2 #include <barvinok/options.h>
3 #include <barvinok/util.h>
5 #include "lattice_point.h"
7 #define ALLOC(type) (type*)malloc(sizeof(type))
8 #define ALLOCN(type,n) (type*)malloc((n) * sizeof(type))
9 #define REALLOCN(ptr,type,n) (type*)realloc(ptr, (n) * sizeof(type))
11 static struct bernoulli_coef bernoulli_coef
;
12 static struct poly_list bernoulli
;
13 static struct poly_list faulhaber
;
15 struct bernoulli_coef
*bernoulli_coef_compute(int n
)
20 if (n
< bernoulli_coef
.n
)
21 return &bernoulli_coef
;
23 if (n
>= bernoulli_coef
.size
) {
24 int size
= 3*(n
+ 5)/2;
27 b
= Vector_Alloc(size
);
28 if (bernoulli_coef
.n
) {
29 Vector_Copy(bernoulli_coef
.num
->p
, b
->p
, bernoulli_coef
.n
);
30 Vector_Free(bernoulli_coef
.num
);
32 bernoulli_coef
.num
= b
;
33 b
= Vector_Alloc(size
);
34 if (bernoulli_coef
.n
) {
35 Vector_Copy(bernoulli_coef
.den
->p
, b
->p
, bernoulli_coef
.n
);
36 Vector_Free(bernoulli_coef
.den
);
38 bernoulli_coef
.den
= b
;
39 b
= Vector_Alloc(size
);
40 if (bernoulli_coef
.n
) {
41 Vector_Copy(bernoulli_coef
.lcm
->p
, b
->p
, bernoulli_coef
.n
);
42 Vector_Free(bernoulli_coef
.lcm
);
44 bernoulli_coef
.lcm
= b
;
46 bernoulli_coef
.size
= size
;
50 for (i
= bernoulli_coef
.n
; i
<= n
; ++i
) {
52 value_set_si(bernoulli_coef
.num
->p
[0], 1);
53 value_set_si(bernoulli_coef
.den
->p
[0], 1);
54 value_set_si(bernoulli_coef
.lcm
->p
[0], 1);
57 value_set_si(bernoulli_coef
.num
->p
[i
], 0);
58 value_set_si(factor
, -(i
+1));
59 for (j
= i
-1; j
>= 0; --j
) {
60 mpz_mul_ui(factor
, factor
, j
+1);
61 mpz_divexact_ui(factor
, factor
, i
+1-j
);
62 value_division(tmp
, bernoulli_coef
.lcm
->p
[i
-1],
63 bernoulli_coef
.den
->p
[j
]);
64 value_multiply(tmp
, tmp
, bernoulli_coef
.num
->p
[j
]);
65 value_multiply(tmp
, tmp
, factor
);
66 value_addto(bernoulli_coef
.num
->p
[i
], bernoulli_coef
.num
->p
[i
], tmp
);
68 mpz_mul_ui(bernoulli_coef
.den
->p
[i
], bernoulli_coef
.lcm
->p
[i
-1], i
+1);
69 value_gcd(tmp
, bernoulli_coef
.num
->p
[i
], bernoulli_coef
.den
->p
[i
]);
70 if (value_notone_p(tmp
)) {
71 value_division(bernoulli_coef
.num
->p
[i
],
72 bernoulli_coef
.num
->p
[i
], tmp
);
73 value_division(bernoulli_coef
.den
->p
[i
],
74 bernoulli_coef
.den
->p
[i
], tmp
);
76 value_lcm(bernoulli_coef
.lcm
->p
[i
],
77 bernoulli_coef
.lcm
->p
[i
-1], bernoulli_coef
.den
->p
[i
]);
79 bernoulli_coef
.n
= n
+1;
83 return &bernoulli_coef
;
87 * Compute either Bernoulli B_n or Faulhaber F_n polynomials.
89 * B_n = sum_{k=0}^n { n \choose k } b_k x^{n-k}
90 * F_n = 1/(n+1) sum_{k=0}^n { n+1 \choose k } b_k x^{n+1-k}
92 static struct poly_list
*bernoulli_faulhaber_compute(int n
, struct poly_list
*pl
,
97 struct bernoulli_coef
*bc
;
103 int size
= 3*(n
+ 5)/2;
106 poly
= ALLOCN(Vector
*, size
);
107 for (i
= 0; i
< pl
->n
; ++i
)
108 poly
[i
] = pl
->poly
[i
];
115 bc
= bernoulli_coef_compute(n
);
118 for (i
= pl
->n
; i
<= n
; ++i
) {
119 pl
->poly
[i
] = Vector_Alloc(i
+faulhaber
+2);
120 value_assign(pl
->poly
[i
]->p
[i
+faulhaber
], bc
->lcm
->p
[i
]);
122 mpz_mul_ui(pl
->poly
[i
]->p
[i
+2], bc
->lcm
->p
[i
], i
+1);
124 value_assign(pl
->poly
[i
]->p
[i
+1], bc
->lcm
->p
[i
]);
125 value_set_si(factor
, 1);
126 for (j
= 1; j
<= i
; ++j
) {
127 mpz_mul_ui(factor
, factor
, i
+faulhaber
+1-j
);
128 mpz_divexact_ui(factor
, factor
, j
);
129 value_division(pl
->poly
[i
]->p
[i
+faulhaber
-j
],
130 bc
->lcm
->p
[i
], bc
->den
->p
[j
]);
131 value_multiply(pl
->poly
[i
]->p
[i
+faulhaber
-j
],
132 pl
->poly
[i
]->p
[i
+faulhaber
-j
], bc
->num
->p
[j
]);
133 value_multiply(pl
->poly
[i
]->p
[i
+faulhaber
-j
],
134 pl
->poly
[i
]->p
[i
+faulhaber
-j
], factor
);
136 Vector_Normalize(pl
->poly
[i
]->p
, i
+faulhaber
+2);
144 struct poly_list
*bernoulli_compute(int n
)
146 return bernoulli_faulhaber_compute(n
, &bernoulli
, 0);
149 struct poly_list
*faulhaber_compute(int n
)
151 return bernoulli_faulhaber_compute(n
, &faulhaber
, 1);
154 static evalue
*shifted_copy(const evalue
*src
)
156 evalue
*e
= ALLOC(evalue
);
159 evalue_shift_variables(e
, -1);
163 /* Computes the argument for the Faulhaber polynomial.
164 * If we are computing a polynomial approximation (exact == 0),
165 * then this is simply arg/denom.
166 * Otherwise, if neg == 0, then we are dealing with an upper bound
167 * and we need to compute floor(arg/denom) = arg/denom - { arg/denom }
168 * If neg == 1, then we are dealing with a lower bound
169 * and we need to compute ceil(arg/denom) = arg/denom + { -arg/denom }
171 * Modifies arg (if exact == 1).
173 static evalue
*power_sums_base(Vector
*arg
, Value denom
, int neg
, int exact
)
176 evalue
*base
= affine2evalue(arg
->p
, denom
, arg
->Size
-1);
178 if (!exact
|| value_one_p(denom
))
182 Vector_Oppose(arg
->p
, arg
->p
, arg
->Size
);
184 fract
= fractional_part(arg
->p
, denom
, arg
->Size
-1, NULL
);
186 value_set_si(arg
->p
[0], -1);
187 evalue_mul(fract
, arg
->p
[0]);
195 static evalue
*power_sums(struct poly_list
*faulhaber
, const evalue
*poly
,
196 Vector
*arg
, Value denom
, int neg
, int alt_neg
,
200 evalue
*base
= power_sums_base(arg
, denom
, neg
, exact
);
201 evalue
*sum
= evalue_zero();
203 for (i
= 1; i
< poly
->x
.p
->size
; ++i
) {
204 evalue
*term
= evalue_polynomial(faulhaber
->poly
[i
], base
);
205 evalue
*factor
= shifted_copy(&poly
->x
.p
->arr
[i
]);
207 if (alt_neg
&& (i
% 2))
220 /* Given a constraint (cst_affine) a x + b y + c >= 0, compate a constraint (c)
221 * +- (b y + c) +- a >=,> 0
224 * sign_affine sign_cst
226 static void bound_constraint(Value
*c
, unsigned dim
,
228 int sign_affine
, int sign_cst
, int strict
)
230 if (sign_affine
== -1)
231 Vector_Oppose(cst_affine
+1, c
, dim
+1);
233 Vector_Copy(cst_affine
+1, c
, dim
+1);
236 value_subtract(c
[dim
], c
[dim
], cst_affine
[0]);
237 else if (sign_cst
== 1)
238 value_addto(c
[dim
], c
[dim
], cst_affine
[0]);
241 value_decrement(c
[dim
], c
[dim
]);
244 struct Bernoulli_data
{
245 struct barvinok_options
*options
;
246 struct evalue_section
*s
;
252 static evalue
*compute_poly_u(evalue
*poly_u
, Value
*upper
, Vector
*row
,
253 unsigned dim
, Value tmp
,
254 struct poly_list
*faulhaber
,
255 struct Bernoulli_data
*data
)
257 int exact
= data
->options
->approximation_method
== BV_APPROX_NONE
;
260 Vector_Copy(upper
+2, row
->p
, dim
+1);
261 value_oppose(tmp
, upper
[1]);
262 value_addto(row
->p
[dim
], row
->p
[dim
], tmp
);
263 return power_sums(faulhaber
, data
->e
, row
, tmp
, 0, 0, exact
);
266 static evalue
*compute_poly_l(evalue
*poly_l
, Value
*lower
, Vector
*row
,
268 struct poly_list
*faulhaber
,
269 struct Bernoulli_data
*data
)
271 int exact
= data
->options
->approximation_method
== BV_APPROX_NONE
;
274 Vector_Copy(lower
+2, row
->p
, dim
+1);
275 value_addto(row
->p
[dim
], row
->p
[dim
], lower
[1]);
276 return power_sums(faulhaber
, data
->e
, row
, lower
[1], 0, 1, exact
);
279 /* Compute sum of constant term.
281 static evalue
*linear_term(const evalue
*cst
, Value
*lower
, Value
*upper
,
282 Vector
*row
, Value tmp
, int exact
)
285 unsigned dim
= row
->Size
- 1;
287 if (EVALUE_IS_ZERO(*cst
))
288 return evalue_zero();
291 value_absolute(tmp
, upper
[1]);
293 Vector_Combine(lower
+2, upper
+2, row
->p
, tmp
, lower
[1], dim
+1);
294 value_multiply(tmp
, tmp
, lower
[1]);
295 /* upper - lower + 1 */
296 value_addto(row
->p
[dim
], row
->p
[dim
], tmp
);
298 linear
= affine2evalue(row
->p
, tmp
, dim
);
302 value_absolute(tmp
, upper
[1]);
303 Vector_Copy(upper
+2, row
->p
, dim
+1);
304 value_addto(row
->p
[dim
], row
->p
[dim
], tmp
);
306 linear
= power_sums_base(row
, tmp
, 0, 1);
308 Vector_Copy(lower
+2, row
->p
, dim
+1);
310 l
= power_sums_base(row
, lower
[1], 0, 1);
312 /* floor(upper+1) + floor(-lower) = floor(upper) - ceil(lower) + 1 */
321 static void Bernoulli_init(unsigned n
, void *cb_data
)
323 struct Bernoulli_data
*data
= (struct Bernoulli_data
*)cb_data
;
324 int exact
= data
->options
->approximation_method
== BV_APPROX_NONE
;
325 int cases
= exact
? 3 : 5;
327 if (cases
* n
<= data
->size
)
330 data
->size
= cases
* (n
+ 16);
331 data
->s
= REALLOCN(data
->s
, struct evalue_section
, data
->size
);
334 static void Bernoulli_cb(Matrix
*M
, Value
*lower
, Value
*upper
, void *cb_data
);
337 * This function requires that either the lower or the upper bound
338 * represented by the constraints "lower" and "upper" is an integer
340 * An affine substitution is performed to make this bound exactly
341 * zero, ensuring that in the recursive call to Bernoulli_cb,
342 * only one of the "cases" will apply.
344 static void transform_to_single_case(Matrix
*M
, Value
*lower
, Value
*upper
,
345 struct Bernoulli_data
*data
)
347 unsigned dim
= M
->NbColumns
-2;
351 const evalue
*e
= data
->e
;
357 subs
= ALLOCN(evalue
*, dim
+1);
358 for (i
= 0; i
< dim
; ++i
)
359 subs
[1+i
] = evalue_var(1+i
);
360 shadow
= Vector_Alloc(2 * (2+dim
+1));
361 if (value_one_p(lower
[1])) {
362 /* Replace i by i + l' when b = 1 */
363 value_set_si(shadow
->p
[0], 1);
364 Vector_Oppose(lower
+2, shadow
->p
+1, dim
+1);
365 subs
[0] = affine2evalue(shadow
->p
, shadow
->p
[0], dim
+1);
369 * (-a i + u') + a (-l') >= 0
371 value_assign(shadow
->p
[2+dim
+1+1], upper
[1]);
372 value_oppose(a
, upper
[1]);
374 Vector_Combine(upper
+2, lower
+2, shadow
->p
+2+dim
+1+2,
376 upper
= shadow
->p
+2+dim
+1;
378 value_set_si(lower
[1], 1);
379 Vector_Set(lower
+2, 0, dim
+1);
381 /* Replace i by i + u' when a = 1 */
382 value_set_si(shadow
->p
[0], 1);
383 Vector_Copy(upper
+2, shadow
->p
+1, dim
+1);
384 subs
[0] = affine2evalue(shadow
->p
, shadow
->p
[0], dim
+1);
386 * (b i - l') + b u' >= 0
390 value_assign(shadow
->p
[1], lower
[1]);
392 value_assign(b
, lower
[1]);
393 Vector_Combine(upper
+2, lower
+2, shadow
->p
+2,
395 upper
= shadow
->p
+2+dim
+1;
397 value_set_si(upper
[1], -1);
398 Vector_Set(upper
+2, 0, dim
+1);
403 t
= evalue_dup(data
->e
);
404 evalue_substitute(t
, subs
);
407 for (i
= 0; i
< dim
+1; ++i
)
408 evalue_free(subs
[i
]);
411 Bernoulli_cb(M
, lower
, upper
, data
);
418 static void Bernoulli_cb(Matrix
*M
, Value
*lower
, Value
*upper
, void *cb_data
)
420 struct Bernoulli_data
*data
= (struct Bernoulli_data
*)cb_data
;
423 const evalue
*factor
= NULL
;
424 evalue
*linear
= NULL
;
427 unsigned dim
= M
->NbColumns
-2;
429 int exact
= data
->options
->approximation_method
== BV_APPROX_NONE
;
430 int cases
= exact
? 3 : 5;
434 assert(data
->ns
+ cases
<= data
->size
);
437 T
= Constraints2Polyhedron(M2
, data
->options
->MaxRays
);
440 POL_ENSURE_VERTICES(T
);
446 constant
= value_notzero_p(data
->e
->d
) ||
447 data
->e
->x
.p
->type
!= polynomial
||
448 data
->e
->x
.p
->pos
!= 1;
449 if (!constant
&& (value_one_p(lower
[1]) || value_mone_p(upper
[1]))) {
451 int lower_cst
, upper_cst
;
453 lower_cst
= First_Non_Zero(lower
+2, dim
) == -1;
454 upper_cst
= First_Non_Zero(upper
+2, dim
) == -1;
456 (lower_cst
&& value_negz_p(lower
[2+dim
])) ||
457 (upper_cst
&& value_negz_p(upper
[2+dim
])) ||
458 (lower_cst
&& upper_cst
&&
459 value_posz_p(lower
[2+dim
]) && value_posz_p(upper
[2+dim
]));
461 transform_to_single_case(M
, lower
, upper
, data
);
467 assert(lower
!= upper
);
469 row
= Vector_Alloc(dim
+1);
471 if (value_notzero_p(data
->e
->d
)) {
475 if (data
->e
->x
.p
->type
== polynomial
&& data
->e
->x
.p
->pos
== 1)
476 factor
= shifted_copy(&data
->e
->x
.p
->arr
[0]);
478 factor
= shifted_copy(data
->e
);
482 linear
= linear_term(factor
, lower
, upper
, row
, tmp
, exact
);
485 data
->s
[data
->ns
].E
= linear
;
486 data
->s
[data
->ns
].D
= T
;
488 data
->options
->stats
->bernoulli_sums
++;
490 evalue
*poly_u
= NULL
, *poly_l
= NULL
;
492 struct poly_list
*faulhaber
;
493 assert(data
->e
->x
.p
->type
== polynomial
);
494 assert(data
->e
->x
.p
->pos
== 1);
495 faulhaber
= faulhaber_compute(data
->e
->x
.p
->size
-1);
496 /* lower is the constraint
497 * b i - l' >= 0 i >= l'/b = l
498 * upper is the constraint
499 * -a i + u' >= 0 i <= u'/a = u
501 M2
= Matrix_Alloc(3, 2+T
->Dimension
);
502 value_set_si(M2
->p
[0][0], 1);
503 value_set_si(M2
->p
[1][0], 1);
504 value_set_si(M2
->p
[2][0], 1);
507 * 0 < l l' - 1 >= 0 if exact
510 bound_constraint(M2
->p
[0]+1, T
->Dimension
, lower
+1, -1, 0, 1);
512 bound_constraint(M2
->p
[0]+1, T
->Dimension
, lower
+1, -1, -1, 0);
513 D
= AddConstraints(M2
->p_Init
, 1, T
, data
->options
->MaxRays
);
514 POL_ENSURE_VERTICES(D
);
519 poly_u
= compute_poly_u(poly_u
, upper
, row
, dim
, tmp
,
521 Vector_Oppose(lower
+2, row
->p
, dim
+1);
522 extra
= power_sums(faulhaber
, data
->e
, row
, lower
[1], 1, 0, exact
);
526 data
->s
[data
->ns
].E
= extra
;
527 data
->s
[data
->ns
].D
= D
;
529 data
->options
->stats
->bernoulli_sums
++;
533 * 1 <= -u -u' - a >= 0
534 * 0 < -u -u' - 1 >= 0 if exact
537 bound_constraint(M2
->p
[0]+1, T
->Dimension
, upper
+1, -1, 0, 1);
539 bound_constraint(M2
->p
[0]+1, T
->Dimension
, upper
+1, -1, 1, 0);
540 D
= AddConstraints(M2
->p_Init
, 1, T
, data
->options
->MaxRays
);
541 POL_ENSURE_VERTICES(D
);
546 poly_l
= compute_poly_l(poly_l
, lower
, row
, dim
, faulhaber
, data
);
547 Vector_Oppose(upper
+2, row
->p
, dim
+1);
548 value_oppose(tmp
, upper
[1]);
549 extra
= power_sums(faulhaber
, data
->e
, row
, tmp
, 1, 1, exact
);
553 data
->s
[data
->ns
].E
= extra
;
554 data
->s
[data
->ns
].D
= D
;
556 data
->options
->stats
->bernoulli_sums
++;
563 bound_constraint(M2
->p
[0]+1, T
->Dimension
, upper
+1, 1, 0, 0);
564 bound_constraint(M2
->p
[1]+1, T
->Dimension
, lower
+1, 1, 0, 0);
565 D
= AddConstraints(M2
->p_Init
, 2, T
, data
->options
->MaxRays
);
566 POL_ENSURE_VERTICES(D
);
570 poly_l
= compute_poly_l(poly_l
, lower
, row
, dim
, faulhaber
, data
);
571 poly_u
= compute_poly_u(poly_u
, upper
, row
, dim
, tmp
,
574 data
->s
[data
->ns
].E
= ALLOC(evalue
);
575 value_init(data
->s
[data
->ns
].E
->d
);
576 evalue_copy(data
->s
[data
->ns
].E
, poly_u
);
577 eadd(poly_l
, data
->s
[data
->ns
].E
);
578 eadd(linear
, data
->s
[data
->ns
].E
);
579 data
->s
[data
->ns
].D
= D
;
581 data
->options
->stats
->bernoulli_sums
++;
586 * l < 1 -l' + b - 1 >= 0
590 bound_constraint(M2
->p
[0]+1, T
->Dimension
, lower
+1, 1, 1, 1);
591 bound_constraint(M2
->p
[1]+1, T
->Dimension
, lower
+1, -1, 0, 1);
592 bound_constraint(M2
->p
[2]+1, T
->Dimension
, upper
+1, 1, 1, 0);
593 D
= AddConstraints(M2
->p_Init
, 3, T
, data
->options
->MaxRays
);
594 POL_ENSURE_VERTICES(D
);
598 poly_u
= compute_poly_u(poly_u
, upper
, row
, dim
, tmp
,
600 eadd(linear
, poly_u
);
601 data
->s
[data
->ns
].E
= poly_u
;
603 data
->s
[data
->ns
].D
= D
;
605 data
->options
->stats
->bernoulli_sums
++;
609 * -u < 1 u' + a - 1 >= 0
610 * 0 < -u -u' - 1 >= 0
611 * l <= -1 -l' - b >= 0
613 bound_constraint(M2
->p
[0]+1, T
->Dimension
, upper
+1, 1, -1, 1);
614 bound_constraint(M2
->p
[1]+1, T
->Dimension
, upper
+1, -1, 0, 1);
615 bound_constraint(M2
->p
[2]+1, T
->Dimension
, lower
+1, 1, -1, 0);
616 D
= AddConstraints(M2
->p_Init
, 3, T
, data
->options
->MaxRays
);
617 POL_ENSURE_VERTICES(D
);
621 poly_l
= compute_poly_l(poly_l
, lower
, row
, dim
,
623 eadd(linear
, poly_l
);
624 data
->s
[data
->ns
].E
= poly_l
;
626 data
->s
[data
->ns
].D
= D
;
628 data
->options
->stats
->bernoulli_sums
++;
640 if (factor
!= data
->e
)
641 evalue_free((evalue
*)factor
);
647 * Move the variable at position pos to the front by exchanging
648 * that variable with the first variable.
650 static void more_var_to_front(Polyhedron
**P_p
, evalue
**E_p
, int pos
)
652 Polyhedron
*P
= *P_p
;
654 unsigned dim
= P
->Dimension
;
658 P
= Polyhedron_Copy(P
);
659 Polyhedron_ExchangeColumns(P
, 1, 1+pos
);
662 if (value_zero_p(E
->d
)) {
666 subs
= ALLOCN(evalue
*, dim
);
667 for (j
= 0; j
< dim
; ++j
)
668 subs
[j
] = evalue_var(j
);
672 E
= evalue_dup(*E_p
);
673 evalue_substitute(E
, subs
);
674 for (j
= 0; j
< dim
; ++j
)
675 evalue_free(subs
[j
]);
681 static int type_offset(enode
*p
)
683 return p
->type
== fractional
? 1 :
684 p
->type
== flooring
? 1 : 0;
687 static void adjust_periods(evalue
*e
, unsigned nvar
, Vector
*periods
)
689 for (; value_zero_p(e
->d
); e
= &e
->x
.p
->arr
[0]) {
691 assert(e
->x
.p
->type
== polynomial
);
692 assert(e
->x
.p
->size
== 2);
693 assert(value_notzero_p(e
->x
.p
->arr
[1].d
));
695 pos
= e
->x
.p
->pos
- 1;
699 value_lcm(periods
->p
[pos
], periods
->p
[pos
], e
->x
.p
->arr
[1].d
);
703 static void fractional_periods_r(evalue
*e
, unsigned nvar
, Vector
*periods
)
707 if (value_notzero_p(e
->d
))
710 assert(e
->x
.p
->type
== polynomial
|| e
->x
.p
->type
== fractional
);
712 if (e
->x
.p
->type
== fractional
)
713 adjust_periods(&e
->x
.p
->arr
[0], nvar
, periods
);
715 for (i
= type_offset(e
->x
.p
); i
< e
->x
.p
->size
; ++i
)
716 fractional_periods_r(&e
->x
.p
->arr
[i
], nvar
, periods
);
720 * For each of the nvar variables, compute the lcm of the
721 * denominators of the coefficients of that variable in
722 * any of the fractional parts.
724 static Vector
*fractional_periods(evalue
*e
, unsigned nvar
)
727 Vector
*periods
= Vector_Alloc(nvar
);
729 for (i
= 0; i
< nvar
; ++i
)
730 value_set_si(periods
->p
[i
], 1);
732 fractional_periods_r(e
, nvar
, periods
);
737 /* Move "best" variable to sum over into the first position,
738 * possibly changing *P_p and *E_p.
740 * If there are any fractional parts (period != NULL), then we
741 * first look for a variable with the smallest lcm of denominators
742 * inside a fractional part. This denominator is assigned to period
743 * and corresponds to the number of "splinters" we need to construct
746 * Of those with this denominator (all if period == NULL or if there
747 * are no fractional parts), we select the variable with the smallest
748 * maximal coefficient, as this coefficient will become a denominator
749 * in new fractional parts (for an exact computation), which may
750 * lead to splintering in the next step.
752 static void move_best_to_front(Polyhedron
**P_p
, evalue
**E_p
, unsigned nvar
,
755 Polyhedron
*P
= *P_p
;
757 int i
, j
, best_i
= -1;
764 periods
= fractional_periods(E
, nvar
);
765 value_assign(*period
, periods
->p
[0]);
766 for (i
= 1; i
< nvar
; ++i
)
767 if (value_lt(periods
->p
[i
], *period
))
768 value_assign(*period
, periods
->p
[i
]);
774 for (i
= 0; i
< nvar
; ++i
) {
775 if (period
&& value_ne(*period
, periods
->p
[i
]))
778 value_set_si(max
, 0);
780 for (j
= 0; j
< P
->NbConstraints
; ++j
) {
781 if (value_zero_p(P
->Constraint
[j
][1+i
]))
783 if (First_Non_Zero(P
->Constraint
[j
]+1, i
) == -1 &&
784 First_Non_Zero(P
->Constraint
[j
]+1+i
+1, nvar
-i
-1) == -1)
786 if (value_abs_gt(P
->Constraint
[j
][1+i
], max
))
787 value_absolute(max
, P
->Constraint
[j
][1+i
]);
790 if (best_i
== -1 || value_lt(max
, best
)) {
791 value_assign(best
, max
);
800 Vector_Free(periods
);
803 more_var_to_front(P_p
, E_p
, best_i
);
808 static evalue
*sum_over_polytope_base(Polyhedron
*P
, evalue
*E
, unsigned nvar
,
809 struct Bernoulli_data
*data
,
810 struct barvinok_options
*options
)
814 assert(P
->NbEq
== 0);
819 for_each_lower_upper_bound(P
, Bernoulli_init
, Bernoulli_cb
, data
);
821 res
= evalue_from_section_array(data
->s
, data
->ns
);
824 evalue
*tmp
= Bernoulli_sum_evalue(res
, nvar
-1, options
);
832 static evalue
*sum_over_polytope(Polyhedron
*P
, evalue
*E
, unsigned nvar
,
833 struct Bernoulli_data
*data
,
834 struct barvinok_options
*options
);
836 static evalue
*sum_over_polytope_with_equalities(Polyhedron
*P
, evalue
*E
,
838 struct Bernoulli_data
*data
,
839 struct barvinok_options
*options
)
841 unsigned dim
= P
->Dimension
;
842 unsigned new_dim
, new_nparam
;
843 Matrix
*T
= NULL
, *CP
= NULL
;
849 return evalue_zero();
853 remove_all_equalities(&P
, NULL
, &CP
, &T
, dim
-nvar
, options
->MaxRays
);
857 return evalue_zero();
860 new_nparam
= CP
? CP
->NbColumns
-1 : dim
- nvar
;
861 new_dim
= T
? T
->NbColumns
-1 : nvar
+ new_nparam
;
863 /* We can avoid these substitutions if E is a constant */
864 subs
= ALLOCN(evalue
*, dim
);
865 for (j
= 0; j
< nvar
; ++j
) {
867 subs
[j
] = affine2evalue(T
->p
[j
], T
->p
[nvar
+new_nparam
][new_dim
],
870 subs
[j
] = evalue_var(j
);
872 for (j
= 0; j
< dim
-nvar
; ++j
) {
874 subs
[nvar
+j
] = affine2evalue(CP
->p
[j
], CP
->p
[dim
-nvar
][new_nparam
],
877 subs
[nvar
+j
] = evalue_var(j
);
878 evalue_shift_variables(subs
[nvar
+j
], new_dim
-new_nparam
);
882 evalue_substitute(E
, subs
);
885 for (j
= 0; j
< dim
; ++j
)
886 evalue_free(subs
[j
]);
889 if (new_dim
-new_nparam
> 0) {
890 sum
= sum_over_polytope(P
, E
, new_dim
-new_nparam
, data
, options
);
896 sum
->x
.p
= new_enode(partition
, 2, new_dim
);
897 EVALUE_SET_DOMAIN(sum
->x
.p
->arr
[0], P
);
898 value_clear(sum
->x
.p
->arr
[1].d
);
899 sum
->x
.p
->arr
[1] = *E
;
904 evalue_backsubstitute(sum
, CP
, options
->MaxRays
);
914 /* Splinter P into period slices along the first variable x = period y + c,
915 * 0 <= c < perdiod, * ensuring no fractional part contains the first variable,
916 * and sum over all slices.
918 static evalue
*sum_over_polytope_slices(Polyhedron
*P
, evalue
*E
,
921 struct Bernoulli_data
*data
,
922 struct barvinok_options
*options
)
924 evalue
*sum
= evalue_zero();
926 unsigned dim
= P
->Dimension
;
934 value_set_si(one
, 1);
936 subs
= ALLOCN(evalue
*, dim
);
938 T
= Matrix_Alloc(dim
+1, dim
+1);
939 value_assign(T
->p
[0][0], period
);
940 for (j
= 1; j
< dim
+1; ++j
)
941 value_set_si(T
->p
[j
][j
], 1);
943 for (j
= 0; j
< dim
; ++j
)
944 subs
[j
] = evalue_var(j
);
945 evalue_mul(subs
[0], period
);
947 for (value_set_si(i
, 0); value_lt(i
, period
); value_increment(i
, i
)) {
949 Polyhedron
*S
= DomainPreimage(P
, T
, options
->MaxRays
);
950 evalue
*e
= evalue_dup(E
);
951 evalue_substitute(e
, subs
);
955 tmp
= sum_over_polytope_with_equalities(S
, e
, nvar
, data
, options
);
957 tmp
= sum_over_polytope_base(S
, e
, nvar
, data
, options
);
966 value_increment(T
->p
[0][dim
], T
->p
[0][dim
]);
967 evalue_add_constant(subs
[0], one
);
973 for (j
= 0; j
< dim
; ++j
)
974 evalue_free(subs
[j
]);
981 static evalue
*sum_over_polytope(Polyhedron
*P
, evalue
*E
, unsigned nvar
,
982 struct Bernoulli_data
*data
,
983 struct barvinok_options
*options
)
985 Polyhedron
*P_orig
= P
;
989 int exact
= options
->approximation_method
== BV_APPROX_NONE
;
992 return sum_over_polytope_with_equalities(P
, E
, nvar
, data
, options
);
996 move_best_to_front(&P
, &E
, nvar
, exact
? &period
: NULL
);
997 if (exact
&& value_notone_p(period
))
998 sum
= sum_over_polytope_slices(P
, E
, nvar
, period
, data
, options
);
1000 sum
= sum_over_polytope_base(P
, E
, nvar
, data
, options
);
1007 value_clear(period
);
1012 evalue
*Bernoulli_sum_evalue(evalue
*e
, unsigned nvar
,
1013 struct barvinok_options
*options
)
1015 struct Bernoulli_data data
;
1017 evalue
*sum
= evalue_zero();
1019 if (EVALUE_IS_ZERO(*e
))
1027 assert(value_zero_p(e
->d
));
1028 assert(e
->x
.p
->type
== partition
);
1031 data
.s
= ALLOCN(struct evalue_section
, data
.size
);
1032 data
.options
= options
;
1034 for (i
= 0; i
< e
->x
.p
->size
/2; ++i
) {
1036 for (D
= EVALUE_DOMAIN(e
->x
.p
->arr
[2*i
]); D
; D
= D
->next
) {
1037 Polyhedron
*next
= D
->next
;
1041 tmp
= sum_over_polytope(D
, &e
->x
.p
->arr
[2*i
+1], nvar
, &data
, options
);