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move bounded division lemmas to nla solver/ nla_divisions.

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This commit is contained in:
Nikolaj Bjorner 2023-01-30 11:11:04 -08:00
parent 03ca330926
commit 304b316314
7 changed files with 110 additions and 216 deletions
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135
src/math/lp/nla_divisions.cpp
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@ -36,13 +36,22 @@ namespace nla {
m_core.trail().push(push_back_vector(m_rdivisions));
}
void divisions::add_bounded_division(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_bounded_divisions.push_back({ q, x, y });
m_core.trail().push(push_back_vector(m_bounded_divisions));
}
typedef lp::lar_term term;
// y1 >= y2 > 0 & x1 <= x2 => x1/y1 <= x2/y2
// y2 <= y1 < 0 & x1 >= x2 >= 0 => x1/y1 <= x2/y2
// y2 <= y1 < 0 & x1 <= x2 <= 0 => x1/y1 >= x2/y2
void divisions::check(vector<lemma>& lemmas) {
void divisions::check() {
core& c = m_core;
if (c.use_nra_model())
return;
@ -155,99 +164,45 @@ namespace nla {
// 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));
void divisions::check_bounded_divisions() {
core& c = m_core;
unsigned offset = c.random(), sz = m_bounded_divisions.size();
if (!is_registered_var(v1))
for (unsigned j = 0; j < sz; ++j) {
unsigned i = (offset + j) % sz;
auto [q, x, y] = m_bounded_divisions[i];
if (!c.is_relevant(q))
continue;
auto xv = c.val(x);
auto yv = c.val(y);
auto qv = c.val(q);
if (xv < 0 || !xv.is_int())
continue;
if (yv <= 0 || !yv.is_int())
continue;
if (qv == div(xv, yv))
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;
rational div_v = div(xv, yv);
// y = yv & x <= yv * div(xv, yv) + yv - 1 => div(x, y) <= div(xv, yv)
// y = yv & x >= y * div(xv, yv) => div(xv, yv) <= div(x, y)
rational mul(1);
rational hi = yv * div_v + yv - 1;
rational lo = yv * div_v;
if (xv > hi) {
new_lemma lemma(c, "y = yv & x <= yv * div(xv, yv) + yv - 1 => div(p, y) <= div(xv, yv)");
lemma |= ineq(y, llc::NE, yv);
lemma |= ineq(x, llc::GT, hi);
lemma |= ineq(q, llc::LE, div_v);
return;
}
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;
if (xv < lo) {
new_lemma lemma(c, "y = yv & x >= yv * div(xv, yv) => div(xv, yv) <= div(x, y)");
lemma |= ineq(y, llc::NE, yv);
lemma |= ineq(x, llc::LT, lo);
lemma |= ineq(q, llc::GE, div_v);
return;
}
}
return all_divs_valid;
}
#endif
}
}