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add notes and unit tests

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2021-09-22 05:04:07 -07:00
parent 6478e789e9
commit dc55fbf30d
2 changed files with 138 additions and 13 deletions
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23
src/math/polysat/ule_constraint.cpp
View file

@ -12,7 +12,8 @@ Author:
Notes:
Rewrite rules to simplify expressions
Rewrite rules to simplify expressions.
In the following let k, k1, k2 be values.
- k1 <= k2 ==> 0 <= 0 if k1 <= k2
- k1 <= k2 ==> 1 <= 0 if k1 > k2
@ -21,9 +22,16 @@ Notes:
- k*2^n*p <= 0 ==> 2^n*p <= 0 if k is odd, leading coeffient is always a power of 2.
- k <= p ==> p - k <= - k - 1
TODO:
- p <= p + q ==> p <= -q - 1
- p + k <= p ==> p + k <= k - 1 for k > 0
TODO: clause simplifications:
- p + k <= p ==> p + k <= k or p = 0 for k != 0
- p*q = 0 ==> p = 0 or q = 0 applies to any factoring
- 2*p <= 2*q ==> (p >= 2^n-1 & q < 2^n-1) or (p >= 2^n-1 = q >= 2^n-1 & p <= q)
==> (p >= 2^n-1 => q < 2^n-1 or p <= q) &
(p < 2^n-1 => p <= q) &
(p < 2^n-1 => q < 2^n-1)
--*/
@ -53,7 +61,11 @@ namespace polysat {
if (m_rhs.is_val() && m_rhs.val() == m_rhs.manager().max_value()) {
m_lhs = 0, m_rhs = 0;
return;
}
}
if (m_lhs == m_rhs) {
m_lhs = m_rhs = 0;
return;
}
if (m_lhs.is_val() && m_rhs.is_val()) {
if (m_lhs.val() <= m_rhs.val())
m_lhs = m_rhs = 0;
@ -75,6 +87,7 @@ namespace polysat {
if (x.is_neg())
x = mod(x, m_lhs.manager().two_to_N());
m_lhs *= x;
SASSERT(m_lhs.leading_coefficient().is_power_of_two());
}
}

128
src/test/polysat.cpp
View file

@ -725,7 +725,7 @@ namespace polysat {
void permute_args(unsigned k, pdd& a, pdd& b, pdd& c) {
SASSERT(k < 6);
unsigned i = k % 3;
unsigned j = i % 2;
unsigned j = k % 2;
if (i == 1)
std::swap(a, b);
else if (i == 2)
@ -734,6 +734,40 @@ namespace polysat {
std::swap(b, c);
}
void permute_args(unsigned n, pdd& a, pdd& b, pdd& c, pdd& d) {
SASSERT(n < 24);
switch (n % 4) {
case 1:
std::swap(a, b);
break;
case 2:
std::swap(a, c);
break;
case 3:
std::swap(a, d);
break;
default:
break;
}
switch (n % 3) {
case 1:
std::swap(b, c);
break;
case 2:
std::swap(b, d);
break;
default:
break;
}
switch (n % 2) {
case 1:
std::swap(c, d);
break;
default:
break;
}
}
// xy < xz and !Omega(x*y) => y < z
static void test_ineq_axiom1(unsigned bw = 32) {
auto const bound = rational::power_of_two(bw-1);
@ -798,9 +832,84 @@ namespace polysat {
}
// xy < b & a <= x & !Omega(x*y) => a*y < b
static void test_ineq_axiom3(unsigned bw = 32) {
auto const bound = rational::power_of_two(bw - 1);
for (unsigned i = 0; i < 24; ++i) {
scoped_solver s(__func__);
auto x = s.var(s.add_var(bw));
auto y = s.var(s.add_var(bw));
auto a = s.var(s.add_var(bw));
auto b = s.var(s.add_var(bw));
permute_args(i, x, y, a, b);
s.add_ult(x * y, b);
s.add_ule(a, x);
s.add_ult(x, bound);
s.add_ult(y, bound);
s.add_ule(b, a * y);
s.check();
s.expect_unsat();
}
}
// xy <= b & a <= x & !Omega(x*y) => a*y <= b
static void test_ineq_axiom4(unsigned bw = 32) {
auto const bound = rational::power_of_two(bw - 1);
for (unsigned i = 0; i < 24; ++i) {
scoped_solver s(__func__);
auto x = s.var(s.add_var(bw));
auto y = s.var(s.add_var(bw));
auto a = s.var(s.add_var(bw));
auto b = s.var(s.add_var(bw));
permute_args(i, x, y, a, b);
s.add_ule(x * y, b);
s.add_ule(a, x);
s.add_ult(x, bound);
s.add_ult(y, bound);
s.add_ult(b, a * y);
s.check();
s.expect_unsat();
}
}
// a < xy & x <= b & !Omega(x*y) => a < b*y
// a <= xy & x <= b & !omega(x*y) => a <= b*y
static void test_ineq_axiom5(unsigned bw = 32) {
auto const bound = rational::power_of_two(bw - 1);
for (unsigned i = 0; i < 24; ++i) {
scoped_solver s(__func__);
auto x = s.var(s.add_var(bw));
auto y = s.var(s.add_var(bw));
auto a = s.var(s.add_var(bw));
auto b = s.var(s.add_var(bw));
permute_args(i, x, y, a, b);
s.add_ult(a, x * y);
s.add_ule(x, b);
s.add_ult(x, bound);
s.add_ult(y, bound);
s.add_ule(b * y, a);
s.check();
s.expect_unsat();
}
}
// a <= xy & x <= b & !Omega(x*y) => a <= b*y
static void test_ineq_axiom6(unsigned bw = 32) {
auto const bound = rational::power_of_two(bw - 1);
for (unsigned i = 0; i < 24; ++i) {
scoped_solver s(__func__);
auto x = s.var(s.add_var(bw));
auto y = s.var(s.add_var(bw));
auto a = s.var(s.add_var(bw));
auto b = s.var(s.add_var(bw));
permute_args(i, x, y, a, b);
s.add_ule(a, x * y);
s.add_ule(x, b);
s.add_ult(x, bound);
s.add_ult(y, bound);
s.add_ult(b * y, a);
s.check();
s.expect_unsat();
}
}
// Goal: we probably mix up polysat variables and PDD variables at several points; try to uncover such cases
@ -930,14 +1039,10 @@ void tst_polysat() {
polysat::test_subst();
// polysat::test_ineq_axiom1();
// return;
// not working
// polysat::test_fixed_point_arith_div_mul_inverse();
//polysat::test_monot_bounds_simple(8);
// polysat::test_fixed_point_arith_div_mul_inverse();
// polysat::test_monot_bounds_simple(8);
// working
polysat::test_fixed_point_arith_mul_div_inverse();
@ -965,6 +1070,13 @@ void tst_polysat() {
polysat::test_monot_bounds(2);
polysat::test_cjust();
polysat::test_ineq_axiom1();
polysat::test_ineq_axiom2();
polysat::test_ineq_axiom3();
polysat::test_ineq_axiom4();
polysat::test_ineq_axiom5();
polysat::test_ineq_axiom6();
// inefficient conflicts:
// Takes time: polysat::test_monot_bounds_full();