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fixed_bits notes

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Jakob Rath 2024-04-03 10:52:25 +02:00
parent 60422d2071
commit d19de4b1d3
2 changed files with 24 additions and 14 deletions
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35
src/sat/smt/polysat/fixed_bits.cpp
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@ -30,28 +30,33 @@ namespace polysat {
}
//
// If x[hi:lo] = value, then
// let K = w - hi - 1 = w - s.length - s.offset
// 2^Kvalue <= 2^Kx < 2^K(value + 1)
// 2^Kx not in [2^K(value + 1), 2^Kvalue[
// bit-width : w - K = s.offset + s.length
// Assume x[hi:lo] = value.
// Then 2^lo value <= x[hi:0] < 2^lo (value + 1),
// and further 2^(lo + k) value <= 2^k x < 2^(lo + k) (value + 1)
// where k = w - hi - 1, lo = s.offset, hi = s.offset + s.length - 1.
//
// k = w - s.offset - s.length
// lo + k = w - s.length
// entry bit-width = w - k = s.offset + s.length
//
bool fixed_bits::check(rational const& val, fi_record& fi) {
unsigned sz = c.size(m_var);
rational bw = rational::power_of_two(sz);
for (auto const& s : m_fixed_slices) {
rational sbw = rational::power_of_two(s.length);
// slice is properly contained in bit-vector variable
if (s.length <= sz && s.value != mod(machine_div2k(val, s.offset), sbw)) {
SASSERT(s.offset + s.length <= sz);
unsigned bw = s.length + s.offset;
// unsigned K = sz - bw;
pdd lo = c.value(rational::power_of_two(sz - s.length) * (s.value + 1), sz);
pdd hi = c.value(rational::power_of_two(sz - s.length) * s.value, sz);
rational hi_val = rational::power_of_two(s.offset) * s.value;
rational lo_val = mod(rational::power_of_two(s.offset) * (s.value + 1), rational::power_of_two(bw));
rational p2lok = rational::power_of_two(sz - s.length);
rational p2lo = rational::power_of_two(s.offset);
pdd lo = c.value(p2lok * (s.value + 1), sz);
pdd hi = c.value(p2lok * s.value, sz);
rational lo_val = mod(p2lo * (s.value + 1), rational::power_of_two(bw));
rational hi_val = p2lo * s.value;
// verbose_stream() << "sz " << sz << "\n";
// verbose_stream() << "slice len " << s.length << " off " << s.offset << " value " << s.value << "\n";
// verbose_stream() << "lo " << lo.val() << " hi " << hi.val() << "\n";
// verbose_stream() << "lo_val " << lo_val << " hi_val " << hi_val << "\n";
fi.reset();
fi.interval = eval_interval::proper(lo, lo_val, hi, hi_val);
@ -61,10 +66,11 @@ namespace polysat {
// verbose_stream() << "fixed bits sub: v" << m_var << " " << sz << " value " << val << " " << fi << "\n";
return false;
}
#if 0
// slice, properly contains variable.
// s.offset refers to offset in containing value.
if (false && s.length > sz && mod(machine_div2k(s.value, s.offset), bw) != val) {
rational bw = rational::power_of_two(sz);
if (s.length > sz && mod(machine_div2k(s.value, s.offset), bw) != val) {
rational hi_val = mod(machine_div2k(s.value, s.offset), bw);
rational lo_val = mod(hi_val + 1, bw);
pdd lo = c.value(lo_val, sz);
@ -77,6 +83,7 @@ namespace polysat {
verbose_stream() << "fixed bits sup: v" << m_var << " " << fi << "\n";
return false;
}
#endif
}
return true;
}

3
src/sat/smt/polysat/forbidden_intervals.h
View file

@ -23,6 +23,9 @@ namespace polysat {
class core;
struct fi_record {
// eval_interval has both symbolic and concrete bounds:
// - symbolic pdd bounds are bounds on 2^(w - bit_width) * coeff * var[w-1:0] (modulo w = size(var))
// - concrete bounds are bounds on coeff * var[bit_width-1:0] (modulo bit_width)
eval_interval interval;
vector<signed_constraint> side_cond;
vector<signed_constraint> src; // there is either 0 or 1 src.