyhedron
*i
, vec_ZZ
& lambda
, ZZ
& sign
, ZZ
& num
, vec_ZZ
& den
)
1388 unsigned dim
= i
->Dimension
;
1392 rays
.SetDims(dim
, dim
);
1393 add_rays(rays
, i
, &r
);
1394 den
= rays
* lambda
;
1397 for (int j
= 0; j
< den
.length(); ++j
) {
1401 den
[j
] = abs(den
[j
]);
1409 struct counter
: public polar_decomposer
{
1421 counter(Polyhedron
*P
) {
1424 randomvector(P
, lambda
, dim
);
1425 rays
.SetDims(dim
, dim
);
1430 void start(unsigned MaxRays
);
1436 virtual void handle_polar(Polyhedron
*P
, int sign
);
1439 void counter::handle_polar(Polyhedron
*C
, int s
)
1442 assert(C
->NbRays
-1 == dim
);
1443 add_rays(rays
, C
, &r
);
1444 for (int k
= 0; k
< dim
; ++k
) {
1445 assert(lambda
* rays
[k
] != 0);
1450 lattice_point(P
->Ray
[j
]+1, C
, vertex
);
1451 num
= vertex
* lambda
;
1452 normalize(C
, lambda
, sign
, num
, den
);
1455 dpoly
n(dim
, den
[0], 1);
1456 for (int k
= 1; k
< dim
; ++k
) {
1457 dpoly
fact(dim
, den
[k
], 1);
1460 d
.div(n
, count
, sign
);
1463 void counter::start(unsigned MaxRays
)
1465 for (j
= 0; j
< P
->NbRays
; ++j
) {
1466 Polyhedron
*C
= supporting_cone(P
, j
);
1467 decompose(C
, MaxRays
);
1471 typedef Polyhedron
* Polyhedron_p
;
1473 void barvinok_count(Polyhedron
*P
, Value
* result
, unsigned NbMaxCons
)
1475 Polyhedron
** vcone
;
1484 value_set_si(*result
, 0);
1488 for (; r
< P
->NbRays
; ++r
)
1489 if (value_zero_p(P
->Ray
[r
][P
->Dimension
+1]))
1491 if (P
->NbBid
!=0 || r
< P
->NbRays
) {
1492 value_set_si(*result
, -1);
1496 P
= remove_equalities(P
);
1499 value_set_si(*result
, 0);
1505 value_set_si(factor
, 1);
1506 Q
= Polyhedron_Reduce(P
, &factor
);
1513 if (P
->Dimension
== 0) {
1514 value_assign(*result
, factor
);
1517 value_clear(factor
);
1522 cnt
.start(NbMaxCons
);
1524 assert(value_one_p(&cnt
.count
[0]._mp_den
));
1525 value_multiply(*result
, &cnt
.count
[0]._mp_num
, factor
);
1529 value_clear(factor
);
1532 static void uni_polynom(int param
, Vector
*c
, evalue
*EP
)
1534 unsigned dim
= c
->Size
-2;
1536 value_set_si(EP
->d
,0);
1537 EP
->x
.p
= new_enode(polynomial
, dim
+1, param
+1);
1538 for (int j
= 0; j
<= dim
; ++j
)
1539 evalue_set(&EP
->x
.p
->arr
[j
], c
->p
[j
], c
->p
[dim
+1]);
1542 static void multi_polynom(Vector
*c
, evalue
* X
, evalue
*EP
)
1544 unsigned dim
= c
->Size
-2;
1548 evalue_set(&EC
, c
->p
[dim
], c
->p
[dim
+1]);
1551 evalue_set(EP
, c
->p
[dim
], c
->p
[dim
+1]);
1553 for (int i
= dim
-1; i
>= 0; --i
) {
1555 value_assign(EC
.x
.n
, c
->p
[i
]);
1558 free_evalue_refs(&EC
);
1561 Polyhedron
*unfringe (Polyhedron
*P
, unsigned MaxRays
)
1563 int len
= P
->Dimension
+2;
1564 Polyhedron
*T
, *R
= P
;
1567 Vector
*row
= Vector_Alloc(len
);
1568 value_set_si(row
->p
[0], 1);
1570 R
= DomainConstraintSimplify(Polyhedron_Copy(P
), MaxRays
);
1572 Matrix
*M
= Matrix_Alloc(2, len
-1);
1573 value_set_si(M
->p
[1][len
-2], 1);
1574 for (int v
= 0; v
< P
->Dimension
; ++v
) {
1575 value_set_si(M
->p
[0][v
], 1);
1576 Polyhedron
*I
= Polyhedron_Image(P
, M
, 2+1);
1577 value_set_si(M
->p
[0][v
], 0);
1578 for (int r
= 0; r
< I
->NbConstraints
; ++r
) {
1579 if (value_zero_p(I
->Constraint
[r
][0]))
1581 if (value_zero_p(I
->Constraint
[r
][1]))
1583 if (value_one_p(I
->Constraint
[r
][1]))
1585 if (value_mone_p(I
->Constraint
[r
][1]))
1587 value_absolute(g
, I
->Constraint
[r
][1]);
1588 Vector_Set(row
->p
+1, 0, len
-2);
1589 value_division(row
->p
[1+v
], I
->Constraint
[r
][1], g
);
1590 mpz_fdiv_q(row
->p
[len
-1], I
->Constraint
[r
][2], g
);
1592 R
= AddConstraints(row
->p
, 1, R
, MaxRays
);
1604 static Polyhedron
*reduce_domain(Polyhedron
*D
, Matrix
*CT
, Polyhedron
*CEq
,
1605 Polyhedron
**fVD
, int nd
, unsigned MaxRays
)
1610 Dt
= CT
? DomainPreimage(D
, CT
, MaxRays
) : D
;
1611 Polyhedron
*rVD
= DomainIntersection(Dt
, CEq
, MaxRays
);
1613 /* if rVD is empty or too small in geometric dimension */
1614 if(!rVD
|| emptyQ(rVD
) ||
1615 (rVD
->Dimension
-rVD
->NbEq
< Dt
->Dimension
-Dt
->NbEq
-CEq
->NbEq
)) {
1620 return 0; /* empty validity domain */
1626 fVD
[nd
] = Domain_Copy(rVD
);
1627 for (int i
= 0 ; i
< nd
; ++i
) {
1628 Polyhedron
*I
= DomainIntersection(fVD
[nd
], fVD
[i
], MaxRays
);
1633 Polyhedron
*F
= DomainSimplify(I
, fVD
[nd
], MaxRays
);
1635 Polyhedron
*T
= rVD
;
1636 rVD
= DomainDifference(rVD
, F
, MaxRays
);
1643 rVD
= DomainConstraintSimplify(rVD
, MaxRays
);
1645 Domain_Free(fVD
[nd
]);
1652 barvinok_count(rVD
, &c
, MaxRays
);
1653 if (value_zero_p(c
)) {
1662 static bool Polyhedron_is_infinite(Polyhedron
*P
, unsigned nparam
)
1665 for (r
= 0; r
< P
->NbRays
; ++r
)
1666 if (value_zero_p(P
->Ray
[r
][0]) ||
1667 value_zero_p(P
->Ray
[r
][P
->Dimension
+1])) {
1669 for (i
= P
->Dimension
- nparam
; i
< P
->Dimension
; ++i
)
1670 if (value_notzero_p(P
->Ray
[r
][i
+1]))
1672 if (i
>= P
->Dimension
)
1675 return r
< P
->NbRays
;
1678 /* Check whether all rays point in the positive directions
1679 * for the parameters
1681 static bool Polyhedron_has_positive_rays(Polyhedron
*P
, unsigned nparam
)
1684 for (r
= 0; r
< P
->NbRays
; ++r
)
1685 if (value_zero_p(P
->Ray
[r
][P
->Dimension
+1])) {
1687 for (i
= P
->Dimension
- nparam
; i
< P
->Dimension
; ++i
)
1688 if (value_neg_p(P
->Ray
[r
][i
+1]))
1694 typedef evalue
* evalue_p
;
1696 struct enumerator
: public polar_decomposer
{
1710 enumerator(Polyhedron
*P
, unsigned dim
, unsigned nbV
) {
1714 randomvector(P
, lambda
, dim
);
1715 rays
.SetDims(dim
, dim
);
1717 c
= Vector_Alloc(dim
+2);
1719 vE
= new evalue_p
[nbV
];
1720 for (int j
= 0; j
< nbV
; ++j
)
1726 void decompose_at(Param_Vertices
*V
, int _i
, unsigned MaxRays
) {
1727 Polyhedron
*C
= supporting_cone_p(P
, V
);
1731 vE
[_i
] = new evalue
;
1732 value_init(vE
[_i
]->d
);
1733 evalue_set_si(vE
[_i
], 0, 1);
1735 decompose(C
, MaxRays
);
1742 for (int j
= 0; j
< nbV
; ++j
)
1744 free_evalue_refs(vE
[j
]);
1750 virtual void handle_polar(Polyhedron
*P
, int sign
);
1753 void enumerator::handle_polar(Polyhedron
*C
, int s
)
1756 assert(C
->NbRays
-1 == dim
);
1757 add_rays(rays
, C
, &r
);
1758 for (int k
= 0; k
< dim
; ++k
) {
1759 assert(lambda
* rays
[k
] != 0);
1764 lattice_point(V
, C
, lambda
, &num
, 0);
1765 normalize(C
, lambda
, sign
, num
.constant
, den
);
1767 dpoly
n(dim
, den
[0], 1);
1768 for (int k
= 1; k
< dim
; ++k
) {
1769 dpoly
fact(dim
, den
[k
], 1);
1772 if (num
.E
!= NULL
) {
1773 ZZ
one(INIT_VAL
, 1);
1774 dpoly_n
d(dim
, num
.constant
, one
);
1777 multi_polynom(c
, num
.E
, &EV
);
1779 free_evalue_refs(&EV
);
1780 free_evalue_refs(num
.E
);
1782 } else if (num
.pos
!= -1) {
1783 dpoly_n
d(dim
, num
.constant
, num
.coeff
);
1786 uni_polynom(num
.pos
, c
, &EV
);
1788 free_evalue_refs(&EV
);
1790 mpq_set_si(count
, 0, 1);
1791 dpoly
d(dim
, num
.constant
);
1792 d
.div(n
, count
, sign
);
1795 evalue_set(&EV
, &count
[0]._mp_num
, &count
[0]._mp_den
);
1797 free_evalue_refs(&EV
);
1801 evalue
* barvinok_enumerate_ev(Polyhedron
*P
, Polyhedron
* C
, unsigned MaxRays
)
1803 //P = unfringe(P, MaxRays);
1804 Polyhedron
*CEq
= NULL
, *rVD
, *pVD
, *CA
;
1806 Param_Polyhedron
*PP
= NULL
;
1807 Param_Domain
*D
, *next
;
1810 unsigned nparam
= C
->Dimension
;
1812 ALLOC(evalue
, eres
);
1813 value_init(eres
->d
);
1814 value_set_si(eres
->d
, 0);
1817 value_init(factor
.d
);
1818 evalue_set_si(&factor
, 1, 1);
1820 CA
= align_context(C
, P
->Dimension
, MaxRays
);
1821 P
= DomainIntersection(P
, CA
, MaxRays
);
1822 Polyhedron_Free(CA
);
1824 if (C
->Dimension
== 0 || emptyQ(P
)) {
1826 eres
->x
.p
= new_enode(partition
, 2, C
->Dimension
);
1827 EVALUE_SET_DOMAIN(eres
->x
.p
->arr
[0],
1828 DomainConstraintSimplify(CEq
? CEq
: Polyhedron_Copy(C
), MaxRays
));
1829 value_set_si(eres
->x
.p
->arr
[1].d
, 1);
1830 value_init(eres
->x
.p
->arr
[1].x
.n
);
1832 value_set_si(eres
->x
.p
->arr
[1].x
.n
, 0);
1834 barvinok_count(P
, &eres
->x
.p
->arr
[1].x
.n
, MaxRays
);
1836 emul(&factor
, eres
);
1837 reduce_evalue(eres
);
1838 free_evalue_refs(&factor
);
1843 Param_Polyhedron_Free(PP
);
1847 if (Polyhedron_is_infinite(P
, nparam
))
1852 P
= remove_equalities_p(P
, P
->Dimension
-nparam
, &f
);
1856 if (P
->Dimension
== nparam
) {
1858 P
= Universe_Polyhedron(0);
1862 Polyhedron
*Q
= ParamPolyhedron_Reduce(P
, P
->Dimension
-nparam
, &factor
);
1865 if (Q
->Dimension
== nparam
) {
1867 P
= Universe_Polyhedron(0);
1872 Polyhedron
*oldP
= P
;
1873 PP
= Polyhedron2Param_SimplifiedDomain(&P
,C
,MaxRays
,&CEq
,&CT
);
1875 Polyhedron_Free(oldP
);
1877 if (isIdentity(CT
)) {
1881 assert(CT
->NbRows
!= CT
->NbColumns
);
1882 if (CT
->NbRows
== 1) // no more parameters
1884 nparam
= CT
->NbRows
- 1;
1887 unsigned dim
= P
->Dimension
- nparam
;
1889 enumerator
et(P
, dim
, PP
->nbV
);
1892 for (nd
= 0, D
=PP
->D
; D
; ++nd
, D
=D
->next
);
1893 struct section
{ Polyhedron
*D
; evalue E
; };
1894 section
*s
= new section
[nd
];
1895 Polyhedron
**fVD
= new Polyhedron_p
[nd
];
1897 for(nd
= 0, D
=PP
->D
; D
; D
=next
) {
1900 Polyhedron
*rVD
= reduce_domain(D
->Domain
, CT
, CEq
,
1905 pVD
= CT
? DomainImage(rVD
,CT
,MaxRays
) : rVD
;
1907 value_init(s
[nd
].E
.d
);
1908 evalue_set_si(&s
[nd
].E
, 0, 1);
1910 FORALL_PVertex_in_ParamPolyhedron(V
,D
,PP
) // _i is internal counter
1912 et
.decompose_at(V
, _i
, MaxRays
);
1913 eadd(et
.vE
[_i
] , &s
[nd
].E
);
1914 END_FORALL_PVertex_in_ParamPolyhedron
;
1915 reduce_in_domain(&s
[nd
].E
, pVD
);
1918 addeliminatedparams_evalue(&s
[nd
].E
, CT
);
1926 evalue_set_si(eres
, 0, 1);
1928 eres
->x
.p
= new_enode(partition
, 2*nd
, C
->Dimension
);
1929 for (int j
= 0; j
< nd
; ++j
) {
1930 EVALUE_SET_DOMAIN(eres
->x
.p
->arr
[2*j
], s
[j
].D
);
1931 value_clear(eres
->x
.p
->arr
[2*j
+1].d
);
1932 eres
->x
.p
->arr
[2*j
+1] = s
[j
].E
;
1933 Domain_Free(fVD
[j
]);
1941 Polyhedron_Free(CEq
);
1946 Enumeration
* barvinok_enumerate(Polyhedron
*P
, Polyhedron
* C
, unsigned MaxRays
)
1948 evalue
*EP
= barvinok_enumerate_ev(P
, C
, MaxRays
);
1950 return partition2enumeration(EP
);
1953 static void SwapColumns(Value
**V
, int n
, int i
, int j
)
1955 for (int r
= 0; r
< n
; ++r
)
1956 value_swap(V
[r
][i
], V
[r
][j
]);
1959 static void SwapColumns(Polyhedron
*P
, int i
, int j
)
1961 SwapColumns(P
->Constraint
, P
->NbConstraints
, i
, j
);
1962 SwapColumns(P
->Ray
, P
->NbRays
, i
, j
);
1965 static void negative_test_constraint(Value
*l
, Value
*u
, Value
*c
, int pos
,
1968 value_oppose(*v
, u
[pos
+1]);
1969 Vector_Combine(l
+1, u
+1, c
+1, *v
, l
[pos
+1], len
-1);
1970 value_multiply(*v
, *v
, l
[pos
+1]);
1971 value_substract(c
[len
-1], c
[len
-1], *v
);
1972 value_set_si(*v
, -1);
1973 Vector_Scale(c
+1, c
+1, *v
, len
-1);
1974 value_decrement(c
[len
-1], c
[len
-1]);
1975 ConstraintSimplify(c
, c
, len
, v
);
1978 static void oppose_constraint(Value
*c
, int len
, Value
*v
)
1980 value_set_si(*v
, -1);
1981 Vector_Scale(c
+1, c
+1, *v
, len
-1);
1982 value_decrement(c
[len
-1], c
[len
-1]);
1985 static bool SplitOnConstraint(Polyhedron
*P
, int i
, int l
, int u
,
1986 int nvar
, int len
, int exist
, int MaxRays
,
1987 Vector
*row
, Value
& f
, bool independent
,
1988 Polyhedron
**pos
, Polyhedron
**neg
)
1990 negative_test_constraint(P
->Constraint
[l
], P
->Constraint
[u
],
1991 row
->p
, nvar
+i
, len
, &f
);
1992 *neg
= AddConstraints(row
->p
, 1, P
, MaxRays
);
1994 /* We found an independent, but useless constraint
1995 * Maybe we should detect this earlier and not
1996 * mark the variable as INDEPENDENT
1998 if (emptyQ((*neg
))) {
1999 Polyhedron_Free(*neg
);
2003 oppose_constraint(row
->p
, len
, &f
);
2004 *pos
= AddConstraints(row
->p
, 1, P
, MaxRays
);
2006 if (emptyQ((*pos
))) {
2007 Polyhedron_Free(*neg
);
2008 Polyhedron_Free(*pos
);
2016 * unimodularly transform P such that constraint r is transformed
2017 * into a constraint that involves only a single (the first)
2018 * existential variable
2021 static Polyhedron
*rotate_along(Polyhedron
*P
, int r
, int nvar
, int exist
,
2027 Vector
*row
= Vector_Alloc(exist
);
2028 Vector_Copy(P
->Constraint
[r
]+1+nvar
, row
->p
, exist
);
2029 Vector_Gcd(row
->p
, exist
, &g
);
2030 if (value_notone_p(g
))
2031 Vector_AntiScale(row
->p
, row
->p
, g
, exist
);
2034 Matrix
*M
= unimodular_complete(row
);
2035 Matrix
*M2
= Matrix_Alloc(P
->Dimension
+1, P
->Dimension
+1);
2036 for (r
= 0; r
< nvar
; ++r
)
2037 value_set_si(M2
->p
[r
][r
], 1);
2038 for ( ; r
< nvar
+exist
; ++r
)
2039 Vector_Copy(M
->p
[r
-nvar
], M2
->p
[r
]+nvar
, exist
);
2040 for ( ; r
< P
->Dimension
+1; ++r
)
2041 value_set_si(M2
->p
[r
][r
], 1);
2042 Polyhedron
*T
= Polyhedron_Image(P
, M2
, MaxRays
);
2051 static bool SplitOnVar(Polyhedron
*P
, int i
,
2052 int nvar
, int len
, int exist
, int MaxRays
,
2053 Vector
*row
, Value
& f
, bool independent
,
2054 Polyhedron
**pos
, Polyhedron
**neg
)
2058 for (int l
= P
->NbEq
; l
< P
->NbConstraints
; ++l
) {
2059 if (value_negz_p(P
->Constraint
[l
][nvar
+i
+1]))
2063 for (j
= 0; j
< exist
; ++j
)
2064 if (j
!= i
&& value_notzero_p(P
->Constraint
[l
][nvar
+j
+1]))
2070 for (int u
= P
->NbEq
; u
< P
->NbConstraints
; ++u
) {
2071 if (value_posz_p(P
->Constraint
[u
][nvar
+i
+1]))
2075 for (j
= 0; j
< exist
; ++j
)
2076 if (j
!= i
&& value_notzero_p(P
->Constraint
[u
][nvar
+j
+1]))
2082 if (SplitOnConstraint(P
, i
, l
, u
,
2083 nvar
, len
, exist
, MaxRays
,
2084 row
, f
, independent
,
2088 SwapColumns(*neg
, nvar
+1, nvar
+1+i
);
2098 static bool double_bound_pair(Polyhedron
*P
, int nvar
, int exist
,
2099 int i
, int l1
, int l2
,
2100 Polyhedron
**pos
, Polyhedron
**neg
)
2104 Vector
*row
= Vector_Alloc(P
->Dimension
+2);
2105 value_set_si(row
->p
[0], 1);
2106 value_oppose(f
, P
->Constraint
[l1
][nvar
+i
+1]);
2107 Vector_Combine(P
->Constraint
[l1
]+1, P
->Constraint
[l2
]+1,
2109 P
->Constraint
[l2
][nvar
+i
+1], f
,
2111 ConstraintSimplify(row
->p
, row
->p
, P
->Dimension
+2, &f
);
2112 *pos
= AddConstraints(row
->p
, 1, P
, 0);
2113 value_set_si(f
, -1);
2114 Vector_Scale(row
->p
+1, row
->p
+1, f
, P
->Dimension
+1);
2115 value_decrement(row
->p
[P
->Dimension
+1], row
->p
[P
->Dimension
+1]);
2116 *neg
= AddConstraints(row
->p
, 1, P
, 0);
2120 return !emptyQ((*pos
)) && !emptyQ((*neg
));
2123 static bool double_bound(Polyhedron
*P
, int nvar
, int exist
,
2124 Polyhedron
**pos
, Polyhedron
**neg
)
2126 for (int i
= 0; i
< exist
; ++i
) {
2128 for (l1
= P
->NbEq
; l1
< P
->NbConstraints
; ++l1
) {
2129 if (value_negz_p(P
->Constraint
[l1
][nvar
+i
+1]))
2131 for (l2
= l1
+ 1; l2
< P
->NbConstraints
; ++l2
) {
2132 if (value_negz_p(P
->Constraint
[l2
][nvar
+i
+1]))
2134 if (double_bound_pair(P
, nvar
, exist
, i
, l1
, l2
, pos
, neg
))
2138 for (l1
= P
->NbEq
; l1
< P
->NbConstraints
; ++l1
) {
2139 if (value_posz_p(P
->Constraint
[l1
][nvar
+i
+1]))
2141 if (l1
< P
->NbConstraints
)
2142 for (l2
= l1
+ 1; l2
< P
->NbConstraints
; ++l2
) {
2143 if (value_posz_p(P
->Constraint
[l2
][nvar
+i
+1]))
2145 if (double_bound_pair(P
, nvar
, exist
, i
, l1
, l2
, pos
, neg
))
2157 INDEPENDENT
= 1 << 2
2160 static evalue
* enumerate_or(Polyhedron
*D
,
2161 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2164 fprintf(stderr
, "\nER: Or\n");
2165 #endif /* DEBUG_ER */
2167 Polyhedron
*N
= D
->next
;
2170 barvinok_enumerate_e(D
, exist
, nparam
, MaxRays
);
2173 for (D
= N
; D
; D
= N
) {
2178 barvinok_enumerate_e(D
, exist
, nparam
, MaxRays
);
2181 free_evalue_refs(EN
);
2191 static evalue
* enumerate_sum(Polyhedron
*P
,
2192 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2194 int nvar
= P
->Dimension
- exist
- nparam
;
2195 int toswap
= nvar
< exist
? nvar
: exist
;
2196 for (int i
= 0; i
< toswap
; ++i
)
2197 SwapColumns(P
, 1 + i
, nvar
+exist
- i
);
2201 fprintf(stderr
, "\nER: Sum\n");
2202 #endif /* DEBUG_ER */
2204 evalue
*EP
= barvinok_enumerate_e(P
, exist
, nparam
, MaxRays
);
2206 for (int i
= 0; i
< /* nvar */ nparam
; ++i
) {
2207 Matrix
*C
= Matrix_Alloc(1, 1 + nparam
+ 1);
2208 value_set_si(C
->p
[0][0], 1);
2210 value_init(split
.d
);
2211 value_set_si(split
.d
, 0);
2212 split
.x
.p
= new_enode(partition
, 4, nparam
);
2213 value_set_si(C
->p
[0][1+i
], 1);
2214 Matrix
*C2
= Matrix_Copy(C
);
2215 EVALUE_SET_DOMAIN(split
.x
.p
->arr
[0],
2216 Constraints2Polyhedron(C2
, MaxRays
));
2218 evalue_set_si(&split
.x
.p
->arr
[1], 1, 1);
2219 value_set_si(C
->p
[0][1+i
], -1);
2220 value_set_si(C
->p
[0][1+nparam
], -1);
2221 EVALUE_SET_DOMAIN(split
.x
.p
->arr
[2],
2222 Constraints2Polyhedron(C
, MaxRays
));
2223 evalue_set_si(&split
.x
.p
->arr
[3], 1, 1);
2225 free_evalue_refs(&split
);
2229 evalue_range_reduction(EP
);
2231 evalue_frac2floor(EP
);
2233 evalue
*sum
= esum(EP
, nvar
);
2235 free_evalue_refs(EP
);
2239 evalue_range_reduction(EP
);
2244 static evalue
* split_sure(Polyhedron
*P
, Polyhedron
*S
,
2245 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2247 int nvar
= P
->Dimension
- exist
- nparam
;
2249 Matrix
*M
= Matrix_Alloc(exist
, S
->Dimension
+2);
2250 for (int i
= 0; i
< exist
; ++i
)
2251 value_set_si(M
->p
[i
][nvar
+i
+1], 1);
2253 S
= DomainAddRays(S
, M
, MaxRays
);
2255 Polyhedron
*F
= DomainAddRays(P
, M
, MaxRays
);
2256 Polyhedron
*D
= DomainDifference(F
, S
, MaxRays
);
2258 D
= Disjoint_Domain(D
, 0, MaxRays
);
2263 M
= Matrix_Alloc(P
->Dimension
+1-exist
, P
->Dimension
+1);
2264 for (int j
= 0; j
< nvar
; ++j
)
2265 value_set_si(M
->p
[j
][j
], 1);
2266 for (int j
= 0; j
< nparam
+1; ++j
)
2267 value_set_si(M
->p
[nvar
+j
][nvar
+exist
+j
], 1);
2268 Polyhedron
*T
= Polyhedron_Image(S
, M
, MaxRays
);
2269 evalue
*EP
= barvinok_enumerate_e(T
, 0, nparam
, MaxRays
);
2274 for (Polyhedron
*Q
= D
; Q
; Q
= Q
->next
) {
2275 Polyhedron
*N
= Q
->next
;
2277 T
= DomainIntersection(P
, Q
, MaxRays
);
2278 evalue
*E
= barvinok_enumerate_e(T
, exist
, nparam
, MaxRays
);
2280 free_evalue_refs(E
);
2289 static evalue
* enumerate_sure(Polyhedron
*P
,
2290 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2294 int nvar
= P
->Dimension
- exist
- nparam
;
2300 for (i
= 0; i
< exist
; ++i
) {
2301 Matrix
*M
= Matrix_Alloc(S
->NbConstraints
, S
->Dimension
+2);
2303 value_set_si(lcm
, 1);
2304 for (int j
= 0; j
< S
->NbConstraints
; ++j
) {
2305 if (value_negz_p(S
->Constraint
[j
][1+nvar
+i
]))
2307 if (value_one_p(S
->Constraint
[j
][1+nvar
+i
]))
2309 value_lcm(lcm
, S
->Constraint
[j
][1+nvar
+i
], &lcm
);
2312 for (int j
= 0; j
< S
->NbConstraints
; ++j
) {
2313 if (value_negz_p(S
->Constraint
[j
][1+nvar
+i
]))
2315 if (value_one_p(S
->Constraint
[j
][1+nvar
+i
]))
2317 value_division(f
, lcm
, S
->Constraint
[j
][1+nvar
+i
]);
2318 Vector_Scale(S
->Constraint
[j
], M
->p
[c
], f
, S
->Dimension
+2);
2319 value_substract(M
->p
[c
][S
->Dimension
+1],
2320 M
->p
[c
][S
->Dimension
+1],
2322 value_increment(M
->p
[c
][S
->Dimension
+1],
2323 M
->p
[c
][S
->Dimension
+1]);
2327 S
= AddConstraints(M
->p
[0], c
, S
, MaxRays
);
2342 fprintf(stderr
, "\nER: Sure\n");
2343 #endif /* DEBUG_ER */
2345 return split_sure(P
, S
, exist
, nparam
, MaxRays
);
2348 static evalue
* enumerate_sure2(Polyhedron
*P
,
2349 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2351 int nvar
= P
->Dimension
- exist
- nparam
;
2353 for (r
= 0; r
< P
->NbRays
; ++r
)
2354 if (value_one_p(P
->Ray
[r
][0]) &&
2355 value_one_p(P
->Ray
[r
][P
->Dimension
+1]))
2361 Matrix
*M
= Matrix_Alloc(nvar
+ 1 + nparam
, P
->Dimension
+2);
2362 for (int i
= 0; i
< nvar
; ++i
)
2363 value_set_si(M
->p
[i
][1+i
], 1);
2364 for (int i
= 0; i
< nparam
; ++i
)
2365 value_set_si(M
->p
[i
+nvar
][1+nvar
+exist
+i
], 1);
2366 Vector_Copy(P
->Ray
[r
]+1+nvar
, M
->p
[nvar
+nparam
]+1+nvar
, exist
);
2367 value_set_si(M
->p
[nvar
+nparam
][0], 1);
2368 value_set_si(M
->p
[nvar
+nparam
][P
->Dimension
+1], 1);
2369 Polyhedron
* F
= Rays2Polyhedron(M
, MaxRays
);
2372 Polyhedron
*I
= DomainIntersection(F
, P
, MaxRays
);
2376 fprintf(stderr
, "\nER: Sure2\n");
2377 #endif /* DEBUG_ER */
2379 return split_sure(P
, I
, exist
, nparam
, MaxRays
);
2382 static evalue
* enumerate_cyclic(Polyhedron
*P
,
2383 unsigned exist
, unsigned nparam
,
2384 evalue
* EP
, int r
, int p
, unsigned MaxRays
)
2386 int nvar
= P
->Dimension
- exist
- nparam
;
2388 /* If EP in its fractional maps only contains references
2389 * to the remainder parameter with appropriate coefficients
2390 * then we could in principle avoid adding existentially
2391 * quantified variables to the validity domains.
2392 * We'd have to replace the remainder by m { p/m }
2393 * and multiply with an appropriate factor that is one
2394 * only in the appropriate range.
2395 * This last multiplication can be avoided if EP
2396 * has a single validity domain with no (further)
2397 * constraints on the remainder parameter
2400 Matrix
*CT
= Matrix_Alloc(nparam
+1, nparam
+3);
2401 Matrix
*M
= Matrix_Alloc(1, 1+nparam
+3);
2402 for (int j
= 0; j
< nparam
; ++j
)
2404 value_set_si(CT
->p
[j
][j
], 1);
2405 value_set_si(CT
->p
[p
][nparam
+1], 1);
2406 value_set_si(CT
->p
[nparam
][nparam
+2], 1);
2407 value_set_si(M
->p
[0][1+p
], -1);
2408 value_absolute(M
->p
[0][1+nparam
], P
->Ray
[0][1+nvar
+exist
+p
]);
2409 value_set_si(M
->p
[0][1+nparam
+1], 1);
2410 Polyhedron
*CEq
= Constraints2Polyhedron(M
, 1);
2412 addeliminatedparams_enum(EP
, CT
, CEq
, MaxRays
, nparam
);
2413 Polyhedron_Free(CEq
);
2419 static void enumerate_vd_add_ray(evalue
*EP
, Matrix
*Rays
, unsigned MaxRays
)
2421 if (value_notzero_p(EP
->d
))
2424 assert(EP
->x
.p
->type
== partition
);
2425 assert(EP
->x
.p
->pos
== EVALUE_DOMAIN(EP
->x
.p
->arr
[0])->Dimension
);
2426 for (int i
= 0; i
< EP
->x
.p
->size
/2; ++i
) {
2427 Polyhedron
*D
= EVALUE_DOMAIN(EP
->x
.p
->arr
[2*i
]);
2428 Polyhedron
*N
= DomainAddRays(D
, Rays
, MaxRays
);
2429 EVALUE_SET_DOMAIN(EP
->x
.p
->arr
[2*i
], N
);
2434 static evalue
* enumerate_line(Polyhedron
*P
,
2435 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2441 fprintf(stderr
, "\nER: Line\n");
2442 #endif /* DEBUG_ER */
2444 int nvar
= P
->Dimension
- exist
- nparam
;
2446 for (i
= 0; i
< nparam
; ++i
)
2447 if (value_notzero_p(P
->Ray
[0][1+nvar
+exist
+i
]))
2450 for (j
= i
+1; j
< nparam
; ++j
)
2451 if (value_notzero_p(P
->Ray
[0][1+nvar
+exist
+i
]))
2453 assert(j
>= nparam
); // for now
2455 Matrix
*M
= Matrix_Alloc(2, P
->Dimension
+2);
2456 value_set_si(M
->p
[0][0], 1);
2457 value_set_si(M
->p
[0][1+nvar
+exist
+i
], 1);
2458 value_set_si(M
->p
[1][0], 1);
2459 value_set_si(M
->p
[1][1+nvar
+exist
+i
], -1);
2460 value_absolute(M
->p
[1][1+P
->Dimension
], P
->Ray
[0][1+nvar
+exist
+i
]);
2461 value_decrement(M
->p
[1][1+P
->Dimension
], M
->p
[1][1+P
->Dimension
]);
2462 Polyhedron
*S
= AddConstraints(M
->p
[0], 2, P
, MaxRays
);
2463 evalue
*EP
= barvinok_enumerate_e(S
, exist
, nparam
, MaxRays
);
2467 return enumerate_cyclic(P
, exist
, nparam
, EP
, 0, i
, MaxRays
);
2470 static int single_param_pos(Polyhedron
*P
, unsigned exist
, unsigned nparam
,
2473 int nvar
= P
->Dimension
- exist
- nparam
;
2474 if (First_Non_Zero(P
->Ray
[r
]+1, nvar
) != -1)
2476 int i
= First_Non_Zero(P
->Ray
[r
]+1+nvar
+exist
, nparam
);
2479 if (First_Non_Zero(P
->Ray
[r
]+1+nvar
+exist
+1, nparam
-i
-1) != -1)
2484 static evalue
* enumerate_remove_ray(Polyhedron
*P
, int r
,
2485 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2488 fprintf(stderr
, "\nER: RedundantRay\n");
2489 #endif /* DEBUG_ER */
2493 value_set_si(one
, 1);
2494 int len
= P
->NbRays
-1;
2495 Matrix
*M
= Matrix_Alloc(2 * len
, P
->Dimension
+2);
2496 Vector_Copy(P
->Ray
[0], M
->p
[0], r
* (P
->Dimension
+2));
2497 Vector_Copy(P
->Ray
[r
+1], M
->p
[r
], (len
-r
) * (P
->Dimension
+2));
2498 for (int j
= 0; j
< P
->NbRays
; ++j
) {
2501 Vector_Combine(P
->Ray
[j
], P
->Ray
[r
], M
->p
[len
+j
-(j
>r
)],
2502 one
, P
->Ray
[j
][P
->Dimension
+1], P
->Dimension
+2);
2505 P
= Rays2Polyhedron(M
, MaxRays
);
2507 evalue
*EP
= barvinok_enumerate_e(P
, exist
, nparam
, MaxRays
);
2514 static evalue
* enumerate_redundant_ray(Polyhedron
*P
,
2515 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2517 assert(P
->NbBid
== 0);
2518 int nvar
= P
->Dimension
- exist
- nparam
;
2522 for (int r
= 0; r
< P
->NbRays
; ++r
) {
2523 if (value_notzero_p(P
->Ray
[r
][P
->Dimension
+1]))
2525 int i1
= single_param_pos(P
, exist
, nparam
, r
);
2528 for (int r2
= r
+1; r2
< P
->NbRays
; ++r2
) {
2529 if (value_notzero_p(P
->Ray
[r2
][P
->Dimension
+1]))
2531 int i2
= single_param_pos(P
, exist
, nparam
, r2
);
2537 value_division(m
, P
->Ray
[r
][1+nvar
+exist
+i1
],
2538 P
->Ray
[r2
][1+nvar
+exist
+i1
]);
2539 value_multiply(m
, m
, P
->Ray
[r2
][1+nvar
+exist
+i1
]);
2540 /* r2 divides r => r redundant */
2541 if (value_eq(m
, P
->Ray
[r
][1+nvar
+exist
+i1
])) {
2543 return enumerate_remove_ray(P
, r
, exist
, nparam
, MaxRays
);
2546 value_division(m
, P
->Ray
[r2
][1+nvar
+exist
+i1
],
2547 P
->Ray
[r
][1+nvar
+exist
+i1
]);
2548 value_multiply(m
, m
, P
->Ray
[r
][1+nvar
+exist
+i1
]);
2549 /* r divides r2 => r2 redundant */
2550 if (value_eq(m
, P
->Ray
[r2
][1+nvar
+exist
+i1
])) {
2552 return enumerate_remove_ray(P
, r2
, exist
, nparam
, MaxRays
);
2560 static Polyhedron
*upper_bound(Polyhedron
*P
,
2561 int pos
, Value
*max
, Polyhedron
**R
)
2570 for (Polyhedron
*Q
= P
; Q
; Q
= N
) {
2572 for (r
= 0; r
< P
->NbRays
; ++r
) {
2573 if (value_zero_p(P
->Ray
[r
][P
->Dimension
+1]) &&
2574 value_pos_p(P
->Ray
[r
][1+pos
]))
2577 if (r
< P
->NbRays
) {
2585 for (r
= 0; r
< P
->NbRays
; ++r
) {
2586 if (value_zero_p(P
->Ray
[r
][P
->Dimension
+1]))
2588 mpz_fdiv_q(v
, P
->Ray
[r
][1+pos
], P
->Ray
[r
][1+P
->Dimension
]);
2589 if ((!Q
->next
&& r
== 0) || value_gt(v
, *max
))
2590 value_assign(*max
, v
);
2597 static evalue
* enumerate_ray(Polyhedron
*P
,
2598 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2600 assert(P
->NbBid
== 0);
2601 int nvar
= P
->Dimension
- exist
- nparam
;
2604 for (r
= 0; r
< P
->NbRays
; ++r
)
2605 if (value_zero_p(P
->Ray
[r
][P
->Dimension
+1]))
2611 for (r2
= r
+1; r2
< P
->NbRays
; ++r2
)
2612 if (value_zero_p(P
->Ray
[r2
][P
->Dimension
+1]))
2614 if (r2
< P
->NbRays
) {
2616 return enumerate_sum(P
, exist
, nparam
, MaxRays
);
2620 fprintf(stderr
, "\nER: Ray\n");
2621 #endif /* DEBUG_ER */
2627 value_set_si(one
, 1);
2628 int i
= single_param_pos(P
, exist
, nparam
, r
);
2629 assert(i
!= -1); // for now;
2631 Matrix
*M
= Matrix_Alloc(P
->NbRays
, P
->Dimension
+2);
2632 for (int j
= 0; j
< P
->NbRays
; ++j
) {
2633 Vector_Combine(P
->Ray
[j
], P
->Ray
[r
], M
->p
[j
],
2634 one
, P
->Ray
[j
][P
->Dimension
+1], P
->Dimension
+2);
2636 Polyhedron
*S
= Rays2Polyhedron(M
, MaxRays
);
2638 Polyhedron
*D
= DomainDifference(P
, S
, MaxRays
);
2640 // Polyhedron_Print(stderr, P_VALUE_FMT, D);
2641 assert(value_pos_p(P
->Ray
[r
][1+nvar
+exist
+i
])); // for now
2643 D
= upper_bound(D
, nvar
+exist
+i
, &m
, &R
);
2647 M
= Matrix_Alloc(2, P
->Dimension
+2);
2648 value_set_si(M
->p
[0][0], 1);
2649 value_set_si(M
->p
[1][0], 1);
2650 value_set_si(M
->p
[0][1+nvar
+exist
+i
], -1);
2651 value_set_si(M
->p
[1][1+nvar
+exist
+i
], 1);
2652 value_assign(M
->p
[0][1+P
->Dimension
], m
);
2653 value_oppose(M
->p
[1][1+P
->Dimension
], m
);
2654 value_addto(M
->p
[1][1+P
->Dimension
], M
->p
[1][1+P
->Dimension
],
2655 P
->Ray
[r
][1+nvar
+exist
+i
]);
2656 value_decrement(M
->p
[1][1+P
->Dimension
], M
->p
[1][1+P
->Dimension
]);
2657 // Matrix_Print(stderr, P_VALUE_FMT, M);
2658 D
= AddConstraints(M
->p
[0], 2, P
, MaxRays
);
2659 // Polyhedron_Print(stderr, P_VALUE_FMT, D);
2660 value_substract(M
->p
[0][1+P
->Dimension
], M
->p
[0][1+P
->Dimension
],
2661 P
->Ray
[r
][1+nvar
+exist
+i
]);
2662 // Matrix_Print(stderr, P_VALUE_FMT, M);
2663 S
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
2664 // Polyhedron_Print(stderr, P_VALUE_FMT, S);
2667 evalue
*EP
= barvinok_enumerate_e(D
, exist
, nparam
, MaxRays
);
2672 if (value_notone_p(P
->Ray
[r
][1+nvar
+exist
+i
]))
2673 EP
= enumerate_cyclic(P
, exist
, nparam
, EP
, r
, i
, MaxRays
);
2675 M
= Matrix_Alloc(1, nparam
+2);
2676 value_set_si(M
->p
[0][0], 1);
2677 value_set_si(M
->p
[0][1+i
], 1);
2678 enumerate_vd_add_ray(EP
, M
, MaxRays
);
2683 evalue
*E
= barvinok_enumerate_e(S
, exist
, nparam
, MaxRays
);
2685 free_evalue_refs(E
);
2692 evalue
*ER
= enumerate_or(R
, exist
, nparam
, MaxRays
);
2694 free_evalue_refs(ER
);
2701 static evalue
* new_zero_ep()
2706 evalue_set_si(EP
, 0, 1);
2710 static evalue
* enumerate_vd(Polyhedron
**PA
,
2711 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2713 Polyhedron
*P
= *PA
;
2714 int nvar
= P
->Dimension
- exist
- nparam
;
2715 Param_Polyhedron
*PP
= NULL
;
2716 Polyhedron
*C
= Universe_Polyhedron(nparam
);
2720 PP
= Polyhedron2Param_SimplifiedDomain(&PR
,C
,MaxRays
,&CEq
,&CT
);
2724 Param_Domain
*D
, *last
;
2727 for (nd
= 0, D
=PP
->D
; D
; D
=D
->next
, ++nd
)
2730 Polyhedron
**VD
= new Polyhedron_p
[nd
];
2731 Polyhedron
**fVD
= new Polyhedron_p
[nd
];
2732 for(nd
= 0, D
=PP
->D
; D
; D
=D
->next
) {
2733 Polyhedron
*rVD
= reduce_domain(D
->Domain
, CT
, CEq
,
2747 /* This doesn't seem to have any effect */
2749 Polyhedron
*CA
= align_context(VD
[0], P
->Dimension
, MaxRays
);
2751 P
= DomainIntersection(P
, CA
, MaxRays
);
2754 Polyhedron_Free(CA
);
2759 if (!EP
&& CT
->NbColumns
!= CT
->NbRows
) {
2760 Polyhedron
*CEqr
= DomainImage(CEq
, CT
, MaxRays
);
2761 Polyhedron
*CA
= align_context(CEqr
, PR
->Dimension
, MaxRays
);
2762 Polyhedron
*I
= DomainIntersection(PR
, CA
, MaxRays
);
2763 Polyhedron_Free(CEqr
);
2764 Polyhedron_Free(CA
);
2766 fprintf(stderr
, "\nER: Eliminate\n");
2767 #endif /* DEBUG_ER */
2768 nparam
-= CT
->NbColumns
- CT
->NbRows
;
2769 EP
= barvinok_enumerate_e(I
, exist
, nparam
, MaxRays
);
2770 nparam
+= CT
->NbColumns
- CT
->NbRows
;
2771 addeliminatedparams_enum(EP
, CT
, CEq
, MaxRays
, nparam
);
2775 Polyhedron_Free(PR
);
2778 if (!EP
&& nd
> 1) {
2780 fprintf(stderr
, "\nER: VD\n");
2781 #endif /* DEBUG_ER */
2782 for (int i
= 0; i
< nd
; ++i
) {
2783 Polyhedron
*CA
= align_context(VD
[i
], P
->Dimension
, MaxRays
);
2784 Polyhedron
*I
= DomainIntersection(P
, CA
, MaxRays
);
2787 EP
= barvinok_enumerate_e(I
, exist
, nparam
, MaxRays
);
2789 evalue
*E
= barvinok_enumerate_e(I
, exist
, nparam
, MaxRays
);
2791 free_evalue_refs(E
);
2795 Polyhedron_Free(CA
);
2799 for (int i
= 0; i
< nd
; ++i
) {
2800 Polyhedron_Free(VD
[i
]);
2801 Polyhedron_Free(fVD
[i
]);
2807 if (!EP
&& nvar
== 0) {
2810 Param_Vertices
*V
, *V2
;
2811 Matrix
* M
= Matrix_Alloc(1, P
->Dimension
+2);
2813 FORALL_PVertex_in_ParamPolyhedron(V
, last
, PP
) {
2815 FORALL_PVertex_in_ParamPolyhedron(V2
, last
, PP
) {
2822 for (int i
= 0; i
< exist
; ++i
) {
2823 value_oppose(f
, V
->Vertex
->p
[i
][nparam
+1]);
2824 Vector_Combine(V
->Vertex
->p
[i
],
2826 M
->p
[0] + 1 + nvar
+ exist
,
2827 V2
->Vertex
->p
[i
][nparam
+1],
2831 for (j
= 0; j
< nparam
; ++j
)
2832 if (value_notzero_p(M
->p
[0][1+nvar
+exist
+j
]))
2836 ConstraintSimplify(M
->p
[0], M
->p
[0],
2837 P
->Dimension
+2, &f
);
2838 value_set_si(M
->p
[0][0], 0);
2839 Polyhedron
*para
= AddConstraints(M
->p
[0], 1, P
,
2842 Polyhedron_Free(para
);
2845 Polyhedron
*pos
, *neg
;
2846 value_set_si(M
->p
[0][0], 1);
2847 value_decrement(M
->p
[0][P
->Dimension
+1],
2848 M
->p
[0][P
->Dimension
+1]);
2849 neg
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
2850 value_set_si(f
, -1);
2851 Vector_Scale(M
->p
[0]+1, M
->p
[0]+1, f
,
2853 value_decrement(M
->p
[0][P
->Dimension
+1],
2854 M
->p
[0][P
->Dimension
+1]);
2855 value_decrement(M
->p
[0][P
->Dimension
+1],
2856 M
->p
[0][P
->Dimension
+1]);
2857 pos
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
2858 if (emptyQ(neg
) && emptyQ(pos
)) {
2859 Polyhedron_Free(para
);
2860 Polyhedron_Free(pos
);
2861 Polyhedron_Free(neg
);
2865 fprintf(stderr
, "\nER: Order\n");
2866 #endif /* DEBUG_ER */
2867 EP
= barvinok_enumerate_e(para
, exist
, nparam
, MaxRays
);
2870 E
= barvinok_enumerate_e(pos
, exist
, nparam
, MaxRays
);
2872 free_evalue_refs(E
);
2876 E
= barvinok_enumerate_e(neg
, exist
, nparam
, MaxRays
);
2878 free_evalue_refs(E
);
2881 Polyhedron_Free(para
);
2882 Polyhedron_Free(pos
);
2883 Polyhedron_Free(neg
);
2888 } END_FORALL_PVertex_in_ParamPolyhedron
;
2891 } END_FORALL_PVertex_in_ParamPolyhedron
;
2894 /* Search for vertex coordinate to split on */
2895 /* First look for one independent of the parameters */
2896 FORALL_PVertex_in_ParamPolyhedron(V
, last
, PP
) {
2897 for (int i
= 0; i
< exist
; ++i
) {
2899 for (j
= 0; j
< nparam
; ++j
)
2900 if (value_notzero_p(V
->Vertex
->p
[i
][j
]))
2904 value_set_si(M
->p
[0][0], 1);
2905 Vector_Set(M
->p
[0]+1, 0, nvar
+exist
);
2906 Vector_Copy(V
->Vertex
->p
[i
],
2907 M
->p
[0] + 1 + nvar
+ exist
, nparam
+1);
2908 value_oppose(M
->p
[0][1+nvar
+i
],
2909 V
->Vertex
->p
[i
][nparam
+1]);
2911 Polyhedron
*pos
, *neg
;
2912 value_set_si(M
->p
[0][0], 1);
2913 value_decrement(M
->p
[0][P
->Dimension
+1],
2914 M
->p
[0][P
->Dimension
+1]);
2915 neg
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
2916 value_set_si(f
, -1);
2917 Vector_Scale(M
->p
[0]+1, M
->p
[0]+1, f
,
2919 value_decrement(M
->p
[0][P
->Dimension
+1],
2920 M
->p
[0][P
->Dimension
+1]);
2921 value_decrement(M
->p
[0][P
->Dimension
+1],
2922 M
->p
[0][P
->Dimension
+1]);
2923 pos
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
2924 if (emptyQ(neg
) || emptyQ(pos
)) {
2925 Polyhedron_Free(pos
);
2926 Polyhedron_Free(neg
);
2929 Polyhedron_Free(pos
);
2930 value_increment(M
->p
[0][P
->Dimension
+1],
2931 M
->p
[0][P
->Dimension
+1]);
2932 pos
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
2934 fprintf(stderr
, "\nER: Vertex\n");
2935 #endif /* DEBUG_ER */
2937 EP
= enumerate_or(pos
, exist
, nparam
, MaxRays
);
2942 } END_FORALL_PVertex_in_ParamPolyhedron
;
2946 /* Search for vertex coordinate to split on */
2947 /* Now look for one that depends on the parameters */
2948 FORALL_PVertex_in_ParamPolyhedron(V
, last
, PP
) {
2949 for (int i
= 0; i
< exist
; ++i
) {
2950 value_set_si(M
->p
[0][0], 1);
2951 Vector_Set(M
->p
[0]+1, 0, nvar
+exist
);
2952 Vector_Copy(V
->Vertex
->p
[i
],
2953 M
->p
[0] + 1 + nvar
+ exist
, nparam
+1);
2954 value_oppose(M
->p
[0][1+nvar
+i
],
2955 V
->Vertex
->p
[i
][nparam
+1]);
2957 Polyhedron
*pos
, *neg
;
2958 value_set_si(M
->p
[0][0], 1);
2959 value_decrement(M
->p
[0][P
->Dimension
+1],
2960 M
->p
[0][P
->Dimension
+1]);
2961 neg
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
2962 value_set_si(f
, -1);
2963 Vector_Scale(M
->p
[0]+1, M
->p
[0]+1, f
,
2965 value_decrement(M
->p
[0][P
->Dimension
+1],
2966 M
->p
[0][P
->Dimension
+1]);
2967 value_decrement(M
->p
[0][P
->Dimension
+1],
2968 M
->p
[0][P
->Dimension
+1]);
2969 pos
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
2970 if (emptyQ(neg
) || emptyQ(pos
)) {
2971 Polyhedron_Free(pos
);
2972 Polyhedron_Free(neg
);
2975 Polyhedron_Free(pos
);
2976 value_increment(M
->p
[0][P
->Dimension
+1],
2977 M
->p
[0][P
->Dimension
+1]);
2978 pos
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
2980 fprintf(stderr
, "\nER: ParamVertex\n");
2981 #endif /* DEBUG_ER */
2983 EP
= enumerate_or(pos
, exist
, nparam
, MaxRays
);
2988 } END_FORALL_PVertex_in_ParamPolyhedron
;
2996 Polyhedron_Free(CEq
);
3000 Param_Polyhedron_Free(PP
);
3007 evalue
*barvinok_enumerate_pip(Polyhedron
*P
,
3008 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
3013 evalue
*barvinok_enumerate_pip(Polyhedron
*P
,
3014 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
3016 int nvar
= P
->Dimension
- exist
- nparam
;
3017 evalue
*EP
= new_zero_ep();
3018 Polyhedron
*Q
, *N
, *T
= 0;
3024 fprintf(stderr
, "\nER: PIP\n");
3025 #endif /* DEBUG_ER */
3027 for (int i
= 0; i
< P
->Dimension
; ++i
) {
3030 bool posray
= false;
3031 bool negray
= false;
3032 value_set_si(min
, 0);
3033 for (int j
= 0; j
< P
->NbRays
; ++j
) {
3034 if (value_pos_p(P
->Ray
[j
][1+i
])) {
3036 if (value_zero_p(P
->Ray
[j
][1+P
->Dimension
]))
3038 } else if (value_neg_p(P
->Ray
[j
][1+i
])) {
3040 if (value_zero_p(P
->Ray
[j
][1+P
->Dimension
]))
3044 P
->Ray
[j
][1+i
], P
->Ray
[j
][1+P
->Dimension
]);
3045 if (value_lt(tmp
, min
))
3046 value_assign(min
, tmp
);
3051 assert(!(posray
&& negray
));
3052 assert(!negray
); // for now
3053 Polyhedron
*O
= T
? T
: P
;
3054 /* shift by a safe amount */
3055 Matrix
*M
= Matrix_Alloc(O
->NbRays
, O
->Dimension
+2);
3056 Vector_Copy(O
->Ray
[0], M
->p
[0], O
->NbRays
* (O
->Dimension
+2));
3057 for (int j
= 0; j
< P
->NbRays
; ++j
) {
3058 if (value_notzero_p(M
->p
[j
][1+P
->Dimension
])) {
3059 value_multiply(tmp
, min
, M
->p
[j
][1+P
->Dimension
]);
3060 value_substract(M
->p
[j
][1+i
], M
->p
[j
][1+i
], tmp
);
3065 T
= Rays2Polyhedron(M
, MaxRays
);
3068 /* negating a parameter requires that we substitute in the
3069 * sign again afterwards.
3072 assert(i
< nvar
+exist
);
3074 T
= Polyhedron_Copy(P
);
3075 for (int j
= 0; j
< T
->NbRays
; ++j
)
3076 value_oppose(T
->Ray
[j
][1+i
], T
->Ray
[j
][1+i
]);
3077 for (int j
= 0; j
< T
->NbConstraints
; ++j
)
3078 value_oppose(T
->Constraint
[j
][1+i
], T
->Constraint
[j
][1+i
]);
3084 Polyhedron
*D
= pip_lexmin(T
? T
: P
, exist
, nparam
);
3085 for (Q
= D
; Q
; Q
= N
) {
3089 exist
= Q
->Dimension
- nvar
- nparam
;
3090 E
= barvinok_enumerate_e(Q
, exist
, nparam
, MaxRays
);
3093 free_evalue_refs(E
);
3105 static bool is_single(Value
*row
, int pos
, int len
)
3107 return First_Non_Zero(row
, pos
) == -1 &&
3108 First_Non_Zero(row
+pos
+1, len
-pos
-1) == -1;
3111 static evalue
* barvinok_enumerate_e_r(Polyhedron
*P
,
3112 unsigned exist
, unsigned nparam
, unsigned MaxRays
);
3115 static int er_level
= 0;
3117 evalue
* barvinok_enumerate_e(Polyhedron
*P
,
3118 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
3120 fprintf(stderr
, "\nER: level %i\n", er_level
);
3121 int nvar
= P
->Dimension
- exist
- nparam
;
3122 fprintf(stderr
, "%d %d %d\n", nvar
, exist
, nparam
);
3124 Polyhedron_Print(stderr
, P_VALUE_FMT
, P
);
3126 P
= DomainConstraintSimplify(Polyhedron_Copy(P
), MaxRays
);
3127 evalue
*EP
= barvinok_enumerate_e_r(P
, exist
, nparam
, MaxRays
);
3133 evalue
* barvinok_enumerate_e(Polyhedron
*P
,
3134 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
3136 P
= DomainConstraintSimplify(Polyhedron_Copy(P
), MaxRays
);
3137 evalue
*EP
= barvinok_enumerate_e_r(P
, exist
, nparam
, MaxRays
);
3143 static evalue
* barvinok_enumerate_e_r(Polyhedron
*P
,
3144 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
3147 Polyhedron
*U
= Universe_Polyhedron(nparam
);
3148 evalue
*EP
= barvinok_enumerate_ev(P
, U
, MaxRays
);
3149 //char *param_name[] = {"P", "Q", "R", "S", "T" };
3150 //print_evalue(stdout, EP, param_name);
3155 int nvar
= P
->Dimension
- exist
- nparam
;
3156 int len
= P
->Dimension
+ 2;
3159 return new_zero_ep();
3161 if (nvar
== 0 && nparam
== 0) {
3162 evalue
*EP
= new_zero_ep();
3163 barvinok_count(P
, &EP
->x
.n
, MaxRays
);
3164 if (value_pos_p(EP
->x
.n
))
3165 value_set_si(EP
->x
.n
, 1);
3170 for (r
= 0; r
< P
->NbRays
; ++r
)
3171 if (value_zero_p(P
->Ray
[r
][0]) ||
3172 value_zero_p(P
->Ray
[r
][P
->Dimension
+1])) {
3174 for (i
= 0; i
< nvar
; ++i
)
3175 if (value_notzero_p(P
->Ray
[r
][i
+1]))
3179 for (i
= nvar
+ exist
; i
< nvar
+ exist
+ nparam
; ++i
)
3180 if (value_notzero_p(P
->Ray
[r
][i
+1]))
3182 if (i
>= nvar
+ exist
+ nparam
)
3185 if (r
< P
->NbRays
) {
3186 evalue
*EP
= new_zero_ep();
3187 value_set_si(EP
->x
.n
, -1);
3192 for (r
= 0; r
< P
->NbEq
; ++r
)
3193 if ((first
= First_Non_Zero(P
->Constraint
[r
]+1+nvar
, exist
)) != -1)
3196 if (First_Non_Zero(P
->Constraint
[r
]+1+nvar
+first
+1,
3197 exist
-first
-1) != -1) {
3198 Polyhedron
*T
= rotate_along(P
, r
, nvar
, exist
, MaxRays
);
3200 fprintf(stderr
, "\nER: Equality\n");
3201 #endif /* DEBUG_ER */
3202 evalue
*EP
= barvinok_enumerate_e(T
, exist
-1, nparam
, MaxRays
);
3207 fprintf(stderr
, "\nER: Fixed\n");
3208 #endif /* DEBUG_ER */
3210 return barvinok_enumerate_e(P
, exist
-1, nparam
, MaxRays
);
3212 Polyhedron
*T
= Polyhedron_Copy(P
);
3213 SwapColumns(T
, nvar
+1, nvar
+1+first
);
3214 evalue
*EP
= barvinok_enumerate_e(T
, exist
-1, nparam
, MaxRays
);
3221 Vector
*row
= Vector_Alloc(len
);
3222 value_set_si(row
->p
[0], 1);
3227 enum constraint
* info
= new constraint
[exist
];
3228 for (int i
= 0; i
< exist
; ++i
) {
3230 for (int l
= P
->NbEq
; l
< P
->NbConstraints
; ++l
) {
3231 if (value_negz_p(P
->Constraint
[l
][nvar
+i
+1]))
3233 bool l_parallel
= is_single(P
->Constraint
[l
]+nvar
+1, i
, exist
);
3234 for (int u
= P
->NbEq
; u
< P
->NbConstraints
; ++u
) {
3235 if (value_posz_p(P
->Constraint
[u
][nvar
+i
+1]))
3237 bool lu_parallel
= l_parallel
||
3238 is_single(P
->Constraint
[u
]+nvar
+1, i
, exist
);
3239 value_oppose(f
, P
->Constraint
[u
][nvar
+i
+1]);
3240 Vector_Combine(P
->Constraint
[l
]+1, P
->Constraint
[u
]+1, row
->p
+1,
3241 f
, P
->Constraint
[l
][nvar
+i
+1], len
-1);
3242 if (!(info
[i
] & INDEPENDENT
)) {
3244 for (j
= 0; j
< exist
; ++j
)
3245 if (j
!= i
&& value_notzero_p(row
->p
[nvar
+j
+1]))
3248 //printf("independent: i: %d, l: %d, u: %d\n", i, l, u);
3249 info
[i
] = (constraint
)(info
[i
] | INDEPENDENT
);
3252 if (info
[i
] & ALL_POS
) {
3253 value_addto(row
->p
[len
-1], row
->p
[len
-1],
3254 P
->Constraint
[l
][nvar
+i
+1]);
3255 value_addto(row
->p
[len
-1], row
->p
[len
-1], f
);
3256 value_multiply(f
, f
, P
->Constraint
[l
][nvar
+i
+1]);
3257 value_substract(row
->p
[len
-1], row
->p
[len
-1], f
);
3258 value_decrement(row
->p
[len
-1], row
->p
[len
-1]);
3259 ConstraintSimplify(row
->p
, row
->p
, len
, &f
);
3260 value_set_si(f
, -1);
3261 Vector_Scale(row
->p
+1, row
->p
+1, f
, len
-1);
3262 value_decrement(row
->p
[len
-1], row
->p
[len
-1]);
3263 Polyhedron
*T
= AddConstraints(row
->p
, 1, P
, MaxRays
);
3265 //printf("not all_pos: i: %d, l: %d, u: %d\n", i, l, u);
3266 info
[i
] = (constraint
)(info
[i
] ^ ALL_POS
);
3268 //puts("pos remainder");
3269 //Polyhedron_Print(stdout, P_VALUE_FMT, T);
3272 if (!(info
[i
] & ONE_NEG
)) {
3274 negative_test_constraint(P
->Constraint
[l
],
3276 row
->p
, nvar
+i
, len
, &f
);
3277 oppose_constraint(row
->p
, len
, &f
);
3278 Polyhedron
*T
= AddConstraints(row
->p
, 1, P
, MaxRays
);
3280 //printf("one_neg i: %d, l: %d, u: %d\n", i, l, u);
3281 info
[i
] = (constraint
)(info
[i
] | ONE_NEG
);
3283 //puts("neg remainder");
3284 //Polyhedron_Print(stdout, P_VALUE_FMT, T);
3288 if (!(info
[i
] & ALL_POS
) && (info
[i
] & ONE_NEG
))
3292 if (info
[i
] & ALL_POS
)
3299 for (int i = 0; i < exist; ++i)
3300 printf("%i: %i\n", i, info[i]);
3302 for (int i
= 0; i
< exist
; ++i
)
3303 if (info
[i
] & ALL_POS
) {
3305 fprintf(stderr
, "\nER: Positive\n");
3306 #endif /* DEBUG_ER */
3308 // Maybe we should chew off some of the fat here
3309 Matrix
*M
= Matrix_Alloc(P
->Dimension
, P
->Dimension
+1);
3310 for (int j
= 0; j
< P
->Dimension
; ++j
)
3311 value_set_si(M
->p
[j
][j
+ (j
>= i
+nvar
)], 1);
3312 Polyhedron
*T
= Polyhedron_Image(P
, M
, MaxRays
);
3314 evalue
*EP
= barvinok_enumerate_e(T
, exist
-1, nparam
, MaxRays
);
3321 for (int i
= 0; i
< exist
; ++i
)
3322 if (info
[i
] & ONE_NEG
) {
3324 fprintf(stderr
, "\nER: Negative\n");
3325 #endif /* DEBUG_ER */
3330 return barvinok_enumerate_e(P
, exist
-1, nparam
, MaxRays
);
3332 Polyhedron
*T
= Polyhedron_Copy(P
);
3333 SwapColumns(T
, nvar
+1, nvar
+1+i
);
3334 evalue
*EP
= barvinok_enumerate_e(T
, exist
-1, nparam
, MaxRays
);
3339 for (int i
= 0; i
< exist
; ++i
)
3340 if (info
[i
] & INDEPENDENT
) {
3341 Polyhedron
*pos
, *neg
;
3343 /* Find constraint again and split off negative part */
3345 if (SplitOnVar(P
, i
, nvar
, len
, exist
, MaxRays
,
3346 row
, f
, true, &pos
, &neg
)) {
3348 fprintf(stderr
, "\nER: Split\n");
3349 #endif /* DEBUG_ER */
3352 barvinok_enumerate_e(neg
, exist
-1, nparam
, MaxRays
);
3354 barvinok_enumerate_e(pos
, exist
, nparam
, MaxRays
);
3356 free_evalue_refs(E
);
3358 Polyhedron_Free(neg
);
3359 Polyhedron_Free(pos
);
3373 EP
= enumerate_line(P
, exist
, nparam
, MaxRays
);
3377 EP
= barvinok_enumerate_pip(P
, exist
, nparam
, MaxRays
);
3381 EP
= enumerate_redundant_ray(P
, exist
, nparam
, MaxRays
);
3385 EP
= enumerate_sure(P
, exist
, nparam
, MaxRays
);
3389 EP
= enumerate_ray(P
, exist
, nparam
, MaxRays
);
3393 EP
= enumerate_sure2(P
, exist
, nparam
, MaxRays
);
3397 F
= unfringe(P
, MaxRays
);
3398 if (!PolyhedronIncludes(F
, P
)) {
3400 fprintf(stderr
, "\nER: Fringed\n");
3401 #endif /* DEBUG_ER */
3402 EP
= barvinok_enumerate_e(F
, exist
, nparam
, MaxRays
);
3409 EP
= enumerate_vd(&P
, exist
, nparam
, MaxRays
);
3414 EP
= enumerate_sum(P
, exist
, nparam
, MaxRays
);
3421 Polyhedron
*pos
, *neg
;
3422 for (i
= 0; i
< exist
; ++i
)
3423 if (SplitOnVar(P
, i
, nvar
, len
, exist
, MaxRays
,
3424 row
, f
, false, &pos
, &neg
))
3430 EP
= enumerate_or(pos
, exist
, nparam
, MaxRays
);
3442 static void normalize(Polyhedron
*i
, vec_ZZ
& lambda
, ZZ
& sign
,
3443 ZZ
& num_s
, vec_ZZ
& num_p
, vec_ZZ
& den_s
, vec_ZZ
& den_p
,
3446 unsigned dim
= i
->Dimension
;
3447 unsigned nparam
= num_p
.length();
3448 unsigned nvar
= dim
- nparam
;
3452 rays
.SetDims(dim
, nvar
);
3453 add_rays(rays
, i
, &r
, nvar
, true);
3454 den_s
= rays
* lambda
;
3458 for (int j
= 0; j
< den_s
.length(); ++j
) {
3459 values2zz(i
->Ray
[j
]+1+nvar
, f
[j
], nparam
);
3460 if (den_s
[j
] == 0) {
3464 if (First_Non_Zero(i
->Ray
[j
]+1+nvar
, nparam
) != -1) {
3475 den_s
[j
] = abs(den_s
[j
]);
3484 gen_fun
* barvinok_series(Polyhedron
*P
, Polyhedron
* C
, unsigned MaxRays
)
3486 Polyhedron
** vcone
;
3488 unsigned nparam
= C
->Dimension
;
3492 sign
.SetLength(ncone
);
3494 CA
= align_context(C
, P
->Dimension
, MaxRays
);
3495 P
= DomainIntersection(P
, CA
, MaxRays
);
3496 Polyhedron_Free(CA
);
3498 assert(!Polyhedron_is_infinite(P
, nparam
));
3499 assert(P
->NbBid
== 0);
3500 assert(Polyhedron_has_positive_rays(P
, nparam
));
3501 assert(P
->NbEq
== 0);
3504 nvar
= dim
- nparam
;
3505 vcone
= new Polyhedron_p
[P
->NbRays
];
3507 for (int j
= 0; j
< P
->NbRays
; ++j
) {
3508 if (!value_pos_p(P
->Ray
[j
][dim
+1]))
3512 Polyhedron
*C
= supporting_cone(P
, j
);
3513 decompose(C
, &vcone
[j
], &npos
, &nneg
, MaxRays
);
3514 ncone
+= npos
+ nneg
;
3515 sign
.SetLength(ncone
);
3516 for (int k
= 0; k
< npos
; ++k
)
3517 sign
[ncone
-nneg
-k
-1] = 1;
3518 for (int k
= 0; k
< nneg
; ++k
)
3519 sign
[ncone
-k
-1] = -1;
3523 rays
.SetDims(ncone
* dim
, nvar
);
3525 for (int j
= 0; j
< P
->NbRays
; ++j
) {
3526 if (!value_pos_p(P
->Ray
[j
][dim
+1]))
3529 for (Polyhedron
*i
= vcone
[j
]; i
; i
= i
->next
) {
3530 add_rays(rays
, i
, &r
, nvar
);
3533 rays
.SetDims(r
, nvar
);
3535 nonorthog(rays
, lambda
);
3536 //randomvector(P, lambda, nvar);
3539 cout << "rays: " << rays;
3540 cout << "lambda: " << lambda;
3546 num_p
.SetLength(nparam
);
3549 den_s
.SetLength(dim
);
3551 den_p
.SetLength(dim
);
3553 den
.SetDims(dim
, nparam
);
3559 gen_fun
* gf
= new gen_fun
;
3561 for (int j
= 0; j
< P
->NbRays
; ++j
) {
3562 if (!value_pos_p(P
->Ray
[j
][dim
+1]))
3565 for (Polyhedron
*i
= vcone
[j
]; i
; i
= i
->next
, ++f
) {
3566 lattice_point(P
->Ray
[j
]+1, i
, vertex
);
3569 for ( ; k
< nvar
; ++k
)
3570 num_s
+= vertex
[k
] * lambda
[k
];
3571 for ( ; k
< dim
; ++k
)
3572 num_p
[k
-nvar
] = vertex
[k
];
3573 normalize(i
, lambda
, sign
[f
], num_s
, num_p
,
3578 for (int k
= 0; k
< dim
; ++k
) {
3581 else if (den_s
[k
] == 0)
3584 if (no_param
== 0) {
3585 for (int k
= 0; k
< dim
; ++k
)
3588 gf
->add(sign
[f
], one
, num_p
, den
);
3589 } else if (no_param
+ only_param
== dim
) {
3592 pden
.SetDims(only_param
, nparam
);
3594 for (k
= 0, l
= 0; k
< dim
; ++k
)
3598 for (k
= 0; k
< dim
; ++k
)
3602 dpoly
n(no_param
, num_s
);
3603 dpoly
d(no_param
, den_s
[k
], 1);
3604 for ( ; k
< dim
; ++k
)
3605 if (den_s
[k
] != 0) {
3606 dpoly
fact(no_param
, den_s
[k
], 1);
3610 mpq_set_si(count
, 0, 1);
3611 n
.div(d
, count
, sign
[f
]);
3614 value2zz(mpq_numref(count
), qn
);
3615 value2zz(mpq_denref(count
), qd
);
3617 gf
->add(qn
, qd
, num_p
, pden
);
3622 pden
.SetDims(only_param
, nparam
);
3624 for (k
= 0, l
= 0; k
< dim
; ++k
)
3628 for (k
= 0; k
< dim
; ++k
)
3632 dpoly
n(no_param
, num_s
);
3633 dpoly
d(no_param
, den_s
[k
], 1);
3634 for ( ; k
< dim
; ++k
)
3635 if (den_p
[k
] == 0) {
3636 dpoly
fact(no_param
, den_s
[k
], 1);
3640 for (k
= 0; k
< dim
; ++k
) {
3641 if (den_s
[k
] == 0 || den_p
[k
] == 0)
3644 dpoly
pd(no_param
-1, den_s
[k
], 1);
3645 int s
= den_p
[k
] < 0 ? -1 : 1;
3648 r
= new dpoly_r(n
, pd
, k
, s
, dim
);
3650 assert(0); // for now
3653 r
->div(d
, sign
[f
], gf
, pden
, den
, num_p
);
3657 cout << "sign: " << sign[f];
3658 cout << "num_s: " << num_s;
3659 cout << "num_p: " << num_p;
3660 cout << "den_s: " << den_s;
3661 cout << "den_p: " << den_p;
3662 cout << "den: " << den;
3663 cout << "only_param: " << only_param;
3664 cout << "no_param: " << no_param;