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fix #2613 fix #2612

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2019-10-05 16:57:51 -07:00
parent 016732aa59
commit 39edf73e78
16 changed files with 222 additions and 162 deletions
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67
src/math/polynomial/algebraic_numbers.cpp
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@ -257,7 +257,7 @@ namespace algebraic_numbers {
SASSERT(bqm().ge(upper(c), candidate));
if (bqm().lt(lower(c), candidate) && upm().eval_sign_at(c->m_p_sz, c->m_p, candidate) == 0) {
if (bqm().lt(lower(c), candidate) && upm().eval_sign_at(c->m_p_sz, c->m_p, candidate) == polynomial::sign_zero) {
m_wrapper.set(a, candidate);
return true;
}
@ -320,7 +320,7 @@ namespace algebraic_numbers {
SASSERT(bqm().ge(upper(c), candidate));
// Find if candidate is an actual root
if (bqm().lt(lower(c), candidate) && upm().eval_sign_at(c->m_p_sz, c->m_p, candidate) == 0) {
if (bqm().lt(lower(c), candidate) && upm().eval_sign_at(c->m_p_sz, c->m_p, candidate) == polynomial::sign_zero) {
saved_a.restore_if_too_small();
set(a, candidate);
return true;
@ -379,11 +379,11 @@ namespace algebraic_numbers {
}
void update_sign_lower(algebraic_cell * c) {
int sl = upm().eval_sign_at(c->m_p_sz, c->m_p, lower(c));
polynomial::sign sl = upm().eval_sign_at(c->m_p_sz, c->m_p, lower(c));
// The isolating intervals are refinable. Thus, the polynomial has opposite signs at lower and upper.
SASSERT(sl != 0);
SASSERT(sl != polynomial::sign_zero);
SASSERT(upm().eval_sign_at(c->m_p_sz, c->m_p, upper(c)) == -sl);
c->m_sign_lower = sl < 0;
c->m_sign_lower = sl == polynomial::sign_neg;
}
// Make sure the GCD of the coefficients is one and the leading coefficient is positive
@ -1594,8 +1594,8 @@ namespace algebraic_numbers {
#define REFINE_LOOP(BOUND, TARGET_SIGN) \
while (true) { \
bqm().div2(BOUND); \
int new_sign = upm().eval_sign_at(cell_a->m_p_sz, cell_a->m_p, BOUND); \
if (new_sign == 0) { \
polynomial::sign new_sign = upm().eval_sign_at(cell_a->m_p_sz, cell_a->m_p, BOUND); \
if (new_sign == polynomial::sign_zero) { \
/* found actual root */ \
scoped_mpq r(qm()); \
to_mpq(qm(), BOUND, r); \
@ -1695,8 +1695,8 @@ namespace algebraic_numbers {
if (bqm().ge(l, b))
return 1;
// b is in the isolating interval (l, u)
int sign_b = upm().eval_sign_at(c->m_p_sz, c->m_p, b);
if (sign_b == 0)
auto sign_b = upm().eval_sign_at(c->m_p_sz, c->m_p, b);
if (sign_b == polynomial::sign_zero)
return 0;
return sign_b == sign_lower(c) ? 1 : -1;
}
@ -1979,7 +1979,7 @@ namespace algebraic_numbers {
};
polynomial::var_vector m_eval_sign_vars;
int eval_sign_at(polynomial_ref const & p, polynomial::var2anum const & x2v) {
polynomial::sign eval_sign_at(polynomial_ref const & p, polynomial::var2anum const & x2v) {
polynomial::manager & ext_pm = p.m();
TRACE("anum_eval_sign", tout << "evaluating sign of: " << p << "\n";);
while (true) {
@ -1990,7 +1990,7 @@ namespace algebraic_numbers {
scoped_mpq r(qm());
ext_pm.eval(p, x2v_basic, r);
TRACE("anum_eval_sign", tout << "all variables are assigned to rationals, value of p: " << r << "\n";);
return qm().sign(r);
return polynomial::to_sign(qm().sign(r));
}
catch (const opt_var2basic::failed &) {
// continue
@ -2004,13 +2004,13 @@ namespace algebraic_numbers {
if (ext_pm.is_zero(p_prime)) {
// polynomial vanished after substituting rational values.
return 0;
return polynomial::sign_zero;
}
if (is_const(p_prime)) {
// polynomial became the constant polynomial after substitution.
SASSERT(size(p_prime) == 1);
return ext_pm.m().sign(ext_pm.coeff(p_prime, 0));
return polynomial::to_sign(ext_pm.m().sign(ext_pm.coeff(p_prime, 0)));
}
// Try to find sign using intervals
@ -2026,7 +2026,7 @@ namespace algebraic_numbers {
ext_pm.eval(p_prime, x2v_interval, ri);
TRACE("anum_eval_sign", tout << "evaluating using intervals: " << ri << "\n";);
if (!bqim().contains_zero(ri)) {
return bqim().is_pos(ri) ? 1 : -1;
return bqim().is_pos(ri) ? polynomial::sign_pos : polynomial::sign_neg;
}
// refine intervals if magnitude > m_min_magnitude
bool refined = false;
@ -2067,7 +2067,7 @@ namespace algebraic_numbers {
// Remark: m_zero_accuracy == 0 means use precise computation.
if (m_zero_accuracy > 0) {
// assuming the value is 0, since the result is in (-1/2^k, 1/2^k), where m_zero_accuracy = k
return 0;
return polynomial::sign_zero;
}
#if 0
// Evaluating sign using algebraic arithmetic
@ -2143,7 +2143,7 @@ namespace algebraic_numbers {
bqm().div2k(mL, k);
bqm().div2k(L, k);
if (bqm().lt(mL, ri.lower()) && bqm().lt(ri.upper(), L))
return 0;
return polynomial::sign_zero;
// keep refining ri until ri is inside (-L, L) or
// ri does not contain zero.
@ -2166,14 +2166,13 @@ namespace algebraic_numbers {
TRACE("anum_eval_sign", tout << "evaluating using intervals: " << ri << "\n";
tout << "zero lower bound is: " << L << "\n";);
if (!bqim().contains_zero(ri)) {
return bqim().is_pos(ri) ? 1 : -1;
return bqim().is_pos(ri) ? polynomial::sign_pos : polynomial::sign_neg;
}
if (bqm().lt(mL, ri.lower()) && bqm().lt(ri.upper(), L))
return 0;
return polynomial::sign_zero;
for (unsigned i = 0; i < xs.size(); i++) {
polynomial::var x = xs[i];
for (auto x : xs) {
SASSERT(x2v.contains(x));
anum const & v = x2v(x);
SASSERT(!v.is_basic());
@ -2242,18 +2241,14 @@ namespace algebraic_numbers {
unsigned sz = roots.size();
unsigned j = 0;
// std::cout << "p: " << p << "\n";
// std::cout << "sz: " << sz << "\n";
for (unsigned i = 0; i < sz; i++) {
checkpoint();
// display_root(std::cout, roots[i]); std::cout << std::endl;
ext_var2num ext_x2v(m_wrapper, x2v, x, roots[i]);
TRACE("isolate_roots", tout << "filter_roots i: " << i << ", ext_x2v: x" << x << " -> "; display_root(tout, roots[i]); tout << "\n";);
int sign = eval_sign_at(p, ext_x2v);
polynomial::sign sign = eval_sign_at(p, ext_x2v);
TRACE("isolate_roots", tout << "filter_roots i: " << i << ", result sign: " << sign << "\n";);
if (sign != 0)
continue;
// display_decimal(std::cout, roots[i], 10); std::cout << " is root" << std::endl;
if (i != j)
set(roots[j], roots[i]);
j++;
@ -2453,7 +2448,7 @@ namespace algebraic_numbers {
}
}
int eval_at_mpbq(polynomial_ref const & p, polynomial::var2anum const & x2v, polynomial::var x, mpbq const & v) {
polynomial::sign eval_at_mpbq(polynomial_ref const & p, polynomial::var2anum const & x2v, polynomial::var x, mpbq const & v) {
scoped_mpq qv(qm());
to_mpq(qm(), v, qv);
scoped_anum av(m_wrapper);
@ -2568,13 +2563,13 @@ namespace algebraic_numbers {
#define DEFAULT_PRECISION 2
void isolate_roots(polynomial_ref const & p, polynomial::var2anum const & x2v, numeral_vector & roots, svector<int> & signs) {
void isolate_roots(polynomial_ref const & p, polynomial::var2anum const & x2v, numeral_vector & roots, svector<polynomial::sign> & signs) {
isolate_roots(p, x2v, roots);
unsigned num_roots = roots.size();
if (num_roots == 0) {
anum zero;
ext2_var2num ext_x2v(m_wrapper, x2v, zero);
int s = eval_sign_at(p, ext_x2v);
polynomial::sign s = eval_sign_at(p, ext_x2v);
signs.push_back(s);
}
else {
@ -2601,8 +2596,8 @@ namespace algebraic_numbers {
TRACE("isolate_roots_bug", tout << "w: "; display_root(tout, w); tout << "\n";);
{
ext2_var2num ext_x2v(m_wrapper, x2v, w);
int s = eval_sign_at(p, ext_x2v);
SASSERT(s != 0);
auto s = eval_sign_at(p, ext_x2v);
SASSERT(s != polynomial::sign_zero);
signs.push_back(s);
}
@ -2611,16 +2606,16 @@ namespace algebraic_numbers {
numeral & curr = roots[i];
select(prev, curr, w);
ext2_var2num ext_x2v(m_wrapper, x2v, w);
int s = eval_sign_at(p, ext_x2v);
SASSERT(s != 0);
auto s = eval_sign_at(p, ext_x2v);
SASSERT(s != polynomial::sign_zero);
signs.push_back(s);
}
int_gt(roots[num_roots - 1], w);
{
ext2_var2num ext_x2v(m_wrapper, x2v, w);
int s = eval_sign_at(p, ext_x2v);
SASSERT(s != 0);
auto s = eval_sign_at(p, ext_x2v);
SASSERT(s != polynomial::sign_zero);
signs.push_back(s);
}
}
@ -2879,7 +2874,7 @@ namespace algebraic_numbers {
m_imp->isolate_roots(p, x2v, roots);
}
void manager::isolate_roots(polynomial_ref const & p, polynomial::var2anum const & x2v, numeral_vector & roots, svector<int> & signs) {
void manager::isolate_roots(polynomial_ref const & p, polynomial::var2anum const & x2v, numeral_vector & roots, svector<polynomial::sign> & signs) {
m_imp->isolate_roots(p, x2v, roots, signs);
}
@ -3037,7 +3032,7 @@ namespace algebraic_numbers {
l = rational(_l);
}
int manager::eval_sign_at(polynomial_ref const & p, polynomial::var2anum const & x2v) {
polynomial::sign manager::eval_sign_at(polynomial_ref const & p, polynomial::var2anum const & x2v) {
SASSERT(&(x2v.m()) == this);
return m_imp->eval_sign_at(p, x2v);
}