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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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207
src/math/lp/nla_solver.cpp
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@ -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
}
}