z3-z3-4.13.0.src.test.nlsat.cpp Maven / Gradle / Ivy
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/*++
Copyright (c) 2012 Microsoft Corporation
Module Name:
nlsat.cpp
Abstract:
nlsat procedure
Author:
Leonardo (leonardo) 2012-01-09
Notes:
--*/
#include "nlsat/nlsat_assignment.h"
#include "nlsat/nlsat_interval_set.h"
#include "nlsat/nlsat_evaluator.h"
#include "nlsat/nlsat_solver.h"
#include "util/util.h"
#include "nlsat/nlsat_explain.h"
#include "math/polynomial/polynomial_cache.h"
#include "util/rlimit.h"
#include
nlsat::interval_set_ref tst_interval(nlsat::interval_set_ref const & s1,
nlsat::interval_set_ref const & s2,
unsigned expected_num_intervals,
bool check_num_intervals = true) {
nlsat::interval_set_manager & ism = s1.m();
nlsat::interval_set_ref r(ism);
std::cout << "s1: " << s1 << "\n";
std::cout << "s2: " << s2 << "\n";
r = ism.mk_union(s1, s2);
std::cout << "union(s1, s2): " << r << std::endl;
ENSURE(!check_num_intervals || ism.num_intervals(r) == expected_num_intervals);
ENSURE(ism.subset(s1, r));
ENSURE(ism.subset(s2, r));
if (ism.set_eq(s1, s2)) {
ENSURE(ism.set_eq(s1, r));
ENSURE(ism.set_eq(s2, r));
}
else {
ENSURE(ism.subset(s1, s2) || !ism.subset(r, s2));
ENSURE(ism.subset(s2, s1) || !ism.subset(r, s1));
}
nlsat::interval_set_ref r2(ism);
r2 = ism.mk_union(s2, s1);
ENSURE(ism.set_eq(r, r2));
anum zero;
nlsat::interval_set_ref full(ism);
nlsat::literal dummy(131, false);
full = ism.mk(true, true, zero, true, true, zero, dummy, nullptr);
ENSURE(ism.set_eq(r, full) == ism.is_full(r));
return r;
}
static void tst3() {
enable_trace("nlsat_interval");
reslimit rl;
unsynch_mpq_manager qm;
anum_manager am(rl, qm);
small_object_allocator allocator;
nlsat::interval_set_manager ism(am, allocator);
scoped_anum sqrt2(am), m_sqrt2(am), two(am), m_two(am), three(am), one(am), zero(am);
am.set(two, 2);
am.set(m_two, -2);
am.set(one, 1);
am.root(two, 2, sqrt2);
am.set(m_sqrt2, sqrt2);
am.neg(m_sqrt2);
am.set(three, 3);
nlsat::literal p1(1, false);
nlsat::literal p2(2, false);
nlsat::literal p3(3, false);
nlsat::literal p4(4, false);
nlsat::literal np2(2, true);
nlsat::interval_set_ref s1(ism), s2(ism), s3(ism), s4(ism);
s1 = ism.mk_empty();
std::cout << "s1: " << s1 << "\n";
s2 = ism.mk(true, true, zero, false, false, sqrt2, np2, nullptr);
std::cout << "s2: " << s2 << "\n";
s3 = ism.mk(false, false, zero, false, false, two, p1, nullptr);
std::cout << "s3: " << s3 << "\n";
s4 = ism.mk_union(s2, s3);
std::cout << "s4: " << s4 << "\n";
// Case
// s1: [ ... ]
// s2: [ ... ]
s1 = ism.mk(false, false, zero, false, false, two, p1, nullptr);
s2 = ism.mk(false, false, zero, false, false, two, p2, nullptr);
tst_interval(s1, s2, 1);
// Case
// s1: [ ... ]
// s2: [ ... ]
s1 = ism.mk(false, false, zero, false, false, two, p1, nullptr);
s2 = ism.mk(false, false, m_sqrt2, false, false, one, p2, nullptr);
s3 = ism.mk_union(s1, s2);
tst_interval(s1, s2, 2);
// Case
// s1: [ ... ]
// s2: [ ... ]
s1 = ism.mk(false, false, m_sqrt2, false, false, one, p1, nullptr);
s2 = ism.mk(false, false, zero, false, false, two, p2, nullptr);
tst_interval(s1, s2, 2);
// Case
// s1: [ ... ]
// s2: [ ... ]
s1 = ism.mk(false, false, m_sqrt2, false, false, one, p1, nullptr);
s2 = ism.mk(false, false, two, false, false, three, p2, nullptr);
tst_interval(s1, s2, 2);
// Case
// s1: [ ... ]
// s2: [ ... ]
s1 = ism.mk(false, false, m_sqrt2, false, false, three, p1, nullptr);
s2 = ism.mk(false, false, zero, false, false, two, p2, nullptr);
tst_interval(s1, s2, 1);
// Case
// s1: [ ... ]
// s2: [ ... ] [ ... ]
s1 = ism.mk(false, false, m_two, false, false, two, p1, nullptr);
s2 = ism.mk(false, false, m_sqrt2, false, false, zero, p2, nullptr);
s3 = ism.mk(false, false, one, false, false, three, p2, nullptr);
s2 = ism.mk_union(s2, s3);
tst_interval(s1, s2, 2);
// Case
// s1: [ ... ]
// s2: [ ... ]
s1 = ism.mk(false, false, m_two, false, false, two, p1, nullptr);
s2 = ism.mk(false, false, two, false, false, three, p2, nullptr);
tst_interval(s1, s2, 2);
s2 = ism.mk(true, false, two, false, false, three, p2, nullptr);
tst_interval(s1, s2, 2);
s2 = ism.mk(true, false, two, false, false, three, p1, nullptr);
tst_interval(s1, s2, 1);
s1 = ism.mk(false, false, m_two, true, false, two, p1, nullptr);
tst_interval(s1, s2, 2);
s1 = ism.mk(false, false, two, false, false, two, p1, nullptr);
s2 = ism.mk(false, false, two, false, false, three, p2, nullptr);
tst_interval(s1, s2, 1);
// Case
// s1: [ ... ] [ ... ]
// s2: [ .. ] [ ... ] [ ... ]
s1 = ism.mk(false, false, m_two, false, false, zero, p1, nullptr);
s3 = ism.mk(false, false, one, false, false, three, p1, nullptr);
s1 = ism.mk_union(s1, s3);
s2 = ism.mk(true, true, zero, false, false, m_sqrt2, p2, nullptr);
tst_interval(s1, s2, 3);
s3 = ism.mk(false, false, one, false, false, sqrt2, p2, nullptr);
s2 = ism.mk_union(s2, s3);
s3 = ism.mk(false, false, two, true, true, zero, p2, nullptr);
s2 = ism.mk_union(s2, s3);
tst_interval(s1, s2, 4);
// Case
s1 = ism.mk(true, true, zero, false, false, one, p1, nullptr);
s2 = ism.mk(true, false, one, true, true, zero, p2, nullptr);
tst_interval(s1, s2, 2);
s2 = ism.mk(true, false, one, false, false, two, p2, nullptr);
s3 = ism.mk(false, false, two, true, true, zero, p1, nullptr);
s2 = ism.mk_union(s2, s3);
tst_interval(s1, s2, 3);
}
static nlsat::interval_set_ref mk_random(nlsat::interval_set_manager & ism, anum_manager & am, int range, int space, int tries, bool minus_inf, bool plus_inf,
nlsat::literal lit) {
static random_gen gen;
ENSURE(range > 0);
ENSURE(space > 0);
nlsat::interval_set_ref r(ism), curr(ism);
scoped_anum lower(am);
scoped_anum upper(am);
int prev = -range + (gen() % (space*4));
if (gen() % 3 == 0 && minus_inf) {
int next = prev + (gen() % space);
bool open = gen() % 2 == 0;
am.set(upper, next);
r = ism.mk(true, true, lower, open, false, upper, lit, nullptr);
prev = next;
}
for (int i = 0; i < tries; i++) {
int l = prev + (gen() % space);
int u = l + (gen() % space);
bool lower_open = gen() % 2 == 0;
bool upper_open = gen() % 2 == 0;
if ((lower_open || upper_open) && l == u)
u++;
am.set(lower, l);
am.set(upper, u);
curr = ism.mk(lower_open, false, lower, upper_open, false, upper, lit, nullptr);
r = ism.mk_union(r, curr);
prev = u;
}
if (gen() % 3 == 0 && plus_inf) {
int next = prev + (gen() % space);
bool open = gen() % 2 == 0;
am.set(lower, next);
curr = ism.mk(open, false, lower, true, true, upper, lit, nullptr);
r = ism.mk_union(r, curr);
}
return r;
}
static void check_subset_result(nlsat::interval_set_ref const & s1,
nlsat::interval_set_ref const & s2,
nlsat::interval_set_ref const & r,
nlsat::literal l1,
nlsat::literal l2) {
nlsat::interval_set_manager ism(s1.m());
nlsat::interval_set_ref tmp(ism);
unsigned num = ism.num_intervals(r);
nlsat::literal_vector lits;
ptr_vector clauses;
ism.get_justifications(r, lits, clauses);
ENSURE(lits.size() <= 2);
for (unsigned i = 0; i < num; i++) {
tmp = ism.get_interval(r, i);
ism.get_justifications(tmp, lits, clauses);
ENSURE(lits.size() == 1);
if (lits[0] == l1) {
ENSURE(ism.subset(tmp, s1));
}
else {
ENSURE(lits[0] == l2);
ENSURE(ism.subset(tmp, s2));
}
}
}
static void tst4() {
enable_trace("nlsat_interval");
reslimit rl;
unsynch_mpq_manager qm;
anum_manager am(rl, qm);
small_object_allocator allocator;
nlsat::interval_set_manager ism(am, allocator);
nlsat::interval_set_ref s1(ism), s2(ism), r(ism);
nlsat::literal l1(1, false);
nlsat::literal l2(2, false);
for (unsigned i = 0; i < 100; i++) {
s1 = mk_random(ism, am, 20, 3, 10, true, true, l1);
s2 = mk_random(ism, am, 20, 3, 10, true, true, l2);
r = tst_interval(s1, s2, 0, false);
check_subset_result(s1, s2, r, l1, l2);
}
for (unsigned i = 0; i < 100; i++) {
s1 = mk_random(ism, am, 200, 100, 20, true, true, l1);
s2 = mk_random(ism, am, 200, 100, 20, true, true, l2);
r = tst_interval(s1, s2, 0, false);
check_subset_result(s1, s2, r, l1, l2);
}
}
static void tst5() {
params_ref ps;
reslimit rlim;
nlsat::solver s(rlim, ps, false);
anum_manager & am = s.am();
nlsat::pmanager & pm = s.pm();
nlsat::assignment as(am);
small_object_allocator allocator;
nlsat::interval_set_manager ism(am, allocator);
nlsat::evaluator ev(s, as, pm, allocator);
nlsat::var x0, x1;
x0 = pm.mk_var();
x1 = pm.mk_var();
polynomial_ref p(pm);
polynomial_ref _x0(pm), _x1(pm);
_x0 = pm.mk_polynomial(x0);
_x1 = pm.mk_polynomial(x1);
p = (_x0^2) + (_x1^2) - 2;
nlsat::poly * _p[1] = { p.get() };
bool is_even[1] = { false };
nlsat::bool_var b = s.mk_ineq_atom(nlsat::atom::GT, 1, _p, is_even);
nlsat::atom * a = s.bool_var2atom(b);
ENSURE(a != nullptr);
scoped_anum zero(am);
am.set(zero, 0);
as.set(0, zero);
auto i = ev.infeasible_intervals(a, true, nullptr);
std::cout << "1) " << i << "\n";
as.set(1, zero);
auto i2 = ev.infeasible_intervals(a, true, nullptr);
std::cout << "2) " << i2 << "\n";
}
static void project(nlsat::solver& s, nlsat::explain& ex, nlsat::var x, unsigned num, nlsat::literal const* lits) {
std::cout << "Project ";
s.display(std::cout, num, lits);
nlsat::scoped_literal_vector result(s);
ex.project(x, num, lits, result);
s.display(std::cout << "\n==>\n", result.size(), result.data());
std::cout << "\n";
}
static void project_fa(nlsat::solver& s, nlsat::explain& ex, nlsat::var x, unsigned num, nlsat::literal const* lits) {
std::cout << "Project ";
nlsat::scoped_literal_vector result(s);
ex(num, lits, result);
std::cout << "(or";
for (auto l : result) {
s.display(std::cout << " ", l);
}
for (unsigned i = 0; i < num; ++i) {
s.display(std::cout << " ", ~lits[i]);
}
std::cout << ")\n";
}
static nlsat::literal mk_gt(nlsat::solver& s, nlsat::poly* p) {
nlsat::poly * _p[1] = { p };
bool is_even[1] = { false };
return s.mk_ineq_literal(nlsat::atom::GT, 1, _p, is_even);
}
static nlsat::literal mk_lt(nlsat::solver& s, nlsat::poly* p) {
nlsat::poly * _p[1] = { p };
bool is_even[1] = { false };
return s.mk_ineq_literal(nlsat::atom::LT, 1, _p, is_even);
}
static nlsat::literal mk_eq(nlsat::solver& s, nlsat::poly* p) {
nlsat::poly * _p[1] = { p };
bool is_even[1] = { false };
return s.mk_ineq_literal(nlsat::atom::EQ, 1, _p, is_even);
}
static void tst6() {
params_ref ps;
reslimit rlim;
nlsat::solver s(rlim, ps, false);
anum_manager & am = s.am();
nlsat::pmanager & pm = s.pm();
nlsat::assignment as(am);
nlsat::explain& ex = s.get_explain();
nlsat::var x0, x1, x2, a, b, c, d;
a = s.mk_var(false);
b = s.mk_var(false);
c = s.mk_var(false);
d = s.mk_var(false);
x0 = s.mk_var(false);
x1 = s.mk_var(false);
x2 = s.mk_var(false);
polynomial_ref p1(pm), p2(pm), p3(pm), p4(pm), p5(pm);
polynomial_ref _x0(pm), _x1(pm), _x2(pm);
polynomial_ref _a(pm), _b(pm), _c(pm), _d(pm);
_x0 = pm.mk_polynomial(x0);
_x1 = pm.mk_polynomial(x1);
_x2 = pm.mk_polynomial(x2);
_a = pm.mk_polynomial(a);
_b = pm.mk_polynomial(b);
_c = pm.mk_polynomial(c);
_d = pm.mk_polynomial(d);
p1 = (_a*(_x0^2)) + _x2 + 2;
p2 = (_b*_x1) - (2*_x2) - _x0 + 8;
nlsat::scoped_literal_vector lits(s);
lits.push_back(mk_gt(s, p1));
lits.push_back(mk_gt(s, p2));
lits.push_back(mk_gt(s, (_c*_x0) + _x2 + 1));
lits.push_back(mk_gt(s, (_d*_x0) - _x1 + 5*_x2));
scoped_anum zero(am), one(am), two(am);
am.set(zero, 0);
am.set(one, 1);
am.set(two, 2);
as.set(0, one);
as.set(1, one);
as.set(2, two);
as.set(3, two);
as.set(4, two);
as.set(5, one);
as.set(6, one);
s.set_rvalues(as);
project(s, ex, x0, 2, lits.data());
project(s, ex, x1, 3, lits.data());
project(s, ex, x2, 3, lits.data());
project(s, ex, x2, 2, lits.data());
project(s, ex, x2, 4, lits.data());
project(s, ex, x2, 3, lits.data()+1);
}
static void tst7() {
params_ref ps;
reslimit rlim;
nlsat::solver s(rlim, ps, false);
nlsat::pmanager & pm = s.pm();
nlsat::var x0, x1, x2, a, b, c, d;
a = s.mk_var(false);
b = s.mk_var(false);
c = s.mk_var(false);
d = s.mk_var(false);
x0 = s.mk_var(false);
x1 = s.mk_var(false);
x2 = s.mk_var(false);
polynomial_ref p1(pm), p2(pm), p3(pm), p4(pm), p5(pm);
polynomial_ref _x0(pm), _x1(pm), _x2(pm);
polynomial_ref _a(pm), _b(pm), _c(pm), _d(pm);
_x0 = pm.mk_polynomial(x0);
_x1 = pm.mk_polynomial(x1);
_x2 = pm.mk_polynomial(x2);
_a = pm.mk_polynomial(a);
_b = pm.mk_polynomial(b);
_c = pm.mk_polynomial(c);
_d = pm.mk_polynomial(d);
p1 = _x0 + _x1;
p2 = _x2 - _x0;
p3 = (-1*_x0) - _x1;
nlsat::scoped_literal_vector lits(s);
lits.push_back(mk_gt(s, p1));
lits.push_back(mk_gt(s, p2));
lits.push_back(mk_gt(s, p3));
nlsat::literal_vector litsv(lits.size(), lits.data());
lbool res = s.check(litsv);
VERIFY(res == l_false);
for (unsigned i = 0; i < litsv.size(); ++i) {
s.display(std::cout, litsv[i]);
std::cout << " ";
}
std::cout << "\n";
litsv.reset();
litsv.append(2, lits.data());
res = s.check(litsv);
ENSURE(res == l_true);
s.display(std::cout);
s.am().display(std::cout, s.value(x0)); std::cout << "\n";
s.am().display(std::cout, s.value(x1)); std::cout << "\n";
s.am().display(std::cout, s.value(x2)); std::cout << "\n";
}
static void tst8() {
params_ref ps;
reslimit rlim;
nlsat::solver s(rlim, ps, false);
anum_manager & am = s.am();
nlsat::pmanager & pm = s.pm();
nlsat::assignment as(am);
nlsat::explain& ex = s.get_explain();
nlsat::var x0, x1, x2, a, b, c, d;
a = s.mk_var(false);
b = s.mk_var(false);
c = s.mk_var(false);
d = s.mk_var(false);
x0 = s.mk_var(false);
x1 = s.mk_var(false);
x2 = s.mk_var(false);
polynomial_ref p1(pm), p2(pm), p3(pm), p4(pm), p5(pm);
polynomial_ref _x0(pm), _x1(pm), _x2(pm);
polynomial_ref _a(pm), _b(pm), _c(pm), _d(pm);
_x0 = pm.mk_polynomial(x0);
_x1 = pm.mk_polynomial(x1);
_x2 = pm.mk_polynomial(x2);
_a = pm.mk_polynomial(a);
_b = pm.mk_polynomial(b);
_c = pm.mk_polynomial(c);
_d = pm.mk_polynomial(d);
scoped_anum zero(am), one(am), two(am), six(am);
am.set(zero, 0);
am.set(one, 1);
am.set(two, 2);
am.set(six, 6);
as.set(0, two); // a
as.set(1, one); // b
as.set(2, six); // c
as.set(3, zero); // d
as.set(4, zero); // x0
as.set(5, zero); // x1
as.set(6, two); // x2
s.set_rvalues(as);
nlsat::scoped_literal_vector lits(s);
lits.push_back(mk_eq(s, (_a*_x2*_x2) - (_b*_x2) - _c));
project(s, ex, x2, 1, lits.data());
}
static void tst9() {
params_ref ps;
reslimit rlim;
nlsat::solver s(rlim, ps, false);
anum_manager & am = s.am();
nlsat::pmanager & pm = s.pm();
nlsat::assignment as(am);
nlsat::explain& ex = s.get_explain();
int num_lo = 4;
int num_hi = 5;
svector los, his;
for (int i = 0; i < num_lo; ++i) {
los.push_back(s.mk_var(false));
scoped_anum num(am);
am.set(num, - i - 1);
as.set(i, num);
}
for (int i = 0; i < num_hi; ++i) {
his.push_back(s.mk_var(false));
scoped_anum num(am);
am.set(num, i + 1);
as.set(num_lo + i, num);
}
nlsat::var _z = s.mk_var(false);
nlsat::var _x = s.mk_var(false);
polynomial_ref x(pm), z(pm);
x = pm.mk_polynomial(_x);
scoped_anum val(am);
am.set(val, 0);
as.set(num_lo + num_hi, val);
as.set(num_lo + num_hi + 1, val);
s.set_rvalues(as);
nlsat::scoped_literal_vector lits(s);
for (int i = 0; i < num_lo; ++i) {
polynomial_ref y(pm);
y = pm.mk_polynomial(los[i]);
lits.push_back(mk_gt(s, x - y));
}
for (int i = 0; i < num_hi; ++i) {
polynomial_ref y(pm);
y = pm.mk_polynomial(his[i]);
lits.push_back(mk_gt(s, y - x));
}
z = pm.mk_polynomial(_z);
lits.push_back(mk_eq(s, x - z));
#define TEST_ON_OFF() \
std::cout << "Off "; \
ex.set_signed_project(false); \
project(s, ex, _x, lits.size()-1, lits.data()); \
std::cout << "On "; \
ex.set_signed_project(true); \
project(s, ex, _x, lits.size()-1, lits.data()); \
std::cout << "Off "; \
ex.set_signed_project(false); \
project(s, ex, _x, lits.size(), lits.data()); \
std::cout << "On "; \
ex.set_signed_project(true); \
project(s, ex, _x, lits.size(), lits.data()) \
TEST_ON_OFF();
lits.reset();
polynomial_ref u(pm);
u = pm.mk_polynomial(his[1]);
for (int i = 0; i < num_lo; ++i) {
polynomial_ref y(pm);
y = pm.mk_polynomial(los[i]);
lits.push_back(mk_gt(s, u*x - y));
}
for (int i = 0; i < num_hi; ++i) {
polynomial_ref y(pm);
y = pm.mk_polynomial(his[i]);
lits.push_back(mk_gt(s, y - u*x));
}
z = pm.mk_polynomial(_z);
lits.push_back(mk_eq(s, u*x - z));
TEST_ON_OFF();
lits.reset();
u = pm.mk_polynomial(los[1]);
for (int i = 0; i < num_lo; ++i) {
polynomial_ref y(pm);
y = pm.mk_polynomial(los[i]);
lits.push_back(mk_gt(s, u*x - y));
}
for (int i = 0; i < num_hi; ++i) {
polynomial_ref y(pm);
y = pm.mk_polynomial(his[i]);
lits.push_back(mk_gt(s, y - u*x));
}
z = pm.mk_polynomial(_z);
lits.push_back(mk_eq(s, x - z));
TEST_ON_OFF();
}
#if 0
#endif
static void test_root_literal(nlsat::solver& s, nlsat::explain& ex, nlsat::var x, nlsat::atom::kind k, unsigned i, nlsat::poly* p) {
nlsat::scoped_literal_vector result(s);
ex.test_root_literal(k, x, 1, p, result);
nlsat::bool_var b = s.mk_root_atom(k, x, i, p);
s.display(std::cout, nlsat::literal(b, false));
s.display(std::cout << " ==> ", result.size(), result.data());
std::cout << "\n";
}
static bool satisfies_root(nlsat::solver& s, nlsat::atom::kind k, nlsat::poly* p) {
nlsat::pmanager & pm = s.pm();
anum_manager & am = s.am();
nlsat::assignment as(am);
s.get_rvalues(as);
polynomial_ref pr(p, pm);
switch (k) {
case nlsat::atom::ROOT_EQ: return am.eval_sign_at(pr, as) == 0;
case nlsat::atom::ROOT_LE: return am.eval_sign_at(pr, as) <= 0;
case nlsat::atom::ROOT_LT: return am.eval_sign_at(pr, as) < 0;
case nlsat::atom::ROOT_GE: return am.eval_sign_at(pr, as) >= 0;
case nlsat::atom::ROOT_GT: return am.eval_sign_at(pr, as) > 0;
default:
UNREACHABLE();
return false;
}
}
static void tst10() {
params_ref ps;
reslimit rlim;
nlsat::solver s(rlim, ps, false);
anum_manager & am = s.am();
nlsat::pmanager & pm = s.pm();
nlsat::assignment as(am);
nlsat::explain& ex = s.get_explain();
nlsat::var _a = s.mk_var(false);
nlsat::var _b = s.mk_var(false);
nlsat::var _c = s.mk_var(false);
nlsat::var _x = s.mk_var(false);
polynomial_ref x(pm), a(pm), b(pm), c(pm), p(pm);
x = pm.mk_polynomial(_x);
a = pm.mk_polynomial(_a);
b = pm.mk_polynomial(_b);
c = pm.mk_polynomial(_c);
p = a*x*x + b*x + c;
scoped_anum one(am), two(am), three(am), mone(am), mtwo(am), mthree(am), zero(am), one_a_half(am);
am.set(zero, 0);
am.set(one, 1);
am.set(two, 2);
am.set(three, 3);
am.set(mone, -1);
am.set(mtwo, -2);
am.set(mthree, -3);
rational oah(1,2);
am.set(one_a_half, oah.to_mpq());
scoped_anum_vector nums(am);
nums.push_back(one);
nums.push_back(two);
nums.push_back(one_a_half);
nums.push_back(mone);
nums.push_back(three);
// a = 1, b = -3, c = 2:
// has roots x = 2, x = 1:
// 2^2 - 3*2 + 2 = 0
// 1 - 3 + 2 = 0
as.set(_a, one);
as.set(_b, mthree);
as.set(_c, two);
for (unsigned i = 0; i < nums.size(); ++i) {
as.set(_x, nums[i]);
s.set_rvalues(as);
std::cout << p << "\n";
as.display(std::cout);
for (unsigned k = nlsat::atom::ROOT_EQ; k <= nlsat::atom::ROOT_GE; ++k) {
if (satisfies_root(s, (nlsat::atom::kind) k, p)) {
test_root_literal(s, ex, _x, (nlsat::atom::kind) k, 1, p);
}
}
}
as.set(_a, mone);
as.set(_b, three);
as.set(_c, mtwo);
for (unsigned i = 0; i < nums.size(); ++i) {
as.set(_x, nums[i]);
s.set_rvalues(as);
std::cout << p << "\n";
as.display(std::cout);
for (unsigned k = nlsat::atom::ROOT_EQ; k <= nlsat::atom::ROOT_GE; ++k) {
if (satisfies_root(s, (nlsat::atom::kind) k, p)) {
test_root_literal(s, ex, _x, (nlsat::atom::kind) k, 1, p);
}
}
}
std::cout << "\n";
}
static void tst11() {
params_ref ps;
reslimit rlim;
nlsat::solver s(rlim, ps, false);
anum_manager & am = s.am();
nlsat::pmanager & pm = s.pm();
nlsat::assignment as(am);
nlsat::explain& ex = s.get_explain();
nlsat::var x, y, z;
y = s.mk_var(false);
z = s.mk_var(false);
x = s.mk_var(false);
polynomial_ref p1(pm), p2(pm), _x(pm), _y(pm), _z(pm);
_x = pm.mk_polynomial(x);
_y = pm.mk_polynomial(y);
_z = pm.mk_polynomial(z);
nlsat::scoped_literal_vector lits(s);
scoped_anum zero(am), one(am), five(am);
am.set(zero, 0);
am.set(one, 1);
am.set(five, 5);
as.set(z, zero);
as.set(y, five);
as.set(x, five);
s.set_rvalues(as);
p1 = (_x - _y);
p2 = ((_x*_x) - (_x*_y) - _z);
lits.reset();
lits.push_back(mk_gt(s, p1));
lits.push_back(mk_eq(s, p2));
project_fa(s, ex, x, 2, lits.data());
// return;
p1 = ((_x * _x) - (2 * _y * _x) - _z + (_y *_y));
p2 = _x + _y;
as.set(_x, one);
as.set(_y, zero);
as.set(_z, one);
lits.reset();
lits.push_back(mk_lt(s, p1));
lits.push_back(mk_eq(s, p2));
project_fa(s, ex, x, 2, lits.data());
return;
as.set(z, zero);
as.set(y, five);
as.set(x, five);
p1 = (_x - _y);
p2 = ((_x*_x) - (_x*_y));
lits.reset();
lits.push_back(mk_gt(s, p1));
lits.push_back(mk_eq(s, p2));
project_fa(s, ex, x, 2, lits.data());
#if 0
!(x5^4 - 2 x3^2 x5^2 - 2 x1^2 x5^2 + 4 x0 x1 x5^2 - 2 x0^2 x5^2 + x3^4 - 2 x1^2 x3^2 + 4 x0 x1 x3^2 - 2 x0^2 x3^2 + x1^4 - 4 x0 x1^3 + 6 x0^2 x1^2 - 4 x0^3 x1 + x0^4 = 0) or !(x5 < 0) or !(x4 > root[1](x1 x4 - x0 x4 + x3)) or !(x3 + x1 - x0 > 0) or !(x1 - x0 < 0) or !(x7 > root[1](x1^2 x7 - 2 x0 x1 x7 + x0^2 x7 + x1 x3 - x0 x3)) or x7 - x4 = 0 or !(x1 x3 x7^2 - x0 x3 x7^2 - x5^2 x7 + x3^2 x7 + x1^2 x7 - 2 x0 x1 x7 + x0^2 x7 + x1 x3 - x0 x3 = 0)
x0 := -1
x1 := -21.25
x2 := 0.0470588235?
x3 := 2
x4 := -0.03125
x5 := -18.25
x6 := -0.5
x7 := 1
#endif
}
void tst_nlsat() {
tst11();
std::cout << "------------------\n";
return;
tst10();
std::cout << "------------------\n";
tst9();
std::cout << "------------------\n";
tst8();
std::cout << "------------------\n";
tst7();
std::cout << "------------------\n";
tst6();
std::cout << "------------------\n";
tst5();
std::cout << "------------------\n";
tst4();
std::cout << "------------------\n";
tst3();
}