blob: 5151ab61761b90ef1bf0e38af9148253e7a357a1 [file] [log] [blame]
/*
* 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_ctx_private.h>
#include <isl_mat_private.h>
#include "isl_map_private.h"
#include "isl_tab.h"
#include <isl/seq.h>
#include <isl_config.h>
/*
* The implementation of tableaus in this file was inspired by Section 8
* of David Detlefs, Greg Nelson and James B. Saxe, "Simplify: a theorem
* prover for program checking".
*/
struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx,
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, off + n_var);
if (!tab->mat)
goto error;
tab->var = isl_alloc_array(ctx, struct isl_tab_var, n_var);
if (!tab->var)
goto error;
tab->con = isl_alloc_array(ctx, struct isl_tab_var, n_row);
if (!tab->con)
goto error;
tab->col_var = isl_alloc_array(ctx, int, n_var);
if (!tab->col_var)
goto error;
tab->row_var = isl_alloc_array(ctx, int, n_row);
if (!tab->row_var)
goto error;
for (i = 0; i < n_var; ++i) {
tab->var[i].index = i;
tab->var[i].is_row = 0;
tab->var[i].is_nonneg = 0;
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->strict_redundant = 0;
tab->need_undo = 0;
tab->rational = 0;
tab->empty = 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(tab);
return NULL;
}
int isl_tab_extend_cons(struct isl_tab *tab, unsigned n_new)
{
unsigned off;
if (!tab)
return -1;
off = 2 + tab->M;
if (tab->max_con < tab->n_con + n_new) {
struct isl_tab_var *con;
con = isl_realloc_array(tab->mat->ctx, tab->con,
struct isl_tab_var, tab->max_con + n_new);
if (!con)
return -1;
tab->con = con;
tab->max_con += n_new;
}
if (tab->mat->n_row < tab->n_row + n_new) {
int *row_var;
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(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;
}
/* 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)
{
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(tab);
return NULL;
}
static void free_undo_record(struct isl_tab_undo *undo)
{
switch (undo->type) {
case isl_tab_undo_saved_basis:
free(undo->u.col_var);
break;
default:;
}
free(undo);
}
static void free_undo(struct isl_tab *tab)
{
struct isl_tab_undo *undo, *next;
for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
next = undo->next;
free_undo_record(undo);
}
tab->top = undo;
}
void isl_tab_free(struct isl_tab *tab)
{
if (!tab)
return;
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);
}
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->mat->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->mat->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->mat->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->mat->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->mat->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->mat->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->strict_redundant = 0;
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);
if (!prod)
return NULL;
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->strict_redundant = tab1->strict_redundant || tab2->strict_redundant;
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];
else
return &tab->con[~i];
}
struct isl_tab_var *isl_tab_var_from_row(struct isl_tab *tab, int i)
{
return var_from_index(tab, tab->row_var[i]);
}
static struct isl_tab_var *var_from_col(struct isl_tab *tab, int 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_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][off + var->index]))
continue;
if (isl_tab_var_from_row(tab, i)->is_nonneg)
return 0;
}
return 1;
}
/* Check if there are any lower bounds on column variable "var",
* 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_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][off + var->index]))
continue;
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.
* If "var" is not NULL, then the row returned will be different from
* the one associated with "var".
*
* Each row in the tableau is of the form
*
* x_r = a_r0 + \sum_i a_ri x_i
*
* Only rows with x_r >= 0 and with the sign of a_ri opposite to "sgn"
* impose any limit on the increase or decrease in the value of x_c
* and this bound is equal to a_r0 / |a_rc|. We are therefore looking
* for the row with the smallest (most stringent) such bound.
* Note that the common denominator of each row drops out of the fraction.
* To check if row j has a smaller bound than row r, i.e.,
* a_j0 / |a_jc| < a_r0 / |a_rc| or a_j0 |a_rc| < a_r0 |a_jc|,
* 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_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 (!isl_tab_var_from_row(tab, j)->is_nonneg)
continue;
if (sgn * isl_int_sgn(tab->mat->row[j][off + c]) >= 0)
continue;
if (r < 0) {
r = j;
continue;
}
tsgn = sgn * row_cmp(tab, r, j, c, t);
if (tsgn < 0 || (tsgn == 0 &&
tab->row_var[j] < tab->row_var[r]))
r = j;
}
isl_int_clear(t);
return r;
}
/* 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
*
* we need to find a column such that the sign of a_ri is equal to "sgn"
* (such that an increase in x_i will have the desired effect) or a
* column with a variable that may attain negative values.
* If a_ri is positive, then we need to move x_i in the same direction
* to obtain the desired effect. Otherwise, x_i has to move in the
* opposite direction.
*/
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(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[j]))
continue;
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[c]);
r = pivot_row(tab, skip_var, sgn, c);
*row = r < 0 ? var->index : r;
*col = c;
}
/* Return 1 if row "row" represents an obviously redundant inequality.
* 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 constraints.
*/
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 && !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->strict_redundant && isl_int_is_zero(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][off + i]))
continue;
if (tab->col_var[i] >= 0)
return 0;
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_tab *tab, int row1, int row2)
{
int t;
enum isl_tab_row_sign s;
t = tab->row_var[row1];
tab->row_var[row1] = tab->row_var[row2];
tab->row_var[row2] = t;
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;
s = tab->row_sign[row1];
tab->row_sign[row1] = tab->row_sign[row2];
tab->row_sign[row2] = s;
}
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 0;
undo = isl_alloc_type(tab->mat->ctx, struct isl_tab_undo);
if (!undo)
return -1;
undo->type = type;
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.
* If we may need to undo the operation or if the row represents
* a variable of the original problem, the row is kept,
* but no longer considered when looking for a pivot row.
* Otherwise, the row is simply removed.
*
* The row may be interchanged with some other row. If it
* is interchanged with a later row, return 1. Otherwise return 0.
* If the rows are checked in order in the calling function,
* 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.
*/
int isl_tab_mark_redundant(struct isl_tab *tab, int row)
{
struct isl_tab_var *var = isl_tab_var_from_row(tab, row);
var->is_redundant = 1;
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 && !var->is_nonneg) {
var->is_nonneg = 1;
if (isl_tab_push_var(tab, isl_tab_undo_nonneg, var) < 0)
return -1;
}
if (row != tab->n_redundant)
swap_rows(tab, row, tab->n_redundant);
tab->n_redundant++;
return isl_tab_push_var(tab, isl_tab_undo_redundant, var);
} else {
if (row != tab->n_row - 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;
}
}
int isl_tab_mark_empty(struct isl_tab *tab)
{
if (!tab)
return -1;
if (!tab->empty && tab->need_undo)
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 variables are interchanged.
* The given row in the tableau expresses
*
* x_r = a_r0 + \sum_i a_ri x_i
*
* or
*
* x_c = 1/a_rc x_r - a_r0/a_rc + sum_{i \ne r} -a_ri/a_rc
*
* Substituting this equality into the other rows
*
* x_j = a_j0 + \sum_i a_ji x_i
*
* with a_jc \ne 0, we obtain
*
* x_j = a_jc/a_rc x_r + a_j0 - a_jc a_r0/a_rc + sum a_ji - a_jc a_ri/a_rc
*
* The tableau
*
* n_rc/d_r n_ri/d_r
* n_jc/d_j n_ji/d_j
*
* where i is any other column and j is any other row,
* is therefore transformed into
*
* s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
* 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)
*
* The transformation is performed along the following steps
*
* d_r/n_rc n_ri/n_rc
* n_jc/d_j n_ji/d_j
*
* s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
* n_jc/d_j n_ji/d_j
*
* s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
* n_jc/(|n_rc| d_j) n_ji/(|n_rc| d_j)
*
* s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
* n_jc/(|n_rc| d_j) (n_ji |n_rc|)/(|n_rc| d_j)
*
* s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
* n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
*
* s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
* 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)
*
*/
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;
if (tab->mat->ctx->abort) {
isl_ctx_set_error(tab->mat->ctx, isl_error_abort);
return -1;
}
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][off + col], mat->row[row][off + col]);
} else
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->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][off + col]))
continue;
isl_int_mul(mat->row[i][0], mat->row[i][0], mat->row[row][0]);
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][off + col], mat->row[row][1 + j]);
}
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 = isl_tab_var_from_row(tab, row);
var->is_row = 1;
var->index = row;
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][off + col]))
continue;
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 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 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);
}
return isl_tab_pivot(tab, r, var->index);
}
/* Check whether all variables that are marked as non-negative
* also have a non-negative sample value. This function is not
* called from the current code but is useful during debugging.
*/
static void check_table(struct isl_tab *tab) __attribute__ ((unused));
static void check_table(struct isl_tab *tab)
{
int i;
if (tab->empty)
return;
for (i = tab->n_redundant; i < tab->n_row; ++i) {
struct isl_tab_var *var;
var = isl_tab_var_from_row(tab, i);
if (!var->is_nonneg)
continue;
if (tab->M) {
isl_assert(tab->mat->ctx,
!isl_int_is_neg(tab->mat->row[i][2]), abort());
if (isl_int_is_pos(tab->mat->row[i][2]))
continue;
}
isl_assert(tab->mat->ctx, !isl_int_is_neg(tab->mat->row[i][1]),
abort());
}
}
/* Return the sign of the maximal value of "var".
* If the sign is not negative, then on return from this function,
* the sample value will also be non-negative.
*
* If "var" is manifestly unbounded wrt positive values, we are done.
* Otherwise, we pivot the variable up to a row if needed
* Then we continue pivoting down until either
* - no more down pivots can be performed
* - the sample value is positive
* - the variable is pivoted into a manifestly unbounded column
*/
static int sign_of_max(struct isl_tab *tab, struct isl_tab_var *var)
{
int row, col;
if (max_is_manifestly_unbounded(tab, var))
return 1;
if (to_row(tab, var, 1) < 0)
return -2;
while (!isl_int_is_pos(tab->mat->row[var->index][1])) {
find_pivot(tab, var, var, 1, &row, &col);
if (row == -1)
return isl_int_sgn(tab->mat->row[var->index][1]);
if (isl_tab_pivot(tab, row, col) < 0)
return -2;
if (!var->is_row) /* manifestly unbounded */
return 1;
}
return 1;
}
int isl_tab_sign_of_max(struct isl_tab *tab, int con)
{
struct isl_tab_var *var;
if (!tab)
return -2;
var = &tab->con[con];
isl_assert(tab->mat->ctx, !var->is_redundant, return -2);
isl_assert(tab->mat->ctx, !var->is_zero, return -2);
return sign_of_max(tab, var);
}
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_tab *tab, struct isl_tab_var *var)
{
int row, col;
while (row_is_neg(tab, var->index)) {
find_pivot(tab, var, var, 1, &row, &col);
if (row == -1)
break;
if (isl_tab_pivot(tab, row, col) < 0)
return -2;
if (!var->is_row) /* manifestly unbounded */
return 1;
}
return row_sgn(tab, var->index);
}
/* Perform pivots until we are sure that the row variable "var"
* can attain non-negative values. After return from this
* 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_tab *tab, struct isl_tab_var *var)
{
int row, col;
while (isl_int_is_neg(tab->mat->row[var->index][1])) {
find_pivot(tab, var, var, 1, &row, &col);
if (row == -1)
break;
if (row == var->index) /* manifestly unbounded */
return 1;
if (isl_tab_pivot(tab, row, col) < 0)
return -1;
}
return !isl_int_is_neg(tab->mat->row[var->index][1]);
}
/* Return a negative value if "var" can attain negative values.
* Return a non-negative value otherwise.
*
* If "var" is manifestly unbounded wrt negative values, we are done.
* Otherwise, if var is in a column, we can pivot it down to a row.
* Then we continue pivoting down until either
* - the pivot would result in a manifestly unbounded column
* => we don't perform the pivot, but simply return -1
* - no more down pivots can be performed
* - the sample value is negative
* If the sample value becomes negative and the variable is supposed
* to be nonnegative, then we undo the last pivot.
* However, if the last pivot has made the pivoting variable
* obviously redundant, then it may have moved to another row.
* In that case we look for upward pivots until we reach a non-negative
* value again.
*/
static int sign_of_min(struct isl_tab *tab, struct isl_tab_var *var)
{
int row, col;
struct isl_tab_var *pivot_var = NULL;
if (min_is_manifestly_unbounded(tab, var))
return -1;
if (!var->is_row) {
col = var->index;
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) {
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(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(tab, col);
if (isl_tab_pivot(tab, row, col) < 0)
return -2;
if (var->is_redundant)
return 0;
}
if (pivot_var && var->is_nonneg) {
/* pivot back to non-negative value */
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 sample value of "var" is assumed to be non-negative when the
* the function is called. If 1 is returned then the constraint
* is not redundant and the sample value is made non-negative again before
* the function returns.
*/
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(tab, var))
return 1;
if (!var->is_row) {
col = var->index;
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 (row_at_most_neg_one(tab, var->index)) {
if (var->is_nonneg) {
if (!pivot_var->is_redundant &&
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(tab, var, var, -1, &row, &col);
if (row == var->index) {
if (restore_row(tab, var) < -1)
return -1;
return 1;
}
if (row == -1)
return 0;
pivot_var = var_from_col(tab, col);
if (isl_tab_pivot(tab, row, col) < 0)
return -1;
if (var->is_redundant)
return 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)
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_tab *tab, struct isl_tab_var *var)
{
int row, col;
isl_int *r;
if (max_is_manifestly_unbounded(tab, var))
return 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(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;
if (isl_tab_pivot(tab, row, col) < 0)
return -1;
}
return 1;
}
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(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.
* If we may need to undo the operation the column is kept,
* but no longer considered.
* Otherwise, the column is simply removed.
*
* The column may be interchanged with some other column. If it
* is interchanged with a later column, return 1. Otherwise return 0.
* If the columns are checked in order in the calling function,
* then a return value of 1 means that the column with the given
* column number may now contain a different column that
* hasn't been checked yet.
*/
int isl_tab_kill_col(struct isl_tab *tab, int col)
{
var_from_col(tab, col)->is_zero = 1;
if (tab->need_undo) {
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(tab, col, tab->n_dead);
tab->n_dead++;
return 0;
} else {
if (col != tab->n_col - 1)
swap_cols(tab, col, tab->n_col - 1);
var_from_col(tab, tab->n_col - 1)->index = -1;
tab->n_col--;
return 1;
}
}
static int row_is_manifestly_non_integral(struct isl_tab *tab, int row)
{
unsigned off = 2 + tab->M;
if (tab->M && !isl_int_eq(tab->mat->row[row][2],
tab->mat->row[row][0]))
return 0;
if (isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
tab->n_col - tab->n_dead) != -1)
return 0;
return !isl_int_is_divisible_by(tab->mat->row[row][1],
tab->mat->row[row][0]);
}
/* For integer tableaus, check if any of the coordinates are stuck
* at a non-integral value.
*/
static int tab_is_manifestly_empty(struct isl_tab *tab)
{
int i;
if (tab->empty)
return 1;
if (tab->rational)
return 0;
for (i = 0; i < tab->n_var; ++i) {
if (!tab->var[i].is_row)
continue;
if (row_is_manifestly_non_integral(tab, tab->var[i].index))
return 1;
}
return 0;
}
/* Row variable "var" is non-negative and cannot attain any values
* larger than zero. This means that the coefficients of the unrestricted
* column variables are zero and that the coefficients of the non-negative
* column variables are zero or negative.
* Each of the non-negative variables with a negative coefficient can
* then also be written as the negative sum of non-negative variables
* and must therefore also be zero.
*/
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(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) {
int recheck;
if (isl_int_is_zero(mat->row[var->index][off + j]))
continue;
isl_assert(tab->mat->ctx,
isl_int_is_neg(mat->row[var->index][off + j]), return -1);
recheck = isl_tab_kill_col(tab, j);
if (recheck < 0)
return -1;
if (recheck)
--j;
}
if (isl_tab_mark_redundant(tab, var->index) < 0)
return -1;
if (tab_is_manifestly_empty(tab) && isl_tab_mark_empty(tab) < 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
* of the original variables and needs to be expressed in terms of the
* column variables.
*
* We add each term in turn.
* If r = n/d_r is the current sum and we need to add k x, then
* if x is a column variable, we increase the numerator of
* this column by k d_r
* if x = f/d_x is a row variable, then the new representation of r is
*
* n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
* --- + --- = ------------------- = -------------------
* d_r d_r d_r d_x/g m
*
* with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
*
* If tab->M is set, then, internally, each variable x is represented
* as x' - M. We then also need no subtract k d_r from the coefficient of M.
*/
int isl_tab_add_row(struct isl_tab *tab, isl_int *line)
{
int i;
int r;
isl_int *row;
isl_int a, b;
unsigned off = 2 + tab->M;
r = isl_tab_allocate_con(tab);
if (r < 0)
return -1;
isl_int_init(a);
isl_int_init(b);
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->M + tab->n_col);
for (i = 0; i < tab->n_var; ++i) {
if (tab->var[i].is_zero)
continue;
if (tab->var[i].is_row) {
isl_int_lcm(a,
row[0], tab->mat->row[tab->var[i].index][0]);
isl_int_swap(a, row[0]);
isl_int_divexact(a, row[0], a);
isl_int_divexact(b,
row[0], tab->mat->row[tab->var[i].index][0]);
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->M + tab->n_col);
} else
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(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] = isl_tab_row_unknown;
return r;
}
static int drop_row(struct isl_tab *tab, int row)
{
isl_assert(tab->mat->ctx, ~tab->row_var[row] == tab->n_con - 1, return -1);
if (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.
*/
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.
*/
int isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq)
{
struct isl_tab_var *var;
int r;
if (!tab)
return -1;
r = isl_tab_add_row(tab, eq);
if (r < 0)
return -1;
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)
return -1;
return 0;
}
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)
return -1;
var->is_nonneg = 0;
if (isl_tab_kill_col(tab, var->index) < 0)
return -1;
return 0;
}
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.
*/
int 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 -1;
isl_assert(tab->mat->ctx, !tab->M, return -1);
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)
return -1;
var = &tab->con[r];
row = var->index;
if (row_is_manifestly_zero(tab, row)) {
if (snap) {
if (isl_tab_rollback(tab, snap) < 0)
return -1;
} else
drop_row(tab, row);
return 0;
}
if (tab->bmap) {
tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq);
if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
return -1;
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)
return -1;
if (!tab->bmap)
return -1;
if (add_zero_row(tab) < 0)
return -1;
}
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)
return -1;
if (sgn < 0) {
if (isl_tab_mark_empty(tab) < 0)
return -1;
return 0;
}
}
var->is_nonneg = 1;
if (to_col(tab, var) < 0)
return -1;
var->is_nonneg = 0;
if (isl_tab_kill_col(tab, var->index) < 0)
return -1;
return 0;
}
/* 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)
{
unsigned total;
unsigned div_pos;
struct isl_vec *ineq;
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;
if (add_ineq) {
if (add_ineq(user, ineq->el) < 0)
goto error;
} else {
if (isl_tab_add_ineq(tab, ineq->el) < 0)
goto error;
}
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;
}
isl_vec_free(ineq);
return 0;
error:
isl_vec_free(ineq);
return -1;
}
/* Check whether the div described by "div" is obviously non-negative.
* If we are using a big parameter, then we will encode the div
* as div' = M + div, which is always non-negative.
* Otherwise, we check whether div is a non-negative affine combination
* of non-negative variables.
*/
static int div_is_nonneg(struct isl_tab *tab, __isl_keep isl_vec *div)
{
int i;
if (tab->M)
return 1;
if (isl_int_is_neg(div->el[1]))
return 0;
for (i = 0; i < tab->n_var; ++i) {
if (isl_int_is_neg(div->el[2 + i]))
return 0;
if (isl_int_is_zero(div->el[2 + i]))
continue;
if (!tab->var[i].is_nonneg)
return 0;
}
return 1;
}
/* Add an extra div, prescribed 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.
*/
int isl_tab_add_div(struct isl_tab *tab, __isl_keep isl_vec *div,
int (*add_ineq)(void *user, isl_int *), void *user)
{
int r;
int k;
int nonneg;
if (!tab || !div)
return -1;
isl_assert(tab->mat->ctx, tab->bmap, return -1);
nonneg = div_is_nonneg(tab, div);
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)
{
int i;
struct isl_tab *tab;
if (!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), 0);
if (!tab)
return NULL;
tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) {
if (isl_tab_mark_empty(tab) < 0)
goto error;
return tab;
}
for (i = 0; i < bmap->n_eq; ++i) {
tab = add_eq(tab, bmap->eq[i]);
if (!tab)
return tab;
}
for (i = 0; i < bmap->n_ineq; ++i) {
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 "bset".
*/
struct isl_tab *isl_tab_from_recession_cone(__isl_keep isl_basic_set *bset,
int parametric)
{
isl_int cst;
int i;
struct isl_tab *tab;
unsigned offset = 0;
if (!bset)
return NULL;
if (parametric)
offset = isl_basic_set_dim(bset, isl_dim_param);
tab = isl_tab_alloc(bset->ctx, bset->n_eq + bset->n_ineq,
isl_basic_set_total_dim(bset) - offset, 0);
if (!tab)
return NULL;
tab->rational = ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL);
tab->cone = 1;
isl_int_init(cst);
for (i = 0; i < bset->n_eq; ++i) {
isl_int_swap(bset->eq[i][offset], cst);
if (offset > 0) {
if (isl_tab_add_eq(tab, bset->eq[i] + offset) < 0)
goto error;
} else
tab = add_eq(tab, bset->eq[i]);
isl_int_swap(bset->eq[i][offset], cst);
if (!tab)
goto done;
}
for (i = 0; i < bset->n_ineq; ++i) {
int r;
isl_int_swap(bset->ineq[i][offset], cst);
r = isl_tab_add_row(tab, bset->ineq[i] + offset);
isl_int_swap(bset->ineq[i][offset], cst);
if (r < 0)
goto error;
tab->con[r].is_nonneg = 1;
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(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_tab *tab)
{
int i;
if (!tab)
return -1;
if (tab->empty)
return 1;
if (tab->n_dead == tab->n_col)
return 1;
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;
}
}
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)
continue;
row = tab->var[i].index;
if (!isl_int_is_divisible_by(tab->mat->row[row][1],
tab->mat->row[row][0]))
return 0;
}
return 1;
}
static struct isl_vec *extract_integer_sample(struct isl_tab *tab)
{
int i;
struct isl_vec *vec;
vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
if (!vec)
return NULL;
isl_int_set_si(vec->block.data[0], 1);
for (i = 0; i < tab->n_var; ++i) {
if (!tab->var[i].is_row)
isl_int_set_si(vec->block.data[1 + i], 0);
else {
int row = tab->var[i].index;
isl_int_divexact(vec->block.data[1 + i],
tab->mat->row[row][1], tab->mat->row[row][0]);
}
}
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
* in "bmap" (unless "bmap" already had an integer sample).
*
* The tableau is assumed to have been created from "bmap" using
* isl_tab_from_basic_map.
*/
struct isl_basic_map *isl_basic_map_update_from_tab(struct isl_basic_map *bmap,
struct isl_tab *tab)
{
int i;
unsigned n_eq;
if (!bmap)
return NULL;
if (!tab)
return bmap;
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(tab, n_eq + i))
isl_basic_map_inequality_to_equality(bmap, 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 && isl_tab_sample_is_integer(tab))
bmap->sample = extract_integer_sample(tab);
return bmap;
}
struct isl_basic_set *isl_basic_set_update_from_tab(struct isl_basic_set *bset,
struct isl_tab *tab)
{
return (struct isl_basic_set *)isl_basic_map_update_from_tab(
(struct isl_basic_map *)bset, tab);
}
/* Given a non-negative variable "var", add a new non-negative variable
* that is the opposite of "var", ensuring that var can only attain the
* value zero.
* If var = n/d is a row variable, then the new variable = -n/d.
* If var is a column variables, then the new variable = -var.
* If the new variable cannot attain non-negative values, then
* the resulting tableau is empty.
* Otherwise, we know the value will be zero and we close the row.
*/
static int 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 0;
isl_assert(tab->mat->ctx, !var->is_redundant, return -1);
isl_assert(tab->mat->ctx, var->is_nonneg, return -1);
if (isl_tab_extend_cons(tab, 1) < 0)
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;
row = tab->mat->row[tab->n_row];