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fix division filter

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2023-01-30 08:20:26 -08:00
parent 8e37e2f913
commit 2c4a9c2f5c
3 changed files with 143 additions and 37 deletions
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172
src/math/lp/nla_divisions.cpp
View file

@ -18,13 +18,22 @@ Description:
namespace nla {
void divisions::add_idivision(lpvar r, lpvar x, lpvar y) {
m_idivisions.push_back({r, x, y});
void divisions::add_idivision(lpvar q, lpvar x, lpvar y) {
if (x == null_lpvar || y == null_lpvar || q == null_lpvar)
return;
if (lp::tv::is_term(x) || lp::tv::is_term(y) || lp::tv::is_term(q))
return;
verbose_stream() << q << " " << x << " " << y << " " << null_lpvar << "\n";
m_idivisions.push_back({q, x, y});
m_core.trail().push(push_back_vector(m_idivisions));
}
void divisions::add_rdivision(lpvar r, lpvar x, lpvar y) {
m_rdivisions.push_back({ r, x, y });
void divisions::add_rdivision(lpvar q, lpvar x, lpvar y) {
if (x == null_lpvar || y == null_lpvar || q == null_lpvar)
return;
if (lp::tv::is_term(x) || lp::tv::is_term(y) || lp::tv::is_term(q))
return;
m_rdivisions.push_back({ q, x, y });
m_core.trail().push(push_back_vector(m_rdivisions));
}
@ -39,60 +48,60 @@ namespace nla {
if (c.use_nra_model())
return;
auto monotonicity1 = [&](auto x1, auto& x1val, auto y1, auto& y1val, auto& r1, auto& r1val,
auto x2, auto& x2val, auto y2, auto& y2val, auto& r2, auto& r2val) {
if (y1val >= y2val && y2val > 0 && x1val <= x2val && r1val > r2val) {
auto monotonicity1 = [&](auto x1, auto& x1val, auto y1, auto& y1val, auto& q1, auto& q1val,
auto x2, auto& x2val, auto y2, auto& y2val, auto& q2, auto& q2val) {
if (y1val >= y2val && y2val > 0 && x1val <= x2val && q1val > q2val) {
new_lemma lemma(c, "y1 >= y2 > 0 & x1 <= x2 => x1/y1 <= x2/y2");
lemma |= ineq(term(y1, rational(-1), y2), llc::LT, 0);
lemma |= ineq(y2, llc::LE, 0);
lemma |= ineq(term(x1, rational(-1), x2), llc::GT, 0);
lemma |= ineq(term(r1, rational(-1), r2), llc::LE, 0);
lemma |= ineq(term(q1, rational(-1), q2), llc::LE, 0);
return true;
}
return false;
};
auto monotonicity2 = [&](auto x1, auto& x1val, auto y1, auto& y1val, auto& r1, auto& r1val,
auto x2, auto& x2val, auto y2, auto& y2val, auto& r2, auto& r2val) {
if (y2val <= y1val && y1val < 0 && x1val >= x2val && x2val >= 0 && r1val > r2val) {
auto monotonicity2 = [&](auto x1, auto& x1val, auto y1, auto& y1val, auto& q1, auto& q1val,
auto x2, auto& x2val, auto y2, auto& y2val, auto& q2, auto& q2val) {
if (y2val <= y1val && y1val < 0 && x1val >= x2val && x2val >= 0 && q1val > q2val) {
new_lemma lemma(c, "y2 <= y1 < 0 & x1 >= x2 >= 0 => x1/y1 <= x2/y2");
lemma |= ineq(term(y1, rational(-1), y2), llc::LT, 0);
lemma |= ineq(y1, llc::GE, 0);
lemma |= ineq(term(x1, rational(-1), x2), llc::LT, 0);
lemma |= ineq(x2, llc::LT, 0);
lemma |= ineq(term(r1, rational(-1), r2), llc::LE, 0);
lemma |= ineq(term(q1, rational(-1), q2), llc::LE, 0);
return true;
}
return false;
};
auto monotonicity3 = [&](auto x1, auto& x1val, auto y1, auto& y1val, auto& r1, auto& r1val,
auto x2, auto& x2val, auto y2, auto& y2val, auto& r2, auto& r2val) {
if (y2val <= y1val && y1val < 0 && x1val <= x2val && x2val <= 0 && r1val < r2val) {
auto monotonicity3 = [&](auto x1, auto& x1val, auto y1, auto& y1val, auto& q1, auto& q1val,
auto x2, auto& x2val, auto y2, auto& y2val, auto& q2, auto& q2val) {
if (y2val <= y1val && y1val < 0 && x1val <= x2val && x2val <= 0 && q1val < q2val) {
new_lemma lemma(c, "y2 <= y1 < 0 & x1 <= x2 <= 0 => x1/y1 >= x2/y2");
lemma |= ineq(term(y1, rational(-1), y2), llc::LT, 0);
lemma |= ineq(y1, llc::GE, 0);
lemma |= ineq(term(x1, rational(-1), x2), llc::GT, 0);
lemma |= ineq(x2, llc::GT, 0);
lemma |= ineq(term(r1, rational(-1), r2), llc::GE, 0);
lemma |= ineq(term(q1, rational(-1), q2), llc::GE, 0);
return true;
}
return false;
};
auto monotonicity = [&](auto x1, auto& x1val, auto y1, auto& y1val, auto& r1, auto& r1val,
auto x2, auto& x2val, auto y2, auto& y2val, auto& r2, auto& r2val) {
if (monotonicity1(x1, x1val, y1, y1val, r1, r1val, x2, x2val, y2, y2val, r2, r2val))
auto monotonicity = [&](auto x1, auto& x1val, auto y1, auto& y1val, auto& q1, auto& q1val,
auto x2, auto& x2val, auto y2, auto& y2val, auto& q2, auto& q2val) {
if (monotonicity1(x1, x1val, y1, y1val, q1, q1val, x2, x2val, y2, y2val, q2, q2val))
return true;
if (monotonicity1(x2, x2val, y2, y2val, r2, r2val, x1, x1val, y1, y1val, r1, r1val))
if (monotonicity1(x2, x2val, y2, y2val, q2, q2val, x1, x1val, y1, y1val, q1, q1val))
return true;
if (monotonicity2(x1, x1val, y1, y1val, r1, r1val, x2, x2val, y2, y2val, r2, r2val))
if (monotonicity2(x1, x1val, y1, y1val, q1, q1val, x2, x2val, y2, y2val, q2, q2val))
return true;
if (monotonicity2(x2, x2val, y2, y2val, r2, r2val, x1, x1val, y1, y1val, r1, r1val))
if (monotonicity2(x2, x2val, y2, y2val, q2, q2val, x1, x1val, y1, y1val, q1, q1val))
return true;
if (monotonicity3(x1, x1val, y1, y1val, r1, r1val, x2, x2val, y2, y2val, r2, r2val))
if (monotonicity3(x1, x1val, y1, y1val, q1, q1val, x2, x2val, y2, y2val, q2, q2val))
return true;
if (monotonicity3(x2, x2val, y2, y2val, r2, r2val, x1, x1val, y1, y1val, r1, r1val))
if (monotonicity3(x2, x2val, y2, y2val, q2, q2val, x1, x1val, y1, y1val, q1, q1val))
return true;
return false;
};
@ -106,15 +115,15 @@ namespace nla {
// idiv semantics
if (!xval.is_int() || !yval.is_int() || yval == 0 || rval == div(xval, yval))
continue;
for (auto const& [r2, x2, y2] : m_idivisions) {
if (r2 == r)
for (auto const& [q2, x2, y2] : m_idivisions) {
if (q2 == r)
continue;
if (!c.is_relevant(r2))
if (!c.is_relevant(q2))
continue;
auto x2val = c.val(x2);
auto y2val = c.val(y2);
auto r2val = c.val(r2);
if (monotonicity(x, xval, y, yval, r, rval, x2, x2val, y2, y2val, r2, r2val))
auto q2val = c.val(q2);
if (monotonicity(x, xval, y, yval, r, rval, x2, x2val, y2, y2val, q2, q2val))
return;
}
}
@ -128,15 +137,15 @@ namespace nla {
// / semantics
if (yval == 0 || rval == xval / yval)
continue;
for (auto const& [r2, x2, y2] : m_rdivisions) {
if (r2 == r)
for (auto const& [q2, x2, y2] : m_rdivisions) {
if (q2 == r)
continue;
if (!c.is_relevant(r2))
if (!c.is_relevant(q2))
continue;
auto x2val = c.val(x2);
auto y2val = c.val(y2);
auto r2val = c.val(r2);
if (monotonicity(x, xval, y, yval, r, rval, x2, x2val, y2, y2val, r2, r2val))
auto q2val = c.val(q2);
if (monotonicity(x, xval, y, yval, r, rval, x2, x2val, y2, y2val, q2, q2val))
return;
}
}
@ -146,5 +155,100 @@ namespace nla {
// if p is bounded, q a value, r = eval(p):
// p <= q * div(r, q) + q - 1 => div(p, q) <= div(r, q)
// p >= q * div(r, q) => div(r, q) <= div(p, q)
#if 0
bool check_idiv_bounds() {
if (m_idiv_terms.empty()) {
return true;
}
bool all_divs_valid = true;
unsigned count = 0;
unsigned offset = ctx().get_random_value();
for (unsigned j = 0; j < m_idiv_terms.size(); ++j) {
unsigned i = (offset + j) % m_idiv_terms.size();
expr* n = m_idiv_terms[i];
if (!ctx().is_relevant(n))
continue;
expr* p = nullptr, * q = nullptr;
VERIFY(a.is_idiv(n, p, q));
theory_var v = internalize_def(to_app(n));
theory_var v1 = internalize_def(to_app(p));
if (!is_registered_var(v1))
continue;
lp::impq q1 = get_ivalue(v1);
rational q2;
if (!q1.x.is_int() || q1.x.is_neg() || !q1.y.is_zero()) {
// TBD
// q1 = 223/4, q2 = 2, r = 219/8
// take ceil(q1), floor(q1), ceil(q2), floor(q2), for floor(q2) > 0
// then
// p/q <= ceil(q1)/floor(q2) => n <= div(ceil(q1), floor(q2))
// p/q >= floor(q1)/ceil(q2) => n >= div(floor(q1), ceil(q2))
continue;
}
if (a.is_numeral(q, q2) && q2.is_pos()) {
if (!a.is_bounded(n)) {
TRACE("arith", tout << "unbounded " << expr_ref(n, m) << "\n";);
continue;
}
if (!is_registered_var(v))
continue;
lp::impq val_v = get_ivalue(v);
if (val_v.y.is_zero() && val_v.x == div(q1.x, q2))
continue;
TRACE("arith", tout << get_value(v) << " != " << q1 << " div " << q2 << "\n";);
rational div_r = div(q1.x, q2);
// p <= q * div(q1, q) + q - 1 => div(p, q) <= div(q1, q2)
// p >= q * div(q1, q) => div(q1, q) <= div(p, q)
rational mul(1);
rational hi = q2 * div_r + q2 - 1;
rational lo = q2 * div_r;
// used to normalize inequalities so they
// don't appear as 8*x >= 15, but x >= 2
expr* n1 = nullptr, * n2 = nullptr;
if (a.is_mul(p, n1, n2) && a.is_extended_numeral(n1, mul) && mul.is_pos()) {
p = n2;
hi = floor(hi / mul);
lo = ceil(lo / mul);
}
literal p_le_q1 = mk_literal(a.mk_le(p, a.mk_numeral(hi, true)));
literal p_ge_q1 = mk_literal(a.mk_ge(p, a.mk_numeral(lo, true)));
literal n_le_div = mk_literal(a.mk_le(n, a.mk_numeral(div_r, true)));
literal n_ge_div = mk_literal(a.mk_ge(n, a.mk_numeral(div_r, true)));
{
scoped_trace_stream _sts(th, ~p_le_q1, n_le_div);
mk_axiom(~p_le_q1, n_le_div);
}
{
scoped_trace_stream _sts(th, ~p_ge_q1, n_ge_div);
mk_axiom(~p_ge_q1, n_ge_div);
}
all_divs_valid = false;
++count;
TRACE("arith",
tout << q1 << " div " << q2 << "\n";
literal_vector lits;
lits.push_back(~p_le_q1);
lits.push_back(n_le_div);
ctx().display_literals_verbose(tout, lits) << "\n\n";
lits[0] = ~p_ge_q1;
lits[1] = n_ge_div;
ctx().display_literals_verbose(tout, lits) << "\n";);
continue;
}
}
return all_divs_valid;
}
#endif
}

6
src/math/lp/nla_divisions.h
View file

@ -24,10 +24,12 @@ namespace nla {
core& m_core;
vector<std::tuple<lpvar, lpvar, lpvar>> m_idivisions;
vector<std::tuple<lpvar, lpvar, lpvar>> m_rdivisions;
vector<std::tuple<lpvar, lpvar, lpvar, lpvar>> m_bounded_divisions;
public:
divisions(core& c):m_core(c) {}
void add_idivision(lpvar r, lpvar x, lpvar y);
void add_rdivision(lpvar r, lpvar x, lpvar y);
void add_idivision(lpvar q, lpvar x, lpvar y);
void add_rdivision(lpvar q, lpvar x, lpvar y);
void add_bounded_division(lpvar q, lpvar r, lpvar x, lpvar y);
void check(vector<lemma>&);
};
}

2
src/smt/theory_lra.cpp
View file

@ -1808,7 +1808,7 @@ public:
for (unsigned j = 0; j < m_idiv_terms.size(); ++j) {
unsigned i = (offset + j) % m_idiv_terms.size();
expr* n = m_idiv_terms[i];
if (!ctx().is_relevant(n))
if (false && !ctx().is_relevant(n))
continue;
expr* p = nullptr, *q = nullptr;
VERIFY(a.is_idiv(n, p, q));