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explain_overlap, notes on case ebw < abw

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Jakob Rath 2024-04-11 11:19:49 +02:00
parent adea39b92e
commit 138c90d52b
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160
src/sat/smt/polysat/viable.cpp
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@ -815,51 +815,94 @@ next:
}
/*
* For two consecutive intervals
*
* - 2^kx \not\in [lo, hi[,
* - 2^k'y \not\in [lo', hi'[
* - a value v such that
* - 2^kv \not\in [lo, hi[
* - 2^k'v \in [lo', hi'[
* - hi \in ] (v - 1) * 2^{bw - ebw} ; v * 2^{bw - ebw} ]
*
* For two consecutive intervals
*
* - 2^k x \not\in [lo, hi[ (entry 'e')
* - 2^k' y \not\in [lo', hi'[ (entry 'after')
* - value v such that
* - 2^k v \not\in [lo, hi[
* - 2^k' v \in [lo', hi'[
* - hi \in ] (v - 1) * 2^k ; v * 2^k ]
*
* Where:
* - bw is the width of x, aw the width of y
* - ebw is the bit-width of x, abw the bit-width of y
* - k = bw - ebw, k' = aw - abw
*
* We want to encode the constraint that (2^k' hi)[w'] in [lo', hi'[
*
* Note that x in [lo, hi[ <=> x - lo < hi - lo
* If bw = aw, ebw = abw there is nothing else to do.
* - hi \in [lo', hi'[
*
* If bw != aw or aw < bw:
* - hi \in ] (v - 1) * 2^{bw - ebw} ; v * 2^{bw - ebw} ]
* - hi := v mod aw
*
* - 2^k'hi \in [lo', hi'[
*
*
* We have the reduced intervals:
* - x[ebw] \not\in [ ceil(lo/2^k), ceil(hi/2^k) [
* - y[abw] \not\in [ ceil(lo'/2^k'), ceil(hi'/2^k') [
* - ceil(lo/2^k) != ceil(hi/2^k) ... ensured by side conditions from interval reduction
* - ceil(lo'/2^k') != ceil(hi'/2^k') ... ensured by side conditions from interval reduction
*
* Case ebw = abw:
* - Regular intervals that link up
* - Encode that ceil(hi/2^k) \in [ ceil(lo'/2^k'), ceil(hi'/2^k') [
* - This is equivalent to 2^k' ceil(hi/2^k) \in [ lo', hi' [
*
* Case ebw < abw:
* - 'e' is last entry of a hole.
* - project 'after' onto the hole: [?,ceil(hi/2^k)[ links up with [ceil(lo'/2^k')[ebw],ceil(hi'/2^k')[ebw][
* - We want to encode: ceil(hi/2^k) \in [ceil(lo'/2^k')[ebw],ceil(hi'/2^k')[ebw][
* - However, if 'after' is too small the projected interval may be empty and we do not get a useful constraint
* - The correct choice is to use the complement of the hole rather than the next interval alone.
* - This case is handled in explain_hole_overlap.
*
* Case ebw > abw:
* - 'after' is first entry of a hole.
* - conceptually: project complement of hole onto lower bit-width,
* i.e., have interval [?,ceil(hi/2^k)[abw][ link up with [ceil(lo'/2^k'),ceil(hi'/2^k')[
* - Encode: ceil(hi/2^k)[abw] \in [ceil(lo'/2^k'),ceil(hi'/2^k')[
* - Equivalently: 2^k' ceil(hi/2^k)[abw] \in [lo',hi'[
* - Equivalently: 2^k' ceil(hi/2^k) \in [lo',hi'[ because k' = aw - abw
*
* In both relevant cases, we want to encode the constraint
* 2^k' ceil(hi/2^k) \in [lo',hi'[
*
* - Note that x in [lo, hi[ <=> x - lo < hi - lo.
* - If k > 0 (i.e., ebw < bw) then evaluate ceil(hi/2^k) (since we cannot express it as pdd).
* TODO: possible exception: if all coefficients of 'hi' are divisible by 2^k
* - If bw != aw, likewise (since we cannot mix different pdd sizes in one expression).
* TODO: possible exception: if lo', hi' are values, just translate them to other pdd manager?
*
* Evaluating ceil(hi/2^k) means:
* - hi \in ] (v - 1) * 2^{bw - ebw} ; v * 2^{bw - ebw} ]
* - hi := v mod aw
*
*/
void viable::explain_overlap(explanation const& e, explanation const& after, dependency_vector& deps) {
auto bw = c.size(e.e->var);
auto ebw = e.e->bit_width;
auto aw = c.size(after.e->var);
auto abw = after.e->bit_width;
auto t = e.e->interval.hi();
auto lo = after.e->interval.lo();
auto hi = after.e->interval.hi();
#define DEBUG_EXPLAIN_OVERLAP 0
unsigned const bw = c.size(e.e->var);
unsigned const ebw = e.e->bit_width;
unsigned const aw = c.size(after.e->var);
unsigned const abw = after.e->bit_width;
pdd t = e.e->interval.hi();
pdd lo = after.e->interval.lo();
pdd hi = after.e->interval.hi();
#if DEBUG_EXPLAIN_OVERLAP
verbose_stream() << "explain_overlap\n";
display_explain(verbose_stream() << " e ", e) << "\n";
display_explain(verbose_stream() << " after ", after) << "\n";
verbose_stream() << " bw " << bw << " ebw " << ebw << " aw " << aw << " abw " << abw << "\n";
#endif
SASSERT(abw <= aw);
SASSERT(ebw <= bw);
SASSERT_EQ(mod2k(e.value, ebw), e.e->interval.hi_val());
SASSERT(r_interval::proper(after.e->interval.lo_val(), after.e->interval.hi_val()).contains(mod2k(e.value, abw)));
if (ebw < abw) {
// 'e' is the last entry of a hole.
// This case is handled in explain_hole_overlap.
return;
}
if (ebw < bw || aw != bw) {
auto const& p2b = rational::power_of_two(bw);
auto const& p2eb = rational::power_of_two(bw - ebw);
// let coeff = 2^{bw - ebw}
// let assume coeff * x \not\in [lo, t[
// let assume coeff * x \not\in [s, t[
// Then value is chosen, min x . coeff * x >= t.
// In other words:
//
@ -874,34 +917,57 @@ next:
auto vlo = c.value(mod((e.value - 1) * p2eb + 1, p2b), bw);
auto vhi = c.value(mod(e.value * p2eb + 1, p2b), bw);
#if 0
verbose_stream() << "value " << e.value << "\n";
verbose_stream() << "t " << t << "\n";
verbose_stream() << "[" << vlo << " " << vhi << "[\n";
verbose_stream() << "before bw " << ebw << " " << bw << " " << *e.e << "\nafter bw " << abw << " " << aw << " " << *after.e << "\n";
if (!t.is_val())
IF_VERBOSE(0, verbose_stream() << "symbolic t : " << t << "\n");
verbose_stream() << t - vlo << " " << vhi - vlo << "\n";
#endif
auto sc = cs.ult(t - vlo, vhi - vlo);
#if DEBUG_EXPLAIN_OVERLAP
verbose_stream() << " assignment: " << c.get_assignment() << "\n";
if (c.is_assigned(1))
verbose_stream() << " v1 = " << c.get_assignment().value(1) << "\n";
verbose_stream() << " value " << e.value << "\n";
verbose_stream() << " t " << t << "\n";
verbose_stream() << " [" << vlo << " " << vhi << "[\n";
verbose_stream() << " before bw " << ebw << " " << bw << " " << *e.e << "\n";
verbose_stream() << " after bw " << abw << " " << aw << " " << *after.e << "\n";
if (!t.is_val())
verbose_stream() << " symbolic t : " << t << "\n";
verbose_stream() << " " << t - vlo << " " << vhi - vlo << "\n";
verbose_stream() << " sc " << sc << "\n";
#endif
CTRACE("bv", sc.is_always_false(), c.display(tout));
VERIFY(!sc.is_always_false());
if (!sc.is_always_true())
deps.push_back(c.propagate(sc, c.explain_weak_eval(sc), "explain_overlap value bounds"));
t.reset(lo.manager());
t = c.value(mod(e.value, rational::power_of_two(aw)), aw);
// verbose_stream() << "after " << t << "\n";
#if DEBUG_EXPLAIN_OVERLAP
verbose_stream() << " t' " << t << "\n";
#endif
if (c.inconsistent())
verbose_stream() << "inconsistent overlap " << sc << " " << "\n";
}
if (abw < aw)
t *= rational::power_of_two(aw - abw);
/*
if (ebw < abw) {
// NOTE: this doesn't work, because the projected interval may be empty if we just project 'after' instead of the hole's complement
t *= rational::power_of_two(abw - ebw);
lo *= rational::power_of_two(abw - ebw);
hi *= rational::power_of_two(abw - ebw);
}
*/
if (abw < aw)
t *= rational::power_of_two(aw - abw);
auto sc = cs.ult(t - lo, hi - lo);
#if DEBUG_EXPLAIN_OVERLAP
// verbose_stream() << " lhs: " << t << " - (" << lo << ") == " << (t - lo) << "\n";
// verbose_stream() << " rhs: " << hi << " - (" << lo << ") == " << (hi - lo) << "\n";
// verbose_stream() << " ult: " << sc << "\n";
// verbose_stream() << " eval " << sc.eval() << "\n";
// verbose_stream() << " weval " << sc.weak_eval(c.get_assignment()) << "\n";
// verbose_stream() << " seval " << sc.strong_eval(c.get_assignment()) << "\n";
#endif
SASSERT(!sc.is_always_false());
if (!sc.is_always_true())
deps.push_back(c.propagate(sc, c.explain_weak_eval(sc), "explain_overlap linking constraint"));