z3-z3-4.13.0.src.math.lp.nla_core.h Maven / Gradle / Ivy
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/*++
Copyright (c) 2017 Microsoft Corporation
Module Name:
nla_core.h
Author:
Lev Nachmanson (levnach)
Nikolaj Bjorner (nbjorner)
--*/
#pragma once
#include "math/lp/factorization.h"
#include "math/lp/lp_types.h"
#include "math/lp/var_eqs.h"
#include "math/lp/nla_tangent_lemmas.h"
#include "math/lp/nla_basics_lemmas.h"
#include "math/lp/nla_order_lemmas.h"
#include "math/lp/nla_monotone_lemmas.h"
#include "math/lp/nla_grobner.h"
#include "math/lp/nla_powers.h"
#include "math/lp/nla_divisions.h"
#include "math/lp/emonics.h"
#include "math/lp/nex.h"
#include "math/lp/horner.h"
#include "math/lp/monomial_bounds.h"
#include "math/lp/nla_intervals.h"
#include "nlsat/nlsat_solver.h"
#include "smt/params/smt_params_helper.hpp"
namespace nra {
class solver;
}
namespace nla {
template
bool try_insert(const A& elem, B& collection) {
auto it = collection.find(elem);
if (it != collection.end())
return false;
collection.insert(elem);
return true;
}
class core {
friend struct common;
friend class new_lemma;
friend class grobner;
friend class order;
friend struct basics;
friend struct tangents;
friend class monotone;
friend class powers;
friend class intervals;
friend class horner;
friend class solver;
friend class monomial_bounds;
friend class nra::solver;
friend class divisions;
unsigned m_nlsat_delay = 0;
unsigned m_nlsat_delay_bound = 0;
bool should_run_bounded_nlsat();
lbool bounded_nlsat();
var_eqs m_evars;
lp::lar_solver& lra;
reslimit& m_reslim;
smt_params_helper m_params;
std::function m_relevant;
vector m_lemmas;
vector m_literals;
vector m_equalities;
vector m_fixed_equalities;
indexed_uint_set m_to_refine;
indexed_uint_set m_monics_with_changed_bounds;
tangents m_tangents;
basics m_basics;
order m_order;
monotone m_monotone;
powers m_powers;
divisions m_divisions;
intervals m_intervals;
monomial_bounds m_monomial_bounds;
unsigned m_conflicts;
bool m_check_feasible = false;
horner m_horner;
grobner m_grobner;
emonics m_emons;
svector m_add_buffer;
mutable indexed_uint_set m_active_var_set;
reslimit m_nra_lim;
bool m_use_nra_model = false;
nra::solver m_nra;
bool m_cautious_patching = true;
lpvar m_patched_var = 0;
monic const* m_patched_monic = nullptr;
void check_weighted(unsigned sz, std::pair>* checks);
void add_bounds();
public:
// constructor
core(lp::lar_solver& s, params_ref const& p, reslimit&);
const auto& monics_with_changed_bounds() const { return m_monics_with_changed_bounds; }
void insert_to_refine(lpvar j);
void erase_from_to_refine(lpvar j);
const indexed_uint_set& active_var_set () const { return m_active_var_set;}
bool active_var_set_contains(unsigned j) const { return m_active_var_set.contains(j); }
void insert_to_active_var_set(unsigned j) const {
m_active_var_set.insert(j);
}
void clear_active_var_set() const { m_active_var_set.reset(); }
unsigned get_var_weight(lpvar) const;
reslimit& reslim() { return m_reslim; }
emonics& emons() { return m_emons; }
const emonics& emons() const { return m_emons; }
monic& emon(unsigned i) { return m_emons[i]; }
monic const& emon(unsigned i) const { return m_emons[i]; }
bool has_relevant_monomial() const;
bool compare_holds(const rational& ls, llc cmp, const rational& rs) const;
rational value(const lp::lar_term& r) const;
bool ineq_holds(const ineq& n) const;
bool lemma_holds(const lemma& l) const;
bool is_monic_var(lpvar j) const { return m_emons.is_monic_var(j); }
const rational& val(lpvar j) const { return lra.get_column_value(j).x; }
const rational& var_val(const monic& m) const { return lra.get_column_value(m.var()).x; }
rational mul_val(const monic& m) const {
rational r(1);
for (lpvar v : m.vars()) r *= lra.get_column_value(v).x;
return r;
}
bool canonize_sign_is_correct(const monic& m) const;
lpvar var(monic const& sv) const { return sv.var(); }
rational val_rooted(const monic& m) const { return m.rsign()*val(m.var()); }
rational val(const factor& f) const { return f.rat_sign() * (f.is_var()? val(f.var()) : var_val(m_emons[f.var()])); }
rational val(const factorization&) const;
lpvar var(const factor& f) const { return f.var(); }
smt_params_helper const & params() const { return m_params; }
// returns true if the combination of the Horner's schema and Grobner Basis should be called
bool need_run_horner() const {
return params().arith_nl_horner() && lp_settings().stats().m_nla_calls % params().arith_nl_horner_frequency() == 0;
}
bool need_run_grobner() const {
return params().arith_nl_grobner();
}
void set_active_vars_weights(nex_creator&);
std::unordered_set get_vars_of_expr_with_opening_terms(const nex* e);
void incremental_linearization(bool);
svector sorted_rvars(const factor& f) const;
bool done() const;
// the value of the factor is equal to the value of the variable multiplied
// by the canonize_sign
bool canonize_sign(const factor& f) const;
bool canonize_sign(const factorization& f) const;
bool canonize_sign(lpvar j) const;
// the value of the rooted monomias is equal to the value of the m.var() variable multiplied
// by the canonize_sign
bool canonize_sign(const monic& m) const;
void deregister_monic_from_monicomials (const monic & m, unsigned i);
void deregister_monic_from_tables(const monic & m, unsigned i);
void add_monic(lpvar v, unsigned sz, lpvar const* vs);
void add_idivision(lpvar q, lpvar x, lpvar y) { m_divisions.add_idivision(q, x, y); }
void add_rdivision(lpvar q, lpvar x, lpvar y) { m_divisions.add_rdivision(q, x, y); }
void add_bounded_division(lpvar q, lpvar x, lpvar y) { m_divisions.add_bounded_division(q, x, y); }
void set_relevant(std::function& is_relevant) { m_relevant = is_relevant; }
bool is_relevant(lpvar v) const { return !m_relevant || m_relevant(v); }
void push();
void pop(unsigned n);
trail_stack& trail() { return m_emons.get_trail_stack(); }
rational mon_value_by_vars(unsigned i) const;
rational product_value(const monic & m) const;
// return true iff the monic value is equal to the product of the values of the factors
bool check_monic(const monic& m) const;
std::ostream & print_ineq(const ineq & in, std::ostream & out) const;
std::ostream & print_var(lpvar j, std::ostream & out) const;
std::ostream & print_monics(std::ostream & out) const;
std::ostream & print_ineqs(const lemma& l, std::ostream & out) const;
std::ostream & print_factorization(const factorization& f, std::ostream& out) const;
template
std::ostream& print_product(const T & m, std::ostream& out) const;
template
std::string product_indices_str(const T & m) const;
std::string var_str(lpvar) const;
std::ostream & print_factor(const factor& f, std::ostream& out) const;
std::ostream & print_factor_with_vars(const factor& f, std::ostream& out) const;
std::ostream & print_factor_with_vars(lpvar j, std::ostream& out) const { return print_var(j, out); }
std::ostream& print_monic(const monic& m, std::ostream& out) const;
std::ostream& print_bfc(const factorization& m, std::ostream& out) const;
std::ostream& print_monic_with_vars(unsigned i, std::ostream& out) const;
template
std::ostream& print_product_with_vars(const T& m, std::ostream& out) const;
std::ostream& print_monic_with_vars(const monic& m, std::ostream& out) const;
std::ostream& print_explanation(const lp::explanation& exp, std::ostream& out) const;
std::ostream& diagnose_pdd_miss(std::ostream& out);
template
void trace_print_rms(const T& p, std::ostream& out);
void trace_print_monic_and_factorization(const monic& rm, const factorization& f, std::ostream& out) const;
void print_monic_stats(const monic& m, std::ostream& out);
void print_stats(std::ostream& out);
pp_var pp(lpvar j) const { return pp_var(*this, j); }
pp_fac pp(factor const& f) const { return pp_fac(*this, f); }
pp_factorization pp(factorization const& f) const { return pp_factorization(*this, f); }
std::ostream& print_lemma(const lemma& l, std::ostream& out) const;
void trace_print_ol(const monic& ac,
const factor& a,
const factor& c,
const monic& bc,
const factor& b,
std::ostream& out);
void mk_ineq_no_expl_check(new_lemma& lemma, lp::lar_term& t, llc cmp, const rational& rs);
void maybe_add_a_factor(lpvar i,
const factor& c,
std::unordered_set& found_vars,
std::unordered_set& found_rm,
vector & r) const;
llc apply_minus(llc cmp);
void fill_explanation_and_lemma_sign(new_lemma& lemma, const monic& a, const monic & b, rational const& sign);
svector reduce_monic_to_rooted(const svector & vars, rational & sign) const;
monic_coeff canonize_monic(monic const& m) const;
int vars_sign(const svector& v);
bool has_upper_bound(lpvar j) const;
bool has_lower_bound(lpvar j) const;
bool no_bounds(lpvar j) const {
return !has_upper_bound(j) && !has_lower_bound(j);
}
const rational& get_upper_bound(unsigned j) const;
const rational& get_lower_bound(unsigned j) const;
bool has_lower_bound(lp::lpvar var, u_dependency*& ci, lp::mpq& value, bool& is_strict) const {
return lra.has_lower_bound(var, ci, value, is_strict);
}
bool has_upper_bound(lp::lpvar var, u_dependency*& ci, lp::mpq& value, bool& is_strict) const {
return lra.has_upper_bound(var, ci, value, is_strict);
}
bool zero_is_an_inner_point_of_bounds(lpvar j) const;
bool var_is_int(lpvar j) const { return lra.column_is_int(j); }
int rat_sign(const monic& m) const;
inline int rat_sign(lpvar j) const { return nla::rat_sign(val(j)); }
bool sign_contradiction(const monic& m) const;
bool var_is_fixed_to_zero(lpvar j) const;
bool var_is_fixed_to_val(lpvar j, const rational& v) const;
bool var_is_fixed(lpvar j) const;
bool var_is_free(lpvar j) const;
bool find_canonical_monic_of_vars(const svector& vars, lpvar & i) const;
bool is_canonical_monic(lpvar) const;
bool elists_are_consistent(bool check_in_model) const;
bool elist_is_consistent(const std::unordered_set&) const;
bool var_has_positive_lower_bound(lpvar j) const;
bool var_has_negative_upper_bound(lpvar j) const;
bool var_is_separated_from_zero(lpvar j) const;
bool vars_are_equiv(lpvar a, lpvar b) const;
bool explain_ineq(new_lemma& lemma, const lp::lar_term& t, llc cmp, const rational& rs);
bool explain_upper_bound(const lp::lar_term& t, const rational& rs, lp::explanation& e) const;
bool explain_lower_bound(const lp::lar_term& t, const rational& rs, lp::explanation& e) const;
bool explain_coeff_lower_bound(const lp::lar_term::ival& p, rational& bound, lp::explanation& e) const;
bool explain_coeff_upper_bound(const lp::lar_term::ival& p, rational& bound, lp::explanation& e) const;
bool explain_by_equiv(const lp::lar_term& t, lp::explanation& e) const;
bool has_zero_factor(const factorization& factorization) const;
template
bool mon_has_zero(const T& product) const;
lp::lp_settings& lp_settings();
const lp::lp_settings& lp_settings() const;
unsigned random();
// we look for octagon constraints here, with a left part +-x +- y
void collect_equivs();
bool is_octagon_term(const lp::lar_term& t, bool & sign, lpvar& i, lpvar &j) const;
void add_equivalence_maybe(const lp::lar_term* t, u_dependency* c0, u_dependency* c1);
void init_vars_equivalence();
bool vars_table_is_ok() const;
bool rm_table_is_ok() const;
bool tables_are_ok() const;
bool var_is_a_root(lpvar j) const;
template
bool vars_are_roots(const T& v) const;
void register_monic_in_tables(unsigned i_mon);
void register_monics_in_tables();
void clear();
void init_search();
void init_to_refine();
bool divide(const monic& bc, const factor& c, factor & b) const;
std::unordered_set collect_vars(const lemma& l) const;
bool rm_check(const monic&) const;
std::unordered_map get_rm_by_arity();
void negate_relation(new_lemma& lemma, unsigned j, const rational& a);
void negate_factor_equality(new_lemma& lemma, const factor& c, const factor& d);
void negate_factor_relation(new_lemma& lemma, const rational& a_sign, const factor& a, const rational& b_sign, const factor& b);
bool find_bfc_to_refine_on_monic(const monic&, factorization & bf);
bool find_bfc_to_refine(const monic* & m, factorization& bf);
bool conflict_found() const;
lbool check();
lbool check_power(lpvar r, lpvar x, lpvar y);
void check_bounded_divisions();
bool no_lemmas_hold() const;
void propagate();
void simplify();
lbool test_check();
lpvar map_to_root(lpvar) const;
std::ostream& print_terms(std::ostream&) const;
std::ostream& print_term(const lp::lar_term&, std::ostream&) const;
template
std::ostream& print_row(const T& row, std::ostream& out) const {
vector> v;
for (auto p : row) {
v.push_back(std::make_pair(p.coeff(), p.var()));
}
return lp::print_linear_combination_customized(v, [this](lpvar j) { return var_str(j); }, out);
}
bool influences_nl_var(lpvar) const;
bool is_nl_var(lpvar) const;
bool is_used_in_monic(lpvar) const;
void patch_monomials();
void patch_monomials_on_to_refine();
void patch_monomial(lpvar);
bool var_breaks_correct_monic(lpvar) const;
bool var_breaks_correct_monic_as_factor(lpvar, const monic&) const;
void update_to_refine_of_var(lpvar j);
bool try_to_patch(const rational&);
bool to_refine_is_correct() const;
bool is_patch_blocked(lpvar u, const lp::impq&) const;
bool has_big_num(const monic&) const;
bool var_is_big(lpvar) const;
bool has_real(const factorization&) const;
bool has_real(const monic& m) const;
void set_use_nra_model(bool m);
bool use_nra_model() const { return m_use_nra_model; }
vector const& lemmas() const { return m_lemmas; }
vector const& literals() const { return m_literals; }
vector const& equalities() const { return m_equalities; }
vector const& fixed_equalities() const { return m_fixed_equalities; }
bool should_check_feasible() const { return m_check_feasible; }
void add_fixed_equality(lp::lpvar v, rational const& k, lp::explanation const& e) { m_fixed_equalities.push_back({v, k, e}); }
void add_equality(lp::lpvar i, lp::lpvar j, lp::explanation const& e) { m_equalities.push_back({i, j, e}); }
}; // end of core
struct pp_mon {
core const& c;
monic const& m;
pp_mon(core const& c, monic const& m): c(c), m(m) {}
pp_mon(core const& c, lpvar v): c(c), m(c.emons()[v]) {}
};
struct pp_mon_with_vars {
core const& c;
monic const& m;
pp_mon_with_vars(core const& c, monic const& m): c(c), m(m) {}
pp_mon_with_vars(core const& c, lpvar v): c(c), m(c.emons()[v]) {}
};
inline std::ostream& operator<<(std::ostream& out, pp_mon const& p) { return p.c.print_monic(p.m, out); }
inline std::ostream& operator<<(std::ostream& out, pp_mon_with_vars const& p) { return p.c.print_monic_with_vars(p.m, out); }
inline std::ostream& operator<<(std::ostream& out, pp_fac const& f) { return f.c.print_factor(f.f, out); }
inline std::ostream& operator<<(std::ostream& out, pp_factorization const& f) { return f.c.print_factorization(f.f, out); }
inline std::ostream& operator<<(std::ostream& out, pp_var const& v) { return v.c.print_var(v.v, out); }
} // end of namespace nla