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/*
* Copyright 2008-2009 Katholieke Universiteit Leuven
* Copyright 2013 Ecole Normale Superieure
* Copyright 2014 INRIA Rocquencourt
* Copyright 2016 Sven Verdoolaege
*
* Use of this software is governed by the MIT license
*
* Written by Sven Verdoolaege, K.U.Leuven, Departement
* Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
* and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
* and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
* B.P. 105 - 78153 Le Chesnay, France
*/
#include <isl_ctx_private.h>
#include <isl_mat_private.h>
#include <isl_vec_private.h>
#include "isl_map_private.h"
#include "isl_tab.h"
#include <isl_seq.h>
#include <isl_config.h>
#include <bset_to_bmap.c>
#include <bset_from_bmap.c>
/*
* 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 (n_var && !tab->var)
goto error;
tab->con = isl_alloc_array(ctx, struct isl_tab_var, n_row);
if (n_row && !tab->con)
goto error;
tab->col_var = isl_alloc_array(ctx, int, n_var);
if (n_var && !tab->col_var)
goto error;
tab->row_var = isl_alloc_array(ctx, int, n_row);
if (n_row && !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;
}
isl_ctx *isl_tab_get_ctx(struct isl_tab *tab)
{
return tab ? isl_mat_get_ctx(tab->mat) : 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 = tab->n_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;
}
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 (tab->max_var && !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 (tab->max_con && !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 ((tab->mat->n_col - off) && !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 (tab->mat->n_row && !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 (tab->mat->n_row && !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 (tab->samples->n_row && !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;
dup->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 __isl_give isl_mat *tab_mat_product(__isl_keep isl_mat *mat1,
__isl_keep 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 ((tab1->max_var + tab2->max_var) && !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 ((tab1->max_con + tab2->max_con) && !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 ((tab1->n_col + tab2->n_col) && !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 ((tab1->mat->n_row + tab2->mat->n_row) && !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 isl_stat push_union(struct isl_tab *tab,
enum isl_tab_undo_type type, union isl_tab_undo_val u) WARN_UNUSED;
/* Push record "u" onto the undo stack of "tab", provided "tab"
* keeps track of undo information.
*
* If the record cannot be pushed, then mark the undo stack as invalid
* such that a later rollback attempt will not try to undo earlier
* records without having been able to undo the current record.
*/
static isl_stat 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)
return isl_stat_error;
if (!tab->need_undo)
return isl_stat_ok;
undo = isl_alloc_type(tab->mat->ctx, struct isl_tab_undo);
if (!undo)
goto error;
undo->type = type;
undo->u = u;
undo->next = tab->top;
tab->top = undo;
return isl_stat_ok;
error:
free_undo(tab);
tab->top = NULL;
return isl_stat_error;
}
isl_stat 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);
}
isl_stat 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.
*/
isl_stat 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 (tab->n_col && !u.col_var)
return isl_stat_error;
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);
}
isl_stat 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;
}
int 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 0;
error:
isl_vec_free(sample);
return -1;
}
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.
*/
isl_stat isl_tab_save_samples(struct isl_tab *tab)
{
union isl_tab_undo_val u;
if (!tab)
return isl_stat_error;
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->preserve || 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;
}
}
/* Mark "tab" as a rational tableau.
* If it wasn't marked as a rational tableau already and if we may
* need to undo changes, then arrange for the marking to be undone
* during the undo.
*/
int isl_tab_mark_rational(struct isl_tab *tab)
{
if (!tab)
return -1;
if (!tab->rational && tab->need_undo)
if (isl_tab_push(tab, isl_tab_undo_rational) < 0)
return -1;
tab->rational = 1;
return 0;
}
isl_stat isl_tab_mark_empty(struct isl_tab *tab)
{
if (!tab)
return isl_stat_error;
if (!tab->empty && tab->need_undo)
if (isl_tab_push(tab, isl_tab_undo_empty) < 0)
return isl_stat_error;
tab->empty = 1;
return isl_stat_ok;
}
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;
isl_ctx *ctx;
struct isl_mat *mat = tab->mat;
struct isl_tab_var *var;
unsigned off = 2 + tab->M;
ctx = isl_tab_get_ctx(tab);
if (isl_ctx_next_operation(ctx) < 0)
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.
*
* If the variable "var" is supposed to be non-negative (is_nonneg is set),
* then 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 (var->is_nonneg && 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.
*
* If "temp_var" is set, then "var" is a temporary variable that
* will be removed after this function returns and for which
* no information is recorded on the undo stack.
* Do not add any undo records involving this variable in this case
* since the variable will have been removed before any future undo
* operations. Also avoid marking the variable as redundant,
* since that either adds an undo record or needlessly removes the row
* (the caller will take care of removing the row).
*/
static isl_stat close_row(struct isl_tab *tab, struct isl_tab_var *var,
int temp_var) WARN_UNUSED;
static isl_stat close_row(struct isl_tab *tab, struct isl_tab_var *var,
int temp_var)
{
int j;
struct isl_mat *mat = tab->mat;
unsigned off = 2 + tab->M;
if (!var->is_nonneg)
isl_die(isl_tab_get_ctx(tab), isl_error_internal,
"expecting non-negative variable",
return isl_stat_error);
var->is_zero = 1;
if (!temp_var && tab->need_undo)
if (isl_tab_push_var(tab, isl_tab_undo_zero, var) < 0)
return isl_stat_error;
for (j = tab->n_dead; j < tab->n_col; ++j) {
int recheck;
if (isl_int_is_zero(mat->row[var->index][off + j]))
continue;
if (isl_int_is_pos(mat->row[var->index][off + j]))
isl_die(isl_tab_get_ctx(tab), isl_error_internal,
"row cannot have positive coefficients",
return isl_stat_error);
recheck = isl_tab_kill_col(tab, j);
if (recheck < 0)
return isl_stat_error;
if (recheck)
--j;
}
if (!temp_var && isl_tab_mark_redundant(tab, var->index) < 0)
return isl_stat_error;
if (tab_is_manifestly_empty(tab) && isl_tab_mark_empty(tab) < 0)
return isl_stat_error;
return isl_stat_ok;
}
/* Add a constraint to the tableau and allocate a row for it.
* Return the index into the constraint array "con".
*
* This function assumes that at least one more row and at least
* one more element in the constraint array are available in the tableau.
*/
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;
}
/* Move the entries in tab->var up one position, starting at "first",
* creating room for an extra entry at position "first".
* Since some of the entries of tab->row_var and tab->col_var contain
* indices into this array, they have to be updated accordingly.
*/
static int var_insert_entry(struct isl_tab *tab, int first)
{
int i;
if (tab->n_var >= tab->max_var)
isl_die(isl_tab_get_ctx(tab), isl_error_internal,
"not enough room for new variable", return -1);
if (first > tab->n_var)
isl_die(isl_tab_get_ctx(tab), isl_error_internal,
"invalid initial position", return -1);
for (i = tab->n_var - 1; i >= first; --i) {
tab->var[i + 1] = tab->var[i];
if (tab->var[i + 1].is_row)
tab->row_var[tab->var[i + 1].index]++;
else
tab->col_var[tab->var[i + 1].index]++;
}
tab->n_var++;
return 0;
}
/* Drop the entry at position "first" in tab->var, moving all
* subsequent entries down.
* Since some of the entries of tab->row_var and tab->col_var contain
* indices into this array, they have to be updated accordingly.
*/
static int var_drop_entry(struct isl_tab *tab, int first)
{
int i;
if (first >= tab->n_var)
isl_die(isl_tab_get_ctx(tab), isl_error_internal,
"invalid initial position", return -1);
tab->n_var--;
for (i = first; i < tab->n_var; ++i) {
tab->var[i] = tab->var[i + 1];
if (tab->var[i + 1].is_row)
tab->row_var[tab->var[i].index]--;
else
tab->col_var[tab->var[i].index]--;
}
return 0;
}
/* Add a variable to the tableau at position "r" and allocate a column for it.
* Return the index into the variable array "var", i.e., "r",
* or -1 on error.
*/
int isl_tab_insert_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);
if (var_insert_entry(tab, r) < 0)
return -1;
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_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.
*
* This function assumes that at least one more row and at least
* one more element in the constraint array are available in the tableau.
*
* 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 isl_stat drop_row(struct isl_tab *tab, int row)
{
isl_assert(tab->mat->ctx, ~tab->row_var[row] == tab->n_con - 1,
return isl_stat_error);
if (row != tab->n_row - 1)
swap_rows(tab, row, tab->n_row - 1);
tab->n_row--;
tab->n_con--;
return isl_stat_ok;
}
/* Drop the variable in column "col" along with the column.
* The column is removed first because it may need to be moved
* into the last position and this process requires
* the contents of the col_var array in a state
* before the removal of the variable.
*/
static isl_stat drop_col(struct isl_tab *tab, int col)
{
int var;
var = tab->col_var[col];
if (col != tab->n_col - 1)
swap_cols(tab, col, tab->n_col - 1);
tab->n_col--;
if (var_drop_entry(tab, var) < 0)
return isl_stat_error;
return isl_stat_ok;
}
/* Add inequality "ineq" and check if it conflicts with the
* previously added constraints or if it is obviously redundant.
*
* This function assumes that at least one more row and at least
* one more element in the constraint array are available in the tableau.
*/
isl_stat isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq)
{
int r;
int sgn;
isl_int cst;
if (!tab)
return isl_stat_error;
if (tab->bmap) {
struct isl_basic_map *bmap = tab->bmap;
isl_assert(tab->mat->ctx, tab->n_eq == bmap->n_eq,
return isl_stat_error);
isl_assert(tab->mat->ctx,
tab->n_con == bmap->n_eq + bmap->n_ineq,
return isl_stat_error);
tab->bmap = isl_basic_map_add_ineq(tab->bmap, ineq);
if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
return isl_stat_error;
if (!tab->bmap)
return isl_stat_error;
}
if (tab->cone) {
isl_int_init(cst);
isl_int_set_si(cst, 0);
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 isl_stat_error;
tab->con[r].is_nonneg = 1;
if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
return isl_stat_error;
if (isl_tab_row_is_redundant(tab, tab->con[r].index)) {
if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
return isl_stat_error;
return isl_stat_ok;
}
sgn = restore_row(tab, &tab->con[r]);
if (sgn < -1)
return isl_stat_error;
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 isl_stat_error;
return isl_stat_ok;
}
/* 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.
*
* This function assumes that at least one more row and at least
* one more element in the constraint array are available in the tableau.
*/
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;
}
/* Does the sample value of row "row" of "tab" involve the big parameter,
* if any?
*/
static int row_is_big(struct isl_tab *tab, int row)
{
return tab->M && !isl_int_is_zero(tab->mat->row[row][2]);
}
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 (row_is_big(tab, row))
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.
*
* This function assumes that at least one more row and at least
* one more element in the constraint array are available in the 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;
}
/* Add a zero row to "tab" and return the corresponding index
* in the constraint array.
*
* This function assumes that at least one more row and at least
* one more element in the constraint array are available in the tableau.
*/
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.
*
* This function assumes that at least one more row and at least
* one more element in the constraint array are available in the tableau.
* If tab->bmap is set, then two rows are needed instead of one.
*/
isl_stat 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 isl_stat_error;
isl_assert(tab->mat->ctx, !tab->M, return isl_stat_error);
if (tab->need_undo)
snap = isl_tab_snap(tab);
if (tab->cone) {
isl_int_init(cst);
isl_int_set_si(cst, 0);
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 isl_stat_error;
var = &tab->con[r];
row = var->index;
if (row_is_manifestly_zero(tab, row)) {
if (snap)
return isl_tab_rollback(tab, snap);
return drop_row(tab, row);
}
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 isl_stat_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)
return isl_stat_error;
if (!tab->bmap)
return isl_stat_error;
if (add_zero_row(tab) < 0)
return isl_stat_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)
return isl_stat_error;
if (sgn < 0) {
if (isl_tab_mark_empty(tab) < 0)
return isl_stat_error;
return isl_stat_ok;
}
}
var->is_nonneg = 1;
if (to_col(tab, var) < 0)
return isl_stat_error;
var->is_nonneg = 0;
if (isl_tab_kill_col(tab, var->index) < 0)
return isl_stat_error;
return isl_stat_ok;
}
/* 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 __isl_give isl_vec *ineq_for_div(__isl_keep isl_basic_map *bmap,
unsigned div)
{
isl_size total;
unsigned div_pos;
struct isl_vec *ineq;
total = isl_basic_map_dim(bmap, isl_dim_all);
if (total < 0)
return NULL;
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.
*
* This function assumes that at least two more rows and at least
* two more elements in the constraint array are available in the tableau.
*/
static isl_stat add_div_constraints(struct isl_tab *tab, unsigned div,
isl_stat (*add_ineq)(void *user, isl_int *), void *user)
{
isl_size total;
unsigned div_pos;
struct isl_vec *ineq;
total = isl_basic_map_dim(tab->bmap, isl_dim_all);
if (total < 0)
return isl_stat_error;
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 isl_stat_ok;
error:
isl_vec_free(ineq);
return isl_stat_error;
}
/* 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;
}
/* Insert an extra div, prescribed by "div", to the tableau and
* the associated bmap (which is assumed to be non-NULL).
* The extra integer division is inserted at (tableau) position "pos".
* Return "pos" or -1 if an error occurred.
*
* 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_insert_div(struct isl_tab *tab, int pos, __isl_keep isl_vec *div,
isl_stat (*add_ineq)(void *user, isl_int *), void *user)
{
int r;
int nonneg;
isl_size n_div;
int o_div;
if (!tab || !div)
return -1;
if (div->size != 1 + 1 + tab->n_var)
isl_die(isl_tab_get_ctx(tab), isl_error_invalid,
"unexpected size", return -1);
n_div = isl_basic_map_dim(tab->bmap, isl_dim_div);
if (n_div < 0)
return -1;
o_div = tab->n_var - n_div;
if (pos < o_div || pos > tab->n_var)
isl_die(isl_tab_get_ctx(tab), isl_error_invalid,
"invalid position", 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_insert_var(tab, pos);
if (r < 0)
return -1;
if (nonneg)
tab->var[r].is_nonneg = 1;
tab->bmap = isl_basic_map_insert_div(tab->bmap, pos - o_div, div);
if (!tab->bmap)
return -1;
if (isl_tab_push_var(tab, isl_tab_undo_bmap_div, &tab->var[r]) < 0)
return -1;
if (add_div_constraints(tab, pos - o_div, add_ineq, user) < 0)
return -1;
return r;
}
/* Add an extra div, prescribed by "div", to the tableau and
* the associated bmap (which is assumed to be non-NULL).
*/
int isl_tab_add_div(struct isl_tab *tab, __isl_keep isl_vec *div)
{
if (!tab)
return -1;
return isl_tab_insert_div(tab, tab->n_var, div, NULL, NULL);
}
/* If "track" is set, then we want to keep track of all constraints in tab
* in its bmap field. This field is initialized from a copy of "bmap",
* so we need to make sure that all constraints in "bmap" also appear
* in the constructed tab.
*/
__isl_give struct isl_tab *isl_tab_from_basic_map(
__isl_keep isl_basic_map *bmap, int track)
{
int i;
struct isl_tab *tab;
isl_size total;
total = isl_basic_map_dim(bmap, isl_dim_all);
if (total < 0)
return NULL;
tab = isl_tab_alloc(bmap->ctx, total + bmap->n_ineq + 1, total, 0);
if (!tab)
return NULL;
tab->preserve = track;
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;
goto done;
}
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)
goto done;
}
done:
if (track && isl_tab_track_bmap(tab, isl_basic_map_copy(bmap)) < 0)
goto error;
return tab;
error:
isl_tab_free(tab);
return NULL;
}
__isl_give struct isl_tab *isl_tab_from_basic_set(
__isl_keep isl_basic_set *bset, int track)
{
return isl_tab_from_basic_map(bset, track);
}
/* 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;
isl_size offset = 0;
isl_size total;
total = isl_basic_set_dim(bset, isl_dim_all);
if (parametric)
offset = isl_basic_set_dim(bset, isl_dim_param);
if (total < 0 || offset < 0)
return NULL;
tab = isl_tab_alloc(bset->ctx, bset->n_eq + bset->n_ineq,
total - offset, 0);
if (!tab)
return NULL;
tab->rational = ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL);
tab->cone = 1;
isl_int_init(cst);
isl_int_set_si(cst, 0);
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.
*/
isl_bool isl_tab_cone_is_bounded(struct isl_tab *tab)
{
int i;
if (!tab)
return isl_bool_error;
if (tab->empty)
return isl_bool_true;
if (tab->n_dead == tab->n_col)
return isl_bool_true;
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 isl_bool_error;
if (sgn != 0)
return isl_bool_false;
if (close_row(tab, var, 0) < 0)
return isl_bool_error;
break;
}
if (tab->n_dead == tab->n_col)
return isl_bool_true;
if (i == tab->n_row)
return isl_bool_false;
}
}
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;
}
__isl_give 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;
}
/* Store the sample value of "var" of "tab" rounded up (if sgn > 0)
* or down (if sgn < 0) to the nearest integer in *v.
*/
static void get_rounded_sample_value(struct isl_tab *tab,
struct isl_tab_var *var, int sgn, isl_int *v)
{
if (!var->is_row)
isl_int_set_si(*v, 0);
else if (sgn > 0)
isl_int_cdiv_q(*v, tab->mat->row[var->index][1],
tab->mat->row[var->index][0]);
else
isl_int_fdiv_q(*v, tab->mat->row[var->index][1],
tab->mat->row[var->index][0]);
}
/* 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.
*/
__isl_give isl_basic_map *isl_basic_map_update_from_tab(
__isl_take 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)
bmap = isl_basic_map_gauss(bmap, NULL);
if (!tab->rational &&
bmap && !bmap->sample && isl_tab_sample_is_integer(tab))
bmap->sample = extract_integer_sample(tab);
return bmap;
}
__isl_give isl_basic_set *isl_basic_set_update_from_tab(
__isl_take isl_basic_set *bset, struct isl_tab *tab)
{
return bset_from_bmap(isl_basic_map_update_from_tab(bset_to_bmap(bset),
tab));
}
/* Drop the last constraint added to "tab" in position "r".
* The constraint is expected to have remained in a row.
*/
static isl_stat drop_last_con_in_row(struct isl_tab *tab, int r)
{
if (!tab->con[r].is_row)
isl_die(isl_tab_get_ctx(tab), isl_error_internal,
"row unexpectedly moved to column",
return isl_stat_error);
if (r + 1 != tab->n_con)
isl_die(isl_tab_get_ctx(tab), isl_error_internal,
"additional constraints added", return isl_stat_error);
if (drop_row(tab, tab->con[r].index) < 0)
return isl_stat_error;
return isl_stat_ok;
}
/* Given a non-negative variable "var", temporarily add a new non-negative
* variable that is the opposite of "var", ensuring that "var" can only attain
* the value zero. The new variable is removed again before this function
* returns. However, the effect of forcing "var" to be zero remains.
* 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 isl_stat 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 isl_stat_ok;
if (var->is_redundant || !var->is_nonneg)
isl_die(isl_tab_get_ctx(tab), isl_error_invalid,
"expecting non-redundant non-negative variable",
return isl_stat_error);
if (isl_tab_extend_cons(tab, 1) < 0)
return isl_stat_error;
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];
if (var->is_row) {
isl_int_set(row[0], tab->mat->row[var->index][0]);
isl_seq_neg(row + 1,
tab->mat->row[var->index] + 1, 1 + tab->n_col);
} else {
isl_int_set_si(row[0], 1);
isl_seq_clr(row + 1, 1 + tab->n_col);
isl_int_set_si(row[off + var->index], -1);
}
tab->n_row++;
tab->n_con++;
sgn = sign_of_max(tab, &tab->con[r]);
if (sgn < -1)
return isl_stat_error;
if (sgn < 0) {
if (drop_last_con_in_row(tab, r) < 0)
return isl_stat_error;
if (isl_tab_mark_empty(tab) < 0)
return isl_stat_error;
return isl_stat_ok;
}
tab->con[r].is_nonneg = 1;
/* sgn == 0 */
if (close_row(tab, &tab->con[r], 1) < 0)
return isl_stat_error;
if (drop_last_con_in_row(tab, r) < 0)
return isl_stat_error;
return isl_stat_ok;
}
/* Check that "con" is a valid constraint position for "tab".
*/
static isl_stat isl_tab_check_con(struct isl_tab *tab, int con)
{
if (!tab)
return isl_stat_error;
if (con < 0 || con >= tab->n_con)
isl_die(isl_tab_get_ctx(tab), isl_error_invalid,
"position out of bounds", return isl_stat_error);
return isl_stat_ok;
}
/* Given a tableau "tab" and an inequality constraint "con" of the tableau,
* relax the inequality by one. That is, the inequality r >= 0 is replaced
* by r' = r + 1 >= 0.
* If r is a row variable, we simply increase the constant term by one
* (taking into account the denominator).
* If r is a column variable, then we need to modify each row that
* refers to r = r' - 1 by substituting this equality, effectively
* subtracting the coefficient of the column from the constant.
* We should only do this if the minimum is manifestly unbounded,
* however. Otherwise, we may end up with negative sample values
* for non-negative variables.
* So, if r is a column variable with a minimum that is not
* manifestly unbounded, then we need to move it to a row.
* However, the sample value of this row may be negative,
* even after the relaxation, so we need to restore it.
* We therefore prefer to pivot a column up to a row, if possible.
*/
int isl_tab_relax(struct isl_tab *tab, int con)
{
struct isl_tab_var *var;
if (!tab)
return -1;
var = &tab->con[con];
if (var->is_row && (var->index < 0 || var->index < tab->n_redundant))
isl_die(tab->mat->ctx, isl_error_invalid,
"cannot relax redundant constraint", return -1);
if (!var->is_row && (var->index < 0 || var->index < tab->n_dead))
isl_die(tab->mat->ctx, isl_error_invalid,
"cannot relax dead constraint", return -1);
if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
if (to_row(tab, var, 1) < 0)
return -1;
if (!var->is_row && !min_is_manifestly_unbounded(tab, var))
if (to_row(tab, var, -1) < 0)
return -1;
if (var->is_row) {
isl_int_add(tab->mat->row[var->index][1],
tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
if (restore_row(tab, var) < 0)
return -1;
} else {
int i;
unsigned off = 2 + tab->M;
for (i = 0; i < tab->n_row; ++i) {
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][off + var->index]);
}
}
if (isl_tab_push_var(tab, isl_tab_undo_relax, var) < 0)
return -1;
return 0;
}
/* Replace the variable v at position "pos" in the tableau "tab"
* by v' = v + shift.
*
* If the variable is in a column, then we first check if we can
* simply plug in v = v' - shift. The effect on a row with
* coefficient f/d for variable v is that the constant term c/d
* is replaced by (c - f * shift)/d. If shift is positive and
* f is negative for each row that needs to remain non-negative,
* then this is clearly safe. In other words, if the minimum of v
* is manifestly unbounded, then we can keep v in a column position.
* Otherwise, we can pivot it down to a row.
* Similarly, if shift is negative, we need to check if the maximum
* of is manifestly unbounded.
*
* If the variable is in a row (from the start or after pivoting),
* then the constant term c/d is replaced by (c + d * shift)/d.
*/
int isl_tab_shift_var(struct isl_tab *tab, int pos, isl_int shift)
{
struct isl_tab_var *var;
if (!tab)
return -1;
if (isl_int_is_zero(shift))
return 0;
var = &tab->var[pos];
if (!var->is_row) {
if (isl_int_is_neg(shift)) {
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;
}
}
if (var->is_row) {
isl_int_addmul(tab->mat->row[var->index][1],
shift, tab->mat->row[var->index][0]);
} else {
int i;
unsigned off = 2 + tab->M;
for (i = 0; i < tab->n_row; ++i) {
if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
continue;
isl_int_submul(tab->mat->row[i][1],
shift, tab->mat->row[i][off + var->index]);
}
}
return 0;
}
/* Remove the sign constraint from constraint "con".
*
* If the constraint variable was originally marked non-negative,
* then we make sure we mark it non-negative again during rollback.
*/
int isl_tab_unrestrict(struct isl_tab *tab, int con)
{
struct isl_tab_var *var;
if (!tab)
return -1;
var = &tab->con[con];
if (!var->is_nonneg)
return 0;
var->is_nonneg = 0;
if (isl_tab_push_var(tab, isl_tab_undo_unrestrict, var) < 0)
return -1;
return 0;
}
int isl_tab_select_facet(struct isl_tab *tab, int con)
{
if (!tab)
return -1;
return cut_to_hyperplane(tab, &tab->con[con]);
}
static int may_be_equality(struct isl_tab *tab, int row)
{
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]);
}
/* Return an isl_tab_var that has been marked or NULL if no such
* variable can be found.
* The marked field has only been set for variables that
* appear in non-redundant rows or non-dead columns.
*
* Pick the last constraint variable that is marked and
* that appears in either a non-redundant row or a non-dead columns.
* Since the returned variable is tested for being a redundant constraint or
* an implicit equality, there is no need to return any tab variable that
* corresponds to a variable.
*/
static struct isl_tab_var *select_marked(struct isl_tab *tab)
{
int i;
struct isl_tab_var *var;
for (i = tab->n_con - 1; i >= 0; --i) {
var = &tab->con[i];
if (var->index < 0)
continue;
if (var->is_row && var->index < tab->n_redundant)
continue;
if (!var->is_row && var->index < tab->n_dead)
continue;
if (var->marked)
return var;
}
return NULL;
}
/* Check for (near) equalities among the constraints.
* A constraint is an equality if it is non-negative and if
* its maximal value is either
* - zero (in case of rational tableaus), or
* - strictly less than 1 (in case of integer tableaus)
*
* 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
* any values larger than zero or at least one.
* If the maximal value is zero, we mark any column variables
* that appear in the row as being zero and mark the row as being redundant.
* Otherwise, if the maximal value is strictly less than one (and the
* tableau is integer), then we restrict the value to being zero
* by adding an opposite non-negative variable.
* The order in which the variables are considered is not important.
*/
int isl_tab_detect_implicit_equalities(struct isl_tab *tab)
{
int i;
unsigned n_marked;
if (!tab)
return -1;
if (tab->empty)
return 0;
if (tab->n_dead == tab->n_col)
return 0;
n_marked = 0;
for (i = tab->n_redundant; i < tab->n_row; ++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(tab, i);
var->marked = !var->frozen && var->is_nonneg;
if (var->marked)
n_marked++;
}
while (n_marked) {
struct isl_tab_var *var;
int sgn;
var = select_marked(tab);
if (!var)
break;
var->marked = 0;
n_marked--;
sgn = sign_of_max(tab, var);
if (sgn < 0)
return -1;
if (sgn == 0) {
if (close_row(tab, var, 0) < 0)
return -1;
} else if (!tab->rational && !at_least_one(tab, var)) {
if (cut_to_hyperplane(tab, var) < 0)
return -1;
return isl_tab_detect_implicit_equalities(tab);
}
for (i = tab->n_redundant; i < tab->n_row; ++i) {
var = isl_tab_var_from_row(tab, i);
if (!var->marked)
continue;
if (may_be_equality(tab, i))
continue;
var->marked = 0;
n_marked--;
}
}
return 0;
}
/* Update the element of row_var or col_var that corresponds to
* constraint tab->con[i] to a move from position "old" to position "i".
*/
static int update_con_after_move(struct isl_tab *tab, int i, int old)
{
int *p;
int index;
index = tab->con[i].index;
if (index == -1)
return 0;
p = tab->con[i].is_row ? tab->row_var : tab->col_var;
if (p[index] != ~old)
isl_die(tab->mat->ctx, isl_error_internal,
"broken internal state", return -1);
p[index] = ~i;
return 0;
}
/* Interchange constraints "con1" and "con2" in "tab".
* In particular, interchange the contents of these entries in tab->con.
* Since tab->col_var and tab->row_var point back into this array,
* they need to be updated accordingly.
*/
isl_stat isl_tab_swap_constraints(struct isl_tab *tab, int con1, int con2)
{
struct isl_tab_var var;
if (isl_tab_check_con(tab, con1) < 0 ||
isl_tab_check_con(tab, con2) < 0)
return isl_stat_error;
var = tab->con[con1];
tab->con[con1] = tab->con[con2];
if (update_con_after_move(tab, con1, con2) < 0)
return isl_stat_error;
tab->con[con2] = var;
if (update_con_after_move(tab, con2, con1) < 0)
return isl_stat_error;
return isl_stat_ok;
}
/* Rotate the "n" constraints starting at "first" to the right,
* putting the last constraint in the position of the first constraint.
*/
static int rotate_constraints(struct isl_tab *tab, int first, int n)
{
int i, last;
struct isl_tab_var var;
if (n <= 1)
return 0;
last = first + n - 1;
var = tab->con[last];
for (i = last; i > first; --i) {
tab->con[i] = tab->con[i - 1];
if (update_con_after_move(tab, i, i - 1) < 0)
return -1;
}
tab->con[first] = var;
if (update_con_after_move(tab, first, last) < 0)
return -1;
return 0;
}
/* Drop the "n" entries starting at position "first" in tab->con, moving all
* subsequent entries down.
* Since some of the entries of tab->row_var and tab->col_var contain
* indices into this array, they have to be updated accordingly.
*/
static isl_stat con_drop_entries(struct isl_tab *tab,
unsigned first, unsigned n)
{
int i;
if (first + n > tab->n_con || first + n < first)
isl_die(isl_tab_get_ctx(tab), isl_error_internal,
"invalid range", return isl_stat_error);
tab->n_con -= n;
for (i = first; i < tab->n_con; ++i) {
tab->con[i] = tab->con[i + n];
if (update_con_after_move(tab, i, i + n) < 0)
return isl_stat_error;
}
return isl_stat_ok;
}
/* isl_basic_map_gauss5 callback that gets called when
* two (equality) constraints "a" and "b" get interchanged
* in the basic map. Perform the same interchange in "tab".
*/
static isl_stat swap_eq(unsigned a, unsigned b, void *user)
{
struct isl_tab *tab = user;
return isl_tab_swap_constraints(tab, a, b);
}
/* isl_basic_map_gauss5 callback that gets called when
* the final "n" equality constraints get removed.
* As a special case, if "n" is equal to the total number
* of equality constraints, then this means the basic map
* turned out to be empty.
* Drop the same number of equality constraints from "tab" or
* mark it empty in the special case.
*/
static isl_stat drop_eq(unsigned n, void *user)
{
struct isl_tab *tab = user;
if (tab->n_eq == n)
return isl_tab_mark_empty(tab);
tab->n_eq -= n;
return con_drop_entries(tab, tab->n_eq, n);
}
/* If "bmap" has more than a single reference, then call
* isl_basic_map_gauss on it, updating "tab" accordingly.
*/
static __isl_give isl_basic_map *gauss_if_shared(__isl_take isl_basic_map *bmap,
struct isl_tab *tab)
{
isl_bool single;
single = isl_basic_map_has_single_reference(bmap);
if (single < 0)
return isl_basic_map_free(bmap);
if (single)
return bmap;
return isl_basic_map_gauss5(bmap, NULL, &swap_eq, &drop_eq, tab);
}
/* Make the equalities that are implicit in "bmap" but that have been
* detected in the corresponding "tab" explicit in "bmap" and update
* "tab" to reflect the new order of the constraints.
*
* In particular, if inequality i is an implicit equality then
* isl_basic_map_inequality_to_equality will move the inequality
* in front of the other equality and it will move the last inequality
* in the position of inequality i.
* In the tableau, the inequalities of "bmap" are stored after the equalities
* and so the original order
*
* E E E E E A A A I B B B B L
*
* is changed into
*
* I E E E E E A A A L B B B B
*
* where I is the implicit equality, the E are equalities,
* the A inequalities before I, the B inequalities after I and
* L the last inequality.
* We therefore need to rotate to the right two sets of constraints,
* those up to and including I and those after I.
*
* If "tab" contains any constraints that are not in "bmap" then they
* appear after those in "bmap" and they should be left untouched.
*
* Note that this function only calls isl_basic_map_gauss
* (in case some equality constraints got detected)
* if "bmap" has more than one reference.
* If it only has a single reference, then it is left in a temporary state,
* because the caller may require this state.
* Calling isl_basic_map_gauss is then the responsibility of the caller.
*/
__isl_give isl_basic_map *isl_tab_make_equalities_explicit(struct isl_tab *tab,
__isl_take isl_basic_map *bmap)
{
int i;
unsigned n_eq;
if (!tab || !bmap)
return isl_basic_map_free(bmap);
if (tab->empty)
return bmap;
n_eq = tab->n_eq;
for (i = bmap->n_ineq - 1; i >= 0; --i) {
if (!isl_tab_is_equality(tab, bmap->n_eq + i))
continue;
isl_basic_map_inequality_to_equality(bmap, i);
if (rotate_constraints(tab, 0, tab->n_eq + i + 1) < 0)
return isl_basic_map_free(bmap);
if (rotate_constraints(tab, tab->n_eq + i + 1,
bmap->n_ineq - i) < 0)
return isl_basic_map_free(bmap);
tab->n_eq++;
}
if (n_eq != tab->n_eq)
bmap = gauss_if_shared(bmap, tab);
return bmap;
}
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.
* A constraint is redundant if it is non-negative and if
* its minimal value (temporarily ignoring the non-negativity) is either
* - zero (in case of rational tableaus), or
* - strictly larger than -1 (in case of integer tableaus)
*
* We first mark all non-redundant and non-dead variables that
* are not frozen and not obviously negatively unbounded.
* Then we iterate over all marked variables if they can attain
* any values smaller than zero or at most negative one.
* If not, we mark the row as being redundant (assuming it hasn't
* been detected as being obviously redundant in the mean time).
*/
int isl_tab_detect_redundant(struct isl_tab *tab)
{
int i;
unsigned n_marked;
if (!tab)
return -1;
if (tab->empty)
return 0;
if (tab->n_redundant == tab->n_row)
return 0;
n_marked = 0;
for (i = tab->n_redundant; i < tab->n_row; ++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(tab, i);
var->marked = !var->frozen && var->is_nonneg &&
!min_is_manifestly_unbounded(tab, var);
if (var->marked)
n_marked++;
}
while (n_marked) {
struct isl_tab_var *var;
int red;
var = select_marked(tab);
if (!var)
break;
var->marked = 0;
n_marked--;
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(tab, i);
if (!var->marked)
continue;
if (!min_is_manifestly_unbounded(tab, var))
continue;
var->marked = 0;
n_marked--;
}
}
return 0;
}
int isl_tab_is_equality(struct isl_tab *tab, int con)
{
int row;
unsigned off;
if (!tab)
return -1;
if (tab->con[con].is_zero)
return 1;
if (tab->con[con].is_redundant)
return 0;
if (!tab->con[con].is_row)
return tab->con[con].index < tab->n_dead;
row = tab->con[con].index;
off = 2 + tab->M;
return isl_int_is_zero(tab->mat->row[row][1]) &&
!row_is_big(tab, row) &&
isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
tab->n_col - tab->n_dead) == -1;
}
/* Return the minimal value of the affine expression "f" with denominator
* "denom" in *opt, *opt_denom, assuming the tableau is not empty and
* the expression cannot attain arbitrarily small values.
* If opt_denom is NULL, then *opt is rounded up to the nearest integer.
* The return value reflects the nature of the result (empty, unbounded,
* minimal value returned in *opt).
*
* This function assumes that at least one more row and at least
* one more element in the constraint array are available in the tableau.
*/
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)
return isl_lp_error;
if (tab->empty)
return isl_lp_empty;
snap = isl_tab_snap(tab);
r = isl_tab_add_row(tab, f);
if (r < 0)
return isl_lp_error;
var = &tab->con[r];
for (;;) {
int row, col;
find_pivot(tab, var, var, -1, &row, &col);
if (row == var->index) {
res = isl_lp_unbounded;
break;
}
if (row == -1)
break;
if (isl_tab_pivot(tab, row, col) < 0)
return isl_lp_error;
}
isl_int_mul(tab->mat->row[var->index][0],
tab->mat->row[var->index][0], denom);
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]);
} else
get_rounded_sample_value(tab, var, 1, opt);
}
if (isl_tab_rollback(tab, snap) < 0)
return isl_lp_error;
return res;
}
/* Is the constraint at position "con" marked as being redundant?
* If it is marked as representing an equality, then it is not
* considered to be redundant.
* Note that isl_tab_mark_redundant marks both the isl_tab_var as
* redundant and moves the corresponding row into the first
* tab->n_redundant positions (or removes the row, assigning it index -1),
* so the final test is actually redundant itself.
*/
int isl_tab_is_redundant(struct isl_tab *tab, int con)
{
if (isl_tab_check_con(tab, con) < 0)
return -1;
if (tab->con[con].is_zero)
return 0;
if (tab->con[con].is_redundant)
return 1;
return tab->con[con].is_row && tab->con[con].index < tab->n_redundant;
}
/* Is variable "var" of "tab" fixed to a constant value by its row
* in the tableau?
* If so and if "value" is not NULL, then store this constant value
* in "value".
*
* That is, is it a row variable that only has non-zero coefficients
* for dead columns?
*/
static isl_bool is_constant(struct isl_tab *tab, struct isl_tab_var *var,
isl_int *value)
{
unsigned off = 2 + tab->M;
isl_mat *mat = tab->mat;
int n;
int row;
int pos;
if (!var->is_row)
return isl_bool_false;
row = var->index;
if (row_is_big(tab, row))
return isl_bool_false;
n = tab->n_col - tab->n_dead;
pos = isl_seq_first_non_zero(mat->row[row] + off + tab->n_dead, n);
if (pos != -1)
return isl_bool_false;
if (value)
isl_int_divexact(*value, mat->row[row][1], mat->row[row][0]);
return isl_bool_true;
}
/* Has the variable "var' of "tab" reached a value that is greater than
* or equal (if sgn > 0) or smaller than or equal (if sgn < 0) to "target"?
* "tmp" has been initialized by the caller and can be used
* to perform local computations.
*
* If the sample value involves the big parameter, then any value
* is reached.
* Otherwise check if n/d >= t, i.e., n >= d * t (if sgn > 0)
* or n/d <= t, i.e., n <= d * t (if sgn < 0).
*/
static int reached(struct isl_tab *tab, struct isl_tab_var *var, int sgn,
isl_int target, isl_int *tmp)
{
if (row_is_big(tab, var->index))
return 1;
isl_int_mul(*tmp, tab->mat->row[var->index][0], target);
if (sgn > 0)
return isl_int_ge(tab->mat->row[var->index][1], *tmp);
else
return isl_int_le(tab->mat->row[var->index][1], *tmp);
}
/* Can variable "var" of "tab" attain the value "target" by
* pivoting up (if sgn > 0) or down (if sgn < 0)?
* If not, then pivot up [down] to the greatest [smallest]
* rational value.
* "tmp" has been initialized by the caller and can be used
* to perform local computations.
*
* If the variable is manifestly unbounded in the desired direction,
* then it can attain any value.
* Otherwise, it can be moved to a row.
* Continue pivoting until the target is reached.
* If no more pivoting can be performed, the maximal [minimal]
* rational value has been reached and the target cannot be reached.
* If the variable would be pivoted into a manifestly unbounded column,
* then the target can be reached.
*/
static isl_bool var_reaches(struct isl_tab *tab, struct isl_tab_var *var,
int sgn, isl_int target, isl_int *tmp)
{
int row, col;
if (sgn < 0 && min_is_manifestly_unbounded(tab, var))
return isl_bool_true;
if (sgn > 0 && max_is_manifestly_unbounded(tab, var))
return isl_bool_true;
if (to_row(tab, var, sgn) < 0)
return isl_bool_error;
while (!reached(tab, var, sgn, target, tmp)) {
find_pivot(tab, var, var, sgn, &row, &col);
if (row == -1)
return isl_bool_false;
if (row == var->index)
return isl_bool_true;
if (isl_tab_pivot(tab, row, col) < 0)
return isl_bool_error;
}
return isl_bool_true;
}
/* Check if variable "var" of "tab" can only attain a single (integer)
* value, and, if so, add an equality constraint to fix the variable
* to this single value and store the result in "target".
* "target" and "tmp" have been initialized by the caller.
*
* Given the current sample value, round it down and check
* whether it is possible to attain a strictly smaller integer value.
* If so, the variable is not restricted to a single integer value.
* Otherwise, the search stops at the smallest rational value.
* Round up this value and check whether it is possible to attain
* a strictly greater integer value.
* If so, the variable is not restricted to a single integer value.
* Otherwise, the search stops at the greatest rational value.
* If rounding down this value yields a value that is different
* from rounding up the smallest rational value, then the variable
* cannot attain any integer value. Mark the tableau empty.
* Otherwise, add an equality constraint that fixes the variable
* to the single integer value found.
*/
static isl_bool detect_constant_with_tmp(struct isl_tab *tab,
struct isl_tab_var *var, isl_int *target, isl_int *tmp)
{
isl_bool reached;
isl_vec *eq;
int pos;
isl_stat r;
get_rounded_sample_value(tab, var, -1, target);
isl_int_sub_ui(*target, *target, 1);
reached = var_reaches(tab, var, -1, *target, tmp);
if (reached < 0 || reached)
return isl_bool_not(reached);
get_rounded_sample_value(tab, var, 1, target);
isl_int_add_ui(*target, *target, 1);
reached = var_reaches(tab, var, 1, *target, tmp);
if (reached < 0 || reached)
return isl_bool_not(reached);
get_rounded_sample_value(tab, var, -1, tmp);
isl_int_sub_ui(*target, *target, 1);
if (isl_int_ne(*target, *tmp)) {
if (isl_tab_mark_empty(tab) < 0)
return isl_bool_error;
return isl_bool_false;
}
if (isl_tab_extend_cons(tab, 1) < 0)
return isl_bool_error;
eq = isl_vec_alloc(isl_tab_get_ctx(tab), 1 + tab->n_var);
if (!eq)
return isl_bool_error;
pos = var - tab->var;
isl_seq_clr(eq->el + 1, tab->n_var);
isl_int_set_si(eq->el[1 + pos], -1);
isl_int_set(eq->el[0], *target);
r = isl_tab_add_eq(tab, eq->el);
isl_vec_free(eq);
return r < 0 ? isl_bool_error : isl_bool_true;
}
/* Check if variable "var" of "tab" can only attain a single (integer)
* value, and, if so, add an equality constraint to fix the variable
* to this single value and store the result in "value" (if "value"
* is not NULL).
*
* If the current sample value involves the big parameter,
* then the variable cannot have a fixed integer value.
* If the variable is already fixed to a single value by its row, then
* there is no need to add another equality constraint.
*
* Otherwise, allocate some temporary variables and continue
* with detect_constant_with_tmp.
*/
static isl_bool get_constant(struct isl_tab *tab, struct isl_tab_var *var,
isl_int *value)
{
isl_int target, tmp;
isl_bool is_cst;
if (var->is_row && row_is_big(tab, var->index))
return isl_bool_false;
is_cst = is_constant(tab, var, value);
if (is_cst < 0 || is_cst)
return is_cst;
if (!value)
isl_int_init(target);
isl_int_init(tmp);
is_cst = detect_constant_with_tmp(tab, var,
value ? value : &target, &tmp);
isl_int_clear(tmp);
if (!value)
isl_int_clear(target);
return is_cst;
}
/* Check if variable "var" of "tab" can only attain a single (integer)
* value, and, if so, add an equality constraint to fix the variable
* to this single value and store the result in "value" (if "value"
* is not NULL).
*
* For rational tableaus, nothing needs to be done.
*/
isl_bool isl_tab_is_constant(struct isl_tab *tab, int var, isl_int *value)
{
if (!tab)
return isl_bool_error;
if (var < 0 || var >= tab->n_var)
isl_die(isl_tab_get_ctx(tab), isl_error_invalid,
"position out of bounds", return isl_bool_error);
if (tab->rational)
return isl_bool_false;
return get_constant(tab, &tab->var[var], value);
}
/* Check if any of the variables of "tab" can only attain a single (integer)
* value, and, if so, add equality constraints to fix those variables
* to these single values.
*
* For rational tableaus, nothing needs to be done.
*/
isl_stat isl_tab_detect_constants(struct isl_tab *tab)
{
int i;
if (!tab)
return isl_stat_error;
if (tab->rational)
return isl_stat_ok;
for (i = 0; i < tab->n_var; ++i) {
if (get_constant(tab, &tab->var[i], NULL) < 0)
return isl_stat_error;
}
return isl_stat_ok;
}
/* Take a snapshot of the tableau that can be restored by a call to
* isl_tab_rollback.
*/
struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab)
{
if (!tab)
return NULL;
tab->need_undo = 1;
return tab->top;
}
/* Does "tab" need to keep track of undo information?
* That is, was a snapshot taken that may need to be restored?
*/
isl_bool isl_tab_need_undo(struct isl_tab *tab)
{
if (!tab)
return isl_bool_error;
return isl_bool_ok(tab->need_undo);
}
/* Remove all tracking of undo information from "tab", invalidating
* any snapshots that may have been taken of the tableau.
* Since all snapshots have been invalidated, there is also
* no need to start keeping track of undo information again.
*/
void isl_tab_clear_undo(struct isl_tab *tab)
{
if (!tab)
return;
free_undo(tab);
tab->need_undo = 0;
}
/* Undo the operation performed by isl_tab_relax.
*/
static isl_stat unrelax(struct isl_tab *tab, struct isl_tab_var *var)
WARN_UNUSED;
static isl_stat unrelax(struct isl_tab *tab, struct isl_tab_var *var)
{
unsigned off = 2 + tab->M;
if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
if (to_row(tab, var, 1) < 0)
return isl_stat_error;
if (var->is_row) {
isl_int_sub(tab->mat->row[var->index][1],
tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
if (var->is_nonneg) {
int sgn = restore_row(tab, var);
isl_assert(tab->mat->ctx, sgn >= 0,
return isl_stat_error);
}
} else {
int i;
for (i = 0; i < tab->n_row; ++i) {
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][off + var->index]);
}
}
return isl_stat_ok;
}
/* Undo the operation performed by isl_tab_unrestrict.
*
* In particular, mark the variable as being non-negative and make
* sure the sample value respects this constraint.
*/
static isl_stat ununrestrict(struct isl_tab *tab, struct isl_tab_var *var)
{
var->is_nonneg = 1;
if (var->is_row && restore_row(tab, var) < -1)
return isl_stat_error;
return isl_stat_ok;
}
/* Unmark the last redundant row in "tab" as being redundant.
* This undoes part of the modifications performed by isl_tab_mark_redundant.
* In particular, remove the redundant mark and make
* sure the sample value respects the constraint again.
* A variable that is marked non-negative by isl_tab_mark_redundant
* is covered by a separate undo record.
*/
static isl_stat restore_last_redundant(struct isl_tab *tab)
{
struct isl_tab_var *var;
if (tab->n_redundant < 1)
isl_die(isl_tab_get_ctx(tab), isl_error_internal,
"no redundant rows", return isl_stat_error);
var = isl_tab_var_from_row(tab, tab->n_redundant - 1);
var->is_redundant = 0;
tab->n_redundant--;
restore_row(tab, var);
return isl_stat_ok;
}
static isl_stat perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo)
WARN_UNUSED;
static isl_stat 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_nonneg:
var->is_nonneg = 0;
break;
case isl_tab_undo_redundant:
if (!var->is_row || var->index != tab->n_redundant - 1)
isl_die(isl_tab_get_ctx(tab), isl_error_internal,
"not undoing last redundant row",
return isl_stat_error);
return restore_last_redundant(tab);
case isl_tab_undo_freeze:
var->frozen = 0;
break;
case isl_tab_undo_zero:
var->is_zero = 0;
if (!var->is_row)
tab->n_dead--;
break;
case isl_tab_undo_allocate:
if (undo->u.var_index >= 0) {
isl_assert(tab->mat->ctx, !var->is_row,
return isl_stat_error);
return drop_col(tab, var->index);
}
if (!var->is_row) {
if (!max_is_manifestly_unbounded(tab, var)) {
if (to_row(tab, var, 1) < 0)
return isl_stat_error;
} else if (!min_is_manifestly_unbounded(tab, var)) {
if (to_row(tab, var, -1) < 0)
return isl_stat_error;
} else
if (to_row(tab, var, 0) < 0)
return isl_stat_error;
}
return drop_row(tab, var->index);
case isl_tab_undo_relax:
return unrelax(tab, var);
case isl_tab_undo_unrestrict:
return ununrestrict(tab, var);
default:
isl_die(tab->mat->ctx, isl_error_internal,
"perform_undo_var called on invalid undo record",
return isl_stat_error);
}
return isl_stat_ok;
}
/* Restore all rows that have been marked redundant by isl_tab_mark_redundant
* and that have been preserved in the tableau.
* Note that isl_tab_mark_redundant may also have marked some variables
* as being non-negative before marking them redundant. These need
* to be removed as well as otherwise some constraints could end up
* getting marked redundant with respect to the variable.
*/
isl_stat isl_tab_restore_redundant(struct isl_tab *tab)
{
if (!tab)
return isl_stat_error;
if (tab->need_undo)
isl_die(isl_tab_get_ctx(tab), isl_error_invalid,
"manually restoring redundant constraints "
"interferes with undo history",
return isl_stat_error);
while (tab->n_redundant > 0) {
if (tab->row_var[tab->n_redundant - 1] >= 0) {
struct isl_tab_var *var;
var = isl_tab_var_from_row(tab, tab->n_redundant - 1);
var->is_nonneg = 0;
}
restore_last_redundant(tab);
}
return isl_stat_ok;
}
/* Undo the addition of an integer division to the basic map representation
* of "tab" in position "pos".
*/
static isl_stat drop_bmap_div(struct isl_tab *tab, int pos)
{
int off;
isl_size n_div;
n_div = isl_basic_map_dim(tab->bmap, isl_dim_div);
if (n_div < 0)
return isl_stat_error;
off = tab->n_var - n_div;
tab->bmap = isl_basic_map_drop_div(tab->bmap, pos - off);
if (!tab->bmap)
return isl_stat_error;
if (tab->samples) {
tab->samples = isl_mat_drop_cols(tab->samples, 1 + pos, 1);
if (!tab->samples)
return isl_stat_error;
}
return isl_stat_ok;
}
/* 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 (tab->n_col && !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);
return 0;
error:
free(extra);
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);
}
tab->n_sample--;
}
}
static isl_stat perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo)
WARN_UNUSED;
static isl_stat perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo)
{
switch (undo->type) {
case isl_tab_undo_rational:
tab->rational = 0;
break;
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:
case isl_tab_undo_unrestrict:
return perform_undo_var(tab, undo);
case isl_tab_undo_bmap_eq:
tab->bmap = isl_basic_map_free_equality(tab->bmap, 1);
return tab->bmap ? isl_stat_ok : isl_stat_error;
case isl_tab_undo_bmap_ineq:
tab->bmap = isl_basic_map_free_inequality(tab->bmap, 1);
return tab->bmap ? isl_stat_ok : isl_stat_error;
case isl_tab_undo_bmap_div:
return drop_bmap_div(tab, undo->u.var_index);
case isl_tab_undo_saved_basis:
if (restore_basis(tab, undo->u.col_var) < 0)
return isl_stat_error;
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 isl_stat_error);
}
return isl_stat_ok;
}
/* Return the tableau to the state it was in when the snapshot "snap"
* was taken.
*/
isl_stat isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap)
{
struct isl_tab_undo *undo, *next;
if (!tab)
return isl_stat_error;
tab->in_undo = 1;
for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
next = undo->next;
if (undo == snap)
break;
if (perform_undo(tab, undo) < 0) {
tab->top = undo;
free_undo(tab);
tab->in_undo = 0;
return isl_stat_error;
}
free_undo_record(undo);
}
tab->in_undo = 0;
tab->top = undo;
if (!undo)
return isl_stat_error;
return isl_stat_ok;
}
/* The given row "row" represents an inequality violated by all
* points in the tableau. Check for some special cases of such
* separating constraints.
* In particular, if the row has been reduced to the constant -1,
* then we know the inequality is adjacent (but opposite) to
* an equality in the tableau.
* If the row has been reduced to r = c*(-1 -r'), with r' an inequality
* of the tableau and c a positive constant, then the inequality
* is adjacent (but opposite) to the inequality r'.
*/
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_one(tab->mat->row[row][0]))
return isl_ineq_separate;
pos = isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
tab->n_col - tab->n_dead);
if (pos == -1) {
if (isl_int_is_negone(tab->mat->row[row][1]))
return isl_ineq_adj_eq;
else
return isl_ineq_separate;
}
if (!isl_int_eq(tab->mat->row[row][1],
tab->mat->row[row][off + tab->n_dead + pos]))
return isl_ineq_separate;
pos = isl_seq_first_non_zero(
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 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_tab *tab, isl_int *ineq)
{
enum isl_ineq_type type = isl_ineq_error;
struct isl_tab_undo *snap = NULL;
int con;
int row;
if (!tab)
return isl_ineq_error;
if (isl_tab_extend_cons(tab, 1) < 0)
return isl_ineq_error;
snap = isl_tab_snap(tab);
con = isl_tab_add_row(tab, ineq);
if (con < 0)
goto error;
row = tab->con[con].index;
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]))) {
int nonneg = at_least_zero(tab, &tab->con[con]);
if (nonneg < 0)
goto error;
if (nonneg)
type = isl_ineq_cut;
else
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(tab, snap))
return isl_ineq_error;
return type;
error:
return isl_ineq_error;
}
isl_stat isl_tab_track_bmap(struct isl_tab *tab, __isl_take isl_basic_map *bmap)
{
bmap = isl_basic_map_cow(bmap);
if (!tab || !bmap)
goto error;
if (tab->empty) {
bmap = isl_basic_map_set_to_empty(bmap);
if (!bmap)
goto error;
tab->bmap = bmap;
return isl_stat_ok;
}
isl_assert(tab->mat->ctx, tab->n_eq == bmap->n_eq, goto error);
isl_assert(tab->mat->ctx,
tab->n_con == bmap->n_eq + bmap->n_ineq, goto error);
tab->bmap = bmap;
return isl_stat_ok;
error:
isl_basic_map_free(bmap);
return isl_stat_error;
}
isl_stat isl_tab_track_bset(struct isl_tab *tab, __isl_take isl_basic_set *bset)
{
return isl_tab_track_bmap(tab, bset_to_bmap(bset));
}
__isl_keep isl_basic_set *isl_tab_peek_bset(struct isl_tab *tab)
{
if (!tab)
return NULL;
return bset_from_bmap(tab->bmap);
}
static void isl_tab_print_internal(__isl_keep struct isl_tab *tab,
FILE *out, int indent)
{
unsigned r, c;
int i;
if (!tab) {
fprintf(out, "%*snull tab\n", indent, "");
return;
}
fprintf(out, "%*sn_redundant: %d, n_dead: %d", indent, "",
tab->n_redundant, tab->n_dead);
if (tab->rational)
fprintf(out, ", rational");
if (tab->empty)
fprintf(out, ", empty");
fprintf(out, "\n");
fprintf(out, "%*s[", indent, "");
for (i = 0; i < tab->n_var; ++i) {
if (i)
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]" :
tab->var[i].is_redundant ? " [R]" : "");
}
fprintf(out, "]\n");
fprintf(out, "%*s[", indent, "");
for (i = 0; i < tab->n_con; ++i) {
if (i)
fprintf(out, ", ");
fprintf(out, "%c%d%s", tab->con[i].is_row ? 'r' : 'c',
tab->con[i].index,
tab->con[i].is_zero ? " [=0]" :
tab->con[i].is_redundant ? " [R]" : "");
}
fprintf(out, "]\n");
fprintf(out, "%*s[", indent, "");
for (i = 0; i < tab->n_row; ++i) {
const char *sign = "";
if (i)
fprintf(out, ", ");
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, "");
for (i = 0; i < tab->n_col; ++i) {
if (i)
fprintf(out, ", ");
fprintf(out, "c%d: %d%s", i, tab->col_var[i],
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->M + tab->n_col;
isl_mat_print_internal(tab->mat, out, indent);
tab->mat->n_row = r;
tab->mat->n_col = c;
if (tab->bmap)
isl_basic_map_print_internal(tab->bmap, out, indent);
}
void isl_tab_dump(__isl_keep struct isl_tab *tab)
{
isl_tab_print_internal(tab, stderr, 0);
}
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