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https://github.com/Z3Prover/z3
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remove stale functionality, finish implementation for super-slices
This commit is contained in:
Nikolaj Bjorner
parent
6b12bd6dcd
commit
0d3a465e75
2 changed files with 18 additions and 178 deletions
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@ -33,15 +33,16 @@ namespace polysat {
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// 2^(w-hi+1)* x >=
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// 2^(w-hi+1)* x >=
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bool fixed_bits::check(rational const& val, fi_record& fi) {
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bool fixed_bits::check(rational const& val, fi_record& fi) {
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unsigned sz = c.size(m_var);
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unsigned sz = c.size(m_var);
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rational bw = rational::power_of_two(sz);
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for (auto const& s : m_fixed_slices) {
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for (auto const& s : m_fixed_slices) {
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rational bw = rational::power_of_two(s.length);
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rational sbw = rational::power_of_two(s.length);
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// slice is properly contained in bit-vector variable
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// slice is properly contained in bit-vector variable
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if (s.length <= sz && s.value != mod(machine_div2k(val, s.offset + 1), bw)) {
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if (s.length <= sz && s.value != mod(machine_div2k(val, s.offset + 1), sbw)) {
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SASSERT(s.offset + s.length <= sz);
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SASSERT(s.offset + s.length <= sz);
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rational hi_val = s.value;
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rational hi_val = s.value;
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rational lo_val = mod(s.value + 1, bw);
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rational lo_val = mod(s.value + 1, sbw);
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pdd lo = c.value(rational::power_of_two(sz - s.offset - s.length) * lo_val, c.size(m_var));
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pdd lo = c.value(rational::power_of_two(sz - s.offset - s.length) * lo_val, sz);
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pdd hi = c.value(rational::power_of_two(sz - s.offset - s.length) * hi_val, c.size(m_var));
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pdd hi = c.value(rational::power_of_two(sz - s.offset - s.length) * hi_val, sz);
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fi.reset();
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fi.reset();
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fi.interval = eval_interval::proper(lo, lo_val, hi, hi_val);
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fi.interval = eval_interval::proper(lo, lo_val, hi, hi_val);
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fi.deps.push_back(dependency({ m_var, s }));
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fi.deps.push_back(dependency({ m_var, s }));
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@ -51,8 +52,17 @@ namespace polysat {
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}
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}
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// slice, properly contains variable.
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// slice, properly contains variable.
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// s.offset refers to offset in containing value.
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// s.offset refers to offset in containing value.
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if (s.length > sz) {
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if (s.length > sz && mod(machine_div2k(s.value, s.offset), bw) != val) {
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NOT_IMPLEMENTED_YET();
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rational hi_val = mod(machine_div2k(s.value, s.offset), bw);
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rational lo_val = mod(hi_val + 1, bw);
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pdd lo = c.value(lo_val, sz);
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pdd hi = c.value(hi_val, sz);
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fi.reset();
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fi.interval = eval_interval::proper(lo, lo_val, hi, hi_val);
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fi.deps.push_back(dependency({ m_var, s }));
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fi.bit_width = sz;
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fi.coeff = 1;
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return false;
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}
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}
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}
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}
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return true;
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return true;
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@ -64,165 +74,4 @@ namespace polysat {
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return out;
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return out;
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}
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}
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/**
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* 2^k * x = 2^k * b
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* ==> x[N-k-1:0] = b[N-k-1:0]
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*/
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bool get_eq_fixed_lsb(pdd const& p, fixed_slice& out) {
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SASSERT(!p.is_val());
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unsigned const N = p.power_of_2();
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// Recognize p = 2^k * a * x - 2^k * b
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if (!p.hi().is_val())
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return false;
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if (!p.lo().is_val())
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return false;
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// p = c * x - d
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rational const c = p.hi().val();
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rational const d = (-p.lo()).val();
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SASSERT(!c.is_zero());
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#if 1
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// NOTE: ule_constraint::simplify removes odd factors of the leading term
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unsigned k;
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VERIFY(c.is_power_of_two(k));
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if (d.parity(N) < k)
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return false;
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rational const b = machine_div2k(d, k);
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out = fixed_slice(b, 0, N - k);
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SASSERT_EQ(d, b * rational::power_of_two(k));
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SASSERT_EQ(p, (p.manager().mk_var(p.var()) - out.value) * rational::power_of_two(k));
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return true;
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#else
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// branch if we want to support non-simplifed constraints (not recommended)
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//
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// 2^k * a * x = 2^k * b
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// ==> x[N-k-1:0] = a^-1 * b[N-k-1:0]
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// for odd a
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unsigned k = c.parity(N);
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if (d.parity(N) < k)
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return false;
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rational const a = machine_div2k(c, k);
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SASSERT(a.is_odd());
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SASSERT(a.is_one()); // TODO: ule-simplify will multiply with a_inv already, so we can drop the check here.
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rational a_inv;
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VERIFY(a.mult_inverse(N, a_inv));
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rational const b = machine_div2k(d, k);
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out.hi = N - k - 1;
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out.lo = 0;
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out.value = a_inv * b;
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SASSERT_EQ(p, (p.manager().mk_var(p.var()) - out.value) * a * rational::power_of_two(k));
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return true;
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#endif
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}
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bool get_eq_fixed_slice(pdd const& p, fixed_slice& out) {
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if (get_eq_fixed_lsb(p, out))
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return true;
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return false;
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}
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/**
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* Constraint lhs <= rhs.
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*
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* -2^(k - 2) * x > 2^(k - 1)
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* <=> 2 + x[1:0] > 2 (mod 4)
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* ==> x[1:0] = 1
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* -- TODO: Generalize [the obvious solution does not work]
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*/
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bool get_ule_fixed_lsb(pdd const& lhs, pdd const& rhs, bool is_positive, fixed_slice& out) {
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return false;
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}
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/**
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* Constraint lhs <= rhs.
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*
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* x <= 2^k - 1 ==> x[N-1:k] = 0
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* x < 2^k ==> x[N-1:k] = 0
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*/
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bool get_ule_fixed_msb(pdd const& p, pdd const& q, bool is_positive, fixed_slice& out) {
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SASSERT(!q.is_zero()); // equalities are handled elsewhere
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unsigned const N = p.power_of_2();
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pdd const& lhs = is_positive ? p : q;
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pdd const& rhs = is_positive ? q : p;
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bool const is_strict = !is_positive;
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if (lhs.is_var() && rhs.is_val()) {
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// x <= c
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// find smallest k such that c <= 2^k - 1, i.e., c+1 <= 2^k
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// ==> x <= 2^k - 1 ==> x[N-1:k] = 0
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//
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// x < c
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// find smallest k such that c <= 2^k
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// ==> x < 2^k ==> x[N-1:k] = 0
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rational const c = is_strict ? rhs.val() : (rhs.val() + 1);
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unsigned const k = c.next_power_of_two();
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if (k < N) {
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out.length = N - k;
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out.offset = k;
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out.value = 0;
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return true;
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}
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}
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return false;
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}
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// 2^(N-1) <= 2^(N-1-i) * x
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bool get_ule_fixed_bit(pdd const& p, pdd const& q, bool is_positive, fixed_slice& out) {
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return false;
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}
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bool get_ule_fixed_slice(pdd const& lhs, pdd const& rhs, bool is_positive, fixed_slice& out) {
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SASSERT(ule_constraint::is_simplified(lhs, rhs));
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if (rhs.is_zero())
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return is_positive ? get_eq_fixed_slice(lhs, out) : false;
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if (get_ule_fixed_msb(lhs, rhs, is_positive, out))
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return true;
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if (get_ule_fixed_lsb(lhs, rhs, is_positive, out))
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return true;
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if (get_ule_fixed_bit(lhs, rhs, is_positive, out))
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return true;
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return false;
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}
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bool get_fixed_slice(signed_constraint c, fixed_slice& out) {
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SASSERT_EQ(c.vars().size(), 1); // this only makes sense for univariate constraints
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if (c.is_ule())
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return get_ule_fixed_slice(c.to_ule().lhs(), c.to_ule().rhs(), c.is_positive(), out);
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// if (c->is_op())
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// ; // TODO: x & constant = constant ==> bitmask ... but we have trouble recognizing that because we introduce a new variable for '&' before we see the equality.
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return false;
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}
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/*
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// 2^(k - d) * x = m * 2^(k - d)
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// Special case [still seems to occur frequently]: -2^(k - 2) * x > 2^(k - 1) - TODO: Generalize [the obvious solution does not work] => lsb(x, 2) = 1
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bool get_lsb(pdd lhs, pdd rhs, pdd& p, trailing_bits& info, bool pos) {
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SASSERT(lhs.is_univariate() && lhs.degree() <= 1);
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SASSERT(rhs.is_univariate() && rhs.degree() <= 1);
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else { // inequality - check for special case
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if (pos || lhs.power_of_2() < 3)
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return false;
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auto it = lhs.begin();
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if (it == lhs.end())
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return false;
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if (it->vars.size() != 1)
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return false;
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rational coeff = it->coeff;
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it++;
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if (it != lhs.end())
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return false;
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if ((mod2k(-coeff, lhs.power_of_2())) != rational::power_of_two(lhs.power_of_2() - 2))
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return false;
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p = lhs.div(coeff);
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SASSERT(p.is_var());
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info.bits = 1;
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info.length = 2;
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info.positive = true; // this is a conjunction
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return true;
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}
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}
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*/
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} // namespace polysat
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} // namespace polysat
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@ -20,15 +20,6 @@ namespace polysat {
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class core;
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class core;
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bool get_eq_fixed_lsb(pdd const& p, fixed_slice& out);
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bool get_eq_fixed_slice(pdd const& p, fixed_slice& out);
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bool get_ule_fixed_lsb(pdd const& lhs, pdd const& rhs, bool is_positive, fixed_slice& out);
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bool get_ule_fixed_msb(pdd const& lhs, pdd const& rhs, bool is_positive, fixed_slice& out);
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bool get_ule_fixed_bit(pdd const& lhs, pdd const& rhs, bool is_positive, fixed_slice& out);
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bool get_ule_fixed_slice(pdd const& lhs, pdd const& rhs, bool is_positive, fixed_slice& out);
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bool get_fixed_slice(signed_constraint c, fixed_slice& out);
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class fixed_bits {
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class fixed_bits {
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core& c;
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core& c;
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pvar m_var = null_var;
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pvar m_var = null_var;
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