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* Copyright 2008-2009 Katholieke Universiteit Leuven
* Use of this software is governed by the GNU LGPLv2.1 license
* Written by Sven Verdoolaege, K.U.Leuven, Departement
* Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
#ifndef ISL_TAB_H
#define ISL_TAB_H
#include <isl/lp.h>
#include <isl/map.h>
#include <isl/mat.h>
#include <isl/set.h>
struct isl_tab_var {
int index;
unsigned is_row : 1;
unsigned is_nonneg : 1;
unsigned is_zero : 1;
unsigned is_redundant : 1;
unsigned marked : 1;
unsigned frozen : 1;
unsigned negated : 1;
enum isl_tab_undo_type {
struct isl_tab_callback {
int (*run)(struct isl_tab_callback *cb);
union isl_tab_undo_val {
int var_index;
int *col_var;
int n;
struct isl_tab_callback *callback;
struct isl_tab_undo {
enum isl_tab_undo_type type;
union isl_tab_undo_val u;
struct isl_tab_undo *next;
/* The tableau maintains equality relations.
* Each column and each row is associated to a variable or a constraint.
* The "value" of an inequality constraint is the value of the corresponding
* slack variable.
* The "row_var" and "col_var" arrays map column and row indices
* to indices in the "var" and "con" arrays. The elements of these
* arrays maintain extra information about the variables and the constraints.
* Each row expresses the corresponding row variable as an affine expression
* of the column variables.
* The first two columns in the matrix contain the common denominator of
* the row and the numerator of the constant term.
* If "M" is set, then the third column represents the "big parameter".
* The third (M = 0) or fourth (M = 1) column
* in the matrix is called column 0 with respect to the col_var array.
* The sample value of the tableau is the value that assigns zero
* to all the column variables and the constant term of each affine
* expression to the corresponding row variable.
* The operations on the tableau maintain the property that the sample
* value satisfies the non-negativity constraints (usually on the slack
* variables).
* The big parameter represents an arbitrarily big (and divisible)
* positive number. If present, then the sign of a row is determined
* lexicographically, with the sign of the big parameter coefficient
* considered first. The big parameter is only used while
* solving PILP problems.
* The first n_dead column variables have their values fixed to zero.
* The corresponding tab_vars are flagged "is_zero".
* Some of the rows that have have zero coefficients in all but
* the dead columns are also flagged "is_zero".
* The first n_redundant rows correspond to inequality constraints
* that are always satisfied for any value satisfying the non-redundant
* rows. The corresponding tab_vars are flagged "is_redundant".
* A row variable that is flagged "is_zero" is also flagged "is_redundant"
* since the constraint has been reduced to 0 = 0 and is therefore always
* satisfied.
* There are "n_var" variables in total. The first "n_param" of these
* are called parameters and the last "n_div" of these are called divs.
* The basic tableau operations makes no distinction between different
* kinds of variables. These special variables are only used while
* solving PILP problems.
* Dead columns and redundant rows are detected on the fly.
* However, the basic operations do not ensure that all dead columns
* or all redundant rows are detected.
* isl_tab_detect_implicit_equalities and isl_tab_detect_redundant can be used
* to perform and exhaustive search for dead columns and redundant rows.
* The samples matrix contains "n_sample" integer points that have at some
* point been elements satisfying the tableau. The first "n_outside"
* of them no longer satisfy the tableau. They are kept because they
* can be reinstated during rollback when the constraint that cut them
* out is removed. These samples are only maintained for the context
* tableau while solving PILP problems.
enum isl_tab_row_sign {
isl_tab_row_unknown = 0,
struct isl_tab {
struct isl_mat *mat;
unsigned n_row;
unsigned n_col;
unsigned n_dead;
unsigned n_redundant;
unsigned n_var;
unsigned n_param;
unsigned n_div;
unsigned max_var;
unsigned n_con;
unsigned n_eq;
unsigned max_con;
struct isl_tab_var *var;
struct isl_tab_var *con;
int *row_var; /* v >= 0 -> var v; v < 0 -> con ~v */
int *col_var; /* v >= 0 -> var v; v < 0 -> con ~v */
enum isl_tab_row_sign *row_sign;
struct isl_tab_undo bottom;
struct isl_tab_undo *top;
struct isl_vec *dual;
struct isl_basic_map *bmap;
unsigned n_sample;
unsigned n_outside;
int *sample_index;
struct isl_mat *samples;
int n_zero;
int n_unbounded;
struct isl_mat *basis;
int (*conflict)(int con, void *user);
void *conflict_user;
unsigned strict_redundant : 1;
unsigned need_undo : 1;
unsigned rational : 1;
unsigned empty : 1;
unsigned in_undo : 1;
unsigned M : 1;
unsigned cone : 1;
struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx,
unsigned n_row, unsigned n_var, unsigned M);
void isl_tab_free(struct isl_tab *tab);
struct isl_tab *isl_tab_from_basic_map(struct isl_basic_map *bmap);
struct isl_tab *isl_tab_from_basic_set(struct isl_basic_set *bset);
struct isl_tab *isl_tab_from_recession_cone(struct isl_basic_set *bset,
int parametric);
int isl_tab_cone_is_bounded(struct isl_tab *tab);
struct isl_basic_map *isl_basic_map_update_from_tab(struct isl_basic_map *bmap,
struct isl_tab *tab);
struct isl_basic_set *isl_basic_set_update_from_tab(struct isl_basic_set *bset,
struct isl_tab *tab);
int isl_tab_detect_implicit_equalities(struct isl_tab *tab) WARN_UNUSED;
int isl_tab_detect_redundant(struct isl_tab *tab) WARN_UNUSED;
#define ISL_TAB_SAVE_DUAL (1 << 0)
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) WARN_UNUSED;
struct isl_tab *isl_tab_extend(struct isl_tab *tab, unsigned n_new) WARN_UNUSED;
int isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq) WARN_UNUSED;
int isl_tab_add_eq(struct isl_tab *tab, isl_int *eq) WARN_UNUSED;
int isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq) WARN_UNUSED;
int isl_tab_freeze_constraint(struct isl_tab *tab, int con) WARN_UNUSED;
int isl_tab_track_bmap(struct isl_tab *tab, __isl_take isl_basic_map *bmap) WARN_UNUSED;
int isl_tab_track_bset(struct isl_tab *tab, __isl_take isl_basic_set *bset) WARN_UNUSED;
__isl_keep isl_basic_set *isl_tab_peek_bset(struct isl_tab *tab);
int isl_tab_is_equality(struct isl_tab *tab, int con);
int isl_tab_is_redundant(struct isl_tab *tab, int con);
int isl_tab_sample_is_integer(struct isl_tab *tab);
struct isl_vec *isl_tab_get_sample_value(struct isl_tab *tab);
enum isl_ineq_type {
isl_ineq_error = -1,
enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq);
struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab);
int isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap) WARN_UNUSED;
struct isl_tab *isl_tab_relax(struct isl_tab *tab, int con) WARN_UNUSED;
int isl_tab_select_facet(struct isl_tab *tab, int con) WARN_UNUSED;
void isl_tab_dump(__isl_keep struct isl_tab *tab);
struct isl_map *isl_tab_basic_map_partial_lexopt(
struct isl_basic_map *bmap, struct isl_basic_set *dom,
struct isl_set **empty, int max);
/* An isl_region represents a sequence of consecutive variables.
* pos is the location (starting at 0) of the first variable in the sequence.
struct isl_region {
int pos;
int len;
__isl_give isl_vec *isl_tab_basic_set_non_trivial_lexmin(
__isl_take isl_basic_set *bset, int n_op, int n_region,
struct isl_region *region,
int (*conflict)(int con, void *user), void *user);
__isl_give isl_vec *isl_tab_basic_set_non_neg_lexmin(
__isl_take isl_basic_set *bset);
/* private */
struct isl_tab_var *isl_tab_var_from_row(struct isl_tab *tab, int i);
int isl_tab_mark_redundant(struct isl_tab *tab, int row) WARN_UNUSED;
int isl_tab_mark_empty(struct isl_tab *tab) WARN_UNUSED;
struct isl_tab *isl_tab_dup(struct isl_tab *tab);
struct isl_tab *isl_tab_product(struct isl_tab *tab1, struct isl_tab *tab2);
int isl_tab_extend_cons(struct isl_tab *tab, unsigned n_new) WARN_UNUSED;
int isl_tab_allocate_con(struct isl_tab *tab) WARN_UNUSED;
int isl_tab_extend_vars(struct isl_tab *tab, unsigned n_new) WARN_UNUSED;
int isl_tab_allocate_var(struct isl_tab *tab) WARN_UNUSED;
int isl_tab_pivot(struct isl_tab *tab, int row, int col) WARN_UNUSED;
int isl_tab_add_row(struct isl_tab *tab, isl_int *line) WARN_UNUSED;
int isl_tab_row_is_redundant(struct isl_tab *tab, int row);
int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var);
int isl_tab_sign_of_max(struct isl_tab *tab, int con);
int isl_tab_kill_col(struct isl_tab *tab, int col) WARN_UNUSED;
int isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type) WARN_UNUSED;
int isl_tab_push_var(struct isl_tab *tab,
enum isl_tab_undo_type type, struct isl_tab_var *var) WARN_UNUSED;
int isl_tab_push_basis(struct isl_tab *tab) WARN_UNUSED;
struct isl_tab *isl_tab_init_samples(struct isl_tab *tab) WARN_UNUSED;
struct isl_tab *isl_tab_add_sample(struct isl_tab *tab,
__isl_take isl_vec *sample) WARN_UNUSED;
struct isl_tab *isl_tab_drop_sample(struct isl_tab *tab, int s);
int isl_tab_save_samples(struct isl_tab *tab) WARN_UNUSED;
struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab,
struct isl_tab *tab_cone) WARN_UNUSED;
int isl_tab_push_callback(struct isl_tab *tab,
struct isl_tab_callback *callback) WARN_UNUSED;
int isl_tab_add_div(struct isl_tab *tab, __isl_keep isl_vec *div,
int (*add_ineq)(void *user, isl_int *), void *user);