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wip based on notes

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2022-12-29 16:55:46 -08:00
parent ab9a9d2308
commit 10589d59ba
2 changed files with 99 additions and 17 deletions
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112
src/math/polysat/saturation.cpp
View file

@ -1498,6 +1498,84 @@ namespace polysat {
}
rational saturation::round(rational const& N, rational const& x) {
SASSERT(0 <= x && x < N);
if (x + N/2 > N)
return x - N;
else
return x;
}
bool saturation::extract_linear_form(pdd const& q, pvar& y, rational& a, rational& b) {
auto & m = q.manager();
auto N = m.two_to_N();
if (q.is_val()) {
a = 0;
b = round(N, q.val());
return true;
}
y = q.var();
if (!q.lo().is_val())
return false;
if (!q.hi().is_val())
return false;
a = round(N, q.hi().val());
b = round(N, q.lo().val());
return true;
}
/**
* write as p := a*x*y + b*x + c*y + d
*/
bool saturation::extract_bilinear_form(pvar x, pdd const& p, pvar& y, rational& a, rational& b, rational& c, rational& d) {
auto & m = s.var2pdd(x);
auto N = m.two_to_N();
auto eval_round = [&](pdd const& p, rational& r) {
if (!s.try_eval(p, r))
return false;
r = round(N, r);
return true;
};
switch (p.degree(x)) {
case 0:
if (!s.try_eval(p, d))
return false;
a = b = c = 0;
return true;
case 1: {
pdd q = p, r = p, u = p, v = p;
p.factor(x, 1, q, r);
if (!extract_linear_form(q, y, a, b))
return false;
if (a == 0) {
c = 0;
return eval_round(r, d);
}
SASSERT(y != null_var);
switch (r.degree(y)) {
case 0:
if (!eval_round(r, d))
return false;
c = 0;
return true;
case 1:
r.factor(y, 1, u, v);
if (!eval_round(u, c))
return false;
if (!eval_round(v, d))
return false;
return true;
default:
return false;
}
return false;
}
default:
return false;
}
}
bool saturation::get_bound(pvar x, rational const& bound_x, pdd const& p, rational& bound_p) {
if (p.degree(x) == 0)
return s.try_eval(p, bound_p);
@ -1535,32 +1613,30 @@ namespace polysat {
x_max = hi;
SASSERT(x_min != x_max);
if (x_min > x_max)
x_min += m.two_to_N();
x_min -= m.two_to_N();
SASSERT(x_min <= x_max);
if (x_max == 0) {
SASSERT(x_min == 0);
return false;
}
auto isolate_y = [&](pvar x, pdd const& p, pdd& y, pdd& b) {
if (p.degree(x) != 1)
return false;
p.factor(x, 1, y, b);
return !y.is_val();
};
pdd y = p, b = p;
rational b_val, y_val;
// handle just one-side with x for now
if (p.degree(x) == 1 && q.degree(x) == 1)
pvar y1 = null_var, y2 = null_var, y;
rational a1, a2, b1, b2, c1, c2, d1, d2;
if (!extract_bilinear_form(x, p, y1, a1, b1, c1, d1))
return false;
if (!isolate_y(x, p, y, b) && !isolate_y(x, q, y, b))
if (!extract_bilinear_form(x, q, y2, a2, b2, c2, d2))
return false;
if (!s.try_eval(b, b_val))
if (y1 != null_var && y2 != null_var && y1 != y2)
return false;
if (!s.try_eval(y, y_val))
if (y1 == null_var && y2 == null_var)
return false;
// at this point p = x*y + b or q = x*y + b
y = (y1 == null_var) ? y2 : y1;
verbose_stream() << p << " v" << y << " " << a1 << " " << b1 << " " << c1 << " " << d1 << "\n";
verbose_stream() << q << " v" << y << " " << a2 << " " << b2 << " " << c2 << " " << d2 << "\n";
#if 0
auto is_bounded = [&](pdd& p, rational& lo, rational& hi) {
verbose_stream() << "is-bounded " << p << "\n";
if (!get_bound(x, x_min, p, lo))
@ -1614,6 +1690,8 @@ namespace polysat {
verbose_stream() << b << " " << b_val << " max-y " << max_y << "\n";
}
#endif
return false;
}

4
src/math/polysat/saturation.h
View file

@ -65,6 +65,10 @@ namespace polysat {
bool try_add_mul_bound(pvar x, conflict& core, inequality const& axb_l_y);
bool try_add_mul_bound2(pvar x, conflict& core, inequality const& axb_l_y);
rational round(rational const& N, rational const& x);
bool extract_linear_form(pdd const& q, pvar& y, rational& a, rational& b);
bool extract_bilinear_form(pvar x, pdd const& p, pvar& y, rational& a, rational& b, rational& c, rational& d);
bool get_bound(pvar x, rational const& bound_x, pdd const& p, rational& bound_p);
// c := lhs ~ v