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add saturation rules for overflow

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2024-02-01 12:55:17 -08:00
parent 32e23b3b6c
commit 60add85c47
1 changed files with 15 additions and 2 deletions
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17
src/sat/smt/polysat/saturation.cpp
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@ -208,9 +208,11 @@ namespace polysat {
/**
* Expand the following axioms:
* Ovfl(x, y) & x <= y => y >= 2^{(N + 1) div 2}
* Ovfl(x, y) & msb(x) <= k => msb(y) >= N - k - 1
* Ovfl(x, y) & msb(x) <= k & msb(y) <= N - k - 1 => 0x * 0y >= 2^{N-1}
*
* ~Ovfl(x, y) & x <= y => x < 2^{(N + 1) div 2}
* ~Ovfl(x,y) & msb(x) >= k => msb(y) <= N - k - 1
* ~Ovfl(x,y) & msb(x) >= k & msb(y) >= N - k - 1 => 0x * 0y < 2^{N-1}
*/
@ -231,6 +233,7 @@ namespace polysat {
if (bx > by) {
std::swap(bx, by);
std::swap(x, y);
std::swap(vx, vy);
}
// Keep in mind that
@ -261,7 +264,12 @@ namespace polysat {
SASSERT(bx > 1 && by > 1);
SASSERT(bx + by >= N + 1);
auto k = bx - 1;
if (bx + by > N + 1)
if (bx > (N + 1) / 2) {
add_clause("~Ovfl(x, y) & x <= y => x < 2^{(N + 1) div 2}",
{ d, ~C.ule(x, y), C.ult(x, rational::power_of_two((N + 1) / 2)) },
true);
}
else if (bx + by > N + 1)
add_clause("~Ovfl(x, y) & msb(x) >= k => msb(y) <= N - k - 1",
{d, ~msb_ge(x, k), msb_le(y, N - k - 1)},
true);
@ -277,9 +285,14 @@ namespace polysat {
}
else {
// Case Ovfl(x,y)
if (bx == 0) {
if (bx <= 1) {
add_clause("Ovfl(x, y) => x > 1", { d, C.ugt(x, 1) }, true);
}
else if (bx < (N + 1) / 2) {
add_clause("Ovfl(x, y) & x <= y => y >= 2^{(N + 1) div 2}",
{ d, ~C.ule(x, y), C.uge(x, rational::power_of_two((N + 1) / 2)) },
true);
}
else if (bx + by < N + 1) {
SASSERT(bx <= by);
auto k = bx - 1;