evalue_isl.c: isl_pw_qpolynomial_from_eval: use isl_val
[barvinok.git] / counter.cc
blob7880d22193d573483a7b1033eb245b42d60f1132
1 #include <assert.h>
2 #include <barvinok/util.h>
3 #include "counter.h"
4 #include "lattice_point.h"
6 using std::cerr;
7 using std::endl;
9 /* Computes the integer points in the fundamental parallelepiped and
10 * passes them along (in num) to the counter specific (i.e., specialization
11 * specific) add_lattice_points.
13 void counter_base::handle(const mat_ZZ& rays, Value *V, const QQ& c,
14 unsigned long det, barvinok_options *options)
16 Matrix* Rays = zz2matrix(rays);
18 assert(c.d == 1);
19 assert(c.n == 1 || c.n == -1);
20 int sign = to_int(c.n);
22 Matrix_Vector_Product(Rays, lambda->p, den->p_Init);
23 for (int k = 0; k < dim; ++k)
24 if (value_zero_p(den->p_Init[k])) {
25 Matrix_Free(Rays);
26 throw Orthogonal;
28 Inner_Product(lambda->p, V, dim, &tmp);
29 lattice_points_fixed(V, &tmp, Rays, den, num, det);
30 num->NbRows = det;
31 Matrix_Free(Rays);
33 if (dim % 2)
34 sign = -sign;
36 add_lattice_points(sign);
39 static void add_falling_powers(dpoly& n, Value degree)
41 value_increment(n.coeff->p[0], n.coeff->p[0]);
42 if (n.coeff->Size == 1)
43 return;
45 int min = n.coeff->Size-1;
46 if (value_posz_p(degree) && value_cmp_si(degree, min) < 0)
47 min = VALUE_TO_INT(degree);
49 Value tmp;
50 value_init(tmp);
51 value_assign(tmp, degree);
52 value_addto(n.coeff->p[1], n.coeff->p[1], tmp);
53 for (int i = 2; i <= min; ++i) {
54 value_decrement(degree, degree);
55 value_multiply(tmp, tmp, degree);
56 mpz_divexact_ui(tmp, tmp, i);
57 value_addto(n.coeff->p[i], n.coeff->p[i], tmp);
59 value_clear(tmp);
62 void counter::add_lattice_points(int sign)
64 dpoly d(dim);
65 for (int k = 0; k < num->NbRows; ++k)
66 add_falling_powers(d, num->p_Init[k]);
67 dpoly n(dim, den->p_Init[0], 1);
68 for (int k = 1; k < dim; ++k) {
69 dpoly fact(dim, den->p_Init[k], 1);
70 n *= fact;
72 d.div(n, count, sign);
78 void tcounter::setup_todd(unsigned dim)
80 value_set_si(todd.coeff->p[0], 1);
82 dpoly d(dim);
83 value_set_si(d.coeff->p[dim], 1);
84 for (int i = dim-1; i >= 0; --i)
85 mpz_mul_ui(d.coeff->p[i], d.coeff->p[i+1], i+2);
87 todd_denom = todd.div(d);
88 /* shift denominators up -> divide by (dim+1)! */
89 for (int i = todd.coeff->Size-1; i >= 1; --i)
90 value_assign(todd_denom->p[i], todd_denom->p[i-1]);
91 value_set_si(todd_denom->p[0], 1);
94 void tcounter::adapt_todd(dpoly& t, const Value c)
96 if (t.coeff->Size <= 1)
97 return;
98 value_assign(tmp, c);
99 value_multiply(t.coeff->p[1], t.coeff->p[1], tmp);
100 for (int i = 2; i < t.coeff->Size; ++i) {
101 value_multiply(tmp, tmp, c);
102 value_multiply(t.coeff->p[i], t.coeff->p[i], tmp);
106 void tcounter::add_powers(dpoly& n, const Value c)
108 value_increment(n.coeff->p[0], n.coeff->p[0]);
109 if (n.coeff->Size == 1)
110 return;
111 value_assign(tmp, c);
112 value_addto(n.coeff->p[1], n.coeff->p[1], tmp);
113 for (int i = 2; i < n.coeff->Size; ++i) {
114 value_multiply(tmp, tmp, c);
115 value_addto(n.coeff->p[i], n.coeff->p[i], tmp);
119 void tcounter::add_lattice_points(int sign)
121 dpoly t(todd);
122 value_assign(denom, den->p_Init[0]);
123 adapt_todd(t, den->p_Init[0]);
124 for (int k = 1; k < dim; ++k) {
125 dpoly fact(todd);
126 value_multiply(denom, denom, den->p_Init[k]);
127 adapt_todd(fact, den->p_Init[k]);
128 t *= fact;
131 dpoly n(dim);
132 for (int k = 0; k < num->NbRows; ++k)
133 add_powers(n, num->p_Init[k]);
135 for (int i = 0; i < n.coeff->Size; ++i)
136 value_multiply(n.coeff->p[i], n.coeff->p[i], todd_denom->p[i]);
137 value_multiply(denom, denom, todd_denom->p[todd_denom->Size-1]);
139 value_set_si(tmp, 1);
140 for (int i = 2; i < n.coeff->Size; ++i) {
141 mpz_mul_ui(tmp, tmp, i);
142 mpz_divexact(n.coeff->p[i], n.coeff->p[i], tmp);
145 value_multiply(tmp, t.coeff->p[0], n.coeff->p[n.coeff->Size-1]);
146 for (int i = 1; i < n.coeff->Size; ++i)
147 value_addmul(tmp, t.coeff->p[i], n.coeff->p[n.coeff->Size-1-i]);
149 value_assign(mpq_numref(tcount), tmp);
150 value_assign(mpq_denref(tcount), denom);
151 mpq_canonicalize(tcount);
152 if (sign == -1)
153 mpq_sub(count, count, tcount);
154 else
155 mpq_add(count, count, tcount);
160 * Set lambda to a random vector that has a positive inner product
161 * with all the rays of the context { x | A x + b >= 0 }.
163 * To do so, we take d rows A' from the constraint matrix A.
164 * For every ray, we have
165 * A' r >= 0
166 * We compute a random positive row vector x' and set x = x' A'.
167 * We then have, for each ray r,
168 * x r = x' A' r >= 0
169 * Although we can take any d rows from A, we choose linearly
170 * independent rows from A to avoid the elements of the transformed
171 * random vector to have simple linear relations, which would
172 * increase the risk of the vector being orthogonal to one of
173 * powers in the denominator of one of the terms in the generating
174 * function.
176 void infinite_counter::init(Polyhedron *context, int n_try)
178 Matrix *M, *H, *Q, *U;
179 mat_ZZ A;
181 randomvector(context, lambda, context->Dimension, n_try);
183 M = Matrix_Alloc(context->NbConstraints, context->Dimension);
184 for (int i = 0; i < context->NbConstraints; ++i)
185 Vector_Copy(context->Constraint[i]+1, M->p[i], context->Dimension);
186 left_hermite(M, &H, &Q, &U);
187 Matrix_Free(Q);
188 Matrix_Free(U);
190 for (int col = 0, row = 0; col < H->NbColumns; ++col, ++row) {
191 for (; row < H->NbRows; ++row)
192 if (value_notzero_p(H->p[row][col]))
193 break;
194 assert(row < H->NbRows);
195 Vector_Copy(M->p[row], M->p[col], M->NbColumns);
197 matrix2zz(M, A, context->Dimension, context->Dimension);
198 Matrix_Free(H);
199 Matrix_Free(M);
201 for (int i = 0; i < lambda.length(); ++i)
202 lambda[i] = abs(lambda[i]);
203 lambda = lambda * A;
206 static ZZ LCM(const ZZ& a, const ZZ& b)
208 return a * b / GCD(a, b);
211 /* Normalize the powers in the denominator to be positive
212 * and return -1 is the sign has to be changed.
214 static int normalized_sign(vec_ZZ& num, vec_ZZ& den)
216 int change = 0;
218 for (int j = 0; j < den.length(); ++j) {
219 if (den[j] > 0)
220 change ^= 1;
221 else {
222 den[j] = abs(den[j]);
223 for (int k = 0; k < num.length(); ++k)
224 num[k] += den[j];
227 return change ? -1 : 1;
230 void infinite_counter::reduce(const vec_QQ& c, const mat_ZZ& num,
231 const mat_ZZ& den_f)
233 mpq_t factor;
234 mpq_init(factor);
235 unsigned len = den_f.NumRows();
237 ZZ lcm = c[0].d;
238 for (int i = 1; i < c.length(); ++i)
239 lcm = LCM(lcm, c[i].d);
241 vec_ZZ coeff;
242 coeff.SetLength(c.length());
243 for (int i = 0; i < c.length(); ++i)
244 coeff[i] = c[i].n * lcm/c[i].d;
246 if (len == 0) {
247 for (int i = 0; i < c.length(); ++i) {
248 zz2value(coeff[i], tz);
249 value_addto(mpq_numref(factor), mpq_numref(factor), tz);
251 zz2value(lcm, tz);
252 value_assign(mpq_denref(factor), tz);
253 mpq_add(count[0], count[0], factor);
254 mpq_clear(factor);
255 return;
258 vec_ZZ num_s = num * lambda;
259 vec_ZZ den_s = den_f * lambda;
260 for (int i = 0; i < den_s.length(); ++i)
261 assert(den_s[i] != 0);
262 int sign = normalized_sign(num_s, den_s);
263 if (sign < 0)
264 coeff = -coeff;
266 dpoly n(len);
267 zz2value(num_s[0], tz);
268 add_falling_powers(n, tz);
269 zz2value(coeff[0], tz);
270 n *= tz;
271 for (int i = 1; i < c.length(); ++i) {
272 dpoly t(len);
273 zz2value(num_s[i], tz);
274 add_falling_powers(t, tz);
275 zz2value(coeff[i], tz);
276 t *= tz;
277 n += t;
279 zz2value(den_s[0], tz);
280 dpoly d(len, tz, 1);
281 for (int i = 1; i < len; ++i) {
282 zz2value(den_s[i], tz);
283 dpoly fact(len, tz, 1);
284 d *= fact;
286 value_set_si(mpq_numref(factor), 1);
287 zz2value(lcm, tz);
288 value_assign(mpq_denref(factor), tz);
289 n.div(d, count, factor);
291 mpq_clear(factor);