/*

 * Copyright 2008-2009 Katholieke Universiteit Leuven

 *

 * 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

 */

#ifndef ISL_TAB_H

#define ISL_TAB_H

#include <isl/lp.h>

#include <isl/map.h>

#include <isl/mat.h>

#include <isl/set.h>

#include <isl_config.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 {

  isl_tab_undo_bottom,

  isl_tab_undo_rational,

  isl_tab_undo_empty,

  isl_tab_undo_nonneg,

  isl_tab_undo_redundant,

  isl_tab_undo_freeze,

  isl_tab_undo_zero,

  isl_tab_undo_allocate,

  isl_tab_undo_relax,

  isl_tab_undo_unrestrict,

  isl_tab_undo_bmap_ineq,

  isl_tab_undo_bmap_eq,

  isl_tab_undo_bmap_div,

  isl_tab_undo_saved_basis,

  isl_tab_undo_drop_sample,

  isl_tab_undo_saved_samples,

  isl_tab_undo_callback,

};

struct isl_tab_callback {

  isl_stat (*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 an 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.

 *

 * If "preserve" is set, then we want to keep all constraints in the

 * tableau, even if they turn out to be redundant.

 */

enum isl_tab_row_sign {

  isl_tab_row_unknown = 0,

  isl_tab_row_pos,

  isl_tab_row_neg,

  isl_tab_row_any,

};

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 preserve : 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);

isl_ctx *isl_tab_get_ctx(struct isl_tab *tab);

__isl_give struct isl_tab *isl_tab_from_basic_map(

  __isl_keep isl_basic_map *bmap, int track);

__isl_give struct isl_tab *isl_tab_from_basic_set(

  __isl_keep isl_basic_set *bset, int track);

struct isl_tab *isl_tab_from_recession_cone(struct isl_basic_set *bset,

  int parametric);

isl_bool 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;

__isl_give isl_basic_map *isl_tab_make_equalities_explicit(struct isl_tab *tab,

  __isl_take isl_basic_map *bmap);

int isl_tab_detect_redundant(struct isl_tab *tab) WARN_UNUSED;

isl_stat isl_tab_restore_redundant(struct isl_tab *tab);

#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;

isl_stat 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;

isl_stat isl_tab_track_bmap(struct isl_tab *tab, __isl_take isl_basic_map *bmap)

  WARN_UNUSED;

isl_stat 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,

  isl_ineq_redundant,

  isl_ineq_separate,

  isl_ineq_cut,

  isl_ineq_adj_eq,

  isl_ineq_adj_ineq,

};

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;

isl_bool isl_tab_need_undo(struct isl_tab *tab);

void isl_tab_clear_undo(struct isl_tab *tab);

int isl_tab_relax(struct isl_tab *tab, int con) WARN_UNUSED;

int isl_tab_select_facet(struct isl_tab *tab, int con) WARN_UNUSED;

int isl_tab_unrestrict(struct isl_tab *tab, int con) WARN_UNUSED;

void isl_tab_dump(__isl_keep struct isl_tab *tab);

/* Compute maximum instead of minimum. */

#define ISL_OPT_MAX   (1 << 0)

/* Compute full instead of partial optimum; also, domain argument is NULL. */

#define ISL_OPT_FULL    (1 << 1)

/* Result should be free of (unknown) quantified variables. */

#define ISL_OPT_QE    (1 << 2)

__isl_give isl_map *isl_tab_basic_map_partial_lexopt(

  __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,

  __isl_give isl_set **empty, unsigned flags);

__isl_give isl_pw_multi_aff *isl_tab_basic_map_partial_lexopt_pw_multi_aff(

  __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,

  __isl_give isl_set **empty, unsigned flags);

/* An isl_trivial_region represents a non-triviality region.

 * The region is trivial if applying "trivial" to a given sequence

 * of variables results in a zero vector.

 * pos is the location (starting at 0) of the first variable in the sequence.

 */

struct isl_trivial_region {

  int pos;

  isl_mat *trivial;

};

__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_trivial_region *region,

  int (*conflict)(int con, void *user), void *user);

struct isl_tab_lexmin;

typedef struct isl_tab_lexmin isl_tab_lexmin;

__isl_give isl_tab_lexmin *isl_tab_lexmin_from_basic_set(

  __isl_take isl_basic_set *bset);

int isl_tab_lexmin_dim(__isl_keep isl_tab_lexmin *tl);

__isl_give isl_tab_lexmin *isl_tab_lexmin_add_eq(__isl_take isl_tab_lexmin *tl,

  isl_int *eq);

__isl_give isl_tab_lexmin *isl_tab_lexmin_cut_to_integer(

  __isl_take isl_tab_lexmin *tl);

__isl_give isl_vec *isl_tab_lexmin_get_solution(__isl_keep isl_tab_lexmin *tl);

__isl_null isl_tab_lexmin *isl_tab_lexmin_free(__isl_take isl_tab_lexmin *tl);

/* 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_rational(struct isl_tab *tab) WARN_UNUSED;

isl_stat 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_insert_var(struct isl_tab *tab, int pos) 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;

isl_stat isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type)

  WARN_UNUSED;

isl_stat isl_tab_push_var(struct isl_tab *tab,

  enum isl_tab_undo_type type, struct isl_tab_var *var) WARN_UNUSED;

isl_stat isl_tab_push_basis(struct isl_tab *tab) WARN_UNUSED;

struct isl_tab *isl_tab_init_samples(struct isl_tab *tab) WARN_UNUSED;

int 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);

isl_stat 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;

isl_bool isl_tab_is_constant(struct isl_tab *tab, int var, isl_int *value);

isl_stat isl_tab_detect_constants(struct isl_tab *tab);

isl_stat isl_tab_push_callback(struct isl_tab *tab,

  struct isl_tab_callback *callback) WARN_UNUSED;

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 isl_tab_add_div(struct isl_tab *tab, __isl_keep isl_vec *div);

int isl_tab_shift_var(struct isl_tab *tab, int pos, isl_int shift) WARN_UNUSED;

#endif