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 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
);
185 Vector
* short_vector(vec_ZZ
& lambda
) {
186 Matrix
*M
= Matrix_Copy(Rays
);
187 Matrix
*inv
= Matrix_Alloc(M
->NbRows
, M
->NbColumns
);
188 int ok
= Matrix_Inverse(M
, inv
);
195 matrix2zz(inv
, B
, inv
->NbRows
- 1, inv
->NbColumns
- 1);
196 long r
= LLL(det2
, B
, U
);
200 for (int i
= 1; i
< B
.NumRows(); ++i
) {
212 Vector
*z
= Vector_Alloc(U
[index
].length()+1);
214 zz2values(U
[index
], z
->p
);
215 value_set_si(z
->p
[U
[index
].length()], 0);
219 Polyhedron
*C
= poly();
221 for (i
= 0; i
< C
->NbConstraints
; ++i
) {
222 Inner_Product(z
->p
, C
->Constraint
[i
]+1, z
->Size
-1, &tmp
);
223 if (value_pos_p(tmp
))
226 if (i
== C
->NbConstraints
) {
227 value_set_si(tmp
, -1);
228 Vector_Scale(z
->p
, z
->p
, tmp
, z
->Size
-1);
235 Polyhedron_Free(Cone
);
241 Matrix
*M
= Matrix_Alloc(Rays
->NbRows
+1, Rays
->NbColumns
+1);
242 for (int i
= 0; i
< Rays
->NbRows
; ++i
) {
243 Vector_Copy(Rays
->p
[i
], M
->p
[i
]+1, Rays
->NbColumns
);
244 value_set_si(M
->p
[i
][0], 1);
246 Vector_Set(M
->p
[Rays
->NbRows
]+1, 0, Rays
->NbColumns
-1);
247 value_set_si(M
->p
[Rays
->NbRows
][0], 1);
248 value_set_si(M
->p
[Rays
->NbRows
][Rays
->NbColumns
], 1);
249 Cone
= Rays2Polyhedron(M
, M
->NbRows
+1);
250 assert(Cone
->NbConstraints
== Cone
->NbRays
);
264 dpoly(int d
, ZZ
& degree
, int offset
= 0) {
265 coeff
.SetLength(d
+1);
267 int min
= d
+ offset
;
268 if (degree
>= 0 && degree
< ZZ(INIT_VAL
, min
))
269 min
= to_int(degree
);
271 ZZ c
= ZZ(INIT_VAL
, 1);
274 for (int i
= 1; i
<= min
; ++i
) {
275 c
*= (degree
-i
+ 1);
280 void operator *= (dpoly
& f
) {
281 assert(coeff
.length() == f
.coeff
.length());
283 coeff
= f
.coeff
[0] * coeff
;
284 for (int i
= 1; i
< coeff
.length(); ++i
)
285 for (int j
= 0; i
+j
< coeff
.length(); ++j
)
286 coeff
[i
+j
] += f
.coeff
[i
] * old
[j
];
288 void div(dpoly
& d
, mpq_t count
, ZZ
& sign
) {
289 int len
= coeff
.length();
292 mpq_t
* c
= new mpq_t
[coeff
.length()];
295 for (int i
= 0; i
< len
; ++i
) {
297 zz2value(coeff
[i
], tmp
);
298 mpq_set_z(c
[i
], tmp
);
300 for (int j
= 1; j
<= i
; ++j
) {
301 zz2value(d
.coeff
[j
], tmp
);
302 mpq_set_z(qtmp
, tmp
);
303 mpq_mul(qtmp
, qtmp
, c
[i
-j
]);
304 mpq_sub(c
[i
], c
[i
], qtmp
);
307 zz2value(d
.coeff
[0], tmp
);
308 mpq_set_z(qtmp
, tmp
);
309 mpq_div(c
[i
], c
[i
], qtmp
);
312 mpq_sub(count
, count
, c
[len
-1]);
314 mpq_add(count
, count
, c
[len
-1]);
318 for (int i
= 0; i
< len
; ++i
)
330 dpoly_n(int d
, ZZ
& degree_0
, ZZ
& degree_1
, int offset
= 0) {
334 zz2value(degree_0
, d0
);
335 zz2value(degree_1
, d1
);
336 coeff
= Matrix_Alloc(d
+1, d
+1+1);
337 value_set_si(coeff
->p
[0][0], 1);
338 value_set_si(coeff
->p
[0][d
+1], 1);
339 for (int i
= 1; i
<= d
; ++i
) {
340 value_multiply(coeff
->p
[i
][0], coeff
->p
[i
-1][0], d0
);
341 Vector_Combine(coeff
->p
[i
-1], coeff
->p
[i
-1]+1, coeff
->p
[i
]+1,
343 value_set_si(coeff
->p
[i
][d
+1], i
);
344 value_multiply(coeff
->p
[i
][d
+1], coeff
->p
[i
][d
+1], coeff
->p
[i
-1][d
+1]);
345 value_decrement(d0
, d0
);
350 void div(dpoly
& d
, Vector
*count
, ZZ
& sign
) {
351 int len
= coeff
->NbRows
;
352 Matrix
* c
= Matrix_Alloc(coeff
->NbRows
, coeff
->NbColumns
);
355 for (int i
= 0; i
< len
; ++i
) {
356 Vector_Copy(coeff
->p
[i
], c
->p
[i
], len
+1);
357 for (int j
= 1; j
<= i
; ++j
) {
358 zz2value(d
.coeff
[j
], tmp
);
359 value_multiply(tmp
, tmp
, c
->p
[i
][len
]);
360 value_oppose(tmp
, tmp
);
361 Vector_Combine(c
->p
[i
], c
->p
[i
-j
], c
->p
[i
],
362 c
->p
[i
-j
][len
], tmp
, len
);
363 value_multiply(c
->p
[i
][len
], c
->p
[i
][len
], c
->p
[i
-j
][len
]);
365 zz2value(d
.coeff
[0], tmp
);
366 value_multiply(c
->p
[i
][len
], c
->p
[i
][len
], tmp
);
369 value_set_si(tmp
, -1);
370 Vector_Scale(c
->p
[len
-1], count
->p
, tmp
, len
);
371 value_assign(count
->p
[len
], c
->p
[len
-1][len
]);
373 Vector_Copy(c
->p
[len
-1], count
->p
, len
+1);
374 Vector_Normalize(count
->p
, len
+1);
380 struct dpoly_r_term
{
385 /* len: number of elements in c
386 * each element in c is the coefficient of a power of t
387 * in the MacLaurin expansion
390 vector
< dpoly_r_term
* > *c
;
395 void add_term(int i
, int * powers
, ZZ
& coeff
) {
396 for (int k
= 0; k
< c
[i
].size(); ++k
) {
397 if (memcmp(c
[i
][k
]->powers
, powers
, dim
* sizeof(int)) == 0) {
398 c
[i
][k
]->coeff
+= coeff
;
402 dpoly_r_term
*t
= new dpoly_r_term
;
403 t
->powers
= new int[dim
];
404 memcpy(t
->powers
, powers
, dim
* sizeof(int));
408 dpoly_r(int len
, int dim
) {
412 c
= new vector
< dpoly_r_term
* > [len
];
414 dpoly_r(dpoly
& num
, dpoly
& den
, int pos
, int sign
, int dim
) {
416 len
= num
.coeff
.length();
417 c
= new vector
< dpoly_r_term
* > [len
];
421 for (int i
= 0; i
< len
; ++i
) {
422 ZZ coeff
= num
.coeff
[i
];
423 memset(powers
, 0, dim
* sizeof(int));
426 add_term(i
, powers
, coeff
);
428 for (int j
= 1; j
<= i
; ++j
) {
429 for (int k
= 0; k
< c
[i
-j
].size(); ++k
) {
430 memcpy(powers
, c
[i
-j
][k
]->powers
, dim
*sizeof(int));
432 coeff
= -den
.coeff
[j
-1] * c
[i
-j
][k
]->coeff
;
433 add_term(i
, powers
, coeff
);
439 dpoly_r(dpoly_r
* num
, dpoly
& den
, int pos
, int sign
, int dim
) {
442 c
= new vector
< dpoly_r_term
* > [len
];
447 for (int i
= 0 ; i
< len
; ++i
) {
448 for (int k
= 0; k
< num
->c
[i
].size(); ++k
) {
449 memcpy(powers
, num
->c
[i
][k
]->powers
, dim
*sizeof(int));
451 add_term(i
, powers
, num
->c
[i
][k
]->coeff
);
454 for (int j
= 1; j
<= i
; ++j
) {
455 for (int k
= 0; k
< c
[i
-j
].size(); ++k
) {
456 memcpy(powers
, c
[i
-j
][k
]->powers
, dim
*sizeof(int));
458 coeff
= -den
.coeff
[j
-1] * c
[i
-j
][k
]->coeff
;
459 add_term(i
, powers
, coeff
);
465 for (int i
= 0 ; i
< len
; ++i
)
466 for (int k
= 0; k
< c
[i
].size(); ++k
) {
467 delete [] c
[i
][k
]->powers
;
472 dpoly_r
*div(dpoly
& d
) {
473 dpoly_r
*rc
= new dpoly_r(len
, dim
);
474 rc
->denom
= power(d
.coeff
[0], len
);
475 ZZ inv_d
= rc
->denom
/ d
.coeff
[0];
478 for (int i
= 0; i
< len
; ++i
) {
479 for (int k
= 0; k
< c
[i
].size(); ++k
) {
480 coeff
= c
[i
][k
]->coeff
* inv_d
;
481 rc
->add_term(i
, c
[i
][k
]->powers
, coeff
);
484 for (int j
= 1; j
<= i
; ++j
) {
485 for (int k
= 0; k
< rc
->c
[i
-j
].size(); ++k
) {
486 coeff
= - d
.coeff
[j
] * rc
->c
[i
-j
][k
]->coeff
/ d
.coeff
[0];
487 rc
->add_term(i
, rc
->c
[i
-j
][k
]->powers
, coeff
);
494 for (int i
= 0; i
< len
; ++i
) {
497 cout
<< c
[i
].size() << endl
;
498 for (int j
= 0; j
< c
[i
].size(); ++j
) {
499 for (int k
= 0; k
< dim
; ++k
) {
500 cout
<< c
[i
][j
]->powers
[k
] << " ";
502 cout
<< ": " << c
[i
][j
]->coeff
<< "/" << denom
<< endl
;
510 void decompose(Polyhedron
*C
);
511 virtual void handle(Polyhedron
*P
, int sign
) = 0;
514 struct polar_decomposer
: public decomposer
{
515 void decompose(Polyhedron
*C
, unsigned MaxRays
);
516 virtual void handle(Polyhedron
*P
, int sign
);
517 virtual void handle_polar(Polyhedron
*P
, int sign
) = 0;
520 void decomposer::decompose(Polyhedron
*C
)
522 vector
<cone
*> nonuni
;
523 cone
* c
= new cone(C
);
534 while (!nonuni
.empty()) {
537 Vector
* v
= c
->short_vector(lambda
);
538 for (int i
= 0; i
< c
->Rays
->NbRows
- 1; ++i
) {
541 Matrix
* M
= Matrix_Copy(c
->Rays
);
542 Vector_Copy(v
->p
, M
->p
[i
], v
->Size
);
543 cone
* pc
= new cone(M
);
544 assert (pc
->det
!= 0);
545 if (abs(pc
->det
) > 1) {
546 assert(abs(pc
->det
) < abs(c
->det
));
547 nonuni
.push_back(pc
);
549 handle(pc
->poly(), sign(pc
->det
) * s
);
559 void polar_decomposer::decompose(Polyhedron
*cone
, unsigned MaxRays
)
561 Polyhedron_Polarize(cone
);
562 if (cone
->NbRays
- 1 != cone
->Dimension
) {
563 Polyhedron
*tmp
= cone
;
564 cone
= triangularize_cone(cone
, MaxRays
);
565 Polyhedron_Free(tmp
);
567 for (Polyhedron
*Polar
= cone
; Polar
; Polar
= Polar
->next
)
568 decomposer::decompose(Polar
);
572 void polar_decomposer::handle(Polyhedron
*P
, int sign
)
574 Polyhedron_Polarize(P
);
575 handle_polar(P
, sign
);
579 * Barvinok's Decomposition of a simplicial cone
581 * Returns two lists of polyhedra
583 void barvinok_decompose(Polyhedron
*C
, Polyhedron
**ppos
, Polyhedron
**pneg
)
585 Polyhedron
*pos
= *ppos
, *neg
= *pneg
;
586 vector
<cone
*> nonuni
;
587 cone
* c
= new cone(C
);
594 Polyhedron
*p
= Polyhedron_Copy(c
->Cone
);
600 while (!nonuni
.empty()) {
603 Vector
* v
= c
->short_vector(lambda
);
604 for (int i
= 0; i
< c
->Rays
->NbRows
- 1; ++i
) {
607 Matrix
* M
= Matrix_Copy(c
->Rays
);
608 Vector_Copy(v
->p
, M
->p
[i
], v
->Size
);
609 cone
* pc
= new cone(M
);
610 assert (pc
->det
!= 0);
611 if (abs(pc
->det
) > 1) {
612 assert(abs(pc
->det
) < abs(c
->det
));
613 nonuni
.push_back(pc
);
615 Polyhedron
*p
= pc
->poly();
617 if (sign(pc
->det
) == s
) {
635 const int MAX_TRY
=10;
637 * Searches for a vector that is not orthogonal to any
638 * of the rays in rays.
640 static void nonorthog(mat_ZZ
& rays
, vec_ZZ
& lambda
)
642 int dim
= rays
.NumCols();
644 lambda
.SetLength(dim
);
648 for (int i
= 2; !found
&& i
<= 50*dim
; i
+=4) {
649 for (int j
= 0; j
< MAX_TRY
; ++j
) {
650 for (int k
= 0; k
< dim
; ++k
) {
651 int r
= random_int(i
)+2;
652 int v
= (2*(r
%2)-1) * (r
>> 1);
656 for (; k
< rays
.NumRows(); ++k
)
657 if (lambda
* rays
[k
] == 0)
659 if (k
== rays
.NumRows()) {
668 static void randomvector(Polyhedron
*P
, vec_ZZ
& lambda
, int nvar
)
672 unsigned int dim
= P
->Dimension
;
675 for (int i
= 0; i
< P
->NbRays
; ++i
) {
676 for (int j
= 1; j
<= dim
; ++j
) {
677 value_absolute(tmp
, P
->Ray
[i
][j
]);
678 int t
= VALUE_TO_LONG(tmp
) * 16;
683 for (int i
= 0; i
< P
->NbConstraints
; ++i
) {
684 for (int j
= 1; j
<= dim
; ++j
) {
685 value_absolute(tmp
, P
->Constraint
[i
][j
]);
686 int t
= VALUE_TO_LONG(tmp
) * 16;
693 lambda
.SetLength(nvar
);
694 for (int k
= 0; k
< nvar
; ++k
) {
695 int r
= random_int(max
*dim
)+2;
696 int v
= (2*(r
%2)-1) * (max
/2*dim
+ (r
>> 1));
701 static void add_rays(mat_ZZ
& rays
, Polyhedron
*i
, int *r
, int nvar
= -1,
704 unsigned dim
= i
->Dimension
;
707 for (int k
= 0; k
< i
->NbRays
; ++k
) {
708 if (!value_zero_p(i
->Ray
[k
][dim
+1]))
710 if (!all
&& nvar
!= dim
&& First_Non_Zero(i
->Ray
[k
]+1, nvar
) == -1)
712 values2zz(i
->Ray
[k
]+1, rays
[(*r
)++], nvar
);
716 void lattice_point(Value
* values
, Polyhedron
*i
, vec_ZZ
& vertex
)
718 unsigned dim
= i
->Dimension
;
719 if(!value_one_p(values
[dim
])) {
720 Matrix
* Rays
= rays(i
);
721 Matrix
*inv
= Matrix_Alloc(Rays
->NbRows
, Rays
->NbColumns
);
722 int ok
= Matrix_Inverse(Rays
, inv
);
726 Vector
*lambda
= Vector_Alloc(dim
+1);
727 Vector_Matrix_Product(values
, inv
, lambda
->p
);
729 for (int j
= 0; j
< dim
; ++j
)
730 mpz_cdiv_q(lambda
->p
[j
], lambda
->p
[j
], lambda
->p
[dim
]);
731 value_set_si(lambda
->p
[dim
], 1);
732 Vector
*A
= Vector_Alloc(dim
+1);
733 Vector_Matrix_Product(lambda
->p
, Rays
, A
->p
);
736 values2zz(A
->p
, vertex
, dim
);
739 values2zz(values
, vertex
, dim
);
742 static evalue
*term(int param
, ZZ
& c
, Value
*den
= NULL
)
744 evalue
*EP
= new evalue();
746 value_set_si(EP
->d
,0);
747 EP
->x
.p
= new_enode(polynomial
, 2, param
+ 1);
748 evalue_set_si(&EP
->x
.p
->arr
[0], 0, 1);
749 value_init(EP
->x
.p
->arr
[1].x
.n
);
751 value_set_si(EP
->x
.p
->arr
[1].d
, 1);
753 value_assign(EP
->x
.p
->arr
[1].d
, *den
);
754 zz2value(c
, EP
->x
.p
->arr
[1].x
.n
);
758 static void vertex_period(
759 Polyhedron
*i
, vec_ZZ
& lambda
, Matrix
*T
,
760 Value lcm
, int p
, Vector
*val
,
761 evalue
*E
, evalue
* ev
,
764 unsigned nparam
= T
->NbRows
- 1;
765 unsigned dim
= i
->Dimension
;
772 Vector
* values
= Vector_Alloc(dim
+ 1);
773 Vector_Matrix_Product(val
->p
, T
, values
->p
);
774 value_assign(values
->p
[dim
], lcm
);
775 lattice_point(values
->p
, i
, vertex
);
776 num
= vertex
* lambda
;
781 zz2value(num
, ev
->x
.n
);
782 value_assign(ev
->d
, lcm
);
789 values2zz(T
->p
[p
], vertex
, dim
);
790 nump
= vertex
* lambda
;
791 if (First_Non_Zero(val
->p
, p
) == -1) {
792 value_assign(tmp
, lcm
);
793 evalue
*ET
= term(p
, nump
, &tmp
);
795 free_evalue_refs(ET
);
799 value_assign(tmp
, lcm
);
800 if (First_Non_Zero(T
->p
[p
], dim
) != -1)
801 Vector_Gcd(T
->p
[p
], dim
, &tmp
);
803 if (value_lt(tmp
, lcm
)) {
806 value_division(tmp
, lcm
, tmp
);
807 value_set_si(ev
->d
, 0);
808 ev
->x
.p
= new_enode(periodic
, VALUE_TO_INT(tmp
), p
+1);
809 value2zz(tmp
, count
);
811 value_decrement(tmp
, tmp
);
813 ZZ new_offset
= offset
- count
* nump
;
814 value_assign(val
->p
[p
], tmp
);
815 vertex_period(i
, lambda
, T
, lcm
, p
+1, val
, E
,
816 &ev
->x
.p
->arr
[VALUE_TO_INT(tmp
)], new_offset
);
817 } while (value_pos_p(tmp
));
819 vertex_period(i
, lambda
, T
, lcm
, p
+1, val
, E
, ev
, offset
);
823 static void mask_r(Matrix
*f
, int nr
, Vector
*lcm
, int p
, Vector
*val
, evalue
*ev
)
825 unsigned nparam
= lcm
->Size
;
828 Vector
* prod
= Vector_Alloc(f
->NbRows
);
829 Matrix_Vector_Product(f
, val
->p
, prod
->p
);
831 for (int i
= 0; i
< nr
; ++i
) {
832 value_modulus(prod
->p
[i
], prod
->p
[i
], f
->p
[i
][nparam
+1]);
833 isint
&= value_zero_p(prod
->p
[i
]);
835 value_set_si(ev
->d
, 1);
837 value_set_si(ev
->x
.n
, isint
);
844 if (value_one_p(lcm
->p
[p
]))
845 mask_r(f
, nr
, lcm
, p
+1, val
, ev
);
847 value_assign(tmp
, lcm
->p
[p
]);
848 value_set_si(ev
->d
, 0);
849 ev
->x
.p
= new_enode(periodic
, VALUE_TO_INT(tmp
), p
+1);
851 value_decrement(tmp
, tmp
);
852 value_assign(val
->p
[p
], tmp
);
853 mask_r(f
, nr
, lcm
, p
+1, val
, &ev
->x
.p
->arr
[VALUE_TO_INT(tmp
)]);
854 } while (value_pos_p(tmp
));
859 static evalue
*multi_monom(vec_ZZ
& p
)
861 evalue
*X
= new evalue();
864 unsigned nparam
= p
.length()-1;
865 zz2value(p
[nparam
], X
->x
.n
);
866 value_set_si(X
->d
, 1);
867 for (int i
= 0; i
< nparam
; ++i
) {
870 evalue
*T
= term(i
, p
[i
]);
879 * Check whether mapping polyhedron P on the affine combination
880 * num yields a range that has a fixed quotient on integer
882 * If zero is true, then we are only interested in the quotient
883 * for the cases where the remainder is zero.
884 * Returns NULL if false and a newly allocated value if true.
886 static Value
*fixed_quotient(Polyhedron
*P
, vec_ZZ
& num
, Value d
, bool zero
)
889 int len
= num
.length();
890 Matrix
*T
= Matrix_Alloc(2, len
);
891 zz2values(num
, T
->p
[0]);
892 value_set_si(T
->p
[1][len
-1], 1);
893 Polyhedron
*I
= Polyhedron_Image(P
, T
, P
->NbConstraints
);
897 for (i
= 0; i
< I
->NbRays
; ++i
)
898 if (value_zero_p(I
->Ray
[i
][2])) {
906 int bounded
= line_minmax(I
, &min
, &max
);
910 mpz_cdiv_q(min
, min
, d
);
912 mpz_fdiv_q(min
, min
, d
);
913 mpz_fdiv_q(max
, max
, d
);
915 if (value_eq(min
, max
)) {
918 value_assign(*ret
, min
);
926 * Normalize linear expression coef modulo m
927 * Removes common factor and reduces coefficients
928 * Returns index of first non-zero coefficient or len
930 static int normal_mod(Value
*coef
, int len
, Value
*m
)
935 Vector_Gcd(coef
, len
, &gcd
);
937 Vector_AntiScale(coef
, coef
, gcd
, len
);
939 value_division(*m
, *m
, gcd
);
946 for (j
= 0; j
< len
; ++j
)
947 mpz_fdiv_r(coef
[j
], coef
[j
], *m
);
948 for (j
= 0; j
< len
; ++j
)
949 if (value_notzero_p(coef
[j
]))
956 static void mask(Matrix
*f
, evalue
*factor
)
958 int nr
= f
->NbRows
, nc
= f
->NbColumns
;
961 for (n
= 0; n
< nr
&& value_notzero_p(f
->p
[n
][nc
-1]); ++n
)
962 if (value_notone_p(f
->p
[n
][nc
-1]) &&
963 value_notmone_p(f
->p
[n
][nc
-1]))
977 value_set_si(EV
.x
.n
, 1);
979 for (n
= 0; n
< nr
; ++n
) {
980 value_assign(m
, f
->p
[n
][nc
-1]);
981 if (value_one_p(m
) || value_mone_p(m
))
984 int j
= normal_mod(f
->p
[n
], nc
-1, &m
);
986 free_evalue_refs(factor
);
987 value_init(factor
->d
);
988 evalue_set_si(factor
, 0, 1);
992 values2zz(f
->p
[n
], row
, nc
-1);
995 if (j
< (nc
-1)-1 && row
[j
] > g
/2) {
996 for (int k
= j
; k
< (nc
-1); ++k
)
1002 value_set_si(EP
.d
, 0);
1003 EP
.x
.p
= new_enode(relation
, 2, 0);
1004 value_clear(EP
.x
.p
->arr
[1].d
);
1005 EP
.x
.p
->arr
[1] = *factor
;
1006 evalue
*ev
= &EP
.x
.p
->arr
[0];
1007 value_set_si(ev
->d
, 0);
1008 ev
->x
.p
= new_enode(fractional
, 3, -1);
1009 evalue_set_si(&ev
->x
.p
->arr
[1], 0, 1);
1010 evalue_set_si(&ev
->x
.p
->arr
[2], 1, 1);
1011 evalue
*E
= multi_monom(row
);
1012 value_assign(EV
.d
, m
);
1014 value_clear(ev
->x
.p
->arr
[0].d
);
1015 ev
->x
.p
->arr
[0] = *E
;
1021 free_evalue_refs(&EV
);
1027 static void mask(Matrix
*f
, evalue
*factor
)
1029 int nr
= f
->NbRows
, nc
= f
->NbColumns
;
1032 for (n
= 0; n
< nr
&& value_notzero_p(f
->p
[n
][nc
-1]); ++n
)
1033 if (value_notone_p(f
->p
[n
][nc
-1]) &&
1034 value_notmone_p(f
->p
[n
][nc
-1]))
1042 unsigned np
= nc
- 2;
1043 Vector
*lcm
= Vector_Alloc(np
);
1044 Vector
*val
= Vector_Alloc(nc
);
1045 Vector_Set(val
->p
, 0, nc
);
1046 value_set_si(val
->p
[np
], 1);
1047 Vector_Set(lcm
->p
, 1, np
);
1048 for (n
= 0; n
< nr
; ++n
) {
1049 if (value_one_p(f
->p
[n
][nc
-1]) ||
1050 value_mone_p(f
->p
[n
][nc
-1]))
1052 for (int j
= 0; j
< np
; ++j
)
1053 if (value_notzero_p(f
->p
[n
][j
])) {
1054 Gcd(f
->p
[n
][j
], f
->p
[n
][nc
-1], &tmp
);
1055 value_division(tmp
, f
->p
[n
][nc
-1], tmp
);
1056 value_lcm(tmp
, lcm
->p
[j
], &lcm
->p
[j
]);
1061 mask_r(f
, nr
, lcm
, 0, val
, &EP
);
1066 free_evalue_refs(&EP
);
1077 static bool mod_needed(Polyhedron
*PD
, vec_ZZ
& num
, Value d
, evalue
*E
)
1079 Value
*q
= fixed_quotient(PD
, num
, d
, false);
1084 value_oppose(*q
, *q
);
1087 value_set_si(EV
.d
, 1);
1089 value_multiply(EV
.x
.n
, *q
, d
);
1091 free_evalue_refs(&EV
);
1097 static void ceil_mod(Value
*coef
, int len
, Value d
, ZZ
& f
, evalue
*EP
, Polyhedron
*PD
)
1101 value_set_si(m
, -1);
1103 Vector_Scale(coef
, coef
, m
, len
);
1106 int j
= normal_mod(coef
, len
, &m
);
1114 values2zz(coef
, num
, len
);
1121 evalue_set_si(&tmp
, 0, 1);
1125 while (j
< len
-1 && (num
[j
] == g
/2 || num
[j
] == 0))
1127 if ((j
< len
-1 && num
[j
] > g
/2) || (j
== len
-1 && num
[j
] >= (g
+1)/2)) {
1128 for (int k
= j
; k
< len
-1; ++k
)
1130 num
[k
] = g
- num
[k
];
1131 num
[len
-1] = g
- 1 - num
[len
-1];
1132 value_assign(tmp
.d
, m
);
1134 zz2value(t
, tmp
.x
.n
);
1140 ZZ t
= num
[len
-1] * f
;
1141 zz2value(t
, tmp
.x
.n
);
1142 value_assign(tmp
.d
, m
);
1145 evalue
*E
= multi_monom(num
);
1149 if (PD
&& !mod_needed(PD
, num
, m
, E
)) {
1151 zz2value(f
, EV
.x
.n
);
1152 value_assign(EV
.d
, m
);
1157 value_set_si(EV
.x
.n
, 1);
1158 value_assign(EV
.d
, m
);
1160 value_clear(EV
.x
.n
);
1161 value_set_si(EV
.d
, 0);
1162 EV
.x
.p
= new_enode(fractional
, 3, -1);
1163 evalue_copy(&EV
.x
.p
->arr
[0], E
);
1164 evalue_set_si(&EV
.x
.p
->arr
[1], 0, 1);
1165 value_init(EV
.x
.p
->arr
[2].x
.n
);
1166 zz2value(f
, EV
.x
.p
->arr
[2].x
.n
);
1167 value_set_si(EV
.x
.p
->arr
[2].d
, 1);
1172 free_evalue_refs(&EV
);
1173 free_evalue_refs(E
);
1177 free_evalue_refs(&tmp
);
1183 evalue
* bv_ceil3(Value
*coef
, int len
, Value d
, Polyhedron
*P
)
1185 Vector
*val
= Vector_Alloc(len
);
1189 value_set_si(t
, -1);
1190 Vector_Scale(coef
, val
->p
, t
, len
);
1191 value_absolute(t
, d
);
1194 values2zz(val
->p
, num
, len
);
1195 evalue
*EP
= multi_monom(num
);
1199 value_init(tmp
.x
.n
);
1200 value_set_si(tmp
.x
.n
, 1);
1201 value_assign(tmp
.d
, t
);
1207 ceil_mod(val
->p
, len
, t
, one
, EP
, P
);
1210 /* copy EP to malloc'ed evalue */
1216 free_evalue_refs(&tmp
);
1223 evalue
* lattice_point(
1224 Polyhedron
*i
, vec_ZZ
& lambda
, Matrix
*W
, Value lcm
, Polyhedron
*PD
)
1226 unsigned nparam
= W
->NbColumns
- 1;
1228 Matrix
* Rays
= rays2(i
);
1229 Matrix
*T
= Transpose(Rays
);
1230 Matrix
*T2
= Matrix_Copy(T
);
1231 Matrix
*inv
= Matrix_Alloc(T2
->NbRows
, T2
->NbColumns
);
1232 int ok
= Matrix_Inverse(T2
, inv
);
1237 matrix2zz(W
, vertex
, W
->NbRows
, W
->NbColumns
);
1240 num
= lambda
* vertex
;
1242 evalue
*EP
= multi_monom(num
);
1246 value_init(tmp
.x
.n
);
1247 value_set_si(tmp
.x
.n
, 1);
1248 value_assign(tmp
.d
, lcm
);
1252 Matrix
*L
= Matrix_Alloc(inv
->NbRows
, W
->NbColumns
);
1253 Matrix_Product(inv
, W
, L
);
1256 matrix2zz(T
, RT
, T
->NbRows
, T
->NbColumns
);
1259 vec_ZZ p
= lambda
* RT
;
1261 for (int i
= 0; i
< L
->NbRows
; ++i
) {
1262 ceil_mod(L
->p
[i
], nparam
+1, lcm
, p
[i
], EP
, PD
);
1268 free_evalue_refs(&tmp
);
1272 evalue
* lattice_point(
1273 Polyhedron
*i
, vec_ZZ
& lambda
, Matrix
*W
, Value lcm
, Polyhedron
*PD
)
1275 Matrix
*T
= Transpose(W
);
1276 unsigned nparam
= T
->NbRows
- 1;
1278 evalue
*EP
= new evalue();
1280 evalue_set_si(EP
, 0, 1);
1283 Vector
*val
= Vector_Alloc(nparam
+1);
1284 value_set_si(val
->p
[nparam
], 1);
1285 ZZ
offset(INIT_VAL
, 0);
1287 vertex_period(i
, lambda
, T
, lcm
, 0, val
, EP
, &ev
, offset
);
1290 free_evalue_refs(&ev
);
1301 Param_Vertices
* V
, Polyhedron
*i
, vec_ZZ
& lambda
, term_info
* term
,
1304 unsigned nparam
= V
->Vertex
->NbColumns
- 2;
1305 unsigned dim
= i
->Dimension
;
1307 vertex
.SetDims(V
->Vertex
->NbRows
, nparam
+1);
1311 value_set_si(lcm
, 1);
1312 for (int j
= 0; j
< V
->Vertex
->NbRows
; ++j
) {
1313 value_lcm(lcm
, V
->Vertex
->p
[j
][nparam
+1], &lcm
);
1315 if (value_notone_p(lcm
)) {
1316 Matrix
* mv
= Matrix_Alloc(dim
, nparam
+1);
1317 for (int j
= 0 ; j
< dim
; ++j
) {
1318 value_division(tmp
, lcm
, V
->Vertex
->p
[j
][nparam
+1]);
1319 Vector_Scale(V
->Vertex
->p
[j
], mv
->p
[j
], tmp
, nparam
+1);
1322 term
->E
= lattice_point(i
, lambda
, mv
, lcm
, PD
);
1330 for (int i
= 0; i
< V
->Vertex
->NbRows
; ++i
) {
1331 assert(value_one_p(V
->Vertex
->p
[i
][nparam
+1])); // for now
1332 values2zz(V
->Vertex
->p
[i
], vertex
[i
], nparam
+1);
1336 num
= lambda
* vertex
;
1340 for (int j
= 0; j
< nparam
; ++j
)
1346 term
->E
= multi_monom(num
);
1350 term
->constant
= num
[nparam
];
1353 term
->coeff
= num
[p
];
1360 static void normalize(ZZ
& sign
, ZZ
& num
, vec_ZZ
& den
)
1362 unsigned dim
= den
.length();
1366 for (int j
= 0; j
< den
.length(); ++j
) {
1370 den
[j
] = abs(den
[j
]);
1379 * f: the powers in the denominator for the remaining vars
1380 * each row refers to a factor
1381 * den_s: for each factor, the power of (s+1)
1383 * num_s: powers in the numerator corresponding to the summed vars
1384 * num_p: powers in the numerator corresponidng to the remaining vars
1385 * number of rays in cone: "dim" = "k"
1386 * length of each ray: "dim" = "d"
1387 * for now, it is assume: k == d
1389 * den_p: for each factor
1390 * 0: independent of remaining vars
1391 * 1: power corresponds to corresponding row in f
1392 * -1: power is inverse of corresponding row in f
1394 static void normalize(ZZ
& sign
,
1395 ZZ
& num_s
, vec_ZZ
& num_p
, vec_ZZ
& den_s
, vec_ZZ
& den_p
,
1398 unsigned dim
= f
.NumRows();
1399 unsigned nparam
= num_p
.length();
1400 unsigned nvar
= dim
- nparam
;
1404 for (int j
= 0; j
< den_s
.length(); ++j
) {
1405 if (den_s
[j
] == 0) {
1410 for (k
= 0; k
< nparam
; ++k
)
1424 den_s
[j
] = abs(den_s
[j
]);
1433 struct counter
: public polar_decomposer
{
1445 counter(Polyhedron
*P
) {
1448 randomvector(P
, lambda
, dim
);
1449 rays
.SetDims(dim
, dim
);
1454 void start(unsigned MaxRays
);
1460 virtual void handle_polar(Polyhedron
*P
, int sign
);
1463 void counter::handle_polar(Polyhedron
*C
, int s
)
1466 assert(C
->NbRays
-1 == dim
);
1467 add_rays(rays
, C
, &r
);
1468 for (int k
= 0; k
< dim
; ++k
) {
1469 assert(lambda
* rays
[k
] != 0);
1474 lattice_point(P
->Ray
[j
]+1, C
, vertex
);
1475 num
= vertex
* lambda
;
1476 den
= rays
* lambda
;
1477 normalize(sign
, num
, den
);
1480 dpoly
n(dim
, den
[0], 1);
1481 for (int k
= 1; k
< dim
; ++k
) {
1482 dpoly
fact(dim
, den
[k
], 1);
1485 d
.div(n
, count
, sign
);
1488 void counter::start(unsigned MaxRays
)
1490 for (j
= 0; j
< P
->NbRays
; ++j
) {
1491 Polyhedron
*C
= supporting_cone(P
, j
);
1492 decompose(C
, MaxRays
);
1496 struct reducer
: public polar_decomposer
{
1509 int lower
; // call base when only this many variables is left
1510 int untouched
; // keep this many variables untouched
1512 reducer(Polyhedron
*P
) {
1515 lambda
.SetLength(1);
1517 //den.SetLength(dim);
1524 void start(unsigned MaxRays
);
1532 virtual void handle_polar(Polyhedron
*P
, int sign
);
1533 void reduce(ZZ c
, ZZ cd
, vec_ZZ
& num
, mat_ZZ
& den_f
);
1534 virtual void base(ZZ
& c
, ZZ
& cd
, vec_ZZ
& num
, mat_ZZ
& den_f
) = 0;
1537 void reducer::reduce(ZZ c
, ZZ cd
, vec_ZZ
& num
, mat_ZZ
& den_f
)
1539 unsigned len
= den_f
.NumRows(); // number of factors in den
1540 unsigned d
= num
.length()-1;
1543 base(c
, cd
, num
, den_f
);
1546 assert(num
.length() > 1);
1549 den_s
.SetLength(len
);
1551 den_r
.SetDims(len
, d
);
1553 /* Since we're working incrementally, we can look
1554 * for the "easiest" parameter first.
1555 * In particular we first handle the parameters such
1556 * that no_param + only_param == len, since that allows
1557 * us to decouple the problem and the split off part
1558 * may very well be zero
1562 for (i
= 0; i
< d
+1-untouched
; ++i
) {
1563 for (r
= 0; r
< len
; ++r
) {
1564 if (den_f
[r
][i
] != 0) {
1565 for (k
= 0; k
<= d
; ++k
)
1566 if (i
!= k
&& den_f
[r
][k
] != 0)
1575 if (i
> d
-untouched
)
1578 for (r
= 0; r
< len
; ++r
) {
1579 den_s
[r
] = den_f
[r
][i
];
1580 for (k
= 0; k
<= d
; ++k
)
1582 den_r
[r
][k
-(k
>i
)] = den_f
[r
][k
];
1588 for (k
= 0 ; k
<= d
; ++k
)
1590 num_p
[k
-(k
>i
)] = num
[k
];
1593 den_p
.SetLength(len
);
1595 normalize(c
, num_s
, num_p
, den_s
, den_p
, den_r
);
1599 for (int k
= 0; k
< len
; ++k
) {
1602 else if (den_s
[k
] == 0)
1605 if (no_param
== 0) {
1606 for (int k
= 0; k
< len
; ++k
)
1608 den_r
[k
] = -den_r
[k
];
1609 reduce(c
, cd
, num_p
, den_r
);
1613 pden
.SetDims(only_param
, d
);
1615 for (k
= 0, l
= 0; k
< len
; ++k
)
1617 pden
[l
++] = den_r
[k
];
1619 for (k
= 0; k
< len
; ++k
)
1623 dpoly
n(no_param
, num_s
);
1624 dpoly
D(no_param
, den_s
[k
], 1);
1625 for ( ; ++k
< len
; )
1626 if (den_p
[k
] == 0) {
1627 dpoly
fact(no_param
, den_s
[k
], 1);
1631 if (no_param
+ only_param
== len
) {
1632 mpq_set_si(tcount
, 0, 1);
1633 n
.div(D
, tcount
, one
);
1636 value2zz(mpq_numref(tcount
), qn
);
1637 value2zz(mpq_denref(tcount
), qd
);
1643 reduce(qn
, qd
, num_p
, pden
);
1647 for (k
= 0; k
< len
; ++k
) {
1648 if (den_s
[k
] == 0 || den_p
[k
] == 0)
1651 dpoly
pd(no_param
-1, den_s
[k
], 1);
1652 int s
= den_p
[k
] < 0 ? -1 : 1;
1655 r
= new dpoly_r(n
, pd
, k
, s
, len
);
1657 dpoly_r
*nr
= new dpoly_r(r
, pd
, k
, s
, len
);
1663 dpoly_r
*rc
= r
->div(D
);
1667 int common
= pden
.NumRows();
1668 vector
< dpoly_r_term
* >& final
= rc
->c
[rc
->len
-1];
1670 for (int j
= 0; j
< final
.size(); ++j
) {
1671 if (final
[j
]->coeff
== 0)
1674 pden
.SetDims(rows
, pden
.NumCols());
1675 for (int k
= 0; k
< rc
->dim
; ++k
) {
1676 int n
= final
[j
]->powers
[k
];
1679 int abs_n
= n
< 0 ? -n
: n
;
1680 pden
.SetDims(rows
+abs_n
, pden
.NumCols());
1681 for (int l
= 0; l
< abs_n
; ++l
) {
1683 pden
[rows
+l
] = den_r
[k
];
1685 pden
[rows
+l
] = -den_r
[k
];
1689 final
[j
]->coeff
*= c
;
1690 reduce(final
[j
]->coeff
, rc
->denom
, num_p
, pden
);
1699 void reducer::handle_polar(Polyhedron
*C
, int s
)
1701 assert(C
->NbRays
-1 == dim
);
1705 lattice_point(P
->Ray
[j
]+1, C
, vertex
);
1708 den
.SetDims(dim
, dim
);
1711 for (r
= 0; r
< dim
; ++r
)
1712 values2zz(C
->Ray
[r
]+1, den
[r
], dim
);
1714 reduce(sgn
, one
, vertex
, den
);
1717 void reducer::start(unsigned MaxRays
)
1719 for (j
= 0; j
< P
->NbRays
; ++j
) {
1720 Polyhedron
*C
= supporting_cone(P
, j
);
1721 decompose(C
, MaxRays
);
1725 // incremental counter
1726 struct icounter
: public reducer
{
1729 icounter(Polyhedron
*P
) : reducer(P
) {
1737 virtual void base(ZZ
& c
, ZZ
& cd
, vec_ZZ
& num
, mat_ZZ
& den_f
);
1740 void icounter::base(ZZ
& c
, ZZ
& cd
, vec_ZZ
& num
, mat_ZZ
& den_f
)
1743 unsigned len
= den_f
.NumRows(); // number of factors in den
1745 den_s
.SetLength(len
);
1747 for (r
= 0; r
< len
; ++r
)
1748 den_s
[r
] = den_f
[r
][0];
1749 normalize(c
, num_s
, den_s
);
1751 dpoly
n(len
, num_s
);
1752 dpoly
D(len
, den_s
[0], 1);
1753 for (int k
= 1; k
< len
; ++k
) {
1754 dpoly
fact(len
, den_s
[k
], 1);
1757 mpq_set_si(tcount
, 0, 1);
1758 n
.div(D
, tcount
, one
);
1761 mpz_mul(mpq_numref(tcount
), mpq_numref(tcount
), tn
);
1762 mpz_mul(mpq_denref(tcount
), mpq_denref(tcount
), td
);
1763 mpq_canonicalize(tcount
);
1764 mpq_add(count
, count
, tcount
);
1767 struct partial_reducer
: public reducer
{
1770 partial_reducer(Polyhedron
*P
, unsigned nparam
) : reducer(P
) {
1775 ~partial_reducer() {
1777 virtual void base(ZZ
& c
, ZZ
& cd
, vec_ZZ
& num
, mat_ZZ
& den_f
);
1778 void start(unsigned MaxRays
);
1781 void partial_reducer::base(ZZ
& c
, ZZ
& cd
, vec_ZZ
& num
, mat_ZZ
& den_f
)
1783 gf
->add(c
, cd
, num
, den_f
);
1786 void partial_reducer::start(unsigned MaxRays
)
1788 for (j
= 0; j
< P
->NbRays
; ++j
) {
1789 if (!value_pos_p(P
->Ray
[j
][dim
+1]))
1792 Polyhedron
*C
= supporting_cone(P
, j
);
1793 decompose(C
, MaxRays
);
1797 typedef Polyhedron
* Polyhedron_p
;
1799 void barvinok_count(Polyhedron
*P
, Value
* result
, unsigned NbMaxCons
)
1801 Polyhedron
** vcone
;
1810 value_set_si(*result
, 0);
1814 for (; r
< P
->NbRays
; ++r
)
1815 if (value_zero_p(P
->Ray
[r
][P
->Dimension
+1]))
1817 if (P
->NbBid
!=0 || r
< P
->NbRays
) {
1818 value_set_si(*result
, -1);
1822 P
= remove_equalities(P
);
1825 value_set_si(*result
, 0);
1831 value_set_si(factor
, 1);
1832 Q
= Polyhedron_Reduce(P
, &factor
);
1839 if (P
->Dimension
== 0) {
1840 value_assign(*result
, factor
);
1843 value_clear(factor
);
1848 cnt
.start(NbMaxCons
);
1850 assert(value_one_p(&cnt
.count
[0]._mp_den
));
1851 value_multiply(*result
, &cnt
.count
[0]._mp_num
, factor
);
1855 value_clear(factor
);
1858 static void uni_polynom(int param
, Vector
*c
, evalue
*EP
)
1860 unsigned dim
= c
->Size
-2;
1862 value_set_si(EP
->d
,0);
1863 EP
->x
.p
= new_enode(polynomial
, dim
+1, param
+1);
1864 for (int j
= 0; j
<= dim
; ++j
)
1865 evalue_set(&EP
->x
.p
->arr
[j
], c
->p
[j
], c
->p
[dim
+1]);
1868 static void multi_polynom(Vector
*c
, evalue
* X
, evalue
*EP
)
1870 unsigned dim
= c
->Size
-2;
1874 evalue_set(&EC
, c
->p
[dim
], c
->p
[dim
+1]);
1877 evalue_set(EP
, c
->p
[dim
], c
->p
[dim
+1]);
1879 for (int i
= dim
-1; i
>= 0; --i
) {
1881 value_assign(EC
.x
.n
, c
->p
[i
]);
1884 free_evalue_refs(&EC
);
1887 Polyhedron
*unfringe (Polyhedron
*P
, unsigned MaxRays
)
1889 int len
= P
->Dimension
+2;
1890 Polyhedron
*T
, *R
= P
;
1893 Vector
*row
= Vector_Alloc(len
);
1894 value_set_si(row
->p
[0], 1);
1896 R
= DomainConstraintSimplify(Polyhedron_Copy(P
), MaxRays
);
1898 Matrix
*M
= Matrix_Alloc(2, len
-1);
1899 value_set_si(M
->p
[1][len
-2], 1);
1900 for (int v
= 0; v
< P
->Dimension
; ++v
) {
1901 value_set_si(M
->p
[0][v
], 1);
1902 Polyhedron
*I
= Polyhedron_Image(P
, M
, 2+1);
1903 value_set_si(M
->p
[0][v
], 0);
1904 for (int r
= 0; r
< I
->NbConstraints
; ++r
) {
1905 if (value_zero_p(I
->Constraint
[r
][0]))
1907 if (value_zero_p(I
->Constraint
[r
][1]))
1909 if (value_one_p(I
->Constraint
[r
][1]))
1911 if (value_mone_p(I
->Constraint
[r
][1]))
1913 value_absolute(g
, I
->Constraint
[r
][1]);
1914 Vector_Set(row
->p
+1, 0, len
-2);
1915 value_division(row
->p
[1+v
], I
->Constraint
[r
][1], g
);
1916 mpz_fdiv_q(row
->p
[len
-1], I
->Constraint
[r
][2], g
);
1918 R
= AddConstraints(row
->p
, 1, R
, MaxRays
);
1930 static Polyhedron
*reduce_domain(Polyhedron
*D
, Matrix
*CT
, Polyhedron
*CEq
,
1931 Polyhedron
**fVD
, int nd
, unsigned MaxRays
)
1936 Dt
= CT
? DomainPreimage(D
, CT
, MaxRays
) : D
;
1937 Polyhedron
*rVD
= DomainIntersection(Dt
, CEq
, MaxRays
);
1939 /* if rVD is empty or too small in geometric dimension */
1940 if(!rVD
|| emptyQ(rVD
) ||
1941 (rVD
->Dimension
-rVD
->NbEq
< Dt
->Dimension
-Dt
->NbEq
-CEq
->NbEq
)) {
1946 return 0; /* empty validity domain */
1952 fVD
[nd
] = Domain_Copy(rVD
);
1953 for (int i
= 0 ; i
< nd
; ++i
) {
1954 Polyhedron
*I
= DomainIntersection(fVD
[nd
], fVD
[i
], MaxRays
);
1959 Polyhedron
*F
= DomainSimplify(I
, fVD
[nd
], MaxRays
);
1961 Polyhedron
*T
= rVD
;
1962 rVD
= DomainDifference(rVD
, F
, MaxRays
);
1969 rVD
= DomainConstraintSimplify(rVD
, MaxRays
);
1971 Domain_Free(fVD
[nd
]);
1978 barvinok_count(rVD
, &c
, MaxRays
);
1979 if (value_zero_p(c
)) {
1988 static bool Polyhedron_is_infinite(Polyhedron
*P
, unsigned nparam
)
1991 for (r
= 0; r
< P
->NbRays
; ++r
)
1992 if (value_zero_p(P
->Ray
[r
][0]) ||
1993 value_zero_p(P
->Ray
[r
][P
->Dimension
+1])) {
1995 for (i
= P
->Dimension
- nparam
; i
< P
->Dimension
; ++i
)
1996 if (value_notzero_p(P
->Ray
[r
][i
+1]))
1998 if (i
>= P
->Dimension
)
2001 return r
< P
->NbRays
;
2004 /* Check whether all rays point in the positive directions
2005 * for the parameters
2007 static bool Polyhedron_has_positive_rays(Polyhedron
*P
, unsigned nparam
)
2010 for (r
= 0; r
< P
->NbRays
; ++r
)
2011 if (value_zero_p(P
->Ray
[r
][P
->Dimension
+1])) {
2013 for (i
= P
->Dimension
- nparam
; i
< P
->Dimension
; ++i
)
2014 if (value_neg_p(P
->Ray
[r
][i
+1]))
2020 typedef evalue
* evalue_p
;
2022 struct enumerator
: public polar_decomposer
{
2036 enumerator(Polyhedron
*P
, unsigned dim
, unsigned nbV
) {
2040 randomvector(P
, lambda
, dim
);
2041 rays
.SetDims(dim
, dim
);
2043 c
= Vector_Alloc(dim
+2);
2045 vE
= new evalue_p
[nbV
];
2046 for (int j
= 0; j
< nbV
; ++j
)
2052 void decompose_at(Param_Vertices
*V
, int _i
, unsigned MaxRays
) {
2053 Polyhedron
*C
= supporting_cone_p(P
, V
);
2057 vE
[_i
] = new evalue
;
2058 value_init(vE
[_i
]->d
);
2059 evalue_set_si(vE
[_i
], 0, 1);
2061 decompose(C
, MaxRays
);
2068 for (int j
= 0; j
< nbV
; ++j
)
2070 free_evalue_refs(vE
[j
]);
2076 virtual void handle_polar(Polyhedron
*P
, int sign
);
2079 void enumerator::handle_polar(Polyhedron
*C
, int s
)
2082 assert(C
->NbRays
-1 == dim
);
2083 add_rays(rays
, C
, &r
);
2084 for (int k
= 0; k
< dim
; ++k
) {
2085 assert(lambda
* rays
[k
] != 0);
2090 lattice_point(V
, C
, lambda
, &num
, 0);
2091 den
= rays
* lambda
;
2092 normalize(sign
, num
.constant
, den
);
2094 dpoly
n(dim
, den
[0], 1);
2095 for (int k
= 1; k
< dim
; ++k
) {
2096 dpoly
fact(dim
, den
[k
], 1);
2099 if (num
.E
!= NULL
) {
2100 ZZ
one(INIT_VAL
, 1);
2101 dpoly_n
d(dim
, num
.constant
, one
);
2104 multi_polynom(c
, num
.E
, &EV
);
2106 free_evalue_refs(&EV
);
2107 free_evalue_refs(num
.E
);
2109 } else if (num
.pos
!= -1) {
2110 dpoly_n
d(dim
, num
.constant
, num
.coeff
);
2113 uni_polynom(num
.pos
, c
, &EV
);
2115 free_evalue_refs(&EV
);
2117 mpq_set_si(count
, 0, 1);
2118 dpoly
d(dim
, num
.constant
);
2119 d
.div(n
, count
, sign
);
2122 evalue_set(&EV
, &count
[0]._mp_num
, &count
[0]._mp_den
);
2124 free_evalue_refs(&EV
);
2128 evalue
* barvinok_enumerate_ev(Polyhedron
*P
, Polyhedron
* C
, unsigned MaxRays
)
2130 //P = unfringe(P, MaxRays);
2131 Polyhedron
*CEq
= NULL
, *rVD
, *pVD
, *CA
;
2133 Param_Polyhedron
*PP
= NULL
;
2134 Param_Domain
*D
, *next
;
2137 unsigned nparam
= C
->Dimension
;
2139 ALLOC(evalue
, eres
);
2140 value_init(eres
->d
);
2141 value_set_si(eres
->d
, 0);
2144 value_init(factor
.d
);
2145 evalue_set_si(&factor
, 1, 1);
2147 CA
= align_context(C
, P
->Dimension
, MaxRays
);
2148 P
= DomainIntersection(P
, CA
, MaxRays
);
2149 Polyhedron_Free(CA
);
2151 if (C
->Dimension
== 0 || emptyQ(P
)) {
2153 eres
->x
.p
= new_enode(partition
, 2, C
->Dimension
);
2154 EVALUE_SET_DOMAIN(eres
->x
.p
->arr
[0],
2155 DomainConstraintSimplify(CEq
? CEq
: Polyhedron_Copy(C
), MaxRays
));
2156 value_set_si(eres
->x
.p
->arr
[1].d
, 1);
2157 value_init(eres
->x
.p
->arr
[1].x
.n
);
2159 value_set_si(eres
->x
.p
->arr
[1].x
.n
, 0);
2161 barvinok_count(P
, &eres
->x
.p
->arr
[1].x
.n
, MaxRays
);
2163 emul(&factor
, eres
);
2164 reduce_evalue(eres
);
2165 free_evalue_refs(&factor
);
2170 Param_Polyhedron_Free(PP
);
2174 if (Polyhedron_is_infinite(P
, nparam
))
2179 P
= remove_equalities_p(P
, P
->Dimension
-nparam
, &f
);
2183 if (P
->Dimension
== nparam
) {
2185 P
= Universe_Polyhedron(0);
2189 Polyhedron
*Q
= ParamPolyhedron_Reduce(P
, P
->Dimension
-nparam
, &factor
);
2192 if (Q
->Dimension
== nparam
) {
2194 P
= Universe_Polyhedron(0);
2199 Polyhedron
*oldP
= P
;
2200 PP
= Polyhedron2Param_SimplifiedDomain(&P
,C
,MaxRays
,&CEq
,&CT
);
2202 Polyhedron_Free(oldP
);
2204 if (isIdentity(CT
)) {
2208 assert(CT
->NbRows
!= CT
->NbColumns
);
2209 if (CT
->NbRows
== 1) // no more parameters
2211 nparam
= CT
->NbRows
- 1;
2214 unsigned dim
= P
->Dimension
- nparam
;
2216 enumerator
et(P
, dim
, PP
->nbV
);
2219 for (nd
= 0, D
=PP
->D
; D
; ++nd
, D
=D
->next
);
2220 struct section
{ Polyhedron
*D
; evalue E
; };
2221 section
*s
= new section
[nd
];
2222 Polyhedron
**fVD
= new Polyhedron_p
[nd
];
2224 for(nd
= 0, D
=PP
->D
; D
; D
=next
) {
2227 Polyhedron
*rVD
= reduce_domain(D
->Domain
, CT
, CEq
,
2232 pVD
= CT
? DomainImage(rVD
,CT
,MaxRays
) : rVD
;
2234 value_init(s
[nd
].E
.d
);
2235 evalue_set_si(&s
[nd
].E
, 0, 1);
2237 FORALL_PVertex_in_ParamPolyhedron(V
,D
,PP
) // _i is internal counter
2239 et
.decompose_at(V
, _i
, MaxRays
);
2240 eadd(et
.vE
[_i
] , &s
[nd
].E
);
2241 END_FORALL_PVertex_in_ParamPolyhedron
;
2242 reduce_in_domain(&s
[nd
].E
, pVD
);
2245 addeliminatedparams_evalue(&s
[nd
].E
, CT
);
2253 evalue_set_si(eres
, 0, 1);
2255 eres
->x
.p
= new_enode(partition
, 2*nd
, C
->Dimension
);
2256 for (int j
= 0; j
< nd
; ++j
) {
2257 EVALUE_SET_DOMAIN(eres
->x
.p
->arr
[2*j
], s
[j
].D
);
2258 value_clear(eres
->x
.p
->arr
[2*j
+1].d
);
2259 eres
->x
.p
->arr
[2*j
+1] = s
[j
].E
;
2260 Domain_Free(fVD
[j
]);
2268 Polyhedron_Free(CEq
);
2273 Enumeration
* barvinok_enumerate(Polyhedron
*P
, Polyhedron
* C
, unsigned MaxRays
)
2275 evalue
*EP
= barvinok_enumerate_ev(P
, C
, MaxRays
);
2277 return partition2enumeration(EP
);
2280 static void SwapColumns(Value
**V
, int n
, int i
, int j
)
2282 for (int r
= 0; r
< n
; ++r
)
2283 value_swap(V
[r
][i
], V
[r
][j
]);
2286 static void SwapColumns(Polyhedron
*P
, int i
, int j
)
2288 SwapColumns(P
->Constraint
, P
->NbConstraints
, i
, j
);
2289 SwapColumns(P
->Ray
, P
->NbRays
, i
, j
);
2292 static void negative_test_constraint(Value
*l
, Value
*u
, Value
*c
, int pos
,
2295 value_oppose(*v
, u
[pos
+1]);
2296 Vector_Combine(l
+1, u
+1, c
+1, *v
, l
[pos
+1], len
-1);
2297 value_multiply(*v
, *v
, l
[pos
+1]);
2298 value_substract(c
[len
-1], c
[len
-1], *v
);
2299 value_set_si(*v
, -1);
2300 Vector_Scale(c
+1, c
+1, *v
, len
-1);
2301 value_decrement(c
[len
-1], c
[len
-1]);
2302 ConstraintSimplify(c
, c
, len
, v
);
2305 static bool parallel_constraints(Value
*l
, Value
*u
, Value
*c
, int pos
,
2314 Vector_Gcd(&l
[1+pos
], len
, &g1
);
2315 Vector_Gcd(&u
[1+pos
], len
, &g2
);
2316 Vector_Combine(l
+1+pos
, u
+1+pos
, c
+1, g2
, g1
, len
);
2317 parallel
= First_Non_Zero(c
+1, len
) == -1;
2325 static void negative_test_constraint7(Value
*l
, Value
*u
, Value
*c
, int pos
,
2326 int exist
, int len
, Value
*v
)
2331 Vector_Gcd(&u
[1+pos
], exist
, v
);
2332 Vector_Gcd(&l
[1+pos
], exist
, &g
);
2333 Vector_Combine(l
+1, u
+1, c
+1, *v
, g
, len
-1);
2334 value_multiply(*v
, *v
, g
);
2335 value_substract(c
[len
-1], c
[len
-1], *v
);
2336 value_set_si(*v
, -1);
2337 Vector_Scale(c
+1, c
+1, *v
, len
-1);
2338 value_decrement(c
[len
-1], c
[len
-1]);
2339 ConstraintSimplify(c
, c
, len
, v
);
2344 static void oppose_constraint(Value
*c
, int len
, Value
*v
)
2346 value_set_si(*v
, -1);
2347 Vector_Scale(c
+1, c
+1, *v
, len
-1);
2348 value_decrement(c
[len
-1], c
[len
-1]);
2351 static bool SplitOnConstraint(Polyhedron
*P
, int i
, int l
, int u
,
2352 int nvar
, int len
, int exist
, int MaxRays
,
2353 Vector
*row
, Value
& f
, bool independent
,
2354 Polyhedron
**pos
, Polyhedron
**neg
)
2356 negative_test_constraint(P
->Constraint
[l
], P
->Constraint
[u
],
2357 row
->p
, nvar
+i
, len
, &f
);
2358 *neg
= AddConstraints(row
->p
, 1, P
, MaxRays
);
2360 /* We found an independent, but useless constraint
2361 * Maybe we should detect this earlier and not
2362 * mark the variable as INDEPENDENT
2364 if (emptyQ((*neg
))) {
2365 Polyhedron_Free(*neg
);
2369 oppose_constraint(row
->p
, len
, &f
);
2370 *pos
= AddConstraints(row
->p
, 1, P
, MaxRays
);
2372 if (emptyQ((*pos
))) {
2373 Polyhedron_Free(*neg
);
2374 Polyhedron_Free(*pos
);
2382 * unimodularly transform P such that constraint r is transformed
2383 * into a constraint that involves only a single (the first)
2384 * existential variable
2387 static Polyhedron
*rotate_along(Polyhedron
*P
, int r
, int nvar
, int exist
,
2393 Vector
*row
= Vector_Alloc(exist
);
2394 Vector_Copy(P
->Constraint
[r
]+1+nvar
, row
->p
, exist
);
2395 Vector_Gcd(row
->p
, exist
, &g
);
2396 if (value_notone_p(g
))
2397 Vector_AntiScale(row
->p
, row
->p
, g
, exist
);
2400 Matrix
*M
= unimodular_complete(row
);
2401 Matrix
*M2
= Matrix_Alloc(P
->Dimension
+1, P
->Dimension
+1);
2402 for (r
= 0; r
< nvar
; ++r
)
2403 value_set_si(M2
->p
[r
][r
], 1);
2404 for ( ; r
< nvar
+exist
; ++r
)
2405 Vector_Copy(M
->p
[r
-nvar
], M2
->p
[r
]+nvar
, exist
);
2406 for ( ; r
< P
->Dimension
+1; ++r
)
2407 value_set_si(M2
->p
[r
][r
], 1);
2408 Polyhedron
*T
= Polyhedron_Image(P
, M2
, MaxRays
);
2417 static bool SplitOnVar(Polyhedron
*P
, int i
,
2418 int nvar
, int len
, int exist
, int MaxRays
,
2419 Vector
*row
, Value
& f
, bool independent
,
2420 Polyhedron
**pos
, Polyhedron
**neg
)
2424 for (int l
= P
->NbEq
; l
< P
->NbConstraints
; ++l
) {
2425 if (value_negz_p(P
->Constraint
[l
][nvar
+i
+1]))
2429 for (j
= 0; j
< exist
; ++j
)
2430 if (j
!= i
&& value_notzero_p(P
->Constraint
[l
][nvar
+j
+1]))
2436 for (int u
= P
->NbEq
; u
< P
->NbConstraints
; ++u
) {
2437 if (value_posz_p(P
->Constraint
[u
][nvar
+i
+1]))
2441 for (j
= 0; j
< exist
; ++j
)
2442 if (j
!= i
&& value_notzero_p(P
->Constraint
[u
][nvar
+j
+1]))
2448 if (SplitOnConstraint(P
, i
, l
, u
,
2449 nvar
, len
, exist
, MaxRays
,
2450 row
, f
, independent
,
2454 SwapColumns(*neg
, nvar
+1, nvar
+1+i
);
2464 static bool double_bound_pair(Polyhedron
*P
, int nvar
, int exist
,
2465 int i
, int l1
, int l2
,
2466 Polyhedron
**pos
, Polyhedron
**neg
)
2470 Vector
*row
= Vector_Alloc(P
->Dimension
+2);
2471 value_set_si(row
->p
[0], 1);
2472 value_oppose(f
, P
->Constraint
[l1
][nvar
+i
+1]);
2473 Vector_Combine(P
->Constraint
[l1
]+1, P
->Constraint
[l2
]+1,
2475 P
->Constraint
[l2
][nvar
+i
+1], f
,
2477 ConstraintSimplify(row
->p
, row
->p
, P
->Dimension
+2, &f
);
2478 *pos
= AddConstraints(row
->p
, 1, P
, 0);
2479 value_set_si(f
, -1);
2480 Vector_Scale(row
->p
+1, row
->p
+1, f
, P
->Dimension
+1);
2481 value_decrement(row
->p
[P
->Dimension
+1], row
->p
[P
->Dimension
+1]);
2482 *neg
= AddConstraints(row
->p
, 1, P
, 0);
2486 return !emptyQ((*pos
)) && !emptyQ((*neg
));
2489 static bool double_bound(Polyhedron
*P
, int nvar
, int exist
,
2490 Polyhedron
**pos
, Polyhedron
**neg
)
2492 for (int i
= 0; i
< exist
; ++i
) {
2494 for (l1
= P
->NbEq
; l1
< P
->NbConstraints
; ++l1
) {
2495 if (value_negz_p(P
->Constraint
[l1
][nvar
+i
+1]))
2497 for (l2
= l1
+ 1; l2
< P
->NbConstraints
; ++l2
) {
2498 if (value_negz_p(P
->Constraint
[l2
][nvar
+i
+1]))
2500 if (double_bound_pair(P
, nvar
, exist
, i
, l1
, l2
, pos
, neg
))
2504 for (l1
= P
->NbEq
; l1
< P
->NbConstraints
; ++l1
) {
2505 if (value_posz_p(P
->Constraint
[l1
][nvar
+i
+1]))
2507 if (l1
< P
->NbConstraints
)
2508 for (l2
= l1
+ 1; l2
< P
->NbConstraints
; ++l2
) {
2509 if (value_posz_p(P
->Constraint
[l2
][nvar
+i
+1]))
2511 if (double_bound_pair(P
, nvar
, exist
, i
, l1
, l2
, pos
, neg
))
2523 INDEPENDENT
= 1 << 2,
2527 static evalue
* enumerate_or(Polyhedron
*D
,
2528 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2531 fprintf(stderr
, "\nER: Or\n");
2532 #endif /* DEBUG_ER */
2534 Polyhedron
*N
= D
->next
;
2537 barvinok_enumerate_e(D
, exist
, nparam
, MaxRays
);
2540 for (D
= N
; D
; D
= N
) {
2545 barvinok_enumerate_e(D
, exist
, nparam
, MaxRays
);
2548 free_evalue_refs(EN
);
2558 static evalue
* enumerate_sum(Polyhedron
*P
,
2559 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2561 int nvar
= P
->Dimension
- exist
- nparam
;
2562 int toswap
= nvar
< exist
? nvar
: exist
;
2563 for (int i
= 0; i
< toswap
; ++i
)
2564 SwapColumns(P
, 1 + i
, nvar
+exist
- i
);
2568 fprintf(stderr
, "\nER: Sum\n");
2569 #endif /* DEBUG_ER */
2571 evalue
*EP
= barvinok_enumerate_e(P
, exist
, nparam
, MaxRays
);
2573 for (int i
= 0; i
< /* nvar */ nparam
; ++i
) {
2574 Matrix
*C
= Matrix_Alloc(1, 1 + nparam
+ 1);
2575 value_set_si(C
->p
[0][0], 1);
2577 value_init(split
.d
);
2578 value_set_si(split
.d
, 0);
2579 split
.x
.p
= new_enode(partition
, 4, nparam
);
2580 value_set_si(C
->p
[0][1+i
], 1);
2581 Matrix
*C2
= Matrix_Copy(C
);
2582 EVALUE_SET_DOMAIN(split
.x
.p
->arr
[0],
2583 Constraints2Polyhedron(C2
, MaxRays
));
2585 evalue_set_si(&split
.x
.p
->arr
[1], 1, 1);
2586 value_set_si(C
->p
[0][1+i
], -1);
2587 value_set_si(C
->p
[0][1+nparam
], -1);
2588 EVALUE_SET_DOMAIN(split
.x
.p
->arr
[2],
2589 Constraints2Polyhedron(C
, MaxRays
));
2590 evalue_set_si(&split
.x
.p
->arr
[3], 1, 1);
2592 free_evalue_refs(&split
);
2596 evalue_range_reduction(EP
);
2598 evalue_frac2floor(EP
);
2600 evalue
*sum
= esum(EP
, nvar
);
2602 free_evalue_refs(EP
);
2606 evalue_range_reduction(EP
);
2611 static evalue
* split_sure(Polyhedron
*P
, Polyhedron
*S
,
2612 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2614 int nvar
= P
->Dimension
- exist
- nparam
;
2616 Matrix
*M
= Matrix_Alloc(exist
, S
->Dimension
+2);
2617 for (int i
= 0; i
< exist
; ++i
)
2618 value_set_si(M
->p
[i
][nvar
+i
+1], 1);
2620 S
= DomainAddRays(S
, M
, MaxRays
);
2622 Polyhedron
*F
= DomainAddRays(P
, M
, MaxRays
);
2623 Polyhedron
*D
= DomainDifference(F
, S
, MaxRays
);
2625 D
= Disjoint_Domain(D
, 0, MaxRays
);
2630 M
= Matrix_Alloc(P
->Dimension
+1-exist
, P
->Dimension
+1);
2631 for (int j
= 0; j
< nvar
; ++j
)
2632 value_set_si(M
->p
[j
][j
], 1);
2633 for (int j
= 0; j
< nparam
+1; ++j
)
2634 value_set_si(M
->p
[nvar
+j
][nvar
+exist
+j
], 1);
2635 Polyhedron
*T
= Polyhedron_Image(S
, M
, MaxRays
);
2636 evalue
*EP
= barvinok_enumerate_e(T
, 0, nparam
, MaxRays
);
2641 for (Polyhedron
*Q
= D
; Q
; Q
= Q
->next
) {
2642 Polyhedron
*N
= Q
->next
;
2644 T
= DomainIntersection(P
, Q
, MaxRays
);
2645 evalue
*E
= barvinok_enumerate_e(T
, exist
, nparam
, MaxRays
);
2647 free_evalue_refs(E
);
2656 static evalue
* enumerate_sure(Polyhedron
*P
,
2657 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2661 int nvar
= P
->Dimension
- exist
- nparam
;
2667 for (i
= 0; i
< exist
; ++i
) {
2668 Matrix
*M
= Matrix_Alloc(S
->NbConstraints
, S
->Dimension
+2);
2670 value_set_si(lcm
, 1);
2671 for (int j
= 0; j
< S
->NbConstraints
; ++j
) {
2672 if (value_negz_p(S
->Constraint
[j
][1+nvar
+i
]))
2674 if (value_one_p(S
->Constraint
[j
][1+nvar
+i
]))
2676 value_lcm(lcm
, S
->Constraint
[j
][1+nvar
+i
], &lcm
);
2679 for (int j
= 0; j
< S
->NbConstraints
; ++j
) {
2680 if (value_negz_p(S
->Constraint
[j
][1+nvar
+i
]))
2682 if (value_one_p(S
->Constraint
[j
][1+nvar
+i
]))
2684 value_division(f
, lcm
, S
->Constraint
[j
][1+nvar
+i
]);
2685 Vector_Scale(S
->Constraint
[j
], M
->p
[c
], f
, S
->Dimension
+2);
2686 value_substract(M
->p
[c
][S
->Dimension
+1],
2687 M
->p
[c
][S
->Dimension
+1],
2689 value_increment(M
->p
[c
][S
->Dimension
+1],
2690 M
->p
[c
][S
->Dimension
+1]);
2694 S
= AddConstraints(M
->p
[0], c
, S
, MaxRays
);
2709 fprintf(stderr
, "\nER: Sure\n");
2710 #endif /* DEBUG_ER */
2712 return split_sure(P
, S
, exist
, nparam
, MaxRays
);
2715 static evalue
* enumerate_sure2(Polyhedron
*P
,
2716 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2718 int nvar
= P
->Dimension
- exist
- nparam
;
2720 for (r
= 0; r
< P
->NbRays
; ++r
)
2721 if (value_one_p(P
->Ray
[r
][0]) &&
2722 value_one_p(P
->Ray
[r
][P
->Dimension
+1]))
2728 Matrix
*M
= Matrix_Alloc(nvar
+ 1 + nparam
, P
->Dimension
+2);
2729 for (int i
= 0; i
< nvar
; ++i
)
2730 value_set_si(M
->p
[i
][1+i
], 1);
2731 for (int i
= 0; i
< nparam
; ++i
)
2732 value_set_si(M
->p
[i
+nvar
][1+nvar
+exist
+i
], 1);
2733 Vector_Copy(P
->Ray
[r
]+1+nvar
, M
->p
[nvar
+nparam
]+1+nvar
, exist
);
2734 value_set_si(M
->p
[nvar
+nparam
][0], 1);
2735 value_set_si(M
->p
[nvar
+nparam
][P
->Dimension
+1], 1);
2736 Polyhedron
* F
= Rays2Polyhedron(M
, MaxRays
);
2739 Polyhedron
*I
= DomainIntersection(F
, P
, MaxRays
);
2743 fprintf(stderr
, "\nER: Sure2\n");
2744 #endif /* DEBUG_ER */
2746 return split_sure(P
, I
, exist
, nparam
, MaxRays
);
2749 static evalue
* enumerate_cyclic(Polyhedron
*P
,
2750 unsigned exist
, unsigned nparam
,
2751 evalue
* EP
, int r
, int p
, unsigned MaxRays
)
2753 int nvar
= P
->Dimension
- exist
- nparam
;
2755 /* If EP in its fractional maps only contains references
2756 * to the remainder parameter with appropriate coefficients
2757 * then we could in principle avoid adding existentially
2758 * quantified variables to the validity domains.
2759 * We'd have to replace the remainder by m { p/m }
2760 * and multiply with an appropriate factor that is one
2761 * only in the appropriate range.
2762 * This last multiplication can be avoided if EP
2763 * has a single validity domain with no (further)
2764 * constraints on the remainder parameter
2767 Matrix
*CT
= Matrix_Alloc(nparam
+1, nparam
+3);
2768 Matrix
*M
= Matrix_Alloc(1, 1+nparam
+3);
2769 for (int j
= 0; j
< nparam
; ++j
)
2771 value_set_si(CT
->p
[j
][j
], 1);
2772 value_set_si(CT
->p
[p
][nparam
+1], 1);
2773 value_set_si(CT
->p
[nparam
][nparam
+2], 1);
2774 value_set_si(M
->p
[0][1+p
], -1);
2775 value_absolute(M
->p
[0][1+nparam
], P
->Ray
[0][1+nvar
+exist
+p
]);
2776 value_set_si(M
->p
[0][1+nparam
+1], 1);
2777 Polyhedron
*CEq
= Constraints2Polyhedron(M
, 1);
2779 addeliminatedparams_enum(EP
, CT
, CEq
, MaxRays
, nparam
);
2780 Polyhedron_Free(CEq
);
2786 static void enumerate_vd_add_ray(evalue
*EP
, Matrix
*Rays
, unsigned MaxRays
)
2788 if (value_notzero_p(EP
->d
))
2791 assert(EP
->x
.p
->type
== partition
);
2792 assert(EP
->x
.p
->pos
== EVALUE_DOMAIN(EP
->x
.p
->arr
[0])->Dimension
);
2793 for (int i
= 0; i
< EP
->x
.p
->size
/2; ++i
) {
2794 Polyhedron
*D
= EVALUE_DOMAIN(EP
->x
.p
->arr
[2*i
]);
2795 Polyhedron
*N
= DomainAddRays(D
, Rays
, MaxRays
);
2796 EVALUE_SET_DOMAIN(EP
->x
.p
->arr
[2*i
], N
);
2801 static evalue
* enumerate_line(Polyhedron
*P
,
2802 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2808 fprintf(stderr
, "\nER: Line\n");
2809 #endif /* DEBUG_ER */
2811 int nvar
= P
->Dimension
- exist
- nparam
;
2813 for (i
= 0; i
< nparam
; ++i
)
2814 if (value_notzero_p(P
->Ray
[0][1+nvar
+exist
+i
]))
2817 for (j
= i
+1; j
< nparam
; ++j
)
2818 if (value_notzero_p(P
->Ray
[0][1+nvar
+exist
+i
]))
2820 assert(j
>= nparam
); // for now
2822 Matrix
*M
= Matrix_Alloc(2, P
->Dimension
+2);
2823 value_set_si(M
->p
[0][0], 1);
2824 value_set_si(M
->p
[0][1+nvar
+exist
+i
], 1);
2825 value_set_si(M
->p
[1][0], 1);
2826 value_set_si(M
->p
[1][1+nvar
+exist
+i
], -1);
2827 value_absolute(M
->p
[1][1+P
->Dimension
], P
->Ray
[0][1+nvar
+exist
+i
]);
2828 value_decrement(M
->p
[1][1+P
->Dimension
], M
->p
[1][1+P
->Dimension
]);
2829 Polyhedron
*S
= AddConstraints(M
->p
[0], 2, P
, MaxRays
);
2830 evalue
*EP
= barvinok_enumerate_e(S
, exist
, nparam
, MaxRays
);
2834 return enumerate_cyclic(P
, exist
, nparam
, EP
, 0, i
, MaxRays
);
2837 static int single_param_pos(Polyhedron
*P
, unsigned exist
, unsigned nparam
,
2840 int nvar
= P
->Dimension
- exist
- nparam
;
2841 if (First_Non_Zero(P
->Ray
[r
]+1, nvar
) != -1)
2843 int i
= First_Non_Zero(P
->Ray
[r
]+1+nvar
+exist
, nparam
);
2846 if (First_Non_Zero(P
->Ray
[r
]+1+nvar
+exist
+1, nparam
-i
-1) != -1)
2851 static evalue
* enumerate_remove_ray(Polyhedron
*P
, int r
,
2852 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2855 fprintf(stderr
, "\nER: RedundantRay\n");
2856 #endif /* DEBUG_ER */
2860 value_set_si(one
, 1);
2861 int len
= P
->NbRays
-1;
2862 Matrix
*M
= Matrix_Alloc(2 * len
, P
->Dimension
+2);
2863 Vector_Copy(P
->Ray
[0], M
->p
[0], r
* (P
->Dimension
+2));
2864 Vector_Copy(P
->Ray
[r
+1], M
->p
[r
], (len
-r
) * (P
->Dimension
+2));
2865 for (int j
= 0; j
< P
->NbRays
; ++j
) {
2868 Vector_Combine(P
->Ray
[j
], P
->Ray
[r
], M
->p
[len
+j
-(j
>r
)],
2869 one
, P
->Ray
[j
][P
->Dimension
+1], P
->Dimension
+2);
2872 P
= Rays2Polyhedron(M
, MaxRays
);
2874 evalue
*EP
= barvinok_enumerate_e(P
, exist
, nparam
, MaxRays
);
2881 static evalue
* enumerate_redundant_ray(Polyhedron
*P
,
2882 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2884 assert(P
->NbBid
== 0);
2885 int nvar
= P
->Dimension
- exist
- nparam
;
2889 for (int r
= 0; r
< P
->NbRays
; ++r
) {
2890 if (value_notzero_p(P
->Ray
[r
][P
->Dimension
+1]))
2892 int i1
= single_param_pos(P
, exist
, nparam
, r
);
2895 for (int r2
= r
+1; r2
< P
->NbRays
; ++r2
) {
2896 if (value_notzero_p(P
->Ray
[r2
][P
->Dimension
+1]))
2898 int i2
= single_param_pos(P
, exist
, nparam
, r2
);
2904 value_division(m
, P
->Ray
[r
][1+nvar
+exist
+i1
],
2905 P
->Ray
[r2
][1+nvar
+exist
+i1
]);
2906 value_multiply(m
, m
, P
->Ray
[r2
][1+nvar
+exist
+i1
]);
2907 /* r2 divides r => r redundant */
2908 if (value_eq(m
, P
->Ray
[r
][1+nvar
+exist
+i1
])) {
2910 return enumerate_remove_ray(P
, r
, exist
, nparam
, MaxRays
);
2913 value_division(m
, P
->Ray
[r2
][1+nvar
+exist
+i1
],
2914 P
->Ray
[r
][1+nvar
+exist
+i1
]);
2915 value_multiply(m
, m
, P
->Ray
[r
][1+nvar
+exist
+i1
]);
2916 /* r divides r2 => r2 redundant */
2917 if (value_eq(m
, P
->Ray
[r2
][1+nvar
+exist
+i1
])) {
2919 return enumerate_remove_ray(P
, r2
, exist
, nparam
, MaxRays
);
2927 static Polyhedron
*upper_bound(Polyhedron
*P
,
2928 int pos
, Value
*max
, Polyhedron
**R
)
2937 for (Polyhedron
*Q
= P
; Q
; Q
= N
) {
2939 for (r
= 0; r
< P
->NbRays
; ++r
) {
2940 if (value_zero_p(P
->Ray
[r
][P
->Dimension
+1]) &&
2941 value_pos_p(P
->Ray
[r
][1+pos
]))
2944 if (r
< P
->NbRays
) {
2952 for (r
= 0; r
< P
->NbRays
; ++r
) {
2953 if (value_zero_p(P
->Ray
[r
][P
->Dimension
+1]))
2955 mpz_fdiv_q(v
, P
->Ray
[r
][1+pos
], P
->Ray
[r
][1+P
->Dimension
]);
2956 if ((!Q
->next
&& r
== 0) || value_gt(v
, *max
))
2957 value_assign(*max
, v
);
2964 static evalue
* enumerate_ray(Polyhedron
*P
,
2965 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
2967 assert(P
->NbBid
== 0);
2968 int nvar
= P
->Dimension
- exist
- nparam
;
2971 for (r
= 0; r
< P
->NbRays
; ++r
)
2972 if (value_zero_p(P
->Ray
[r
][P
->Dimension
+1]))
2978 for (r2
= r
+1; r2
< P
->NbRays
; ++r2
)
2979 if (value_zero_p(P
->Ray
[r2
][P
->Dimension
+1]))
2981 if (r2
< P
->NbRays
) {
2983 return enumerate_sum(P
, exist
, nparam
, MaxRays
);
2987 fprintf(stderr
, "\nER: Ray\n");
2988 #endif /* DEBUG_ER */
2994 value_set_si(one
, 1);
2995 int i
= single_param_pos(P
, exist
, nparam
, r
);
2996 assert(i
!= -1); // for now;
2998 Matrix
*M
= Matrix_Alloc(P
->NbRays
, P
->Dimension
+2);
2999 for (int j
= 0; j
< P
->NbRays
; ++j
) {
3000 Vector_Combine(P
->Ray
[j
], P
->Ray
[r
], M
->p
[j
],
3001 one
, P
->Ray
[j
][P
->Dimension
+1], P
->Dimension
+2);
3003 Polyhedron
*S
= Rays2Polyhedron(M
, MaxRays
);
3005 Polyhedron
*D
= DomainDifference(P
, S
, MaxRays
);
3007 // Polyhedron_Print(stderr, P_VALUE_FMT, D);
3008 assert(value_pos_p(P
->Ray
[r
][1+nvar
+exist
+i
])); // for now
3010 D
= upper_bound(D
, nvar
+exist
+i
, &m
, &R
);
3014 M
= Matrix_Alloc(2, P
->Dimension
+2);
3015 value_set_si(M
->p
[0][0], 1);
3016 value_set_si(M
->p
[1][0], 1);
3017 value_set_si(M
->p
[0][1+nvar
+exist
+i
], -1);
3018 value_set_si(M
->p
[1][1+nvar
+exist
+i
], 1);
3019 value_assign(M
->p
[0][1+P
->Dimension
], m
);
3020 value_oppose(M
->p
[1][1+P
->Dimension
], m
);
3021 value_addto(M
->p
[1][1+P
->Dimension
], M
->p
[1][1+P
->Dimension
],
3022 P
->Ray
[r
][1+nvar
+exist
+i
]);
3023 value_decrement(M
->p
[1][1+P
->Dimension
], M
->p
[1][1+P
->Dimension
]);
3024 // Matrix_Print(stderr, P_VALUE_FMT, M);
3025 D
= AddConstraints(M
->p
[0], 2, P
, MaxRays
);
3026 // Polyhedron_Print(stderr, P_VALUE_FMT, D);
3027 value_substract(M
->p
[0][1+P
->Dimension
], M
->p
[0][1+P
->Dimension
],
3028 P
->Ray
[r
][1+nvar
+exist
+i
]);
3029 // Matrix_Print(stderr, P_VALUE_FMT, M);
3030 S
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
3031 // Polyhedron_Print(stderr, P_VALUE_FMT, S);
3034 evalue
*EP
= barvinok_enumerate_e(D
, exist
, nparam
, MaxRays
);
3039 if (value_notone_p(P
->Ray
[r
][1+nvar
+exist
+i
]))
3040 EP
= enumerate_cyclic(P
, exist
, nparam
, EP
, r
, i
, MaxRays
);
3042 M
= Matrix_Alloc(1, nparam
+2);
3043 value_set_si(M
->p
[0][0], 1);
3044 value_set_si(M
->p
[0][1+i
], 1);
3045 enumerate_vd_add_ray(EP
, M
, MaxRays
);
3050 evalue
*E
= barvinok_enumerate_e(S
, exist
, nparam
, MaxRays
);
3052 free_evalue_refs(E
);
3059 evalue
*ER
= enumerate_or(R
, exist
, nparam
, MaxRays
);
3061 free_evalue_refs(ER
);
3068 static evalue
* new_zero_ep()
3073 evalue_set_si(EP
, 0, 1);
3077 static evalue
* enumerate_vd(Polyhedron
**PA
,
3078 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
3080 Polyhedron
*P
= *PA
;
3081 int nvar
= P
->Dimension
- exist
- nparam
;
3082 Param_Polyhedron
*PP
= NULL
;
3083 Polyhedron
*C
= Universe_Polyhedron(nparam
);
3087 PP
= Polyhedron2Param_SimplifiedDomain(&PR
,C
,MaxRays
,&CEq
,&CT
);
3091 Param_Domain
*D
, *last
;
3094 for (nd
= 0, D
=PP
->D
; D
; D
=D
->next
, ++nd
)
3097 Polyhedron
**VD
= new Polyhedron_p
[nd
];
3098 Polyhedron
**fVD
= new Polyhedron_p
[nd
];
3099 for(nd
= 0, D
=PP
->D
; D
; D
=D
->next
) {
3100 Polyhedron
*rVD
= reduce_domain(D
->Domain
, CT
, CEq
,
3114 /* This doesn't seem to have any effect */
3116 Polyhedron
*CA
= align_context(VD
[0], P
->Dimension
, MaxRays
);
3118 P
= DomainIntersection(P
, CA
, MaxRays
);
3121 Polyhedron_Free(CA
);
3126 if (!EP
&& CT
->NbColumns
!= CT
->NbRows
) {
3127 Polyhedron
*CEqr
= DomainImage(CEq
, CT
, MaxRays
);
3128 Polyhedron
*CA
= align_context(CEqr
, PR
->Dimension
, MaxRays
);
3129 Polyhedron
*I
= DomainIntersection(PR
, CA
, MaxRays
);
3130 Polyhedron_Free(CEqr
);
3131 Polyhedron_Free(CA
);
3133 fprintf(stderr
, "\nER: Eliminate\n");
3134 #endif /* DEBUG_ER */
3135 nparam
-= CT
->NbColumns
- CT
->NbRows
;
3136 EP
= barvinok_enumerate_e(I
, exist
, nparam
, MaxRays
);
3137 nparam
+= CT
->NbColumns
- CT
->NbRows
;
3138 addeliminatedparams_enum(EP
, CT
, CEq
, MaxRays
, nparam
);
3142 Polyhedron_Free(PR
);
3145 if (!EP
&& nd
> 1) {
3147 fprintf(stderr
, "\nER: VD\n");
3148 #endif /* DEBUG_ER */
3149 for (int i
= 0; i
< nd
; ++i
) {
3150 Polyhedron
*CA
= align_context(VD
[i
], P
->Dimension
, MaxRays
);
3151 Polyhedron
*I
= DomainIntersection(P
, CA
, MaxRays
);
3154 EP
= barvinok_enumerate_e(I
, exist
, nparam
, MaxRays
);
3156 evalue
*E
= barvinok_enumerate_e(I
, exist
, nparam
, MaxRays
);
3158 free_evalue_refs(E
);
3162 Polyhedron_Free(CA
);
3166 for (int i
= 0; i
< nd
; ++i
) {
3167 Polyhedron_Free(VD
[i
]);
3168 Polyhedron_Free(fVD
[i
]);
3174 if (!EP
&& nvar
== 0) {
3177 Param_Vertices
*V
, *V2
;
3178 Matrix
* M
= Matrix_Alloc(1, P
->Dimension
+2);
3180 FORALL_PVertex_in_ParamPolyhedron(V
, last
, PP
) {
3182 FORALL_PVertex_in_ParamPolyhedron(V2
, last
, PP
) {
3189 for (int i
= 0; i
< exist
; ++i
) {
3190 value_oppose(f
, V
->Vertex
->p
[i
][nparam
+1]);
3191 Vector_Combine(V
->Vertex
->p
[i
],
3193 M
->p
[0] + 1 + nvar
+ exist
,
3194 V2
->Vertex
->p
[i
][nparam
+1],
3198 for (j
= 0; j
< nparam
; ++j
)
3199 if (value_notzero_p(M
->p
[0][1+nvar
+exist
+j
]))
3203 ConstraintSimplify(M
->p
[0], M
->p
[0],
3204 P
->Dimension
+2, &f
);
3205 value_set_si(M
->p
[0][0], 0);
3206 Polyhedron
*para
= AddConstraints(M
->p
[0], 1, P
,
3209 Polyhedron_Free(para
);
3212 Polyhedron
*pos
, *neg
;
3213 value_set_si(M
->p
[0][0], 1);
3214 value_decrement(M
->p
[0][P
->Dimension
+1],
3215 M
->p
[0][P
->Dimension
+1]);
3216 neg
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
3217 value_set_si(f
, -1);
3218 Vector_Scale(M
->p
[0]+1, M
->p
[0]+1, f
,
3220 value_decrement(M
->p
[0][P
->Dimension
+1],
3221 M
->p
[0][P
->Dimension
+1]);
3222 value_decrement(M
->p
[0][P
->Dimension
+1],
3223 M
->p
[0][P
->Dimension
+1]);
3224 pos
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
3225 if (emptyQ(neg
) && emptyQ(pos
)) {
3226 Polyhedron_Free(para
);
3227 Polyhedron_Free(pos
);
3228 Polyhedron_Free(neg
);
3232 fprintf(stderr
, "\nER: Order\n");
3233 #endif /* DEBUG_ER */
3234 EP
= barvinok_enumerate_e(para
, exist
, nparam
, MaxRays
);
3237 E
= barvinok_enumerate_e(pos
, exist
, nparam
, MaxRays
);
3239 free_evalue_refs(E
);
3243 E
= barvinok_enumerate_e(neg
, exist
, nparam
, MaxRays
);
3245 free_evalue_refs(E
);
3248 Polyhedron_Free(para
);
3249 Polyhedron_Free(pos
);
3250 Polyhedron_Free(neg
);
3255 } END_FORALL_PVertex_in_ParamPolyhedron
;
3258 } END_FORALL_PVertex_in_ParamPolyhedron
;
3261 /* Search for vertex coordinate to split on */
3262 /* First look for one independent of the parameters */
3263 FORALL_PVertex_in_ParamPolyhedron(V
, last
, PP
) {
3264 for (int i
= 0; i
< exist
; ++i
) {
3266 for (j
= 0; j
< nparam
; ++j
)
3267 if (value_notzero_p(V
->Vertex
->p
[i
][j
]))
3271 value_set_si(M
->p
[0][0], 1);
3272 Vector_Set(M
->p
[0]+1, 0, nvar
+exist
);
3273 Vector_Copy(V
->Vertex
->p
[i
],
3274 M
->p
[0] + 1 + nvar
+ exist
, nparam
+1);
3275 value_oppose(M
->p
[0][1+nvar
+i
],
3276 V
->Vertex
->p
[i
][nparam
+1]);
3278 Polyhedron
*pos
, *neg
;
3279 value_set_si(M
->p
[0][0], 1);
3280 value_decrement(M
->p
[0][P
->Dimension
+1],
3281 M
->p
[0][P
->Dimension
+1]);
3282 neg
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
3283 value_set_si(f
, -1);
3284 Vector_Scale(M
->p
[0]+1, M
->p
[0]+1, f
,
3286 value_decrement(M
->p
[0][P
->Dimension
+1],
3287 M
->p
[0][P
->Dimension
+1]);
3288 value_decrement(M
->p
[0][P
->Dimension
+1],
3289 M
->p
[0][P
->Dimension
+1]);
3290 pos
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
3291 if (emptyQ(neg
) || emptyQ(pos
)) {
3292 Polyhedron_Free(pos
);
3293 Polyhedron_Free(neg
);
3296 Polyhedron_Free(pos
);
3297 value_increment(M
->p
[0][P
->Dimension
+1],
3298 M
->p
[0][P
->Dimension
+1]);
3299 pos
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
3301 fprintf(stderr
, "\nER: Vertex\n");
3302 #endif /* DEBUG_ER */
3304 EP
= enumerate_or(pos
, exist
, nparam
, MaxRays
);
3309 } END_FORALL_PVertex_in_ParamPolyhedron
;
3313 /* Search for vertex coordinate to split on */
3314 /* Now look for one that depends on the parameters */
3315 FORALL_PVertex_in_ParamPolyhedron(V
, last
, PP
) {
3316 for (int i
= 0; i
< exist
; ++i
) {
3317 value_set_si(M
->p
[0][0], 1);
3318 Vector_Set(M
->p
[0]+1, 0, nvar
+exist
);
3319 Vector_Copy(V
->Vertex
->p
[i
],
3320 M
->p
[0] + 1 + nvar
+ exist
, nparam
+1);
3321 value_oppose(M
->p
[0][1+nvar
+i
],
3322 V
->Vertex
->p
[i
][nparam
+1]);
3324 Polyhedron
*pos
, *neg
;
3325 value_set_si(M
->p
[0][0], 1);
3326 value_decrement(M
->p
[0][P
->Dimension
+1],
3327 M
->p
[0][P
->Dimension
+1]);
3328 neg
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
3329 value_set_si(f
, -1);
3330 Vector_Scale(M
->p
[0]+1, M
->p
[0]+1, f
,
3332 value_decrement(M
->p
[0][P
->Dimension
+1],
3333 M
->p
[0][P
->Dimension
+1]);
3334 value_decrement(M
->p
[0][P
->Dimension
+1],
3335 M
->p
[0][P
->Dimension
+1]);
3336 pos
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
3337 if (emptyQ(neg
) || emptyQ(pos
)) {
3338 Polyhedron_Free(pos
);
3339 Polyhedron_Free(neg
);
3342 Polyhedron_Free(pos
);
3343 value_increment(M
->p
[0][P
->Dimension
+1],
3344 M
->p
[0][P
->Dimension
+1]);
3345 pos
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
3347 fprintf(stderr
, "\nER: ParamVertex\n");
3348 #endif /* DEBUG_ER */
3350 EP
= enumerate_or(pos
, exist
, nparam
, MaxRays
);
3355 } END_FORALL_PVertex_in_ParamPolyhedron
;
3363 Polyhedron_Free(CEq
);
3367 Param_Polyhedron_Free(PP
);
3374 evalue
*barvinok_enumerate_pip(Polyhedron
*P
,
3375 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
3380 evalue
*barvinok_enumerate_pip(Polyhedron
*P
,
3381 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
3383 int nvar
= P
->Dimension
- exist
- nparam
;
3384 evalue
*EP
= new_zero_ep();
3385 Polyhedron
*Q
, *N
, *T
= 0;
3391 fprintf(stderr
, "\nER: PIP\n");
3392 #endif /* DEBUG_ER */
3394 for (int i
= 0; i
< P
->Dimension
; ++i
) {
3397 bool posray
= false;
3398 bool negray
= false;
3399 value_set_si(min
, 0);
3400 for (int j
= 0; j
< P
->NbRays
; ++j
) {
3401 if (value_pos_p(P
->Ray
[j
][1+i
])) {
3403 if (value_zero_p(P
->Ray
[j
][1+P
->Dimension
]))
3405 } else if (value_neg_p(P
->Ray
[j
][1+i
])) {
3407 if (value_zero_p(P
->Ray
[j
][1+P
->Dimension
]))
3411 P
->Ray
[j
][1+i
], P
->Ray
[j
][1+P
->Dimension
]);
3412 if (value_lt(tmp
, min
))
3413 value_assign(min
, tmp
);
3418 assert(!(posray
&& negray
));
3419 assert(!negray
); // for now
3420 Polyhedron
*O
= T
? T
: P
;
3421 /* shift by a safe amount */
3422 Matrix
*M
= Matrix_Alloc(O
->NbRays
, O
->Dimension
+2);
3423 Vector_Copy(O
->Ray
[0], M
->p
[0], O
->NbRays
* (O
->Dimension
+2));
3424 for (int j
= 0; j
< P
->NbRays
; ++j
) {
3425 if (value_notzero_p(M
->p
[j
][1+P
->Dimension
])) {
3426 value_multiply(tmp
, min
, M
->p
[j
][1+P
->Dimension
]);
3427 value_substract(M
->p
[j
][1+i
], M
->p
[j
][1+i
], tmp
);
3432 T
= Rays2Polyhedron(M
, MaxRays
);
3435 /* negating a parameter requires that we substitute in the
3436 * sign again afterwards.
3439 assert(i
< nvar
+exist
);
3441 T
= Polyhedron_Copy(P
);
3442 for (int j
= 0; j
< T
->NbRays
; ++j
)
3443 value_oppose(T
->Ray
[j
][1+i
], T
->Ray
[j
][1+i
]);
3444 for (int j
= 0; j
< T
->NbConstraints
; ++j
)
3445 value_oppose(T
->Constraint
[j
][1+i
], T
->Constraint
[j
][1+i
]);
3451 Polyhedron
*D
= pip_lexmin(T
? T
: P
, exist
, nparam
);
3452 for (Q
= D
; Q
; Q
= N
) {
3456 exist
= Q
->Dimension
- nvar
- nparam
;
3457 E
= barvinok_enumerate_e(Q
, exist
, nparam
, MaxRays
);
3460 free_evalue_refs(E
);
3472 static bool is_single(Value
*row
, int pos
, int len
)
3474 return First_Non_Zero(row
, pos
) == -1 &&
3475 First_Non_Zero(row
+pos
+1, len
-pos
-1) == -1;
3478 static evalue
* barvinok_enumerate_e_r(Polyhedron
*P
,
3479 unsigned exist
, unsigned nparam
, unsigned MaxRays
);
3482 static int er_level
= 0;
3484 evalue
* barvinok_enumerate_e(Polyhedron
*P
,
3485 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
3487 fprintf(stderr
, "\nER: level %i\n", er_level
);
3488 int nvar
= P
->Dimension
- exist
- nparam
;
3489 fprintf(stderr
, "%d %d %d\n", nvar
, exist
, nparam
);
3491 Polyhedron_Print(stderr
, P_VALUE_FMT
, P
);
3493 P
= DomainConstraintSimplify(Polyhedron_Copy(P
), MaxRays
);
3494 evalue
*EP
= barvinok_enumerate_e_r(P
, exist
, nparam
, MaxRays
);
3500 evalue
* barvinok_enumerate_e(Polyhedron
*P
,
3501 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
3503 P
= DomainConstraintSimplify(Polyhedron_Copy(P
), MaxRays
);
3504 evalue
*EP
= barvinok_enumerate_e_r(P
, exist
, nparam
, MaxRays
);
3510 static evalue
* barvinok_enumerate_e_r(Polyhedron
*P
,
3511 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
3514 Polyhedron
*U
= Universe_Polyhedron(nparam
);
3515 evalue
*EP
= barvinok_enumerate_ev(P
, U
, MaxRays
);
3516 //char *param_name[] = {"P", "Q", "R", "S", "T" };
3517 //print_evalue(stdout, EP, param_name);
3522 int nvar
= P
->Dimension
- exist
- nparam
;
3523 int len
= P
->Dimension
+ 2;
3526 return new_zero_ep();
3528 if (nvar
== 0 && nparam
== 0) {
3529 evalue
*EP
= new_zero_ep();
3530 barvinok_count(P
, &EP
->x
.n
, MaxRays
);
3531 if (value_pos_p(EP
->x
.n
))
3532 value_set_si(EP
->x
.n
, 1);
3537 for (r
= 0; r
< P
->NbRays
; ++r
)
3538 if (value_zero_p(P
->Ray
[r
][0]) ||
3539 value_zero_p(P
->Ray
[r
][P
->Dimension
+1])) {
3541 for (i
= 0; i
< nvar
; ++i
)
3542 if (value_notzero_p(P
->Ray
[r
][i
+1]))
3546 for (i
= nvar
+ exist
; i
< nvar
+ exist
+ nparam
; ++i
)
3547 if (value_notzero_p(P
->Ray
[r
][i
+1]))
3549 if (i
>= nvar
+ exist
+ nparam
)
3552 if (r
< P
->NbRays
) {
3553 evalue
*EP
= new_zero_ep();
3554 value_set_si(EP
->x
.n
, -1);
3559 for (r
= 0; r
< P
->NbEq
; ++r
)
3560 if ((first
= First_Non_Zero(P
->Constraint
[r
]+1+nvar
, exist
)) != -1)
3563 if (First_Non_Zero(P
->Constraint
[r
]+1+nvar
+first
+1,
3564 exist
-first
-1) != -1) {
3565 Polyhedron
*T
= rotate_along(P
, r
, nvar
, exist
, MaxRays
);
3567 fprintf(stderr
, "\nER: Equality\n");
3568 #endif /* DEBUG_ER */
3569 evalue
*EP
= barvinok_enumerate_e(T
, exist
-1, nparam
, MaxRays
);
3574 fprintf(stderr
, "\nER: Fixed\n");
3575 #endif /* DEBUG_ER */
3577 return barvinok_enumerate_e(P
, exist
-1, nparam
, MaxRays
);
3579 Polyhedron
*T
= Polyhedron_Copy(P
);
3580 SwapColumns(T
, nvar
+1, nvar
+1+first
);
3581 evalue
*EP
= barvinok_enumerate_e(T
, exist
-1, nparam
, MaxRays
);
3588 Vector
*row
= Vector_Alloc(len
);
3589 value_set_si(row
->p
[0], 1);
3594 enum constraint
* info
= new constraint
[exist
];
3595 for (int i
= 0; i
< exist
; ++i
) {
3597 for (int l
= P
->NbEq
; l
< P
->NbConstraints
; ++l
) {
3598 if (value_negz_p(P
->Constraint
[l
][nvar
+i
+1]))
3600 bool l_parallel
= is_single(P
->Constraint
[l
]+nvar
+1, i
, exist
);
3601 for (int u
= P
->NbEq
; u
< P
->NbConstraints
; ++u
) {
3602 if (value_posz_p(P
->Constraint
[u
][nvar
+i
+1]))
3604 bool lu_parallel
= l_parallel
||
3605 is_single(P
->Constraint
[u
]+nvar
+1, i
, exist
);
3606 value_oppose(f
, P
->Constraint
[u
][nvar
+i
+1]);
3607 Vector_Combine(P
->Constraint
[l
]+1, P
->Constraint
[u
]+1, row
->p
+1,
3608 f
, P
->Constraint
[l
][nvar
+i
+1], len
-1);
3609 if (!(info
[i
] & INDEPENDENT
)) {
3611 for (j
= 0; j
< exist
; ++j
)
3612 if (j
!= i
&& value_notzero_p(row
->p
[nvar
+j
+1]))
3615 //printf("independent: i: %d, l: %d, u: %d\n", i, l, u);
3616 info
[i
] = (constraint
)(info
[i
] | INDEPENDENT
);
3619 if (info
[i
] & ALL_POS
) {
3620 value_addto(row
->p
[len
-1], row
->p
[len
-1],
3621 P
->Constraint
[l
][nvar
+i
+1]);
3622 value_addto(row
->p
[len
-1], row
->p
[len
-1], f
);
3623 value_multiply(f
, f
, P
->Constraint
[l
][nvar
+i
+1]);
3624 value_substract(row
->p
[len
-1], row
->p
[len
-1], f
);
3625 value_decrement(row
->p
[len
-1], row
->p
[len
-1]);
3626 ConstraintSimplify(row
->p
, row
->p
, len
, &f
);
3627 value_set_si(f
, -1);
3628 Vector_Scale(row
->p
+1, row
->p
+1, f
, len
-1);
3629 value_decrement(row
->p
[len
-1], row
->p
[len
-1]);
3630 Polyhedron
*T
= AddConstraints(row
->p
, 1, P
, MaxRays
);
3632 //printf("not all_pos: i: %d, l: %d, u: %d\n", i, l, u);
3633 info
[i
] = (constraint
)(info
[i
] ^ ALL_POS
);
3635 //puts("pos remainder");
3636 //Polyhedron_Print(stdout, P_VALUE_FMT, T);
3639 if (!(info
[i
] & ONE_NEG
)) {
3641 negative_test_constraint(P
->Constraint
[l
],
3643 row
->p
, nvar
+i
, len
, &f
);
3644 oppose_constraint(row
->p
, len
, &f
);
3645 Polyhedron
*T
= AddConstraints(row
->p
, 1, P
, MaxRays
);
3647 //printf("one_neg i: %d, l: %d, u: %d\n", i, l, u);
3648 info
[i
] = (constraint
)(info
[i
] | ONE_NEG
);
3650 //puts("neg remainder");
3651 //Polyhedron_Print(stdout, P_VALUE_FMT, T);
3653 } else if (!(info
[i
] & ROT_NEG
)) {
3654 if (parallel_constraints(P
->Constraint
[l
],
3656 row
->p
, nvar
, exist
)) {
3657 negative_test_constraint7(P
->Constraint
[l
],
3659 row
->p
, nvar
, exist
,
3661 oppose_constraint(row
->p
, len
, &f
);
3662 Polyhedron
*T
= AddConstraints(row
->p
, 1, P
, MaxRays
);
3664 // printf("rot_neg i: %d, l: %d, u: %d\n", i, l, u);
3665 info
[i
] = (constraint
)(info
[i
] | ROT_NEG
);
3668 //puts("neg remainder");
3669 //Polyhedron_Print(stdout, P_VALUE_FMT, T);
3674 if (!(info
[i
] & ALL_POS
) && (info
[i
] & (ONE_NEG
| ROT_NEG
)))
3678 if (info
[i
] & ALL_POS
)
3685 for (int i = 0; i < exist; ++i)
3686 printf("%i: %i\n", i, info[i]);
3688 for (int i
= 0; i
< exist
; ++i
)
3689 if (info
[i
] & ALL_POS
) {
3691 fprintf(stderr
, "\nER: Positive\n");
3692 #endif /* DEBUG_ER */
3694 // Maybe we should chew off some of the fat here
3695 Matrix
*M
= Matrix_Alloc(P
->Dimension
, P
->Dimension
+1);
3696 for (int j
= 0; j
< P
->Dimension
; ++j
)
3697 value_set_si(M
->p
[j
][j
+ (j
>= i
+nvar
)], 1);
3698 Polyhedron
*T
= Polyhedron_Image(P
, M
, MaxRays
);
3700 evalue
*EP
= barvinok_enumerate_e(T
, exist
-1, nparam
, MaxRays
);
3707 for (int i
= 0; i
< exist
; ++i
)
3708 if (info
[i
] & ONE_NEG
) {
3710 fprintf(stderr
, "\nER: Negative\n");
3711 #endif /* DEBUG_ER */
3716 return barvinok_enumerate_e(P
, exist
-1, nparam
, MaxRays
);
3718 Polyhedron
*T
= Polyhedron_Copy(P
);
3719 SwapColumns(T
, nvar
+1, nvar
+1+i
);
3720 evalue
*EP
= barvinok_enumerate_e(T
, exist
-1, nparam
, MaxRays
);
3725 for (int i
= 0; i
< exist
; ++i
)
3726 if (info
[i
] & ROT_NEG
) {
3728 fprintf(stderr
, "\nER: Rotate\n");
3729 #endif /* DEBUG_ER */
3733 Polyhedron
*T
= rotate_along(P
, r
, nvar
, exist
, MaxRays
);
3734 evalue
*EP
= barvinok_enumerate_e(T
, exist
-1, nparam
, MaxRays
);
3738 for (int i
= 0; i
< exist
; ++i
)
3739 if (info
[i
] & INDEPENDENT
) {
3740 Polyhedron
*pos
, *neg
;
3742 /* Find constraint again and split off negative part */
3744 if (SplitOnVar(P
, i
, nvar
, len
, exist
, MaxRays
,
3745 row
, f
, true, &pos
, &neg
)) {
3747 fprintf(stderr
, "\nER: Split\n");
3748 #endif /* DEBUG_ER */
3751 barvinok_enumerate_e(neg
, exist
-1, nparam
, MaxRays
);
3753 barvinok_enumerate_e(pos
, exist
, nparam
, MaxRays
);
3755 free_evalue_refs(E
);
3757 Polyhedron_Free(neg
);
3758 Polyhedron_Free(pos
);
3772 EP
= enumerate_line(P
, exist
, nparam
, MaxRays
);
3776 EP
= barvinok_enumerate_pip(P
, exist
, nparam
, MaxRays
);
3780 EP
= enumerate_redundant_ray(P
, exist
, nparam
, MaxRays
);
3784 EP
= enumerate_sure(P
, exist
, nparam
, MaxRays
);
3788 EP
= enumerate_ray(P
, exist
, nparam
, MaxRays
);
3792 EP
= enumerate_sure2(P
, exist
, nparam
, MaxRays
);
3796 F
= unfringe(P
, MaxRays
);
3797 if (!PolyhedronIncludes(F
, P
)) {
3799 fprintf(stderr
, "\nER: Fringed\n");
3800 #endif /* DEBUG_ER */
3801 EP
= barvinok_enumerate_e(F
, exist
, nparam
, MaxRays
);
3808 EP
= enumerate_vd(&P
, exist
, nparam
, MaxRays
);
3813 EP
= enumerate_sum(P
, exist
, nparam
, MaxRays
);
3820 Polyhedron
*pos
, *neg
;
3821 for (i
= 0; i
< exist
; ++i
)
3822 if (SplitOnVar(P
, i
, nvar
, len
, exist
, MaxRays
,
3823 row
, f
, false, &pos
, &neg
))
3829 EP
= enumerate_or(pos
, exist
, nparam
, MaxRays
);
3841 gen_fun
* barvinok_series(Polyhedron
*P
, Polyhedron
* C
, unsigned MaxRays
)
3843 Polyhedron
** vcone
;
3845 unsigned nparam
= C
->Dimension
;
3849 sign
.SetLength(ncone
);
3851 CA
= align_context(C
, P
->Dimension
, MaxRays
);
3852 P
= DomainIntersection(P
, CA
, MaxRays
);
3853 Polyhedron_Free(CA
);
3855 assert(!Polyhedron_is_infinite(P
, nparam
));
3856 assert(P
->NbBid
== 0);
3857 assert(Polyhedron_has_positive_rays(P
, nparam
));
3858 assert(P
->NbEq
== 0);
3860 partial_reducer
red(P
, nparam
);