+/*
+ * Copyright 2008-2009 Katholieke Universiteit Leuven
+ *
+ * Use of this software is governed by the GNU LGPLv2.1 license
+ *
+ * Written by Sven Verdoolaege, K.U.Leuven, Departement
+ * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
+ */
+
+#include "isl_mat.h"
#include "isl_map_private.h"
#include "isl_tab.h"
+#include "isl_seq.h"
/*
* The implementation of tableaus in this file was inspired by Section 8
*/
struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx,
- unsigned n_row, unsigned n_var)
+ unsigned n_row, unsigned n_var, unsigned M)
{
int i;
struct isl_tab *tab;
+ unsigned off = 2 + M;
tab = isl_calloc_type(ctx, struct isl_tab);
if (!tab)
return NULL;
- tab->mat = isl_mat_alloc(ctx, n_row, 2 + n_var);
+ tab->mat = isl_mat_alloc(ctx, n_row, off + n_var);
if (!tab->mat)
goto error;
tab->var = isl_alloc_array(ctx, struct isl_tab_var, n_var);
tab->var[i].is_zero = 0;
tab->var[i].is_redundant = 0;
tab->var[i].frozen = 0;
+ tab->var[i].negated = 0;
tab->col_var[i] = i;
}
tab->n_row = 0;
tab->n_con = 0;
+ tab->n_eq = 0;
tab->max_con = n_row;
tab->n_col = n_var;
tab->n_var = n_var;
+ tab->max_var = n_var;
+ tab->n_param = 0;
+ tab->n_div = 0;
tab->n_dead = 0;
tab->n_redundant = 0;
tab->need_undo = 0;
tab->rational = 0;
tab->empty = 0;
- tab->killed_col = 0;
+ tab->in_undo = 0;
+ tab->M = M;
+ tab->cone = 0;
tab->bottom.type = isl_tab_undo_bottom;
tab->bottom.next = NULL;
tab->top = &tab->bottom;
+
+ tab->n_zero = 0;
+ tab->n_unbounded = 0;
+ tab->basis = NULL;
+
return tab;
error:
- isl_tab_free(ctx, tab);
+ isl_tab_free(tab);
return NULL;
}
-static int extend_cons(struct isl_ctx *ctx, struct isl_tab *tab, unsigned n_new)
+int isl_tab_extend_cons(struct isl_tab *tab, unsigned n_new)
{
+ unsigned off = 2 + tab->M;
+
+ if (!tab)
+ return -1;
+
if (tab->max_con < tab->n_con + n_new) {
struct isl_tab_var *con;
- con = isl_realloc_array(ctx, tab->con,
+ con = isl_realloc_array(tab->mat->ctx, tab->con,
struct isl_tab_var, tab->max_con + n_new);
if (!con)
return -1;
if (tab->mat->n_row < tab->n_row + n_new) {
int *row_var;
- tab->mat = isl_mat_extend(ctx, tab->mat,
- tab->n_row + n_new, tab->n_col);
+ tab->mat = isl_mat_extend(tab->mat,
+ tab->n_row + n_new, off + tab->n_col);
if (!tab->mat)
return -1;
- row_var = isl_realloc_array(ctx, tab->row_var,
+ row_var = isl_realloc_array(tab->mat->ctx, tab->row_var,
int, tab->mat->n_row);
if (!row_var)
return -1;
tab->row_var = row_var;
+ if (tab->row_sign) {
+ enum isl_tab_row_sign *s;
+ s = isl_realloc_array(tab->mat->ctx, tab->row_sign,
+ enum isl_tab_row_sign, tab->mat->n_row);
+ if (!s)
+ return -1;
+ tab->row_sign = s;
+ }
}
return 0;
}
-struct isl_tab *isl_tab_extend(struct isl_ctx *ctx, struct isl_tab *tab,
- unsigned n_new)
+/* Make room for at least n_new extra variables.
+ * Return -1 if anything went wrong.
+ */
+int isl_tab_extend_vars(struct isl_tab *tab, unsigned n_new)
{
- if (extend_cons(ctx, tab, n_new) >= 0)
+ struct isl_tab_var *var;
+ unsigned off = 2 + tab->M;
+
+ if (tab->max_var < tab->n_var + n_new) {
+ var = isl_realloc_array(tab->mat->ctx, tab->var,
+ struct isl_tab_var, tab->n_var + n_new);
+ if (!var)
+ return -1;
+ tab->var = var;
+ tab->max_var += n_new;
+ }
+
+ if (tab->mat->n_col < off + tab->n_col + n_new) {
+ int *p;
+
+ tab->mat = isl_mat_extend(tab->mat,
+ tab->mat->n_row, off + tab->n_col + n_new);
+ if (!tab->mat)
+ return -1;
+ p = isl_realloc_array(tab->mat->ctx, tab->col_var,
+ int, tab->n_col + n_new);
+ if (!p)
+ return -1;
+ tab->col_var = p;
+ }
+
+ return 0;
+}
+
+struct isl_tab *isl_tab_extend(struct isl_tab *tab, unsigned n_new)
+{
+ if (isl_tab_extend_cons(tab, n_new) >= 0)
return tab;
- isl_tab_free(ctx, tab);
+ isl_tab_free(tab);
return NULL;
}
-static void free_undo(struct isl_ctx *ctx, struct isl_tab *tab)
+static void free_undo(struct isl_tab *tab)
{
struct isl_tab_undo *undo, *next;
tab->top = undo;
}
-void isl_tab_free(struct isl_ctx *ctx, struct isl_tab *tab)
+void isl_tab_free(struct isl_tab *tab)
{
if (!tab)
return;
- free_undo(ctx, tab);
- isl_mat_free(ctx, tab->mat);
+ free_undo(tab);
+ isl_mat_free(tab->mat);
+ isl_vec_free(tab->dual);
+ isl_basic_map_free(tab->bmap);
free(tab->var);
free(tab->con);
free(tab->row_var);
free(tab->col_var);
+ free(tab->row_sign);
+ isl_mat_free(tab->samples);
+ free(tab->sample_index);
+ isl_mat_free(tab->basis);
free(tab);
}
-static struct isl_tab_var *var_from_index(struct isl_ctx *ctx,
- struct isl_tab *tab, int i)
+struct isl_tab *isl_tab_dup(struct isl_tab *tab)
+{
+ int i;
+ struct isl_tab *dup;
+ unsigned off;
+
+ if (!tab)
+ return NULL;
+
+ off = 2 + tab->M;
+ dup = isl_calloc_type(tab->ctx, struct isl_tab);
+ if (!dup)
+ return NULL;
+ dup->mat = isl_mat_dup(tab->mat);
+ if (!dup->mat)
+ goto error;
+ dup->var = isl_alloc_array(tab->ctx, struct isl_tab_var, tab->max_var);
+ if (!dup->var)
+ goto error;
+ for (i = 0; i < tab->n_var; ++i)
+ dup->var[i] = tab->var[i];
+ dup->con = isl_alloc_array(tab->ctx, struct isl_tab_var, tab->max_con);
+ if (!dup->con)
+ goto error;
+ for (i = 0; i < tab->n_con; ++i)
+ dup->con[i] = tab->con[i];
+ dup->col_var = isl_alloc_array(tab->ctx, int, tab->mat->n_col - off);
+ if (!dup->col_var)
+ goto error;
+ for (i = 0; i < tab->n_col; ++i)
+ dup->col_var[i] = tab->col_var[i];
+ dup->row_var = isl_alloc_array(tab->ctx, int, tab->mat->n_row);
+ if (!dup->row_var)
+ goto error;
+ for (i = 0; i < tab->n_row; ++i)
+ dup->row_var[i] = tab->row_var[i];
+ if (tab->row_sign) {
+ dup->row_sign = isl_alloc_array(tab->ctx, enum isl_tab_row_sign,
+ tab->mat->n_row);
+ if (!dup->row_sign)
+ goto error;
+ for (i = 0; i < tab->n_row; ++i)
+ dup->row_sign[i] = tab->row_sign[i];
+ }
+ if (tab->samples) {
+ dup->samples = isl_mat_dup(tab->samples);
+ if (!dup->samples)
+ goto error;
+ dup->sample_index = isl_alloc_array(tab->mat->ctx, int,
+ tab->samples->n_row);
+ if (!dup->sample_index)
+ goto error;
+ dup->n_sample = tab->n_sample;
+ dup->n_outside = tab->n_outside;
+ }
+ dup->n_row = tab->n_row;
+ dup->n_con = tab->n_con;
+ dup->n_eq = tab->n_eq;
+ dup->max_con = tab->max_con;
+ dup->n_col = tab->n_col;
+ dup->n_var = tab->n_var;
+ dup->max_var = tab->max_var;
+ dup->n_param = tab->n_param;
+ dup->n_div = tab->n_div;
+ dup->n_dead = tab->n_dead;
+ dup->n_redundant = tab->n_redundant;
+ dup->rational = tab->rational;
+ dup->empty = tab->empty;
+ dup->need_undo = 0;
+ dup->in_undo = 0;
+ dup->M = tab->M;
+ tab->cone = tab->cone;
+ dup->bottom.type = isl_tab_undo_bottom;
+ dup->bottom.next = NULL;
+ dup->top = &dup->bottom;
+
+ dup->n_zero = tab->n_zero;
+ dup->n_unbounded = tab->n_unbounded;
+ dup->basis = isl_mat_dup(tab->basis);
+
+ return dup;
+error:
+ isl_tab_free(dup);
+ return NULL;
+}
+
+/* Construct the coefficient matrix of the product tableau
+ * of two tableaus.
+ * mat{1,2} is the coefficient matrix of tableau {1,2}
+ * row{1,2} is the number of rows in tableau {1,2}
+ * col{1,2} is the number of columns in tableau {1,2}
+ * off is the offset to the coefficient column (skipping the
+ * denominator, the constant term and the big parameter if any)
+ * r{1,2} is the number of redundant rows in tableau {1,2}
+ * d{1,2} is the number of dead columns in tableau {1,2}
+ *
+ * The order of the rows and columns in the result is as explained
+ * in isl_tab_product.
+ */
+static struct isl_mat *tab_mat_product(struct isl_mat *mat1,
+ struct isl_mat *mat2, unsigned row1, unsigned row2,
+ unsigned col1, unsigned col2,
+ unsigned off, unsigned r1, unsigned r2, unsigned d1, unsigned d2)
+{
+ int i;
+ struct isl_mat *prod;
+ unsigned n;
+
+ prod = isl_mat_alloc(mat1->ctx, mat1->n_row + mat2->n_row,
+ off + col1 + col2);
+
+ n = 0;
+ for (i = 0; i < r1; ++i) {
+ isl_seq_cpy(prod->row[n + i], mat1->row[i], off + d1);
+ isl_seq_clr(prod->row[n + i] + off + d1, d2);
+ isl_seq_cpy(prod->row[n + i] + off + d1 + d2,
+ mat1->row[i] + off + d1, col1 - d1);
+ isl_seq_clr(prod->row[n + i] + off + col1 + d1, col2 - d2);
+ }
+
+ n += r1;
+ for (i = 0; i < r2; ++i) {
+ isl_seq_cpy(prod->row[n + i], mat2->row[i], off);
+ isl_seq_clr(prod->row[n + i] + off, d1);
+ isl_seq_cpy(prod->row[n + i] + off + d1,
+ mat2->row[i] + off, d2);
+ isl_seq_clr(prod->row[n + i] + off + d1 + d2, col1 - d1);
+ isl_seq_cpy(prod->row[n + i] + off + col1 + d1,
+ mat2->row[i] + off + d2, col2 - d2);
+ }
+
+ n += r2;
+ for (i = 0; i < row1 - r1; ++i) {
+ isl_seq_cpy(prod->row[n + i], mat1->row[r1 + i], off + d1);
+ isl_seq_clr(prod->row[n + i] + off + d1, d2);
+ isl_seq_cpy(prod->row[n + i] + off + d1 + d2,
+ mat1->row[r1 + i] + off + d1, col1 - d1);
+ isl_seq_clr(prod->row[n + i] + off + col1 + d1, col2 - d2);
+ }
+
+ n += row1 - r1;
+ for (i = 0; i < row2 - r2; ++i) {
+ isl_seq_cpy(prod->row[n + i], mat2->row[r2 + i], off);
+ isl_seq_clr(prod->row[n + i] + off, d1);
+ isl_seq_cpy(prod->row[n + i] + off + d1,
+ mat2->row[r2 + i] + off, d2);
+ isl_seq_clr(prod->row[n + i] + off + d1 + d2, col1 - d1);
+ isl_seq_cpy(prod->row[n + i] + off + col1 + d1,
+ mat2->row[r2 + i] + off + d2, col2 - d2);
+ }
+
+ return prod;
+}
+
+/* Update the row or column index of a variable that corresponds
+ * to a variable in the first input tableau.
+ */
+static void update_index1(struct isl_tab_var *var,
+ unsigned r1, unsigned r2, unsigned d1, unsigned d2)
+{
+ if (var->index == -1)
+ return;
+ if (var->is_row && var->index >= r1)
+ var->index += r2;
+ if (!var->is_row && var->index >= d1)
+ var->index += d2;
+}
+
+/* Update the row or column index of a variable that corresponds
+ * to a variable in the second input tableau.
+ */
+static void update_index2(struct isl_tab_var *var,
+ unsigned row1, unsigned col1,
+ unsigned r1, unsigned r2, unsigned d1, unsigned d2)
+{
+ if (var->index == -1)
+ return;
+ if (var->is_row) {
+ if (var->index < r2)
+ var->index += r1;
+ else
+ var->index += row1;
+ } else {
+ if (var->index < d2)
+ var->index += d1;
+ else
+ var->index += col1;
+ }
+}
+
+/* Create a tableau that represents the Cartesian product of the sets
+ * represented by tableaus tab1 and tab2.
+ * The order of the rows in the product is
+ * - redundant rows of tab1
+ * - redundant rows of tab2
+ * - non-redundant rows of tab1
+ * - non-redundant rows of tab2
+ * The order of the columns is
+ * - denominator
+ * - constant term
+ * - coefficient of big parameter, if any
+ * - dead columns of tab1
+ * - dead columns of tab2
+ * - live columns of tab1
+ * - live columns of tab2
+ * The order of the variables and the constraints is a concatenation
+ * of order in the two input tableaus.
+ */
+struct isl_tab *isl_tab_product(struct isl_tab *tab1, struct isl_tab *tab2)
+{
+ int i;
+ struct isl_tab *prod;
+ unsigned off;
+ unsigned r1, r2, d1, d2;
+
+ if (!tab1 || !tab2)
+ return NULL;
+
+ isl_assert(tab1->mat->ctx, tab1->M == tab2->M, return NULL);
+ isl_assert(tab1->mat->ctx, tab1->rational == tab2->rational, return NULL);
+ isl_assert(tab1->mat->ctx, tab1->cone == tab2->cone, return NULL);
+ isl_assert(tab1->mat->ctx, !tab1->row_sign, return NULL);
+ isl_assert(tab1->mat->ctx, !tab2->row_sign, return NULL);
+ isl_assert(tab1->mat->ctx, tab1->n_param == 0, return NULL);
+ isl_assert(tab1->mat->ctx, tab2->n_param == 0, return NULL);
+ isl_assert(tab1->mat->ctx, tab1->n_div == 0, return NULL);
+ isl_assert(tab1->mat->ctx, tab2->n_div == 0, return NULL);
+
+ off = 2 + tab1->M;
+ r1 = tab1->n_redundant;
+ r2 = tab2->n_redundant;
+ d1 = tab1->n_dead;
+ d2 = tab2->n_dead;
+ prod = isl_calloc_type(tab1->mat->ctx, struct isl_tab);
+ if (!prod)
+ return NULL;
+ prod->mat = tab_mat_product(tab1->mat, tab2->mat,
+ tab1->n_row, tab2->n_row,
+ tab1->n_col, tab2->n_col, off, r1, r2, d1, d2);
+ if (!prod->mat)
+ goto error;
+ prod->var = isl_alloc_array(tab1->mat->ctx, struct isl_tab_var,
+ tab1->max_var + tab2->max_var);
+ if (!prod->var)
+ goto error;
+ for (i = 0; i < tab1->n_var; ++i) {
+ prod->var[i] = tab1->var[i];
+ update_index1(&prod->var[i], r1, r2, d1, d2);
+ }
+ for (i = 0; i < tab2->n_var; ++i) {
+ prod->var[tab1->n_var + i] = tab2->var[i];
+ update_index2(&prod->var[tab1->n_var + i],
+ tab1->n_row, tab1->n_col,
+ r1, r2, d1, d2);
+ }
+ prod->con = isl_alloc_array(tab1->mat->ctx, struct isl_tab_var,
+ tab1->max_con + tab2->max_con);
+ if (!prod->con)
+ goto error;
+ for (i = 0; i < tab1->n_con; ++i) {
+ prod->con[i] = tab1->con[i];
+ update_index1(&prod->con[i], r1, r2, d1, d2);
+ }
+ for (i = 0; i < tab2->n_con; ++i) {
+ prod->con[tab1->n_con + i] = tab2->con[i];
+ update_index2(&prod->con[tab1->n_con + i],
+ tab1->n_row, tab1->n_col,
+ r1, r2, d1, d2);
+ }
+ prod->col_var = isl_alloc_array(tab1->mat->ctx, int,
+ tab1->n_col + tab2->n_col);
+ if (!prod->col_var)
+ goto error;
+ for (i = 0; i < tab1->n_col; ++i) {
+ int pos = i < d1 ? i : i + d2;
+ prod->col_var[pos] = tab1->col_var[i];
+ }
+ for (i = 0; i < tab2->n_col; ++i) {
+ int pos = i < d2 ? d1 + i : tab1->n_col + i;
+ int t = tab2->col_var[i];
+ if (t >= 0)
+ t += tab1->n_var;
+ else
+ t -= tab1->n_con;
+ prod->col_var[pos] = t;
+ }
+ prod->row_var = isl_alloc_array(tab1->mat->ctx, int,
+ tab1->mat->n_row + tab2->mat->n_row);
+ if (!prod->row_var)
+ goto error;
+ for (i = 0; i < tab1->n_row; ++i) {
+ int pos = i < r1 ? i : i + r2;
+ prod->row_var[pos] = tab1->row_var[i];
+ }
+ for (i = 0; i < tab2->n_row; ++i) {
+ int pos = i < r2 ? r1 + i : tab1->n_row + i;
+ int t = tab2->row_var[i];
+ if (t >= 0)
+ t += tab1->n_var;
+ else
+ t -= tab1->n_con;
+ prod->row_var[pos] = t;
+ }
+ prod->samples = NULL;
+ prod->sample_index = NULL;
+ prod->n_row = tab1->n_row + tab2->n_row;
+ prod->n_con = tab1->n_con + tab2->n_con;
+ prod->n_eq = 0;
+ prod->max_con = tab1->max_con + tab2->max_con;
+ prod->n_col = tab1->n_col + tab2->n_col;
+ prod->n_var = tab1->n_var + tab2->n_var;
+ prod->max_var = tab1->max_var + tab2->max_var;
+ prod->n_param = 0;
+ prod->n_div = 0;
+ prod->n_dead = tab1->n_dead + tab2->n_dead;
+ prod->n_redundant = tab1->n_redundant + tab2->n_redundant;
+ prod->rational = tab1->rational;
+ prod->empty = tab1->empty || tab2->empty;
+ prod->need_undo = 0;
+ prod->in_undo = 0;
+ prod->M = tab1->M;
+ prod->cone = tab1->cone;
+ prod->bottom.type = isl_tab_undo_bottom;
+ prod->bottom.next = NULL;
+ prod->top = &prod->bottom;
+
+ prod->n_zero = 0;
+ prod->n_unbounded = 0;
+ prod->basis = NULL;
+
+ return prod;
+error:
+ isl_tab_free(prod);
+ return NULL;
+}
+
+static struct isl_tab_var *var_from_index(struct isl_tab *tab, int i)
{
if (i >= 0)
return &tab->var[i];
return &tab->con[~i];
}
-static struct isl_tab_var *var_from_row(struct isl_ctx *ctx,
- struct isl_tab *tab, int i)
+struct isl_tab_var *isl_tab_var_from_row(struct isl_tab *tab, int i)
{
- return var_from_index(ctx, tab, tab->row_var[i]);
+ return var_from_index(tab, tab->row_var[i]);
}
-static struct isl_tab_var *var_from_col(struct isl_ctx *ctx,
- struct isl_tab *tab, int i)
+static struct isl_tab_var *var_from_col(struct isl_tab *tab, int i)
{
- return var_from_index(ctx, tab, tab->col_var[i]);
+ return var_from_index(tab, tab->col_var[i]);
}
/* Check if there are any upper bounds on column variable "var",
* i.e., non-negative rows where var appears with a negative coefficient.
* Return 1 if there are no such bounds.
*/
-static int max_is_manifestly_unbounded(struct isl_ctx *ctx,
- struct isl_tab *tab, struct isl_tab_var *var)
+static int max_is_manifestly_unbounded(struct isl_tab *tab,
+ struct isl_tab_var *var)
{
int i;
+ unsigned off = 2 + tab->M;
if (var->is_row)
return 0;
for (i = tab->n_redundant; i < tab->n_row; ++i) {
- if (!isl_int_is_neg(tab->mat->row[i][2 + var->index]))
+ if (!isl_int_is_neg(tab->mat->row[i][off + var->index]))
continue;
- if (var_from_row(ctx, tab, i)->is_nonneg)
+ if (isl_tab_var_from_row(tab, i)->is_nonneg)
return 0;
}
return 1;
* i.e., non-negative rows where var appears with a positive coefficient.
* Return 1 if there are no such bounds.
*/
-static int min_is_manifestly_unbounded(struct isl_ctx *ctx,
- struct isl_tab *tab, struct isl_tab_var *var)
+static int min_is_manifestly_unbounded(struct isl_tab *tab,
+ struct isl_tab_var *var)
{
int i;
+ unsigned off = 2 + tab->M;
if (var->is_row)
return 0;
for (i = tab->n_redundant; i < tab->n_row; ++i) {
- if (!isl_int_is_pos(tab->mat->row[i][2 + var->index]))
+ if (!isl_int_is_pos(tab->mat->row[i][off + var->index]))
continue;
- if (var_from_row(ctx, tab, i)->is_nonneg)
+ if (isl_tab_var_from_row(tab, i)->is_nonneg)
return 0;
}
return 1;
}
+static int row_cmp(struct isl_tab *tab, int r1, int r2, int c, isl_int t)
+{
+ unsigned off = 2 + tab->M;
+
+ if (tab->M) {
+ int s;
+ isl_int_mul(t, tab->mat->row[r1][2], tab->mat->row[r2][off+c]);
+ isl_int_submul(t, tab->mat->row[r2][2], tab->mat->row[r1][off+c]);
+ s = isl_int_sgn(t);
+ if (s)
+ return s;
+ }
+ isl_int_mul(t, tab->mat->row[r1][1], tab->mat->row[r2][off + c]);
+ isl_int_submul(t, tab->mat->row[r2][1], tab->mat->row[r1][off + c]);
+ return isl_int_sgn(t);
+}
+
/* Given the index of a column "c", return the index of a row
* that can be used to pivot the column in, with either an increase
* (sgn > 0) or a decrease (sgn < 0) of the corresponding variable.
* we check if -sign(a_jc) (a_j0 a_rc - a_r0 a_jc) < 0,
* where -sign(a_jc) is equal to "sgn".
*/
-static int pivot_row(struct isl_ctx *ctx, struct isl_tab *tab,
+static int pivot_row(struct isl_tab *tab,
struct isl_tab_var *var, int sgn, int c)
{
int j, r, tsgn;
isl_int t;
+ unsigned off = 2 + tab->M;
isl_int_init(t);
r = -1;
for (j = tab->n_redundant; j < tab->n_row; ++j) {
if (var && j == var->index)
continue;
- if (!var_from_row(ctx, tab, j)->is_nonneg)
+ if (!isl_tab_var_from_row(tab, j)->is_nonneg)
continue;
- if (sgn * isl_int_sgn(tab->mat->row[j][2 + c]) >= 0)
+ if (sgn * isl_int_sgn(tab->mat->row[j][off + c]) >= 0)
continue;
if (r < 0) {
r = j;
continue;
}
- isl_int_mul(t, tab->mat->row[r][1], tab->mat->row[j][2 + c]);
- isl_int_submul(t, tab->mat->row[j][1], tab->mat->row[r][2 + c]);
- tsgn = sgn * isl_int_sgn(t);
+ tsgn = sgn * row_cmp(tab, r, j, c, t);
if (tsgn < 0 || (tsgn == 0 &&
tab->row_var[j] < tab->row_var[r]))
r = j;
/* Find a pivot (row and col) that will increase (sgn > 0) or decrease
* (sgn < 0) the value of row variable var.
+ * If not NULL, then skip_var is a row variable that should be ignored
+ * while looking for a pivot row. It is usually equal to var.
+ *
* As the given row in the tableau is of the form
*
* x_r = a_r0 + \sum_i a_ri x_i
* to obtain the desired effect. Otherwise, x_i has to move in the
* opposite direction.
*/
-static void find_pivot(struct isl_ctx *ctx, struct isl_tab *tab,
- struct isl_tab_var *var, int sgn, int *row, int *col)
+static void find_pivot(struct isl_tab *tab,
+ struct isl_tab_var *var, struct isl_tab_var *skip_var,
+ int sgn, int *row, int *col)
{
int j, r, c;
isl_int *tr;
*row = *col = -1;
- isl_assert(ctx, var->is_row, return);
- tr = tab->mat->row[var->index];
+ isl_assert(tab->mat->ctx, var->is_row, return);
+ tr = tab->mat->row[var->index] + 2 + tab->M;
c = -1;
for (j = tab->n_dead; j < tab->n_col; ++j) {
- if (isl_int_is_zero(tr[2 + j]))
+ if (isl_int_is_zero(tr[j]))
continue;
- if (isl_int_sgn(tr[2 + j]) != sgn &&
- var_from_col(ctx, tab, j)->is_nonneg)
+ if (isl_int_sgn(tr[j]) != sgn &&
+ var_from_col(tab, j)->is_nonneg)
continue;
if (c < 0 || tab->col_var[j] < tab->col_var[c])
c = j;
if (c < 0)
return;
- sgn *= isl_int_sgn(tr[2 + c]);
- r = pivot_row(ctx, tab, var, sgn, c);
+ sgn *= isl_int_sgn(tr[c]);
+ r = pivot_row(tab, skip_var, sgn, c);
*row = r < 0 ? var->index : r;
*col = c;
}
* This means
* - it represents an inequality or a variable
* - that is the sum of a non-negative sample value and a positive
- * combination of zero or more non-negative variables.
+ * combination of zero or more non-negative constraints.
*/
-static int is_redundant(struct isl_ctx *ctx, struct isl_tab *tab, int row)
+int isl_tab_row_is_redundant(struct isl_tab *tab, int row)
{
int i;
+ unsigned off = 2 + tab->M;
- if (tab->row_var[row] < 0 && !var_from_row(ctx, tab, row)->is_nonneg)
+ if (tab->row_var[row] < 0 && !isl_tab_var_from_row(tab, row)->is_nonneg)
return 0;
if (isl_int_is_neg(tab->mat->row[row][1]))
return 0;
+ if (tab->M && isl_int_is_neg(tab->mat->row[row][2]))
+ return 0;
for (i = tab->n_dead; i < tab->n_col; ++i) {
- if (isl_int_is_zero(tab->mat->row[row][2 + i]))
+ if (isl_int_is_zero(tab->mat->row[row][off + i]))
continue;
- if (isl_int_is_neg(tab->mat->row[row][2 + i]))
+ if (tab->col_var[i] >= 0)
return 0;
- if (!var_from_col(ctx, tab, i)->is_nonneg)
+ if (isl_int_is_neg(tab->mat->row[row][off + i]))
+ return 0;
+ if (!var_from_col(tab, i)->is_nonneg)
return 0;
}
return 1;
}
-static void swap_rows(struct isl_ctx *ctx,
- struct isl_tab *tab, int row1, int row2)
+static void swap_rows(struct isl_tab *tab, int row1, int row2)
{
int t;
t = tab->row_var[row1];
tab->row_var[row1] = tab->row_var[row2];
tab->row_var[row2] = t;
- var_from_row(ctx, tab, row1)->index = row1;
- var_from_row(ctx, tab, row2)->index = row2;
- tab->mat = isl_mat_swap_rows(ctx, tab->mat, row1, row2);
+ isl_tab_var_from_row(tab, row1)->index = row1;
+ isl_tab_var_from_row(tab, row2)->index = row2;
+ tab->mat = isl_mat_swap_rows(tab->mat, row1, row2);
+
+ if (!tab->row_sign)
+ return;
+ t = tab->row_sign[row1];
+ tab->row_sign[row1] = tab->row_sign[row2];
+ tab->row_sign[row2] = t;
}
-static void push(struct isl_ctx *ctx, struct isl_tab *tab,
- enum isl_tab_undo_type type, struct isl_tab_var *var)
+static int push_union(struct isl_tab *tab,
+ enum isl_tab_undo_type type, union isl_tab_undo_val u) WARN_UNUSED;
+static int push_union(struct isl_tab *tab,
+ enum isl_tab_undo_type type, union isl_tab_undo_val u)
{
struct isl_tab_undo *undo;
if (!tab->need_undo)
- return;
+ return 0;
- undo = isl_alloc_type(ctx, struct isl_tab_undo);
- if (!undo) {
- free_undo(ctx, tab);
- tab->top = NULL;
- return;
- }
+ undo = isl_alloc_type(tab->mat->ctx, struct isl_tab_undo);
+ if (!undo)
+ return -1;
undo->type = type;
- undo->var = var;
+ undo->u = u;
undo->next = tab->top;
tab->top = undo;
+
+ return 0;
+}
+
+int isl_tab_push_var(struct isl_tab *tab,
+ enum isl_tab_undo_type type, struct isl_tab_var *var)
+{
+ union isl_tab_undo_val u;
+ if (var->is_row)
+ u.var_index = tab->row_var[var->index];
+ else
+ u.var_index = tab->col_var[var->index];
+ return push_union(tab, type, u);
+}
+
+int isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type)
+{
+ union isl_tab_undo_val u = { 0 };
+ return push_union(tab, type, u);
+}
+
+/* Push a record on the undo stack describing the current basic
+ * variables, so that the this state can be restored during rollback.
+ */
+int isl_tab_push_basis(struct isl_tab *tab)
+{
+ int i;
+ union isl_tab_undo_val u;
+
+ u.col_var = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
+ if (!u.col_var)
+ return -1;
+ for (i = 0; i < tab->n_col; ++i)
+ u.col_var[i] = tab->col_var[i];
+ return push_union(tab, isl_tab_undo_saved_basis, u);
+}
+
+int isl_tab_push_callback(struct isl_tab *tab, struct isl_tab_callback *callback)
+{
+ union isl_tab_undo_val u;
+ u.callback = callback;
+ return push_union(tab, isl_tab_undo_callback, u);
+}
+
+struct isl_tab *isl_tab_init_samples(struct isl_tab *tab)
+{
+ if (!tab)
+ return NULL;
+
+ tab->n_sample = 0;
+ tab->n_outside = 0;
+ tab->samples = isl_mat_alloc(tab->mat->ctx, 1, 1 + tab->n_var);
+ if (!tab->samples)
+ goto error;
+ tab->sample_index = isl_alloc_array(tab->mat->ctx, int, 1);
+ if (!tab->sample_index)
+ goto error;
+ return tab;
+error:
+ isl_tab_free(tab);
+ return NULL;
+}
+
+struct isl_tab *isl_tab_add_sample(struct isl_tab *tab,
+ __isl_take isl_vec *sample)
+{
+ if (!tab || !sample)
+ goto error;
+
+ if (tab->n_sample + 1 > tab->samples->n_row) {
+ int *t = isl_realloc_array(tab->mat->ctx,
+ tab->sample_index, int, tab->n_sample + 1);
+ if (!t)
+ goto error;
+ tab->sample_index = t;
+ }
+
+ tab->samples = isl_mat_extend(tab->samples,
+ tab->n_sample + 1, tab->samples->n_col);
+ if (!tab->samples)
+ goto error;
+
+ isl_seq_cpy(tab->samples->row[tab->n_sample], sample->el, sample->size);
+ isl_vec_free(sample);
+ tab->sample_index[tab->n_sample] = tab->n_sample;
+ tab->n_sample++;
+
+ return tab;
+error:
+ isl_vec_free(sample);
+ isl_tab_free(tab);
+ return NULL;
+}
+
+struct isl_tab *isl_tab_drop_sample(struct isl_tab *tab, int s)
+{
+ if (s != tab->n_outside) {
+ int t = tab->sample_index[tab->n_outside];
+ tab->sample_index[tab->n_outside] = tab->sample_index[s];
+ tab->sample_index[s] = t;
+ isl_mat_swap_rows(tab->samples, tab->n_outside, s);
+ }
+ tab->n_outside++;
+ if (isl_tab_push(tab, isl_tab_undo_drop_sample) < 0) {
+ isl_tab_free(tab);
+ return NULL;
+ }
+
+ return tab;
+}
+
+/* Record the current number of samples so that we can remove newer
+ * samples during a rollback.
+ */
+int isl_tab_save_samples(struct isl_tab *tab)
+{
+ union isl_tab_undo_val u;
+
+ if (!tab)
+ return -1;
+
+ u.n = tab->n_sample;
+ return push_union(tab, isl_tab_undo_saved_samples, u);
}
/* Mark row with index "row" as being redundant.
* then a return value of 1 means that the row with the given
* row number may now contain a different row that hasn't been checked yet.
*/
-static int mark_redundant(struct isl_ctx *ctx,
- struct isl_tab *tab, int row)
+int isl_tab_mark_redundant(struct isl_tab *tab, int row)
{
- struct isl_tab_var *var = var_from_row(ctx, tab, row);
+ struct isl_tab_var *var = isl_tab_var_from_row(tab, row);
var->is_redundant = 1;
- isl_assert(ctx, row >= tab->n_redundant, return);
+ isl_assert(tab->mat->ctx, row >= tab->n_redundant, return -1);
if (tab->need_undo || tab->row_var[row] >= 0) {
- if (tab->row_var[row] >= 0) {
+ if (tab->row_var[row] >= 0 && !var->is_nonneg) {
var->is_nonneg = 1;
- push(ctx, tab, isl_tab_undo_nonneg, var);
+ if (isl_tab_push_var(tab, isl_tab_undo_nonneg, var) < 0)
+ return -1;
}
if (row != tab->n_redundant)
- swap_rows(ctx, tab, row, tab->n_redundant);
- push(ctx, tab, isl_tab_undo_redundant, var);
+ swap_rows(tab, row, tab->n_redundant);
tab->n_redundant++;
- return 0;
+ return isl_tab_push_var(tab, isl_tab_undo_redundant, var);
} else {
if (row != tab->n_row - 1)
- swap_rows(ctx, tab, row, tab->n_row - 1);
- var_from_row(ctx, tab, tab->n_row - 1)->index = -1;
+ swap_rows(tab, row, tab->n_row - 1);
+ isl_tab_var_from_row(tab, tab->n_row - 1)->index = -1;
tab->n_row--;
return 1;
}
}
-static void mark_empty(struct isl_ctx *ctx, struct isl_tab *tab)
+int isl_tab_mark_empty(struct isl_tab *tab)
{
+ if (!tab)
+ return -1;
if (!tab->empty && tab->need_undo)
- push(ctx, tab, isl_tab_undo_empty, NULL);
+ if (isl_tab_push(tab, isl_tab_undo_empty) < 0)
+ return -1;
tab->empty = 1;
+ return 0;
+}
+
+int isl_tab_freeze_constraint(struct isl_tab *tab, int con)
+{
+ struct isl_tab_var *var;
+
+ if (!tab)
+ return -1;
+
+ var = &tab->con[con];
+ if (var->frozen)
+ return 0;
+ if (var->index < 0)
+ return 0;
+ var->frozen = 1;
+
+ if (tab->need_undo)
+ return isl_tab_push_var(tab, isl_tab_undo_freeze, var);
+
+ return 0;
+}
+
+/* Update the rows signs after a pivot of "row" and "col", with "row_sgn"
+ * the original sign of the pivot element.
+ * We only keep track of row signs during PILP solving and in this case
+ * we only pivot a row with negative sign (meaning the value is always
+ * non-positive) using a positive pivot element.
+ *
+ * For each row j, the new value of the parametric constant is equal to
+ *
+ * a_j0 - a_jc a_r0/a_rc
+ *
+ * where a_j0 is the original parametric constant, a_rc is the pivot element,
+ * a_r0 is the parametric constant of the pivot row and a_jc is the
+ * pivot column entry of the row j.
+ * Since a_r0 is non-positive and a_rc is positive, the sign of row j
+ * remains the same if a_jc has the same sign as the row j or if
+ * a_jc is zero. In all other cases, we reset the sign to "unknown".
+ */
+static void update_row_sign(struct isl_tab *tab, int row, int col, int row_sgn)
+{
+ int i;
+ struct isl_mat *mat = tab->mat;
+ unsigned off = 2 + tab->M;
+
+ if (!tab->row_sign)
+ return;
+
+ if (tab->row_sign[row] == 0)
+ return;
+ isl_assert(mat->ctx, row_sgn > 0, return);
+ isl_assert(mat->ctx, tab->row_sign[row] == isl_tab_row_neg, return);
+ tab->row_sign[row] = isl_tab_row_pos;
+ for (i = 0; i < tab->n_row; ++i) {
+ int s;
+ if (i == row)
+ continue;
+ s = isl_int_sgn(mat->row[i][off + col]);
+ if (!s)
+ continue;
+ if (!tab->row_sign[i])
+ continue;
+ if (s < 0 && tab->row_sign[i] == isl_tab_row_neg)
+ continue;
+ if (s > 0 && tab->row_sign[i] == isl_tab_row_pos)
+ continue;
+ tab->row_sign[i] = isl_tab_row_unknown;
+ }
}
/* Given a row number "row" and a column number "col", pivot the tableau
- * such that the associated variable are interchanged.
+ * such that the associated variables are interchanged.
* The given row in the tableau expresses
*
* x_r = a_r0 + \sum_i a_ri x_i
* s(n_rc)d_r n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
*
*/
-static void pivot(struct isl_ctx *ctx,
- struct isl_tab *tab, int row, int col)
+int isl_tab_pivot(struct isl_tab *tab, int row, int col)
{
int i, j;
int sgn;
int t;
struct isl_mat *mat = tab->mat;
struct isl_tab_var *var;
+ unsigned off = 2 + tab->M;
- isl_int_swap(mat->row[row][0], mat->row[row][2 + col]);
+ isl_int_swap(mat->row[row][0], mat->row[row][off + col]);
sgn = isl_int_sgn(mat->row[row][0]);
if (sgn < 0) {
isl_int_neg(mat->row[row][0], mat->row[row][0]);
- isl_int_neg(mat->row[row][2 + col], mat->row[row][2 + col]);
+ isl_int_neg(mat->row[row][off + col], mat->row[row][off + col]);
} else
- for (j = 0; j < 1 + tab->n_col; ++j) {
- if (j == 1 + col)
+ for (j = 0; j < off - 1 + tab->n_col; ++j) {
+ if (j == off - 1 + col)
continue;
isl_int_neg(mat->row[row][1 + j], mat->row[row][1 + j]);
}
if (!isl_int_is_one(mat->row[row][0]))
- isl_seq_normalize(mat->row[row], 2 + tab->n_col);
+ isl_seq_normalize(mat->ctx, mat->row[row], off + tab->n_col);
for (i = 0; i < tab->n_row; ++i) {
if (i == row)
continue;
- if (isl_int_is_zero(mat->row[i][2 + col]))
+ if (isl_int_is_zero(mat->row[i][off + col]))
continue;
isl_int_mul(mat->row[i][0], mat->row[i][0], mat->row[row][0]);
- for (j = 0; j < 1 + tab->n_col; ++j) {
- if (j == 1 + col)
+ for (j = 0; j < off - 1 + tab->n_col; ++j) {
+ if (j == off - 1 + col)
continue;
isl_int_mul(mat->row[i][1 + j],
mat->row[i][1 + j], mat->row[row][0]);
isl_int_addmul(mat->row[i][1 + j],
- mat->row[i][2 + col], mat->row[row][1 + j]);
+ mat->row[i][off + col], mat->row[row][1 + j]);
}
- isl_int_mul(mat->row[i][2 + col],
- mat->row[i][2 + col], mat->row[row][2 + col]);
- if (!isl_int_is_one(mat->row[row][0]))
- isl_seq_normalize(mat->row[i], 2 + tab->n_col);
+ isl_int_mul(mat->row[i][off + col],
+ mat->row[i][off + col], mat->row[row][off + col]);
+ if (!isl_int_is_one(mat->row[i][0]))
+ isl_seq_normalize(mat->ctx, mat->row[i], off + tab->n_col);
}
t = tab->row_var[row];
tab->row_var[row] = tab->col_var[col];
tab->col_var[col] = t;
- var = var_from_row(ctx, tab, row);
+ var = isl_tab_var_from_row(tab, row);
var->is_row = 1;
var->index = row;
- var = var_from_col(ctx, tab, col);
+ var = var_from_col(tab, col);
var->is_row = 0;
var->index = col;
+ update_row_sign(tab, row, col, sgn);
+ if (tab->in_undo)
+ return 0;
for (i = tab->n_redundant; i < tab->n_row; ++i) {
- if (isl_int_is_zero(mat->row[i][2 + col]))
+ if (isl_int_is_zero(mat->row[i][off + col]))
continue;
- if (!var_from_row(ctx, tab, i)->frozen &&
- is_redundant(ctx, tab, i))
- if (mark_redundant(ctx, tab, i))
+ if (!isl_tab_var_from_row(tab, i)->frozen &&
+ isl_tab_row_is_redundant(tab, i)) {
+ int redo = isl_tab_mark_redundant(tab, i);
+ if (redo < 0)
+ return -1;
+ if (redo)
--i;
+ }
}
+ return 0;
}
/* If "var" represents a column variable, then pivot is up (sgn > 0)
* or down (sgn < 0) to a row. The variable is assumed not to be
* unbounded in the specified direction.
+ * If sgn = 0, then the variable is unbounded in both directions,
+ * and we pivot with any row we can find.
*/
-static void to_row(struct isl_ctx *ctx,
- struct isl_tab *tab, struct isl_tab_var *var, int sign)
+static int to_row(struct isl_tab *tab, struct isl_tab_var *var, int sign) WARN_UNUSED;
+static int to_row(struct isl_tab *tab, struct isl_tab_var *var, int sign)
{
int r;
+ unsigned off = 2 + tab->M;
if (var->is_row)
- return;
+ return 0;
+
+ if (sign == 0) {
+ for (r = tab->n_redundant; r < tab->n_row; ++r)
+ if (!isl_int_is_zero(tab->mat->row[r][off+var->index]))
+ break;
+ isl_assert(tab->mat->ctx, r < tab->n_row, return -1);
+ } else {
+ r = pivot_row(tab, NULL, sign, var->index);
+ isl_assert(tab->mat->ctx, r >= 0, return -1);
+ }
- r = pivot_row(ctx, tab, NULL, sign, var->index);
- isl_assert(ctx, r >= 0, return);
- pivot(ctx, tab, r, var->index);
+ return isl_tab_pivot(tab, r, var->index);
}
-static void check_table(struct isl_ctx *ctx, struct isl_tab *tab)
+static void check_table(struct isl_tab *tab)
{
int i;
if (tab->empty)
return;
for (i = 0; i < tab->n_row; ++i) {
- if (!var_from_row(ctx, tab, i)->is_nonneg)
+ if (!isl_tab_var_from_row(tab, i)->is_nonneg)
continue;
assert(!isl_int_is_neg(tab->mat->row[i][1]));
}
* - the sample value is positive
* - the variable is pivoted into a manifestly unbounded column
*/
-static int sign_of_max(struct isl_ctx *ctx,
- struct isl_tab *tab, struct isl_tab_var *var)
+static int sign_of_max(struct isl_tab *tab, struct isl_tab_var *var)
{
int row, col;
- if (max_is_manifestly_unbounded(ctx, tab, var))
+ if (max_is_manifestly_unbounded(tab, var))
return 1;
- to_row(ctx, tab, var, 1);
+ if (to_row(tab, var, 1) < 0)
+ return -2;
while (!isl_int_is_pos(tab->mat->row[var->index][1])) {
- find_pivot(ctx, tab, var, 1, &row, &col);
+ find_pivot(tab, var, var, 1, &row, &col);
if (row == -1)
return isl_int_sgn(tab->mat->row[var->index][1]);
- pivot(ctx, tab, row, col);
+ if (isl_tab_pivot(tab, row, col) < 0)
+ return -2;
if (!var->is_row) /* manifestly unbounded */
return 1;
}
return 1;
}
+static int row_is_neg(struct isl_tab *tab, int row)
+{
+ if (!tab->M)
+ return isl_int_is_neg(tab->mat->row[row][1]);
+ if (isl_int_is_pos(tab->mat->row[row][2]))
+ return 0;
+ if (isl_int_is_neg(tab->mat->row[row][2]))
+ return 1;
+ return isl_int_is_neg(tab->mat->row[row][1]);
+}
+
+static int row_sgn(struct isl_tab *tab, int row)
+{
+ if (!tab->M)
+ return isl_int_sgn(tab->mat->row[row][1]);
+ if (!isl_int_is_zero(tab->mat->row[row][2]))
+ return isl_int_sgn(tab->mat->row[row][2]);
+ else
+ return isl_int_sgn(tab->mat->row[row][1]);
+}
+
/* Perform pivots until the row variable "var" has a non-negative
* sample value or until no more upward pivots can be performed.
* Return the sign of the sample value after the pivots have been
* performed.
*/
-static int restore_row(struct isl_ctx *ctx,
- struct isl_tab *tab, struct isl_tab_var *var)
+static int restore_row(struct isl_tab *tab, struct isl_tab_var *var)
{
int row, col;
- while (isl_int_is_neg(tab->mat->row[var->index][1])) {
- find_pivot(ctx, tab, var, 1, &row, &col);
+ while (row_is_neg(tab, var->index)) {
+ find_pivot(tab, var, var, 1, &row, &col);
if (row == -1)
- return;
- pivot(ctx, tab, row, col);
+ break;
+ if (isl_tab_pivot(tab, row, col) < 0)
+ return -2;
if (!var->is_row) /* manifestly unbounded */
- return;
+ return 1;
}
+ return row_sgn(tab, var->index);
}
/* Perform pivots until we are sure that the row variable "var"
* function, "var" is still a row variable, but its sample
* value may not be non-negative, even if the function returns 1.
*/
-static int at_least_zero(struct isl_ctx *ctx,
- struct isl_tab *tab, struct isl_tab_var *var)
+static int at_least_zero(struct isl_tab *tab, struct isl_tab_var *var)
{
int row, col;
while (isl_int_is_neg(tab->mat->row[var->index][1])) {
- find_pivot(ctx, tab, var, 1, &row, &col);
+ find_pivot(tab, var, var, 1, &row, &col);
if (row == -1)
break;
if (row == var->index) /* manifestly unbounded */
return 1;
- pivot(ctx, tab, row, col);
+ if (isl_tab_pivot(tab, row, col) < 0)
+ return -1;
}
return !isl_int_is_neg(tab->mat->row[var->index][1]);
}
* In that case we look for upward pivots until we reach a non-negative
* value again.
*/
-static int sign_of_min(struct isl_ctx *ctx,
- struct isl_tab *tab, struct isl_tab_var *var)
+static int sign_of_min(struct isl_tab *tab, struct isl_tab_var *var)
{
int row, col;
- struct isl_tab_var *pivot_var;
+ struct isl_tab_var *pivot_var = NULL;
- if (min_is_manifestly_unbounded(ctx, tab, var))
+ if (min_is_manifestly_unbounded(tab, var))
return -1;
if (!var->is_row) {
col = var->index;
- row = pivot_row(ctx, tab, NULL, -1, col);
- pivot_var = var_from_col(ctx, tab, col);
- pivot(ctx, tab, row, col);
+ row = pivot_row(tab, NULL, -1, col);
+ pivot_var = var_from_col(tab, col);
+ if (isl_tab_pivot(tab, row, col) < 0)
+ return -2;
if (var->is_redundant)
return 0;
if (isl_int_is_neg(tab->mat->row[var->index][1])) {
if (var->is_nonneg) {
if (!pivot_var->is_redundant &&
- pivot_var->index == row)
- pivot(ctx, tab, row, col);
- else
- restore_row(ctx, tab, var);
+ pivot_var->index == row) {
+ if (isl_tab_pivot(tab, row, col) < 0)
+ return -2;
+ } else
+ if (restore_row(tab, var) < -1)
+ return -2;
}
return -1;
}
if (var->is_redundant)
return 0;
while (!isl_int_is_neg(tab->mat->row[var->index][1])) {
- find_pivot(ctx, tab, var, -1, &row, &col);
+ find_pivot(tab, var, var, -1, &row, &col);
if (row == var->index)
return -1;
if (row == -1)
return isl_int_sgn(tab->mat->row[var->index][1]);
- pivot_var = var_from_col(ctx, tab, col);
- pivot(ctx, tab, row, col);
+ pivot_var = var_from_col(tab, col);
+ if (isl_tab_pivot(tab, row, col) < 0)
+ return -2;
if (var->is_redundant)
return 0;
}
- if (var->is_nonneg) {
+ if (pivot_var && var->is_nonneg) {
/* pivot back to non-negative value */
- if (!pivot_var->is_redundant && pivot_var->index == row)
- pivot(ctx, tab, row, col);
- else
- restore_row(ctx, tab, var);
+ if (!pivot_var->is_redundant && pivot_var->index == row) {
+ if (isl_tab_pivot(tab, row, col) < 0)
+ return -2;
+ } else
+ if (restore_row(tab, var) < -1)
+ return -2;
}
return -1;
}
+static int row_at_most_neg_one(struct isl_tab *tab, int row)
+{
+ if (tab->M) {
+ if (isl_int_is_pos(tab->mat->row[row][2]))
+ return 0;
+ if (isl_int_is_neg(tab->mat->row[row][2]))
+ return 1;
+ }
+ return isl_int_is_neg(tab->mat->row[row][1]) &&
+ isl_int_abs_ge(tab->mat->row[row][1],
+ tab->mat->row[row][0]);
+}
+
/* Return 1 if "var" can attain values <= -1.
* Return 0 otherwise.
*
* the function is called and will be made non-negative again before
* the function returns.
*/
-static int min_at_most_neg_one(struct isl_ctx *ctx,
- struct isl_tab *tab, struct isl_tab_var *var)
+int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var)
{
int row, col;
struct isl_tab_var *pivot_var;
- if (min_is_manifestly_unbounded(ctx, tab, var))
+ if (min_is_manifestly_unbounded(tab, var))
return 1;
if (!var->is_row) {
col = var->index;
- row = pivot_row(ctx, tab, NULL, -1, col);
- pivot_var = var_from_col(ctx, tab, col);
- pivot(ctx, tab, row, col);
+ row = pivot_row(tab, NULL, -1, col);
+ pivot_var = var_from_col(tab, col);
+ if (isl_tab_pivot(tab, row, col) < 0)
+ return -1;
if (var->is_redundant)
return 0;
- if (isl_int_is_neg(tab->mat->row[var->index][1]) &&
- isl_int_abs_ge(tab->mat->row[var->index][1],
- tab->mat->row[var->index][0])) {
+ if (row_at_most_neg_one(tab, var->index)) {
if (var->is_nonneg) {
if (!pivot_var->is_redundant &&
- pivot_var->index == row)
- pivot(ctx, tab, row, col);
- else
- restore_row(ctx, tab, var);
+ pivot_var->index == row) {
+ if (isl_tab_pivot(tab, row, col) < 0)
+ return -1;
+ } else
+ if (restore_row(tab, var) < -1)
+ return -1;
}
return 1;
}
if (var->is_redundant)
return 0;
do {
- find_pivot(ctx, tab, var, -1, &row, &col);
+ find_pivot(tab, var, var, -1, &row, &col);
if (row == var->index)
return 1;
if (row == -1)
return 0;
- pivot_var = var_from_col(ctx, tab, col);
- pivot(ctx, tab, row, col);
+ pivot_var = var_from_col(tab, col);
+ if (isl_tab_pivot(tab, row, col) < 0)
+ return -1;
if (var->is_redundant)
return 0;
- } while (!isl_int_is_neg(tab->mat->row[var->index][1]) ||
- isl_int_abs_lt(tab->mat->row[var->index][1],
- tab->mat->row[var->index][0]));
+ } while (!row_at_most_neg_one(tab, var->index));
if (var->is_nonneg) {
/* pivot back to non-negative value */
if (!pivot_var->is_redundant && pivot_var->index == row)
- pivot(ctx, tab, row, col);
- restore_row(ctx, tab, var);
+ if (isl_tab_pivot(tab, row, col) < 0)
+ return -1;
+ if (restore_row(tab, var) < -1)
+ return -1;
}
return 1;
}
/* Return 1 if "var" can attain values >= 1.
* Return 0 otherwise.
*/
-static int at_least_one(struct isl_ctx *ctx,
- struct isl_tab *tab, struct isl_tab_var *var)
+static int at_least_one(struct isl_tab *tab, struct isl_tab_var *var)
{
int row, col;
isl_int *r;
- if (max_is_manifestly_unbounded(ctx, tab, var))
+ if (max_is_manifestly_unbounded(tab, var))
return 1;
- to_row(ctx, tab, var, 1);
+ if (to_row(tab, var, 1) < 0)
+ return -1;
r = tab->mat->row[var->index];
while (isl_int_lt(r[1], r[0])) {
- find_pivot(ctx, tab, var, 1, &row, &col);
+ find_pivot(tab, var, var, 1, &row, &col);
if (row == -1)
return isl_int_ge(r[1], r[0]);
if (row == var->index) /* manifestly unbounded */
return 1;
- pivot(ctx, tab, row, col);
+ if (isl_tab_pivot(tab, row, col) < 0)
+ return -1;
}
return 1;
}
-static void swap_cols(struct isl_ctx *ctx,
- struct isl_tab *tab, int col1, int col2)
+static void swap_cols(struct isl_tab *tab, int col1, int col2)
{
int t;
+ unsigned off = 2 + tab->M;
t = tab->col_var[col1];
tab->col_var[col1] = tab->col_var[col2];
tab->col_var[col2] = t;
- var_from_col(ctx, tab, col1)->index = col1;
- var_from_col(ctx, tab, col2)->index = col2;
- tab->mat = isl_mat_swap_cols(ctx, tab->mat, 2 + col1, 2 + col2);
+ var_from_col(tab, col1)->index = col1;
+ var_from_col(tab, col2)->index = col2;
+ tab->mat = isl_mat_swap_cols(tab->mat, off + col1, off + col2);
}
/* Mark column with index "col" as representing a zero variable.
* column number may now contain a different column that
* hasn't been checked yet.
*/
-static int kill_col(struct isl_ctx *ctx,
- struct isl_tab *tab, int col)
+int isl_tab_kill_col(struct isl_tab *tab, int col)
{
- tab->killed_col = 1;
- var_from_col(ctx, tab, col)->is_zero = 1;
+ var_from_col(tab, col)->is_zero = 1;
if (tab->need_undo) {
- push(ctx, tab, isl_tab_undo_zero, var_from_col(ctx, tab, col));
+ if (isl_tab_push_var(tab, isl_tab_undo_zero,
+ var_from_col(tab, col)) < 0)
+ return -1;
if (col != tab->n_dead)
- swap_cols(ctx, tab, col, tab->n_dead);
+ swap_cols(tab, col, tab->n_dead);
tab->n_dead++;
return 0;
} else {
if (col != tab->n_col - 1)
- swap_cols(ctx, tab, col, tab->n_col - 1);
- var_from_col(ctx, tab, tab->n_col - 1)->index = -1;
+ swap_cols(tab, col, tab->n_col - 1);
+ var_from_col(tab, tab->n_col - 1)->index = -1;
tab->n_col--;
return 1;
}
* then also be written as the negative sum of non-negative variables
* and must therefore also be zero.
*/
-static void close_row(struct isl_ctx *ctx,
- struct isl_tab *tab, struct isl_tab_var *var)
+static int close_row(struct isl_tab *tab, struct isl_tab_var *var) WARN_UNUSED;
+static int close_row(struct isl_tab *tab, struct isl_tab_var *var)
{
int j;
struct isl_mat *mat = tab->mat;
+ unsigned off = 2 + tab->M;
- isl_assert(ctx, var->is_nonneg, return);
+ isl_assert(tab->mat->ctx, var->is_nonneg, return -1);
var->is_zero = 1;
+ if (tab->need_undo)
+ if (isl_tab_push_var(tab, isl_tab_undo_zero, var) < 0)
+ return -1;
for (j = tab->n_dead; j < tab->n_col; ++j) {
- if (isl_int_is_zero(mat->row[var->index][2 + j]))
+ if (isl_int_is_zero(mat->row[var->index][off + j]))
continue;
- isl_assert(ctx, isl_int_is_neg(mat->row[var->index][2 + j]),
- return);
- if (kill_col(ctx, tab, j))
+ isl_assert(tab->mat->ctx,
+ isl_int_is_neg(mat->row[var->index][off + j]), return -1);
+ if (isl_tab_kill_col(tab, j))
--j;
}
- mark_redundant(ctx, tab, var->index);
+ if (isl_tab_mark_redundant(tab, var->index) < 0)
+ return -1;
+ return 0;
+}
+
+/* Add a constraint to the tableau and allocate a row for it.
+ * Return the index into the constraint array "con".
+ */
+int isl_tab_allocate_con(struct isl_tab *tab)
+{
+ int r;
+
+ isl_assert(tab->mat->ctx, tab->n_row < tab->mat->n_row, return -1);
+ isl_assert(tab->mat->ctx, tab->n_con < tab->max_con, return -1);
+
+ r = tab->n_con;
+ tab->con[r].index = tab->n_row;
+ tab->con[r].is_row = 1;
+ tab->con[r].is_nonneg = 0;
+ tab->con[r].is_zero = 0;
+ tab->con[r].is_redundant = 0;
+ tab->con[r].frozen = 0;
+ tab->con[r].negated = 0;
+ tab->row_var[tab->n_row] = ~r;
+
+ tab->n_row++;
+ tab->n_con++;
+ if (isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]) < 0)
+ return -1;
+
+ return r;
+}
+
+/* Add a variable to the tableau and allocate a column for it.
+ * Return the index into the variable array "var".
+ */
+int isl_tab_allocate_var(struct isl_tab *tab)
+{
+ int r;
+ int i;
+ unsigned off = 2 + tab->M;
+
+ isl_assert(tab->mat->ctx, tab->n_col < tab->mat->n_col, return -1);
+ isl_assert(tab->mat->ctx, tab->n_var < tab->max_var, return -1);
+
+ r = tab->n_var;
+ tab->var[r].index = tab->n_col;
+ tab->var[r].is_row = 0;
+ tab->var[r].is_nonneg = 0;
+ tab->var[r].is_zero = 0;
+ tab->var[r].is_redundant = 0;
+ tab->var[r].frozen = 0;
+ tab->var[r].negated = 0;
+ tab->col_var[tab->n_col] = r;
+
+ for (i = 0; i < tab->n_row; ++i)
+ isl_int_set_si(tab->mat->row[i][off + tab->n_col], 0);
+
+ tab->n_var++;
+ tab->n_col++;
+ if (isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->var[r]) < 0)
+ return -1;
+
+ return r;
}
/* Add a row to the tableau. The row is given as an affine combination
*
* with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
*/
-static int add_row(struct isl_ctx *ctx, struct isl_tab *tab, isl_int *line)
+int isl_tab_add_row(struct isl_tab *tab, isl_int *line)
{
int i;
- unsigned r;
+ int r;
isl_int *row;
isl_int a, b;
+ unsigned off = 2 + tab->M;
- isl_assert(ctx, tab->n_row < tab->mat->n_row, return -1);
+ r = isl_tab_allocate_con(tab);
+ if (r < 0)
+ return -1;
isl_int_init(a);
isl_int_init(b);
- r = tab->n_con;
- tab->con[r].index = tab->n_row;
- tab->con[r].is_row = 1;
- tab->con[r].is_nonneg = 0;
- tab->con[r].is_zero = 0;
- tab->con[r].is_redundant = 0;
- tab->con[r].frozen = 0;
- tab->row_var[tab->n_row] = ~r;
- row = tab->mat->row[tab->n_row];
+ row = tab->mat->row[tab->con[r].index];
isl_int_set_si(row[0], 1);
isl_int_set(row[1], line[0]);
- isl_seq_clr(row + 2, tab->n_col);
+ isl_seq_clr(row + 2, tab->M + tab->n_col);
for (i = 0; i < tab->n_var; ++i) {
if (tab->var[i].is_zero)
continue;
isl_int_mul(b, b, line[1 + i]);
isl_seq_combine(row + 1, a, row + 1,
b, tab->mat->row[tab->var[i].index] + 1,
- 1 + tab->n_col);
+ 1 + tab->M + tab->n_col);
} else
- isl_int_addmul(row[2 + tab->var[i].index],
+ isl_int_addmul(row[off + tab->var[i].index],
line[1 + i], row[0]);
+ if (tab->M && i >= tab->n_param && i < tab->n_var - tab->n_div)
+ isl_int_submul(row[2], line[1 + i], row[0]);
}
- isl_seq_normalize(row, 2 + tab->n_col);
- tab->n_row++;
- tab->n_con++;
- push(ctx, tab, isl_tab_undo_allocate, &tab->con[r]);
+ isl_seq_normalize(tab->mat->ctx, row, off + tab->n_col);
isl_int_clear(a);
isl_int_clear(b);
+ if (tab->row_sign)
+ tab->row_sign[tab->con[r].index] = 0;
+
return r;
}
-static int drop_row(struct isl_ctx *ctx, struct isl_tab *tab, int row)
+static int drop_row(struct isl_tab *tab, int row)
{
- isl_assert(ctx, ~tab->row_var[row] == tab->n_con - 1, return -1);
+ isl_assert(tab->mat->ctx, ~tab->row_var[row] == tab->n_con - 1, return -1);
if (row != tab->n_row - 1)
- swap_rows(ctx, tab, row, tab->n_row - 1);
+ swap_rows(tab, row, tab->n_row - 1);
tab->n_row--;
tab->n_con--;
return 0;
}
+static int drop_col(struct isl_tab *tab, int col)
+{
+ isl_assert(tab->mat->ctx, tab->col_var[col] == tab->n_var - 1, return -1);
+ if (col != tab->n_col - 1)
+ swap_cols(tab, col, tab->n_col - 1);
+ tab->n_col--;
+ tab->n_var--;
+ return 0;
+}
+
/* Add inequality "ineq" and check if it conflicts with the
* previously added constraints or if it is obviously redundant.
*/
-struct isl_tab *isl_tab_add_ineq(struct isl_ctx *ctx,
- struct isl_tab *tab, isl_int *ineq)
+int isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq)
+{
+ int r;
+ int sgn;
+ isl_int cst;
+
+ if (!tab)
+ return -1;
+ if (tab->bmap) {
+ struct isl_basic_map *bmap = tab->bmap;
+
+ isl_assert(tab->mat->ctx, tab->n_eq == bmap->n_eq, return -1);
+ isl_assert(tab->mat->ctx,
+ tab->n_con == bmap->n_eq + bmap->n_ineq, return -1);
+ tab->bmap = isl_basic_map_add_ineq(tab->bmap, ineq);
+ if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
+ return -1;
+ if (!tab->bmap)
+ return -1;
+ }
+ if (tab->cone) {
+ isl_int_init(cst);
+ isl_int_swap(ineq[0], cst);
+ }
+ r = isl_tab_add_row(tab, ineq);
+ if (tab->cone) {
+ isl_int_swap(ineq[0], cst);
+ isl_int_clear(cst);
+ }
+ if (r < 0)
+ return -1;
+ tab->con[r].is_nonneg = 1;
+ if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
+ return -1;
+ if (isl_tab_row_is_redundant(tab, tab->con[r].index)) {
+ if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
+ return -1;
+ return 0;
+ }
+
+ sgn = restore_row(tab, &tab->con[r]);
+ if (sgn < -1)
+ return -1;
+ if (sgn < 0)
+ return isl_tab_mark_empty(tab);
+ if (tab->con[r].is_row && isl_tab_row_is_redundant(tab, tab->con[r].index))
+ if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
+ return -1;
+ return 0;
+}
+
+/* Pivot a non-negative variable down until it reaches the value zero
+ * and then pivot the variable into a column position.
+ */
+static int to_col(struct isl_tab *tab, struct isl_tab_var *var) WARN_UNUSED;
+static int to_col(struct isl_tab *tab, struct isl_tab_var *var)
+{
+ int i;
+ int row, col;
+ unsigned off = 2 + tab->M;
+
+ if (!var->is_row)
+ return 0;
+
+ while (isl_int_is_pos(tab->mat->row[var->index][1])) {
+ find_pivot(tab, var, NULL, -1, &row, &col);
+ isl_assert(tab->mat->ctx, row != -1, return -1);
+ if (isl_tab_pivot(tab, row, col) < 0)
+ return -1;
+ if (!var->is_row)
+ return 0;
+ }
+
+ for (i = tab->n_dead; i < tab->n_col; ++i)
+ if (!isl_int_is_zero(tab->mat->row[var->index][off + i]))
+ break;
+
+ isl_assert(tab->mat->ctx, i < tab->n_col, return -1);
+ if (isl_tab_pivot(tab, var->index, i) < 0)
+ return -1;
+
+ return 0;
+}
+
+/* We assume Gaussian elimination has been performed on the equalities.
+ * The equalities can therefore never conflict.
+ * Adding the equalities is currently only really useful for a later call
+ * to isl_tab_ineq_type.
+ */
+static struct isl_tab *add_eq(struct isl_tab *tab, isl_int *eq)
+{
+ int i;
+ int r;
+
+ if (!tab)
+ return NULL;
+ r = isl_tab_add_row(tab, eq);
+ if (r < 0)
+ goto error;
+
+ r = tab->con[r].index;
+ i = isl_seq_first_non_zero(tab->mat->row[r] + 2 + tab->M + tab->n_dead,
+ tab->n_col - tab->n_dead);
+ isl_assert(tab->mat->ctx, i >= 0, goto error);
+ i += tab->n_dead;
+ if (isl_tab_pivot(tab, r, i) < 0)
+ goto error;
+ if (isl_tab_kill_col(tab, i) < 0)
+ goto error;
+ tab->n_eq++;
+
+ return tab;
+error:
+ isl_tab_free(tab);
+ return NULL;
+}
+
+static int row_is_manifestly_zero(struct isl_tab *tab, int row)
+{
+ unsigned off = 2 + tab->M;
+
+ if (!isl_int_is_zero(tab->mat->row[row][1]))
+ return 0;
+ if (tab->M && !isl_int_is_zero(tab->mat->row[row][2]))
+ return 0;
+ return isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
+ tab->n_col - tab->n_dead) == -1;
+}
+
+/* Add an equality that is known to be valid for the given tableau.
+ */
+struct isl_tab *isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq)
+{
+ struct isl_tab_var *var;
+ int r;
+
+ if (!tab)
+ return NULL;
+ r = isl_tab_add_row(tab, eq);
+ if (r < 0)
+ goto error;
+
+ var = &tab->con[r];
+ r = var->index;
+ if (row_is_manifestly_zero(tab, r)) {
+ var->is_zero = 1;
+ if (isl_tab_mark_redundant(tab, r) < 0)
+ goto error;
+ return tab;
+ }
+
+ if (isl_int_is_neg(tab->mat->row[r][1])) {
+ isl_seq_neg(tab->mat->row[r] + 1, tab->mat->row[r] + 1,
+ 1 + tab->n_col);
+ var->negated = 1;
+ }
+ var->is_nonneg = 1;
+ if (to_col(tab, var) < 0)
+ goto error;
+ var->is_nonneg = 0;
+ if (isl_tab_kill_col(tab, var->index) < 0)
+ goto error;
+
+ return tab;
+error:
+ isl_tab_free(tab);
+ return NULL;
+}
+
+static int add_zero_row(struct isl_tab *tab)
+{
+ int r;
+ isl_int *row;
+
+ r = isl_tab_allocate_con(tab);
+ if (r < 0)
+ return -1;
+
+ row = tab->mat->row[tab->con[r].index];
+ isl_seq_clr(row + 1, 1 + tab->M + tab->n_col);
+ isl_int_set_si(row[0], 1);
+
+ return r;
+}
+
+/* Add equality "eq" and check if it conflicts with the
+ * previously added constraints or if it is obviously redundant.
+ */
+struct isl_tab *isl_tab_add_eq(struct isl_tab *tab, isl_int *eq)
+{
+ struct isl_tab_undo *snap = NULL;
+ struct isl_tab_var *var;
+ int r;
+ int row;
+ int sgn;
+ isl_int cst;
+
+ if (!tab)
+ return NULL;
+ isl_assert(tab->mat->ctx, !tab->M, goto error);
+
+ if (tab->need_undo)
+ snap = isl_tab_snap(tab);
+
+ if (tab->cone) {
+ isl_int_init(cst);
+ isl_int_swap(eq[0], cst);
+ }
+ r = isl_tab_add_row(tab, eq);
+ if (tab->cone) {
+ isl_int_swap(eq[0], cst);
+ isl_int_clear(cst);
+ }
+ if (r < 0)
+ goto error;
+
+ var = &tab->con[r];
+ row = var->index;
+ if (row_is_manifestly_zero(tab, row)) {
+ if (snap) {
+ if (isl_tab_rollback(tab, snap) < 0)
+ goto error;
+ } else
+ drop_row(tab, row);
+ return tab;
+ }
+
+ if (tab->bmap) {
+ tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq);
+ if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
+ goto error;
+ isl_seq_neg(eq, eq, 1 + tab->n_var);
+ tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq);
+ isl_seq_neg(eq, eq, 1 + tab->n_var);
+ if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
+ goto error;
+ if (!tab->bmap)
+ goto error;
+ if (add_zero_row(tab) < 0)
+ goto error;
+ }
+
+ sgn = isl_int_sgn(tab->mat->row[row][1]);
+
+ if (sgn > 0) {
+ isl_seq_neg(tab->mat->row[row] + 1, tab->mat->row[row] + 1,
+ 1 + tab->n_col);
+ var->negated = 1;
+ sgn = -1;
+ }
+
+ if (sgn < 0) {
+ sgn = sign_of_max(tab, var);
+ if (sgn < -1)
+ goto error;
+ if (sgn < 0) {
+ if (isl_tab_mark_empty(tab) < 0)
+ goto error;
+ return tab;
+ }
+ }
+
+ var->is_nonneg = 1;
+ if (to_col(tab, var) < 0)
+ goto error;
+ var->is_nonneg = 0;
+ if (isl_tab_kill_col(tab, var->index) < 0)
+ goto error;
+
+ return tab;
+error:
+ isl_tab_free(tab);
+ return NULL;
+}
+
+/* Construct and return an inequality that expresses an upper bound
+ * on the given div.
+ * In particular, if the div is given by
+ *
+ * d = floor(e/m)
+ *
+ * then the inequality expresses
+ *
+ * m d <= e
+ */
+static struct isl_vec *ineq_for_div(struct isl_basic_map *bmap, unsigned div)
+{
+ unsigned total;
+ unsigned div_pos;
+ struct isl_vec *ineq;
+
+ if (!bmap)
+ return NULL;
+
+ total = isl_basic_map_total_dim(bmap);
+ div_pos = 1 + total - bmap->n_div + div;
+
+ ineq = isl_vec_alloc(bmap->ctx, 1 + total);
+ if (!ineq)
+ return NULL;
+
+ isl_seq_cpy(ineq->el, bmap->div[div] + 1, 1 + total);
+ isl_int_neg(ineq->el[div_pos], bmap->div[div][0]);
+ return ineq;
+}
+
+/* For a div d = floor(f/m), add the constraints
+ *
+ * f - m d >= 0
+ * -(f-(m-1)) + m d >= 0
+ *
+ * Note that the second constraint is the negation of
+ *
+ * f - m d >= m
+ *
+ * If add_ineq is not NULL, then this function is used
+ * instead of isl_tab_add_ineq to effectively add the inequalities.
+ */
+static int add_div_constraints(struct isl_tab *tab, unsigned div,
+ int (*add_ineq)(void *user, isl_int *), void *user)
{
- int r;
- int sgn;
+ unsigned total;
+ unsigned div_pos;
+ struct isl_vec *ineq;
- if (!tab)
- return NULL;
- r = add_row(ctx, tab, ineq);
- if (r < 0)
+ total = isl_basic_map_total_dim(tab->bmap);
+ div_pos = 1 + total - tab->bmap->n_div + div;
+
+ ineq = ineq_for_div(tab->bmap, div);
+ if (!ineq)
goto error;
- tab->con[r].is_nonneg = 1;
- push(ctx, tab, isl_tab_undo_nonneg, &tab->con[r]);
- if (is_redundant(ctx, tab, tab->con[r].index)) {
- mark_redundant(ctx, tab, tab->con[r].index);
- return tab;
+
+ if (add_ineq) {
+ if (add_ineq(user, ineq->el) < 0)
+ goto error;
+ } else {
+ if (isl_tab_add_ineq(tab, ineq->el) < 0)
+ goto error;
}
- sgn = sign_of_max(ctx, tab, &tab->con[r]);
- if (sgn < 0)
- mark_empty(ctx, tab);
- else {
- if (sgn == 0)
- close_row(ctx, tab, &tab->con[r]);
- else if (tab->con[r].is_row &&
- is_redundant(ctx, tab, tab->con[r].index))
- mark_redundant(ctx, tab, tab->con[r].index);
+ isl_seq_neg(ineq->el, tab->bmap->div[div] + 1, 1 + total);
+ isl_int_set(ineq->el[div_pos], tab->bmap->div[div][0]);
+ isl_int_add(ineq->el[0], ineq->el[0], ineq->el[div_pos]);
+ isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
+
+ if (add_ineq) {
+ if (add_ineq(user, ineq->el) < 0)
+ goto error;
+ } else {
+ if (isl_tab_add_ineq(tab, ineq->el) < 0)
+ goto error;
}
- return tab;
+
+ isl_vec_free(ineq);
+
+ return 0;
error:
- isl_tab_free(ctx, tab);
- return NULL;
+ isl_vec_free(ineq);
+ return -1;
}
-/* We assume Gaussian elimination has been performed on the equalities.
- * The equalities can therefore never conflict.
- * Adding the equalities is currently only really useful for a later call
- * to isl_tab_ineq_type.
+/* Add an extra div, prescrived by "div" to the tableau and
+ * the associated bmap (which is assumed to be non-NULL).
+ *
+ * If add_ineq is not NULL, then this function is used instead
+ * of isl_tab_add_ineq to add the div constraints.
+ * This complication is needed because the code in isl_tab_pip
+ * wants to perform some extra processing when an inequality
+ * is added to the tableau.
*/
-static struct isl_tab *add_eq(struct isl_ctx *ctx,
- struct isl_tab *tab, isl_int *eq)
+int isl_tab_add_div(struct isl_tab *tab, __isl_keep isl_vec *div,
+ int (*add_ineq)(void *user, isl_int *), void *user)
{
int i;
int r;
+ int k;
+ int nonneg;
- if (!tab)
- return NULL;
- r = add_row(ctx, tab, eq);
- if (r < 0)
- goto error;
+ if (!tab || !div)
+ return -1;
- r = tab->con[r].index;
- for (i = tab->n_dead; i < tab->n_col; ++i) {
- if (isl_int_is_zero(tab->mat->row[r][2 + i]))
+ isl_assert(tab->mat->ctx, tab->bmap, return -1);
+
+ for (i = 0; i < tab->n_var; ++i) {
+ if (isl_int_is_neg(div->el[2 + i]))
+ break;
+ if (isl_int_is_zero(div->el[2 + i]))
continue;
- pivot(ctx, tab, r, i);
- kill_col(ctx, tab, i);
- break;
+ if (!tab->var[i].is_nonneg)
+ break;
}
+ nonneg = i == tab->n_var && !isl_int_is_neg(div->el[1]);
- return tab;
-error:
- isl_tab_free(ctx, tab);
- return NULL;
+ if (isl_tab_extend_cons(tab, 3) < 0)
+ return -1;
+ if (isl_tab_extend_vars(tab, 1) < 0)
+ return -1;
+ r = isl_tab_allocate_var(tab);
+ if (r < 0)
+ return -1;
+
+ if (nonneg)
+ tab->var[r].is_nonneg = 1;
+
+ tab->bmap = isl_basic_map_extend_dim(tab->bmap,
+ isl_basic_map_get_dim(tab->bmap), 1, 0, 2);
+ k = isl_basic_map_alloc_div(tab->bmap);
+ if (k < 0)
+ return -1;
+ isl_seq_cpy(tab->bmap->div[k], div->el, div->size);
+ if (isl_tab_push(tab, isl_tab_undo_bmap_div) < 0)
+ return -1;
+
+ if (add_div_constraints(tab, k, add_ineq, user) < 0)
+ return -1;
+
+ return r;
}
struct isl_tab *isl_tab_from_basic_map(struct isl_basic_map *bmap)
return NULL;
tab = isl_tab_alloc(bmap->ctx,
isl_basic_map_total_dim(bmap) + bmap->n_ineq + 1,
- isl_basic_map_total_dim(bmap));
+ isl_basic_map_total_dim(bmap), 0);
if (!tab)
return NULL;
tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) {
- mark_empty(bmap->ctx, tab);
+ if (isl_tab_mark_empty(tab) < 0)
+ goto error;
return tab;
}
for (i = 0; i < bmap->n_eq; ++i) {
- tab = add_eq(bmap->ctx, tab, bmap->eq[i]);
+ tab = add_eq(tab, bmap->eq[i]);
if (!tab)
return tab;
}
- tab->killed_col = 0;
for (i = 0; i < bmap->n_ineq; ++i) {
- tab = isl_tab_add_ineq(bmap->ctx, tab, bmap->ineq[i]);
- if (!tab || tab->empty)
+ if (isl_tab_add_ineq(tab, bmap->ineq[i]) < 0)
+ goto error;
+ if (tab->empty)
return tab;
}
return tab;
+error:
+ isl_tab_free(tab);
+ return NULL;
}
struct isl_tab *isl_tab_from_basic_set(struct isl_basic_set *bset)
return isl_tab_from_basic_map((struct isl_basic_map *)bset);
}
-/* Construct a tableau corresponding to the recession cone of "bmap".
+/* Construct a tableau corresponding to the recession cone of "bset".
*/
-struct isl_tab *isl_tab_from_recession_cone(struct isl_basic_map *bmap)
+struct isl_tab *isl_tab_from_recession_cone(struct isl_basic_set *bset)
{
isl_int cst;
int i;
struct isl_tab *tab;
- if (!bmap)
+ if (!bset)
return NULL;
- tab = isl_tab_alloc(bmap->ctx, bmap->n_eq + bmap->n_ineq,
- isl_basic_map_total_dim(bmap));
+ tab = isl_tab_alloc(bset->ctx, bset->n_eq + bset->n_ineq,
+ isl_basic_set_total_dim(bset), 0);
if (!tab)
return NULL;
- tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
+ tab->rational = ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL);
+ tab->cone = 1;
isl_int_init(cst);
- for (i = 0; i < bmap->n_eq; ++i) {
- isl_int_swap(bmap->eq[i][0], cst);
- tab = add_eq(bmap->ctx, tab, bmap->eq[i]);
- isl_int_swap(bmap->eq[i][0], cst);
+ for (i = 0; i < bset->n_eq; ++i) {
+ isl_int_swap(bset->eq[i][0], cst);
+ tab = add_eq(tab, bset->eq[i]);
+ isl_int_swap(bset->eq[i][0], cst);
if (!tab)
goto done;
}
- tab->killed_col = 0;
- for (i = 0; i < bmap->n_ineq; ++i) {
+ for (i = 0; i < bset->n_ineq; ++i) {
int r;
- isl_int_swap(bmap->ineq[i][0], cst);
- r = add_row(bmap->ctx, tab, bmap->ineq[i]);
- isl_int_swap(bmap->ineq[i][0], cst);
+ isl_int_swap(bset->ineq[i][0], cst);
+ r = isl_tab_add_row(tab, bset->ineq[i]);
+ isl_int_swap(bset->ineq[i][0], cst);
if (r < 0)
goto error;
tab->con[r].is_nonneg = 1;
- push(bmap->ctx, tab, isl_tab_undo_nonneg, &tab->con[r]);
+ if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
+ goto error;
}
done:
isl_int_clear(cst);
return tab;
error:
isl_int_clear(cst);
- isl_tab_free(bmap->ctx, tab);
+ isl_tab_free(tab);
return NULL;
}
/* Assuming "tab" is the tableau of a cone, check if the cone is
* bounded, i.e., if it is empty or only contains the origin.
*/
-int isl_tab_cone_is_bounded(struct isl_ctx *ctx, struct isl_tab *tab)
+int isl_tab_cone_is_bounded(struct isl_tab *tab)
{
int i;
if (tab->n_dead == tab->n_col)
return 1;
- for (i = tab->n_redundant; i < tab->n_row; ++i) {
- struct isl_tab_var *var;
- var = var_from_row(ctx, tab, i);
- if (!var->is_nonneg)
- continue;
- if (sign_of_max(ctx, tab, var) == 0)
- close_row(ctx, tab, var);
- else
- return 0;
+ for (;;) {
+ for (i = tab->n_redundant; i < tab->n_row; ++i) {
+ struct isl_tab_var *var;
+ int sgn;
+ var = isl_tab_var_from_row(tab, i);
+ if (!var->is_nonneg)
+ continue;
+ sgn = sign_of_max(tab, var);
+ if (sgn < -1)
+ return -1;
+ if (sgn != 0)
+ return 0;
+ if (close_row(tab, var) < 0)
+ return -1;
+ break;
+ }
if (tab->n_dead == tab->n_col)
return 1;
+ if (i == tab->n_row)
+ return 0;
}
- return 0;
}
-static int sample_is_integer(struct isl_ctx *ctx, struct isl_tab *tab)
+int isl_tab_sample_is_integer(struct isl_tab *tab)
{
int i;
+ if (!tab)
+ return -1;
+
for (i = 0; i < tab->n_var; ++i) {
int row;
if (!tab->var[i].is_row)
return 1;
}
-static struct isl_vec *extract_integer_sample(struct isl_ctx *ctx,
- struct isl_tab *tab)
+static struct isl_vec *extract_integer_sample(struct isl_tab *tab)
{
int i;
struct isl_vec *vec;
- vec = isl_vec_alloc(ctx, 1 + tab->n_var);
+ vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
if (!vec)
return NULL;
return vec;
}
+struct isl_vec *isl_tab_get_sample_value(struct isl_tab *tab)
+{
+ int i;
+ struct isl_vec *vec;
+ isl_int m;
+
+ if (!tab)
+ return NULL;
+
+ vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
+ if (!vec)
+ return NULL;
+
+ isl_int_init(m);
+
+ isl_int_set_si(vec->block.data[0], 1);
+ for (i = 0; i < tab->n_var; ++i) {
+ int row;
+ if (!tab->var[i].is_row) {
+ isl_int_set_si(vec->block.data[1 + i], 0);
+ continue;
+ }
+ row = tab->var[i].index;
+ isl_int_gcd(m, vec->block.data[0], tab->mat->row[row][0]);
+ isl_int_divexact(m, tab->mat->row[row][0], m);
+ isl_seq_scale(vec->block.data, vec->block.data, m, 1 + i);
+ isl_int_divexact(m, vec->block.data[0], tab->mat->row[row][0]);
+ isl_int_mul(vec->block.data[1 + i], m, tab->mat->row[row][1]);
+ }
+ vec = isl_vec_normalize(vec);
+
+ isl_int_clear(m);
+ return vec;
+}
+
/* Update "bmap" based on the results of the tableau "tab".
* In particular, implicit equalities are made explicit, redundant constraints
* are removed and if the sample value happens to be integer, it is stored
if (!tab)
return bmap;
- n_eq = bmap->n_eq;
+ n_eq = tab->n_eq;
if (tab->empty)
bmap = isl_basic_map_set_to_empty(bmap);
else
for (i = bmap->n_ineq - 1; i >= 0; --i) {
- if (isl_tab_is_equality(bmap->ctx, tab, n_eq + i))
+ if (isl_tab_is_equality(tab, n_eq + i))
isl_basic_map_inequality_to_equality(bmap, i);
- else if (isl_tab_is_redundant(bmap->ctx, tab, n_eq + i))
+ else if (isl_tab_is_redundant(tab, n_eq + i))
isl_basic_map_drop_inequality(bmap, i);
}
+ if (bmap->n_eq != n_eq)
+ isl_basic_map_gauss(bmap, NULL);
if (!tab->rational &&
- !bmap->sample && sample_is_integer(bmap->ctx, tab))
- bmap->sample = extract_integer_sample(bmap->ctx, tab);
+ !bmap->sample && isl_tab_sample_is_integer(tab))
+ bmap->sample = extract_integer_sample(tab);
return bmap;
}
* the resulting tableau is empty.
* Otherwise, we know the value will be zero and we close the row.
*/
-static struct isl_tab *cut_to_hyperplane(struct isl_ctx *ctx,
- struct isl_tab *tab, struct isl_tab_var *var)
+static struct isl_tab *cut_to_hyperplane(struct isl_tab *tab,
+ struct isl_tab_var *var)
{
unsigned r;
isl_int *row;
int sgn;
+ unsigned off = 2 + tab->M;
+
+ if (var->is_zero)
+ return tab;
+ isl_assert(tab->mat->ctx, !var->is_redundant, goto error);
+ isl_assert(tab->mat->ctx, var->is_nonneg, goto error);
- if (extend_cons(ctx, tab, 1) < 0)
+ if (isl_tab_extend_cons(tab, 1) < 0)
goto error;
r = tab->n_con;
tab->con[r].is_zero = 0;
tab->con[r].is_redundant = 0;
tab->con[r].frozen = 0;
+ tab->con[r].negated = 0;
tab->row_var[tab->n_row] = ~r;
row = tab->mat->row[tab->n_row];
} else {
isl_int_set_si(row[0], 1);
isl_seq_clr(row + 1, 1 + tab->n_col);
- isl_int_set_si(row[2 + var->index], -1);
+ isl_int_set_si(row[off + var->index], -1);
}
tab->n_row++;
tab->n_con++;
- push(ctx, tab, isl_tab_undo_allocate, &tab->con[r]);
+ if (isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]) < 0)
+ goto error;
- sgn = sign_of_max(ctx, tab, &tab->con[r]);
- if (sgn < 0)
- mark_empty(ctx, tab);
- else {
- tab->con[r].is_nonneg = 1;
- push(ctx, tab, isl_tab_undo_nonneg, &tab->con[r]);
- /* sgn == 0 */
- close_row(ctx, tab, &tab->con[r]);
+ sgn = sign_of_max(tab, &tab->con[r]);
+ if (sgn < -1)
+ goto error;
+ if (sgn < 0) {
+ if (isl_tab_mark_empty(tab) < 0)
+ goto error;
+ return tab;
}
+ tab->con[r].is_nonneg = 1;
+ if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
+ goto error;
+ /* sgn == 0 */
+ if (close_row(tab, &tab->con[r]) < 0)
+ goto error;
return tab;
error:
- isl_tab_free(ctx, tab);
+ isl_tab_free(tab);
return NULL;
}
* refers to r = r' - 1 by substituting this equality, effectively
* subtracting the coefficient of the column from the constant.
*/
-struct isl_tab *isl_tab_relax(struct isl_ctx *ctx,
- struct isl_tab *tab, int con)
+struct isl_tab *isl_tab_relax(struct isl_tab *tab, int con)
{
struct isl_tab_var *var;
+ unsigned off = 2 + tab->M;
+
if (!tab)
return NULL;
var = &tab->con[con];
- if (!var->is_row && !max_is_manifestly_unbounded(ctx, tab, var))
- to_row(ctx, tab, var, 1);
+ if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
+ if (to_row(tab, var, 1) < 0)
+ goto error;
if (var->is_row)
isl_int_add(tab->mat->row[var->index][1],
int i;
for (i = 0; i < tab->n_row; ++i) {
- if (isl_int_is_zero(tab->mat->row[i][2 + var->index]))
+ if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
continue;
isl_int_sub(tab->mat->row[i][1], tab->mat->row[i][1],
- tab->mat->row[i][2 + var->index]);
+ tab->mat->row[i][off + var->index]);
}
}
- push(ctx, tab, isl_tab_undo_relax, var);
+ if (isl_tab_push_var(tab, isl_tab_undo_relax, var) < 0)
+ goto error;
return tab;
+error:
+ isl_tab_free(tab);
+ return NULL;
}
-struct isl_tab *isl_tab_select_facet(struct isl_ctx *ctx,
- struct isl_tab *tab, int con)
+struct isl_tab *isl_tab_select_facet(struct isl_tab *tab, int con)
{
if (!tab)
return NULL;
- return cut_to_hyperplane(ctx, tab, &tab->con[con]);
+ return cut_to_hyperplane(tab, &tab->con[con]);
}
static int may_be_equality(struct isl_tab *tab, int row)
{
+ unsigned off = 2 + tab->M;
return (tab->rational ? isl_int_is_zero(tab->mat->row[row][1])
: isl_int_lt(tab->mat->row[row][1],
tab->mat->row[row][0])) &&
- isl_seq_first_non_zero(tab->mat->row[row] + 2 + tab->n_dead,
+ isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
tab->n_col - tab->n_dead) != -1;
}
* - zero (in case of rational tableaus), or
* - strictly less than 1 (in case of integer tableaus)
*
- * When the rows are added to the tableau, they are already
- * checked for being equal to zero. If none of the rows
- * have been determined to be zero (killed_col is not set)
- * and we are dealing with a rational tableau, then we wouldn't
- * be able to find any zero row, so we can return immediately.
- *
* We first mark all non-redundant and non-dead variables that
* are not frozen and not obviously not an equality.
* Then we iterate over all marked variables if they can attain
* tableau is integer), then we restrict the value to being zero
* by adding an opposite non-negative variable.
*/
-struct isl_tab *isl_tab_detect_equalities(struct isl_ctx *ctx,
- struct isl_tab *tab)
+struct isl_tab *isl_tab_detect_implicit_equalities(struct isl_tab *tab)
{
int i;
unsigned n_marked;
return NULL;
if (tab->empty)
return tab;
- if (tab->rational && !tab->killed_col)
- return tab;
if (tab->n_dead == tab->n_col)
return tab;
n_marked = 0;
for (i = tab->n_redundant; i < tab->n_row; ++i) {
- struct isl_tab_var *var = var_from_row(ctx, tab, i);
+ struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
var->marked = !var->frozen && var->is_nonneg &&
may_be_equality(tab, i);
if (var->marked)
n_marked++;
}
for (i = tab->n_dead; i < tab->n_col; ++i) {
- struct isl_tab_var *var = var_from_col(ctx, tab, i);
+ struct isl_tab_var *var = var_from_col(tab, i);
var->marked = !var->frozen && var->is_nonneg;
if (var->marked)
n_marked++;
}
while (n_marked) {
struct isl_tab_var *var;
+ int sgn;
for (i = tab->n_redundant; i < tab->n_row; ++i) {
- var = var_from_row(ctx, tab, i);
+ var = isl_tab_var_from_row(tab, i);
if (var->marked)
break;
}
if (i == tab->n_row) {
for (i = tab->n_dead; i < tab->n_col; ++i) {
- var = var_from_col(ctx, tab, i);
+ var = var_from_col(tab, i);
if (var->marked)
break;
}
}
var->marked = 0;
n_marked--;
- if (sign_of_max(ctx, tab, var) == 0)
- close_row(ctx, tab, var);
- else if (!tab->rational && !at_least_one(ctx, tab, var)) {
- tab = cut_to_hyperplane(ctx, tab, var);
- return isl_tab_detect_equalities(ctx, tab);
+ sgn = sign_of_max(tab, var);
+ if (sgn < 0)
+ goto error;
+ if (sgn == 0) {
+ if (close_row(tab, var) < 0)
+ goto error;
+ } else if (!tab->rational && !at_least_one(tab, var)) {
+ tab = cut_to_hyperplane(tab, var);
+ return isl_tab_detect_implicit_equalities(tab);
}
for (i = tab->n_redundant; i < tab->n_row; ++i) {
- var = var_from_row(ctx, tab, i);
+ var = isl_tab_var_from_row(tab, i);
if (!var->marked)
continue;
if (may_be_equality(tab, i))
}
}
- tab->killed_col = 0;
return tab;
+error:
+ isl_tab_free(tab);
+ return NULL;
+}
+
+static int con_is_redundant(struct isl_tab *tab, struct isl_tab_var *var)
+{
+ if (!tab)
+ return -1;
+ if (tab->rational) {
+ int sgn = sign_of_min(tab, var);
+ if (sgn < -1)
+ return -1;
+ return sgn >= 0;
+ } else {
+ int irred = isl_tab_min_at_most_neg_one(tab, var);
+ if (irred < 0)
+ return -1;
+ return !irred;
+ }
}
/* Check for (near) redundant constraints.
* If not, we mark the row as being redundant (assuming it hasn't
* been detected as being obviously redundant in the mean time).
*/
-struct isl_tab *isl_tab_detect_redundant(struct isl_ctx *ctx,
- struct isl_tab *tab)
+int isl_tab_detect_redundant(struct isl_tab *tab)
{
int i;
unsigned n_marked;
if (!tab)
- return NULL;
+ return -1;
if (tab->empty)
- return tab;
+ return 0;
if (tab->n_redundant == tab->n_row)
- return tab;
+ return 0;
n_marked = 0;
for (i = tab->n_redundant; i < tab->n_row; ++i) {
- struct isl_tab_var *var = var_from_row(ctx, tab, i);
+ struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
var->marked = !var->frozen && var->is_nonneg;
if (var->marked)
n_marked++;
}
for (i = tab->n_dead; i < tab->n_col; ++i) {
- struct isl_tab_var *var = var_from_col(ctx, tab, i);
+ struct isl_tab_var *var = var_from_col(tab, i);
var->marked = !var->frozen && var->is_nonneg &&
- !min_is_manifestly_unbounded(ctx, tab, var);
+ !min_is_manifestly_unbounded(tab, var);
if (var->marked)
n_marked++;
}
while (n_marked) {
struct isl_tab_var *var;
+ int red;
for (i = tab->n_redundant; i < tab->n_row; ++i) {
- var = var_from_row(ctx, tab, i);
+ var = isl_tab_var_from_row(tab, i);
if (var->marked)
break;
}
if (i == tab->n_row) {
for (i = tab->n_dead; i < tab->n_col; ++i) {
- var = var_from_col(ctx, tab, i);
+ var = var_from_col(tab, i);
if (var->marked)
break;
}
}
var->marked = 0;
n_marked--;
- if ((tab->rational ? (sign_of_min(ctx, tab, var) >= 0)
- : !min_at_most_neg_one(ctx, tab, var)) &&
- !var->is_redundant)
- mark_redundant(ctx, tab, var->index);
+ red = con_is_redundant(tab, var);
+ if (red < 0)
+ return -1;
+ if (red && !var->is_redundant)
+ if (isl_tab_mark_redundant(tab, var->index) < 0)
+ return -1;
for (i = tab->n_dead; i < tab->n_col; ++i) {
- var = var_from_col(ctx, tab, i);
+ var = var_from_col(tab, i);
if (!var->marked)
continue;
- if (!min_is_manifestly_unbounded(ctx, tab, var))
+ if (!min_is_manifestly_unbounded(tab, var))
continue;
var->marked = 0;
n_marked--;
}
}
- return tab;
+ return 0;
}
-int isl_tab_is_equality(struct isl_ctx *ctx, struct isl_tab *tab, int con)
+int isl_tab_is_equality(struct isl_tab *tab, int con)
{
int row;
+ unsigned off;
if (!tab)
return -1;
row = tab->con[con].index;
+ off = 2 + tab->M;
return isl_int_is_zero(tab->mat->row[row][1]) &&
isl_seq_first_non_zero(tab->mat->row[row] + 2 + tab->n_dead,
tab->n_col - tab->n_dead) == -1;
* The return value reflects the nature of the result (empty, unbounded,
* minmimal value returned in *opt).
*/
-enum isl_lp_result isl_tab_min(struct isl_ctx *ctx, struct isl_tab *tab,
- isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom)
+enum isl_lp_result isl_tab_min(struct isl_tab *tab,
+ isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom,
+ unsigned flags)
{
int r;
enum isl_lp_result res = isl_lp_ok;
struct isl_tab_var *var;
+ struct isl_tab_undo *snap;
if (tab->empty)
return isl_lp_empty;
- r = add_row(ctx, tab, f);
+ snap = isl_tab_snap(tab);
+ r = isl_tab_add_row(tab, f);
if (r < 0)
return isl_lp_error;
var = &tab->con[r];
tab->mat->row[var->index][0], denom);
for (;;) {
int row, col;
- find_pivot(ctx, tab, var, -1, &row, &col);
+ find_pivot(tab, var, var, -1, &row, &col);
if (row == var->index) {
res = isl_lp_unbounded;
break;
}
if (row == -1)
break;
- pivot(ctx, tab, row, col);
+ if (isl_tab_pivot(tab, row, col) < 0)
+ return isl_lp_error;
}
- if (drop_row(ctx, tab, var->index) < 0)
- return isl_lp_error;
- if (res == isl_lp_ok) {
+ if (ISL_FL_ISSET(flags, ISL_TAB_SAVE_DUAL)) {
+ int i;
+
+ isl_vec_free(tab->dual);
+ tab->dual = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_con);
+ if (!tab->dual)
+ return isl_lp_error;
+ isl_int_set(tab->dual->el[0], tab->mat->row[var->index][0]);
+ for (i = 0; i < tab->n_con; ++i) {
+ int pos;
+ if (tab->con[i].is_row) {
+ isl_int_set_si(tab->dual->el[1 + i], 0);
+ continue;
+ }
+ pos = 2 + tab->M + tab->con[i].index;
+ if (tab->con[i].negated)
+ isl_int_neg(tab->dual->el[1 + i],
+ tab->mat->row[var->index][pos]);
+ else
+ isl_int_set(tab->dual->el[1 + i],
+ tab->mat->row[var->index][pos]);
+ }
+ }
+ if (opt && res == isl_lp_ok) {
if (opt_denom) {
isl_int_set(*opt, tab->mat->row[var->index][1]);
isl_int_set(*opt_denom, tab->mat->row[var->index][0]);
isl_int_cdiv_q(*opt, tab->mat->row[var->index][1],
tab->mat->row[var->index][0]);
}
+ if (isl_tab_rollback(tab, snap) < 0)
+ return isl_lp_error;
return res;
}
-int isl_tab_is_redundant(struct isl_ctx *ctx, struct isl_tab *tab, int con)
+int isl_tab_is_redundant(struct isl_tab *tab, int con)
{
- int row;
- unsigned n_col;
-
if (!tab)
return -1;
if (tab->con[con].is_zero)
/* Take a snapshot of the tableau that can be restored by s call to
* isl_tab_rollback.
*/
-struct isl_tab_undo *isl_tab_snap(struct isl_ctx *ctx, struct isl_tab *tab)
+struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab)
{
if (!tab)
return NULL;
/* Undo the operation performed by isl_tab_relax.
*/
-static void unrelax(struct isl_ctx *ctx,
- struct isl_tab *tab, struct isl_tab_var *var)
+static int unrelax(struct isl_tab *tab, struct isl_tab_var *var) WARN_UNUSED;
+static int unrelax(struct isl_tab *tab, struct isl_tab_var *var)
{
- if (!var->is_row && !max_is_manifestly_unbounded(ctx, tab, var))
- to_row(ctx, tab, var, 1);
+ unsigned off = 2 + tab->M;
+
+ if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
+ if (to_row(tab, var, 1) < 0)
+ return -1;
if (var->is_row)
isl_int_sub(tab->mat->row[var->index][1],
int i;
for (i = 0; i < tab->n_row; ++i) {
- if (isl_int_is_zero(tab->mat->row[i][2 + var->index]))
+ if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
continue;
isl_int_add(tab->mat->row[i][1], tab->mat->row[i][1],
- tab->mat->row[i][2 + var->index]);
+ tab->mat->row[i][off + var->index]);
}
}
+
+ return 0;
}
-static void perform_undo(struct isl_ctx *ctx, struct isl_tab *tab,
- struct isl_tab_undo *undo)
+static int perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo) WARN_UNUSED;
+static int perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo)
{
+ struct isl_tab_var *var = var_from_index(tab, undo->u.var_index);
switch(undo->type) {
- case isl_tab_undo_empty:
- tab->empty = 0;
- break;
case isl_tab_undo_nonneg:
- undo->var->is_nonneg = 0;
+ var->is_nonneg = 0;
break;
case isl_tab_undo_redundant:
- undo->var->is_redundant = 0;
+ var->is_redundant = 0;
tab->n_redundant--;
break;
+ case isl_tab_undo_freeze:
+ var->frozen = 0;
+ break;
case isl_tab_undo_zero:
- undo->var->is_zero = 0;
- tab->n_dead--;
+ var->is_zero = 0;
+ if (!var->is_row)
+ tab->n_dead--;
break;
case isl_tab_undo_allocate:
- if (!undo->var->is_row) {
- if (max_is_manifestly_unbounded(ctx, tab, undo->var))
- to_row(ctx, tab, undo->var, -1);
- else
- to_row(ctx, tab, undo->var, 1);
+ if (undo->u.var_index >= 0) {
+ isl_assert(tab->mat->ctx, !var->is_row, return -1);
+ drop_col(tab, var->index);
+ break;
+ }
+ if (!var->is_row) {
+ if (!max_is_manifestly_unbounded(tab, var)) {
+ if (to_row(tab, var, 1) < 0)
+ return -1;
+ } else if (!min_is_manifestly_unbounded(tab, var)) {
+ if (to_row(tab, var, -1) < 0)
+ return -1;
+ } else
+ if (to_row(tab, var, 0) < 0)
+ return -1;
+ }
+ drop_row(tab, var->index);
+ break;
+ case isl_tab_undo_relax:
+ return unrelax(tab, var);
+ }
+
+ return 0;
+}
+
+/* Restore the tableau to the state where the basic variables
+ * are those in "col_var".
+ * We first construct a list of variables that are currently in
+ * the basis, but shouldn't. Then we iterate over all variables
+ * that should be in the basis and for each one that is currently
+ * not in the basis, we exchange it with one of the elements of the
+ * list constructed before.
+ * We can always find an appropriate variable to pivot with because
+ * the current basis is mapped to the old basis by a non-singular
+ * matrix and so we can never end up with a zero row.
+ */
+static int restore_basis(struct isl_tab *tab, int *col_var)
+{
+ int i, j;
+ int n_extra = 0;
+ int *extra = NULL; /* current columns that contain bad stuff */
+ unsigned off = 2 + tab->M;
+
+ extra = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
+ if (!extra)
+ goto error;
+ for (i = 0; i < tab->n_col; ++i) {
+ for (j = 0; j < tab->n_col; ++j)
+ if (tab->col_var[i] == col_var[j])
+ break;
+ if (j < tab->n_col)
+ continue;
+ extra[n_extra++] = i;
+ }
+ for (i = 0; i < tab->n_col && n_extra > 0; ++i) {
+ struct isl_tab_var *var;
+ int row;
+
+ for (j = 0; j < tab->n_col; ++j)
+ if (col_var[i] == tab->col_var[j])
+ break;
+ if (j < tab->n_col)
+ continue;
+ var = var_from_index(tab, col_var[i]);
+ row = var->index;
+ for (j = 0; j < n_extra; ++j)
+ if (!isl_int_is_zero(tab->mat->row[row][off+extra[j]]))
+ break;
+ isl_assert(tab->mat->ctx, j < n_extra, goto error);
+ if (isl_tab_pivot(tab, row, extra[j]) < 0)
+ goto error;
+ extra[j] = extra[--n_extra];
+ }
+
+ free(extra);
+ free(col_var);
+ return 0;
+error:
+ free(extra);
+ free(col_var);
+ return -1;
+}
+
+/* Remove all samples with index n or greater, i.e., those samples
+ * that were added since we saved this number of samples in
+ * isl_tab_save_samples.
+ */
+static void drop_samples_since(struct isl_tab *tab, int n)
+{
+ int i;
+
+ for (i = tab->n_sample - 1; i >= 0 && tab->n_sample > n; --i) {
+ if (tab->sample_index[i] < n)
+ continue;
+
+ if (i != tab->n_sample - 1) {
+ int t = tab->sample_index[tab->n_sample-1];
+ tab->sample_index[tab->n_sample-1] = tab->sample_index[i];
+ tab->sample_index[i] = t;
+ isl_mat_swap_rows(tab->samples, tab->n_sample-1, i);
}
- drop_row(ctx, tab, undo->var->index);
+ tab->n_sample--;
+ }
+}
+
+static int perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo) WARN_UNUSED;
+static int perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo)
+{
+ switch (undo->type) {
+ case isl_tab_undo_empty:
+ tab->empty = 0;
break;
+ case isl_tab_undo_nonneg:
+ case isl_tab_undo_redundant:
+ case isl_tab_undo_freeze:
+ case isl_tab_undo_zero:
+ case isl_tab_undo_allocate:
case isl_tab_undo_relax:
- unrelax(ctx, tab, undo->var);
+ return perform_undo_var(tab, undo);
+ case isl_tab_undo_bmap_eq:
+ return isl_basic_map_free_equality(tab->bmap, 1);
+ case isl_tab_undo_bmap_ineq:
+ return isl_basic_map_free_inequality(tab->bmap, 1);
+ case isl_tab_undo_bmap_div:
+ if (isl_basic_map_free_div(tab->bmap, 1) < 0)
+ return -1;
+ if (tab->samples)
+ tab->samples->n_col--;
+ break;
+ case isl_tab_undo_saved_basis:
+ if (restore_basis(tab, undo->u.col_var) < 0)
+ return -1;
+ break;
+ case isl_tab_undo_drop_sample:
+ tab->n_outside--;
break;
+ case isl_tab_undo_saved_samples:
+ drop_samples_since(tab, undo->u.n);
+ break;
+ case isl_tab_undo_callback:
+ return undo->u.callback->run(undo->u.callback);
+ default:
+ isl_assert(tab->mat->ctx, 0, return -1);
}
+ return 0;
}
/* Return the tableau to the state it was in when the snapshot "snap"
* was taken.
*/
-int isl_tab_rollback(struct isl_ctx *ctx, struct isl_tab *tab,
- struct isl_tab_undo *snap)
+int isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap)
{
struct isl_tab_undo *undo, *next;
if (!tab)
return -1;
+ tab->in_undo = 1;
for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
next = undo->next;
if (undo == snap)
break;
- perform_undo(ctx, tab, undo);
+ if (perform_undo(tab, undo) < 0) {
+ free_undo(tab);
+ tab->in_undo = 0;
+ return -1;
+ }
free(undo);
}
+ tab->in_undo = 0;
tab->top = undo;
if (!undo)
return -1;
* of the tableau, then the inequality is adjacent (but opposite)
* to the inequality r'.
*/
-static enum isl_ineq_type separation_type(struct isl_ctx *ctx,
- struct isl_tab *tab, unsigned row)
+static enum isl_ineq_type separation_type(struct isl_tab *tab, unsigned row)
{
int pos;
+ unsigned off = 2 + tab->M;
if (tab->rational)
return isl_ineq_separate;
if (!isl_int_is_negone(tab->mat->row[row][1]))
return isl_ineq_separate;
- pos = isl_seq_first_non_zero(tab->mat->row[row] + 2 + tab->n_dead,
+ pos = isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
tab->n_col - tab->n_dead);
if (pos == -1)
return isl_ineq_adj_eq;
- if (!isl_int_is_negone(tab->mat->row[row][2 + tab->n_dead + pos]))
+ if (!isl_int_is_negone(tab->mat->row[row][off + tab->n_dead + pos]))
return isl_ineq_separate;
pos = isl_seq_first_non_zero(
- tab->mat->row[row] + 2 + tab->n_dead + pos + 1,
+ tab->mat->row[row] + off + tab->n_dead + pos + 1,
tab->n_col - tab->n_dead - pos - 1);
return pos == -1 ? isl_ineq_adj_ineq : isl_ineq_separate;
/* Check the effect of inequality "ineq" on the tableau "tab".
* The result may be
* isl_ineq_redundant: satisfied by all points in the tableau
- * isl_ineq_separate: satisfied by no point in tha tableau
+ * isl_ineq_separate: satisfied by no point in the tableau
* isl_ineq_cut: satisfied by some by not all points
* isl_ineq_adj_eq: adjacent to an equality
* isl_ineq_adj_ineq: adjacent to an inequality.
*/
-enum isl_ineq_type isl_tab_ineq_type(struct isl_ctx *ctx, struct isl_tab *tab,
- isl_int *ineq)
+enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq)
{
enum isl_ineq_type type = isl_ineq_error;
struct isl_tab_undo *snap = NULL;
if (!tab)
return isl_ineq_error;
- if (extend_cons(ctx, tab, 1) < 0)
+ if (isl_tab_extend_cons(tab, 1) < 0)
return isl_ineq_error;
- snap = isl_tab_snap(ctx, tab);
+ snap = isl_tab_snap(tab);
- con = add_row(ctx, tab, ineq);
+ con = isl_tab_add_row(tab, ineq);
if (con < 0)
goto error;
row = tab->con[con].index;
- if (is_redundant(ctx, tab, row))
+ if (isl_tab_row_is_redundant(tab, row))
type = isl_ineq_redundant;
else if (isl_int_is_neg(tab->mat->row[row][1]) &&
(tab->rational ||
isl_int_abs_ge(tab->mat->row[row][1],
tab->mat->row[row][0]))) {
- if (at_least_zero(ctx, tab, &tab->con[con]))
+ int nonneg = at_least_zero(tab, &tab->con[con]);
+ if (nonneg < 0)
+ goto error;
+ if (nonneg)
type = isl_ineq_cut;
else
- type = separation_type(ctx, tab, row);
- } else if (tab->rational ? (sign_of_min(ctx, tab, &tab->con[con]) < 0)
- : min_at_most_neg_one(ctx, tab, &tab->con[con]))
- type = isl_ineq_cut;
- else
- type = isl_ineq_redundant;
+ type = separation_type(tab, row);
+ } else {
+ int red = con_is_redundant(tab, &tab->con[con]);
+ if (red < 0)
+ goto error;
+ if (!red)
+ type = isl_ineq_cut;
+ else
+ type = isl_ineq_redundant;
+ }
- if (isl_tab_rollback(ctx, tab, snap))
+ if (isl_tab_rollback(tab, snap))
return isl_ineq_error;
return type;
error:
- isl_tab_rollback(ctx, tab, snap);
return isl_ineq_error;
}
-void isl_tab_dump(struct isl_ctx *ctx, struct isl_tab *tab,
- FILE *out, int indent)
+int isl_tab_track_bmap(struct isl_tab *tab, __isl_take isl_basic_map *bmap)
+{
+ if (!tab || !bmap)
+ goto error;
+
+ isl_assert(tab->mat->ctx, tab->n_eq == bmap->n_eq, return -1);
+ isl_assert(tab->mat->ctx,
+ tab->n_con == bmap->n_eq + bmap->n_ineq, return -1);
+
+ tab->bmap = bmap;
+
+ return 0;
+error:
+ isl_basic_map_free(bmap);
+ return -1;
+}
+
+int isl_tab_track_bset(struct isl_tab *tab, __isl_take isl_basic_set *bset)
+{
+ return isl_tab_track_bmap(tab, (isl_basic_map *)bset);
+}
+
+__isl_keep isl_basic_set *isl_tab_peek_bset(struct isl_tab *tab)
+{
+ if (!tab)
+ return NULL;
+
+ return (isl_basic_set *)tab->bmap;
+}
+
+void isl_tab_dump(struct isl_tab *tab, FILE *out, int indent)
{
unsigned r, c;
int i;
fprintf(out, ", rational");
if (tab->empty)
fprintf(out, ", empty");
- if (tab->killed_col)
- fprintf(out, ", killed_col");
fprintf(out, "\n");
fprintf(out, "%*s[", indent, "");
for (i = 0; i < tab->n_var; ++i) {
if (i)
- fprintf(out, ", ");
+ fprintf(out, (i == tab->n_param ||
+ i == tab->n_var - tab->n_div) ? "; "
+ : ", ");
fprintf(out, "%c%d%s", tab->var[i].is_row ? 'r' : 'c',
tab->var[i].index,
tab->var[i].is_zero ? " [=0]" :
fprintf(out, "]\n");
fprintf(out, "%*s[", indent, "");
for (i = 0; i < tab->n_row; ++i) {
+ const char *sign = "";
if (i)
fprintf(out, ", ");
- fprintf(out, "r%d: %d%s", i, tab->row_var[i],
- var_from_row(ctx, tab, i)->is_nonneg ? " [>=0]" : "");
+ if (tab->row_sign) {
+ if (tab->row_sign[i] == isl_tab_row_unknown)
+ sign = "?";
+ else if (tab->row_sign[i] == isl_tab_row_neg)
+ sign = "-";
+ else if (tab->row_sign[i] == isl_tab_row_pos)
+ sign = "+";
+ else
+ sign = "+-";
+ }
+ fprintf(out, "r%d: %d%s%s", i, tab->row_var[i],
+ isl_tab_var_from_row(tab, i)->is_nonneg ? " [>=0]" : "", sign);
}
fprintf(out, "]\n");
fprintf(out, "%*s[", indent, "");
if (i)
fprintf(out, ", ");
fprintf(out, "c%d: %d%s", i, tab->col_var[i],
- var_from_col(ctx, tab, i)->is_nonneg ? " [>=0]" : "");
+ var_from_col(tab, i)->is_nonneg ? " [>=0]" : "");
}
fprintf(out, "]\n");
r = tab->mat->n_row;
tab->mat->n_row = tab->n_row;
c = tab->mat->n_col;
- tab->mat->n_col = 2 + tab->n_col;
- isl_mat_dump(ctx, tab->mat, out, indent);
+ tab->mat->n_col = 2 + tab->M + tab->n_col;
+ isl_mat_dump(tab->mat, out, indent);
tab->mat->n_row = r;
tab->mat->n_col = c;
+ if (tab->bmap)
+ isl_basic_map_dump(tab->bmap, out, indent);
}