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1/*2 * Copyright 2008-2009 Katholieke Universiteit Leuven3 *4 * Use of this software is governed by the MIT license5 *6 * Written by Sven Verdoolaege, K.U.Leuven, Departement7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium8 */9 10#ifndef ISL_TAB_H11#define ISL_TAB_H12 13#include "isl_int.h"14#include <isl/lp.h>15#include <isl/map.h>16#include <isl/mat.h>17#include <isl/set.h>18#include <isl_config.h>19 20struct isl_tab_var {21 int index;22 unsigned is_row : 1;23 unsigned is_nonneg : 1;24 unsigned is_zero : 1;25 unsigned is_redundant : 1;26 unsigned marked : 1;27 unsigned frozen : 1;28 unsigned negated : 1;29};30 31enum isl_tab_undo_type {32 isl_tab_undo_bottom,33 isl_tab_undo_rational,34 isl_tab_undo_empty,35 isl_tab_undo_nonneg,36 isl_tab_undo_redundant,37 isl_tab_undo_freeze,38 isl_tab_undo_zero,39 isl_tab_undo_allocate,40 isl_tab_undo_relax,41 isl_tab_undo_unrestrict,42 isl_tab_undo_bmap_ineq,43 isl_tab_undo_bmap_eq,44 isl_tab_undo_bmap_div,45 isl_tab_undo_saved_basis,46 isl_tab_undo_drop_sample,47 isl_tab_undo_saved_samples,48 isl_tab_undo_callback,49};50 51struct isl_tab_callback {52 isl_stat (*run)(struct isl_tab_callback *cb);53};54 55union isl_tab_undo_val {56 int var_index;57 int *col_var;58 int n;59 struct isl_tab_callback *callback;60};61 62struct isl_tab_undo {63 enum isl_tab_undo_type type;64 union isl_tab_undo_val u;65 struct isl_tab_undo *next;66};67 68/* The tableau maintains equality relations.69 * Each column and each row is associated to a variable or a constraint.70 * The "value" of an inequality constraint is the value of the corresponding71 * slack variable.72 * The "row_var" and "col_var" arrays map column and row indices73 * to indices in the "var" and "con" arrays. The elements of these74 * arrays maintain extra information about the variables and the constraints.75 * Each row expresses the corresponding row variable as an affine expression76 * of the column variables.77 * The first two columns in the matrix contain the common denominator of78 * the row and the numerator of the constant term.79 * If "M" is set, then the third column represents the "big parameter".80 * The third (M = 0) or fourth (M = 1) column81 * in the matrix is called column 0 with respect to the col_var array.82 * The sample value of the tableau is the value that assigns zero83 * to all the column variables and the constant term of each affine84 * expression to the corresponding row variable.85 * The operations on the tableau maintain the property that the sample86 * value satisfies the non-negativity constraints (usually on the slack87 * variables).88 *89 * The big parameter represents an arbitrarily big (and divisible)90 * positive number. If present, then the sign of a row is determined91 * lexicographically, with the sign of the big parameter coefficient92 * considered first. The big parameter is only used while93 * solving PILP problems.94 *95 * The first n_dead column variables have their values fixed to zero.96 * The corresponding tab_vars are flagged "is_zero".97 * Some of the rows that have have zero coefficients in all but98 * the dead columns are also flagged "is_zero".99 *100 * The first n_redundant rows correspond to inequality constraints101 * that are always satisfied for any value satisfying the non-redundant102 * rows. The corresponding tab_vars are flagged "is_redundant".103 * A row variable that is flagged "is_zero" is also flagged "is_redundant"104 * since the constraint has been reduced to 0 = 0 and is therefore always105 * satisfied.106 *107 * There are "n_var" variables in total. The first "n_param" of these108 * are called parameters and the last "n_div" of these are called divs.109 * The basic tableau operations makes no distinction between different110 * kinds of variables. These special variables are only used while111 * solving PILP problems.112 *113 * Dead columns and redundant rows are detected on the fly.114 * However, the basic operations do not ensure that all dead columns115 * or all redundant rows are detected.116 * isl_tab_detect_implicit_equalities and isl_tab_detect_redundant can be used117 * to perform an exhaustive search for dead columns and redundant rows.118 *119 * The samples matrix contains "n_sample" integer points that have at some120 * point been elements satisfying the tableau. The first "n_outside"121 * of them no longer satisfy the tableau. They are kept because they122 * can be reinstated during rollback when the constraint that cut them123 * out is removed. These samples are only maintained for the context124 * tableau while solving PILP problems.125 *126 * If "preserve" is set, then we want to keep all constraints in the127 * tableau, even if they turn out to be redundant.128 */129enum isl_tab_row_sign {130 isl_tab_row_unknown = 0,131 isl_tab_row_pos,132 isl_tab_row_neg,133 isl_tab_row_any,134};135struct isl_tab {136 struct isl_mat *mat;137 138 unsigned n_row;139 unsigned n_col;140 unsigned n_dead;141 unsigned n_redundant;142 143 unsigned n_var;144 unsigned n_param;145 unsigned n_div;146 unsigned max_var;147 unsigned n_con;148 unsigned n_eq;149 unsigned max_con;150 struct isl_tab_var *var;151 struct isl_tab_var *con;152 int *row_var; /* v >= 0 -> var v; v < 0 -> con ~v */153 int *col_var; /* v >= 0 -> var v; v < 0 -> con ~v */154 enum isl_tab_row_sign *row_sign;155 156 struct isl_tab_undo bottom;157 struct isl_tab_undo *top;158 159 struct isl_vec *dual;160 struct isl_basic_map *bmap;161 162 unsigned n_sample;163 unsigned n_outside;164 int *sample_index;165 struct isl_mat *samples;166 167 int n_zero;168 int n_unbounded;169 struct isl_mat *basis;170 171 int (*conflict)(int con, void *user);172 void *conflict_user;173 174 unsigned strict_redundant : 1;175 unsigned need_undo : 1;176 unsigned preserve : 1;177 unsigned rational : 1;178 unsigned empty : 1;179 unsigned in_undo : 1;180 unsigned M : 1;181 unsigned cone : 1;182};183 184struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx,185 unsigned n_row, unsigned n_var, unsigned M);186void isl_tab_free(struct isl_tab *tab);187 188isl_ctx *isl_tab_get_ctx(struct isl_tab *tab);189 190__isl_give struct isl_tab *isl_tab_from_basic_map(191 __isl_keep isl_basic_map *bmap, int track);192__isl_give struct isl_tab *isl_tab_from_basic_set(193 __isl_keep isl_basic_set *bset, int track);194struct isl_tab *isl_tab_from_recession_cone(__isl_keep isl_basic_set *bset,195 int parametric);196isl_bool isl_tab_cone_is_bounded(struct isl_tab *tab);197__isl_give isl_basic_map *isl_basic_map_update_from_tab(198 __isl_take isl_basic_map *bmap, struct isl_tab *tab);199__isl_give isl_basic_set *isl_basic_set_update_from_tab(200 __isl_take isl_basic_set *bset, struct isl_tab *tab);201int isl_tab_detect_implicit_equalities(struct isl_tab *tab) WARN_UNUSED;202__isl_give isl_basic_map *isl_tab_make_equalities_explicit(struct isl_tab *tab,203 __isl_take isl_basic_map *bmap);204int isl_tab_detect_redundant(struct isl_tab *tab) WARN_UNUSED;205isl_stat isl_tab_restore_redundant(struct isl_tab *tab);206#define ISL_TAB_SAVE_DUAL (1 << 0)207enum isl_lp_result isl_tab_min(struct isl_tab *tab,208 isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom,209 unsigned flags) WARN_UNUSED;210 211isl_stat isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq) WARN_UNUSED;212isl_stat isl_tab_add_eq(struct isl_tab *tab, isl_int *eq) WARN_UNUSED;213int isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq) WARN_UNUSED;214 215int isl_tab_freeze_constraint(struct isl_tab *tab, int con) WARN_UNUSED;216 217isl_stat isl_tab_track_bmap(struct isl_tab *tab, __isl_take isl_basic_map *bmap)218 WARN_UNUSED;219isl_stat isl_tab_track_bset(struct isl_tab *tab, __isl_take isl_basic_set *bset)220 WARN_UNUSED;221__isl_keep isl_basic_set *isl_tab_peek_bset(struct isl_tab *tab);222 223int isl_tab_is_equality(struct isl_tab *tab, int con);224int isl_tab_is_redundant(struct isl_tab *tab, int con);225 226int isl_tab_sample_is_integer(struct isl_tab *tab);227__isl_give isl_vec *isl_tab_get_sample_value(struct isl_tab *tab);228 229enum isl_ineq_type {230 isl_ineq_error = -1,231 isl_ineq_redundant,232 isl_ineq_separate,233 isl_ineq_cut,234 isl_ineq_adj_eq,235 isl_ineq_adj_ineq,236};237 238enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq);239 240struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab);241isl_stat isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap) WARN_UNUSED;242isl_bool isl_tab_need_undo(struct isl_tab *tab);243void isl_tab_clear_undo(struct isl_tab *tab);244 245int isl_tab_relax(struct isl_tab *tab, int con) WARN_UNUSED;246int isl_tab_select_facet(struct isl_tab *tab, int con) WARN_UNUSED;247int isl_tab_unrestrict(struct isl_tab *tab, int con) WARN_UNUSED;248 249void isl_tab_dump(__isl_keep struct isl_tab *tab);250 251/* Compute maximum instead of minimum. */252#define ISL_OPT_MAX (1 << 0)253/* Compute full instead of partial optimum; also, domain argument is NULL. */254#define ISL_OPT_FULL (1 << 1)255/* Result should be free of (unknown) quantified variables. */256#define ISL_OPT_QE (1 << 2)257__isl_give isl_map *isl_tab_basic_map_partial_lexopt(258 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,259 __isl_give isl_set **empty, unsigned flags);260__isl_give isl_pw_multi_aff *isl_tab_basic_map_partial_lexopt_pw_multi_aff(261 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,262 __isl_give isl_set **empty, unsigned flags);263 264/* An isl_trivial_region represents a non-triviality region.265 * The region is trivial if applying "trivial" to a given sequence266 * of variables results in a zero vector.267 * pos is the location (starting at 0) of the first variable in the sequence.268 */269struct isl_trivial_region {270 int pos;271 isl_mat *trivial;272};273 274__isl_give isl_vec *isl_tab_basic_set_non_trivial_lexmin(275 __isl_take isl_basic_set *bset, int n_op, int n_region,276 struct isl_trivial_region *region,277 int (*conflict)(int con, void *user), void *user);278 279struct isl_tab_lexmin;280typedef struct isl_tab_lexmin isl_tab_lexmin;281 282__isl_give isl_tab_lexmin *isl_tab_lexmin_from_basic_set(283 __isl_take isl_basic_set *bset);284int isl_tab_lexmin_dim(__isl_keep isl_tab_lexmin *tl);285__isl_give isl_tab_lexmin *isl_tab_lexmin_add_eq(__isl_take isl_tab_lexmin *tl,286 isl_int *eq);287__isl_give isl_tab_lexmin *isl_tab_lexmin_cut_to_integer(288 __isl_take isl_tab_lexmin *tl);289__isl_give isl_vec *isl_tab_lexmin_get_solution(__isl_keep isl_tab_lexmin *tl);290__isl_null isl_tab_lexmin *isl_tab_lexmin_free(__isl_take isl_tab_lexmin *tl);291 292/* private */293 294struct isl_tab_var *isl_tab_var_from_row(struct isl_tab *tab, int i);295int isl_tab_mark_redundant(struct isl_tab *tab, int row) WARN_UNUSED;296int isl_tab_mark_rational(struct isl_tab *tab) WARN_UNUSED;297isl_stat isl_tab_mark_empty(struct isl_tab *tab) WARN_UNUSED;298struct isl_tab *isl_tab_dup(struct isl_tab *tab);299struct isl_tab *isl_tab_product(struct isl_tab *tab1, struct isl_tab *tab2);300int isl_tab_extend_cons(struct isl_tab *tab, unsigned n_new) WARN_UNUSED;301int isl_tab_allocate_con(struct isl_tab *tab) WARN_UNUSED;302int isl_tab_extend_vars(struct isl_tab *tab, unsigned n_new) WARN_UNUSED;303int isl_tab_insert_var(struct isl_tab *tab, int pos) WARN_UNUSED;304int isl_tab_pivot(struct isl_tab *tab, int row, int col) WARN_UNUSED;305int isl_tab_add_row(struct isl_tab *tab, isl_int *line) WARN_UNUSED;306int isl_tab_row_is_redundant(struct isl_tab *tab, int row);307int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var);308int isl_tab_sign_of_max(struct isl_tab *tab, int con);309int isl_tab_kill_col(struct isl_tab *tab, int col) WARN_UNUSED;310 311isl_stat isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type)312 WARN_UNUSED;313isl_stat isl_tab_push_var(struct isl_tab *tab,314 enum isl_tab_undo_type type, struct isl_tab_var *var) WARN_UNUSED;315isl_stat isl_tab_push_basis(struct isl_tab *tab) WARN_UNUSED;316 317struct isl_tab *isl_tab_init_samples(struct isl_tab *tab) WARN_UNUSED;318int isl_tab_add_sample(struct isl_tab *tab,319 __isl_take isl_vec *sample) WARN_UNUSED;320struct isl_tab *isl_tab_drop_sample(struct isl_tab *tab, int s);321isl_stat isl_tab_save_samples(struct isl_tab *tab) WARN_UNUSED;322 323struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab,324 struct isl_tab *tab_cone) WARN_UNUSED;325isl_bool isl_tab_is_constant(struct isl_tab *tab, int var, isl_int *value);326isl_stat isl_tab_detect_constants(struct isl_tab *tab);327 328isl_stat isl_tab_push_callback(struct isl_tab *tab,329 struct isl_tab_callback *callback) WARN_UNUSED;330 331int isl_tab_insert_div(struct isl_tab *tab, int pos, __isl_keep isl_vec *div,332 isl_stat (*add_ineq)(void *user, isl_int *), void *user);333int isl_tab_add_div(struct isl_tab *tab, __isl_keep isl_vec *div);334 335int isl_tab_shift_var(struct isl_tab *tab, int pos, isl_int shift) WARN_UNUSED;336 337isl_stat isl_tab_swap_constraints(struct isl_tab *tab, int con1, int con2);338 339#endif340