/* Make first row entries in column col of bset1 identical to
* those of bset2, using the fact that entry bset1->eq[row][col]=a
* is non-zero. Initially, these elements of bset1 are all zero.
* For each row i < row, we set
* A[i] = a * A[i] + B[i][col] * A[row]
* B[i] = a * B[i]
* so that
* A[i][col] = B[i][col] = a * old(B[i][col])
*/
static void construct_column(
struct isl_basic_set *bset1, struct isl_basic_set *bset2,
unsigned row, unsigned col)
{
int r;
isl_int a;
isl_int b;
unsigned total;
isl_int_init(a);
isl_int_init(b);
total = 1 + isl_basic_set_n_dim(bset1);
for (r = 0; r < row; ++r) {
if (isl_int_is_zero(bset2->eq[r][col]))
continue;
isl_int_gcd(b, bset2->eq[r][col], bset1->eq[row][col]);
isl_int_divexact(a, bset1->eq[row][col], b);
isl_int_divexact(b, bset2->eq[r][col], b);
isl_seq_combine(bset1->eq[r], a, bset1->eq[r],
b, bset1->eq[row], total);
isl_seq_scale(bset2->eq[r], bset2->eq[r], a, total);
}
isl_int_clear(a);
isl_int_clear(b);
delete_row(bset1, row);
}
/* Find an integer point in the set represented by "tab"
* that lies outside of the equality "eq" e(x) = 0.
* If "up" is true, look for a point satisfying e(x) - 1 >= 0.
* Otherwise, look for a point satisfying -e(x) - 1 >= 0 (i.e., e(x) <= -1).
* The point, if found, is returned.
* If no point can be found, a zero-length vector is returned.
*
* Before solving an ILP problem, we first check if simply
* adding the normal of the constraint to one of the known
* integer points in the basic set represented by "tab"
* yields another point inside the basic set.
*
* The caller of this function ensures that the tableau is bounded or
* that tab->basis and tab->n_unbounded have been set appropriately.
*/
static struct isl_vec *outside_point(struct isl_tab *tab, isl_int *eq, int up)
{
struct isl_ctx *ctx;
struct isl_vec *sample = NULL;
struct isl_tab_undo *snap;
unsigned dim;
if (!tab)
return NULL;
ctx = tab->mat->ctx;
dim = tab->n_var;
sample = isl_vec_alloc(ctx, 1 + dim);
if (!sample)
return NULL;
isl_int_set_si(sample->el[0], 1);
isl_seq_combine(sample->el + 1,
ctx->one, tab->bmap->sample->el + 1,
up ? ctx->one : ctx->negone, eq + 1, dim);
if (isl_basic_map_contains(tab->bmap, sample))
return sample;
isl_vec_free(sample);
sample = NULL;
snap = isl_tab_snap(tab);
if (!up)
isl_seq_neg(eq, eq, 1 + dim);
isl_int_sub_ui(eq[0], eq[0], 1);
if (isl_tab_extend_cons(tab, 1) < 0)
goto error;
if (isl_tab_add_ineq(tab, eq) < 0)
goto error;
sample = isl_tab_sample(tab);
isl_int_add_ui(eq[0], eq[0], 1);
if (!up)
isl_seq_neg(eq, eq, 1 + dim);
if (sample && isl_tab_rollback(tab, snap) < 0)
goto error;
return sample;
error:
isl_vec_free(sample);
return NULL;
}
/* Make first row entries in column col of bset1 identical to
* those of bset2, using only these entries of the two matrices.
* Let t be the last row with different entries.
* For each row i < t, we set
* A[i] = (A[t][col]-B[t][col]) * A[i] + (B[i][col]-A[i][col) * A[t]
* B[i] = (A[t][col]-B[t][col]) * B[i] + (B[i][col]-A[i][col) * B[t]
* so that
* A[i][col] = B[i][col] = old(A[t][col]*B[i][col]-A[i][col]*B[t][col])
*/
static int transform_column(
struct isl_basic_set *bset1, struct isl_basic_set *bset2,
unsigned row, unsigned col)
{
int i, t;
isl_int a, b, g;
unsigned total;
for (t = row-1; t >= 0; --t)
if (isl_int_ne(bset1->eq[t][col], bset2->eq[t][col]))
break;
if (t < 0)
return 0;
total = 1 + isl_basic_set_n_dim(bset1);
isl_int_init(a);
isl_int_init(b);
isl_int_init(g);
isl_int_sub(b, bset1->eq[t][col], bset2->eq[t][col]);
for (i = 0; i < t; ++i) {
isl_int_sub(a, bset2->eq[i][col], bset1->eq[i][col]);
isl_int_gcd(g, a, b);
isl_int_divexact(a, a, g);
isl_int_divexact(g, b, g);
isl_seq_combine(bset1->eq[i], g, bset1->eq[i], a, bset1->eq[t],
total);
isl_seq_combine(bset2->eq[i], g, bset2->eq[i], a, bset2->eq[t],
total);
}
isl_int_clear(a);
isl_int_clear(b);
isl_int_clear(g);
delete_row(bset1, t);
delete_row(bset2, t);
return 1;
}
/* Compute a reduced basis for the set represented by the tableau "tab".
* tab->basis, which must be initialized by the calling function to an affine
* unimodular basis, is updated to reflect the reduced basis.
* The first tab->n_zero rows of the basis (ignoring the constant row)
* are assumed to correspond to equalities and are left untouched.
* tab->n_zero is updated to reflect any additional equalities that
* have been detected in the first rows of the new basis.
* The final tab->n_unbounded rows of the basis are assumed to correspond
* to unbounded directions and are also left untouched.
* In particular this means that the remaining rows are assumed to
* correspond to bounded directions.
*
* This function implements the algorithm described in
* "An Implementation of the Generalized Basis Reduction Algorithm
* for Integer Programming" of Cook el al. to compute a reduced basis.
* We use \epsilon = 1/4.
*
* If ctx->opt->gbr_only_first is set, the user is only interested
* in the first direction. In this case we stop the basis reduction when
* the width in the first direction becomes smaller than 2.
*/
struct isl_tab *isl_tab_compute_reduced_basis(struct isl_tab *tab)
{
unsigned dim;
struct isl_ctx *ctx;
struct isl_mat *B;
int unbounded;
int i;
GBR_LP *lp = NULL;
GBR_type F_old, alpha, F_new;
int row;
isl_int tmp;
struct isl_vec *b_tmp;
GBR_type *F = NULL;
GBR_type *alpha_buffer[2] = { NULL, NULL };
GBR_type *alpha_saved;
GBR_type F_saved;
int use_saved = 0;
isl_int mu[2];
GBR_type mu_F[2];
GBR_type two;
GBR_type one;
int empty = 0;
int fixed = 0;
int fixed_saved = 0;
int mu_fixed[2];
int n_bounded;
int gbr_only_first;
if (!tab)
return NULL;
if (tab->empty)
return tab;
ctx = tab->mat->ctx;
gbr_only_first = ctx->opt->gbr_only_first;
dim = tab->n_var;
B = tab->basis;
if (!B)
return tab;
n_bounded = dim - tab->n_unbounded;
if (n_bounded <= tab->n_zero + 1)
return tab;
isl_int_init(tmp);
isl_int_init(mu[0]);
isl_int_init(mu[1]);
GBR_init(alpha);
GBR_init(F_old);
GBR_init(F_new);
GBR_init(F_saved);
GBR_init(mu_F[0]);
GBR_init(mu_F[1]);
GBR_init(two);
GBR_init(one);
b_tmp = isl_vec_alloc(ctx, dim);
if (!b_tmp)
goto error;
F = isl_alloc_array(ctx, GBR_type, n_bounded);
alpha_buffer[0] = isl_alloc_array(ctx, GBR_type, n_bounded);
alpha_buffer[1] = isl_alloc_array(ctx, GBR_type, n_bounded);
alpha_saved = alpha_buffer[0];
if (!F || !alpha_buffer[0] || !alpha_buffer[1])
goto error;
for (i = 0; i < n_bounded; ++i) {
GBR_init(F[i]);
GBR_init(alpha_buffer[0][i]);
GBR_init(alpha_buffer[1][i]);
}
GBR_set_ui(two, 2);
GBR_set_ui(one, 1);
lp = GBR_lp_init(tab);
if (!lp)
goto error;
i = tab->n_zero;
GBR_lp_set_obj(lp, B->row[1+i]+1, dim);
ctx->stats->gbr_solved_lps++;
unbounded = GBR_lp_solve(lp);
isl_assert(ctx, !unbounded, goto error);
GBR_lp_get_obj_val(lp, &F[i]);
if (GBR_lt(F[i], one)) {
if (!GBR_is_zero(F[i])) {
empty = GBR_lp_cut(lp, B->row[1+i]+1);
if (empty)
goto done;
GBR_set_ui(F[i], 0);
}
tab->n_zero++;
}
do {
if (i+1 == tab->n_zero) {
GBR_lp_set_obj(lp, B->row[1+i+1]+1, dim);
ctx->stats->gbr_solved_lps++;
unbounded = GBR_lp_solve(lp);
isl_assert(ctx, !unbounded, goto error);
GBR_lp_get_obj_val(lp, &F_new);
fixed = GBR_lp_is_fixed(lp);
GBR_set_ui(alpha, 0);
} else if (use_saved) {
row = GBR_lp_next_row(lp);
GBR_set(F_new, F_saved);
fixed = fixed_saved;
GBR_set(alpha, alpha_saved[i]);
} else {
row = GBR_lp_add_row(lp, B->row[1+i]+1, dim);
GBR_lp_set_obj(lp, B->row[1+i+1]+1, dim);
ctx->stats->gbr_solved_lps++;
unbounded = GBR_lp_solve(lp);
isl_assert(ctx, !unbounded, goto error);
GBR_lp_get_obj_val(lp, &F_new);
fixed = GBR_lp_is_fixed(lp);
GBR_lp_get_alpha(lp, row, &alpha);
if (i > 0)
save_alpha(lp, row-i, i, alpha_saved);
if (GBR_lp_del_row(lp) < 0)
goto error;
}
GBR_set(F[i+1], F_new);
GBR_floor(mu[0], alpha);
GBR_ceil(mu[1], alpha);
if (isl_int_eq(mu[0], mu[1]))
isl_int_set(tmp, mu[0]);
else {
int j;
for (j = 0; j <= 1; ++j) {
isl_int_set(tmp, mu[j]);
isl_seq_combine(b_tmp->el,
ctx->one, B->row[1+i+1]+1,
tmp, B->row[1+i]+1, dim);
GBR_lp_set_obj(lp, b_tmp->el, dim);
ctx->stats->gbr_solved_lps++;
unbounded = GBR_lp_solve(lp);
isl_assert(ctx, !unbounded, goto error);
GBR_lp_get_obj_val(lp, &mu_F[j]);
mu_fixed[j] = GBR_lp_is_fixed(lp);
if (i > 0)
save_alpha(lp, row-i, i, alpha_buffer[j]);
}
if (GBR_lt(mu_F[0], mu_F[1]))
j = 0;
else
j = 1;
isl_int_set(tmp, mu[j]);
GBR_set(F_new, mu_F[j]);
fixed = mu_fixed[j];
alpha_saved = alpha_buffer[j];
}
isl_seq_combine(B->row[1+i+1]+1, ctx->one, B->row[1+i+1]+1,
tmp, B->row[1+i]+1, dim);
if (i+1 == tab->n_zero && fixed) {
if (!GBR_is_zero(F[i+1])) {
empty = GBR_lp_cut(lp, B->row[1+i+1]+1);
if (empty)
goto done;
GBR_set_ui(F[i+1], 0);
}
tab->n_zero++;
}
GBR_set(F_old, F[i]);
use_saved = 0;
/* mu_F[0] = 4 * F_new; mu_F[1] = 3 * F_old */
GBR_set_ui(mu_F[0], 4);
GBR_mul(mu_F[0], mu_F[0], F_new);
GBR_set_ui(mu_F[1], 3);
GBR_mul(mu_F[1], mu_F[1], F_old);
if (GBR_lt(mu_F[0], mu_F[1])) {
B = isl_mat_swap_rows(B, 1 + i, 1 + i + 1);
if (i > tab->n_zero) {
use_saved = 1;
GBR_set(F_saved, F_new);
fixed_saved = fixed;
if (GBR_lp_del_row(lp) < 0)
goto error;
--i;
} else {
GBR_set(F[tab->n_zero], F_new);
if (gbr_only_first && GBR_lt(F[tab->n_zero], two))
break;
if (fixed) {
if (!GBR_is_zero(F[tab->n_zero])) {
empty = GBR_lp_cut(lp, B->row[1+tab->n_zero]+1);
if (empty)
goto done;
GBR_set_ui(F[tab->n_zero], 0);
}
tab->n_zero++;
}
}
} else {
GBR_lp_add_row(lp, B->row[1+i]+1, dim);
++i;
}
} while (i < n_bounded - 1);
