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initial outline of exponentiation

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2023-01-23 17:38:34 -08:00
parent 3032c9315d
commit 2ae476416c
4 changed files with 207 additions and 116 deletions
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2
src/math/lp/nla_core.h
View file

@ -465,6 +465,8 @@ public:
lbool check(vector<lemma>& l_vec);
void set_lemma_vec(vector<lemma>& l_vec) { m_lemma_vec = &l_vec; }
bool no_lemmas_hold() const;
lbool test_check(vector<lemma>& l);

207
src/math/lp/nla_solver.cpp
View file

@ -13,63 +13,168 @@
#include "math/lp/factorization.h"
#include "math/lp/nla_solver.h"
#include "math/lp/nla_core.h"
#include "math/polynomial/algebraic_numbers.h"
namespace nla {
nla_settings& solver::settings() { return m_core->m_nla_settings; }
nla_settings& solver::settings() { return m_core->m_nla_settings; }
void solver::add_monic(lpvar v, unsigned sz, lpvar const* vs) {
m_core->add_monic(v, sz, vs);
}
bool solver::is_monic_var(lpvar v) const {
return m_core->is_monic_var(v);
}
bool solver::need_check() { return true; }
lbool solver::check(vector<lemma>& l) {
return m_core->check(l);
}
void solver::push(){
m_core->push();
}
void solver::pop(unsigned n) {
m_core->pop(n);
}
solver::solver(lp::lar_solver& s, reslimit& limit):
m_core(alloc(core, s, limit)) {
}
bool solver::influences_nl_var(lpvar j) const {
return m_core->influences_nl_var(j);
}
solver::~solver() {
dealloc(m_core);
}
std::ostream& solver::display(std::ostream& out) const {
m_core->print_monics(out);
if( use_nra_model()) {
m_core->m_nra.display(out);
void solver::add_monic(lpvar v, unsigned sz, lpvar const* vs) {
m_core->add_monic(v, sz, vs);
}
return out;
}
bool solver::is_monic_var(lpvar v) const {
return m_core->is_monic_var(v);
}
bool solver::need_check() { return true; }
lbool solver::check(vector<lemma>& l) {
return m_core->check(l);
}
void solver::push(){
m_core->push();
}
void solver::pop(unsigned n) {
m_core->pop(n);
}
solver::solver(lp::lar_solver& s, reslimit& limit):
m_core(alloc(core, s, limit)) {
}
bool solver::influences_nl_var(lpvar j) const {
return m_core->influences_nl_var(j);
}
solver::~solver() {
dealloc(m_core);
}
std::ostream& solver::display(std::ostream& out) const {
m_core->print_monics(out);
if (use_nra_model())
m_core->m_nra.display(out);
return out;
}
bool solver::use_nra_model() const { return m_core->use_nra_model(); }
bool solver::use_nra_model() const { return m_core->use_nra_model(); }
core& solver::get_core() { return *m_core; }
nlsat::anum_manager& solver::am() { return m_core->m_nra.am(); }
nlsat::anum const& solver::am_value(lp::var_index v) const {
SASSERT(use_nra_model());
return m_core->m_nra.value(v);
}
core& solver::get_core() { return *m_core; }
void solver::collect_statistics(::statistics & st) {
m_core->collect_statistics(st);
}
nlsat::anum_manager& solver::am() { return m_core->m_nra.am(); }
nlsat::anum const& solver::am_value(lp::var_index v) const {
SASSERT(use_nra_model());
return m_core->m_nra.value(v);
}
void solver::collect_statistics(::statistics & st) {
m_core->collect_statistics(st);
}
// ensure r = x^y, add abstraction/refinement lemmas
lbool solver::check_power(lpvar r, lpvar x, lpvar y, vector<lemma>& lemmas) {
if (x == null_lpvar || y == null_lpvar || r == null_lpvar)
return l_undef;
if (use_nra_model())
return l_undef;
auto xval = m_core->val(x);
auto yval = m_core->val(y);
auto rval = m_core->val(r);
core& c = get_core();
c.set_lemma_vec(lemmas);
lemmas.reset();
// x >= x0 > 0, y >= y0 > 0 => r >= x0^y0
// x >= x0 > 0, y <= y0 => r <= x0^y0
// x != 0, y = 0 => r = 1
// x = 0, y != 0 => r = 0
//
// for x fixed, it is exponentiation
// => use tangent lemmas and error tolerance.
if (xval > 0 && yval.is_unsigned()) {
auto r2val = power(xval, yval.get_unsigned());
if (rval == r2val)
return l_true;
if (xval != 0 && yval == 0) {
new_lemma lemma(c, "x != 0 => x^0 = 1");
lemma |= ineq(x, llc::EQ, rational::zero());
lemma |= ineq(y, llc::NE, rational::zero());
lemma |= ineq(r, llc::EQ, rational::one());
return l_false;
}
if (xval == 0 && yval > 0) {
new_lemma lemma(c, "y != 0 => 0^y = 0");
lemma |= ineq(x, llc::NE, rational::zero());
lemma |= ineq(y, llc::EQ, rational::zero());
lemma |= ineq(r, llc::EQ, rational::zero());
return l_false;
}
if (xval > 0 && r2val < rval) {
SASSERT(yval > 0);
new_lemma lemma(c, "x >= x0 > 0, y >= y0 > 0 => r >= x0^y0");
lemma |= ineq(x, llc::LT, xval);
lemma |= ineq(y, llc::LT, yval);
lemma |= ineq(r, llc::GE, r2val);
return l_false;
}
if (xval > 0 && r2val < rval) {
new_lemma lemma(c, "x >= x0 > 0, y <= y0 => r <= x0^y0");
lemma |= ineq(x, llc::LT, xval);
lemma |= ineq(y, llc::GT, yval);
lemma |= ineq(r, llc::LE, r2val);
return l_false;
}
}
if (xval > 0 && yval > 0 && !yval.is_int()) {
auto ynum = numerator(yval);
auto yden = denominator(yval);
if (!ynum.is_unsigned())
return l_undef;
if (!yden.is_unsigned())
return l_undef;
// r = x^{yn/yd}
// <=>
// r^yd = x^yn
auto ryd = power(rval, yden.get_unsigned());
auto xyn = power(xval, ynum.get_unsigned());
if (ryd == xyn)
return l_true;
#if 0
// try some root approximation instead?
if (ryd > xyn) {
// todo
}
if (ryd < xyn) {
// todo
}
#endif
}
return l_undef;
// anum isn't initialized unless nra_solver is invoked.
// there is no proviso for using algebraic numbers outside of the nra solver.
// so either we have a rational refinement version _and_ an algebraic numeral refinement
// loop or we introduce algebraic numerals outside of the nra_solver
#if 0
scoped_anum xval(am()), yval(am()), rval(am());
am().set(xval, am_value(x));
am().set(yval, am_value(y));
am().set(rval, am_value(r));
#endif
}
}

47
src/math/lp/nla_solver.h
View file

@ -16,29 +16,30 @@ Author:
#include "math/lp/nla_settings.h"
#include "math/lp/nla_core.h"
namespace nra {
class solver;
class solver;
}
namespace nla {
class core;
// nonlinear integer incremental linear solver
class solver {
core* m_core;
public:
void add_monic(lpvar v, unsigned sz, lpvar const* vs);
solver(lp::lar_solver& s, reslimit& limit);
~solver();
nla_settings& settings();
void push();
void pop(unsigned scopes);
bool need_check();
lbool check(vector<lemma>&);
bool is_monic_var(lpvar) const;
bool influences_nl_var(lpvar) const;
std::ostream& display(std::ostream& out) const;
bool use_nra_model() const;
core& get_core();
nlsat::anum_manager& am();
nlsat::anum const& am_value(lp::var_index v) const;
void collect_statistics(::statistics & st);
};
class core;
// nonlinear integer incremental linear solver
class solver {
core* m_core;
public:
void add_monic(lpvar v, unsigned sz, lpvar const* vs);
solver(lp::lar_solver& s, reslimit& limit);
~solver();
nla_settings& settings();
void push();
void pop(unsigned scopes);
bool need_check();
lbool check(vector<lemma>&);
lbool check_power(lpvar r, lpvar x, lpvar y, vector<lemma>&);
bool is_monic_var(lpvar) const;
bool influences_nl_var(lpvar) const;
std::ostream& display(std::ostream& out) const;
bool use_nra_model() const;
core& get_core();
nlsat::anum_manager& am();
nlsat::anum const& am_value(lp::var_index v) const;
void collect_statistics(::statistics & st);
};
}

67
src/smt/theory_lra.cpp
View file

@ -797,8 +797,17 @@ class theory_lra::imp {
return internalize_linearized_def(term, st);
}
lpvar get_lpvar(expr* e) {
return get_lpvar(get_enode(e));
}
lpvar get_lpvar(enode* n) {
ensure_column(n);
return n ? get_lpvar(n->get_th_var(get_id())) : lp::null_lpvar;
}
lpvar get_lpvar(theory_var v) const {
return lp().external_to_local(v);
return v == null_theory_var ? lp::null_lpvar : lp().external_to_local(v);
}
lp::tv get_tv(theory_var v) const {
@ -1424,10 +1433,13 @@ public:
return v != null_theory_var && lp().external_is_used(v);
}
void ensure_column(enode* n) {
ensure_column(n->get_th_var(get_id()));
}
void ensure_column(theory_var v) {
if (!lp().external_is_used(v)) {
if (!lp().external_is_used(v) && v != null_theory_var)
register_theory_var_in_lar_solver(v);
}
}
mutable vector<std::pair<lp::tv, rational>> m_todo_terms;
@ -1570,47 +1582,18 @@ public:
final_check_status eval_power(expr* e) {
expr* x, * y;
VERIFY(a.is_power(e, x, y));
enode* n = get_enode(e);
enode* xn = get_enode(x);
enode* yn = get_enode(y);
if (!n || !xn || !yn)
return FC_GIVEUP;
rational valx, valy, valn;
theory_var v = n->get_th_var(get_id());
if (!get_value(xn, valx))
return FC_GIVEUP;
if (!get_value(yn, valy))
return FC_GIVEUP;
if (!get_value(n, valn))
return FC_GIVEUP;
// TBD - check that values align so return FC_DONE.
if (valn < 0 && valx > 0 && valy > 0) {
mk_axiom(mk_literal(a.mk_le(x, a.mk_numeral(rational(0), x->get_sort()))),
~mk_literal(a.mk_le(e, a.mk_numeral(rational(0), e->get_sort()))));
switch (m_nla->check_power(get_lpvar(e), get_lpvar(x), get_lpvar(y), m_nla_lemma_vector)) {
case l_true:
return FC_DONE;
case l_false:
for (const nla::lemma & l : m_nla_lemma_vector)
false_case_of_check_nla(l);
return FC_CONTINUE;
}
// add tangent lemmas for power:
// establish equality using algebraic numerals
// appears to be useless:
if (false && !valy.is_int() && numerator(valy) == 1 && denominator(valy) > 0) {
rational d = denominator(valy);
if (!d.is_unsigned())
return FC_GIVEUP;
unsigned den = d.get_unsigned();
// e = x^{1/y}
// => e^y = x
ptr_vector<expr> es;
for (unsigned i = 0; i < den; ++i)
es.push_back(e);
expr* em = a.mk_mul(es.size(), es.data());
mk_axiom(~mk_literal(m.mk_eq(y, a.mk_real(valy))), mk_literal(m.mk_eq(em, x)));
return FC_CONTINUE;
case l_undef:
return FC_GIVEUP;
default:
break;
}
return FC_GIVEUP;
}