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fix ashr axioms

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This commit is contained in:
Jakob Rath 2024-01-11 18:09:17 +01:00
parent 9fb9e659b0
commit 80184c6ee2
1 changed files with 12 additions and 6 deletions
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14
src/sat/smt/polysat/op_constraint.cpp
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@ -364,6 +364,8 @@ namespace polysat {
// r*2^k = a0 // r*2^k = a0
// ab - a0 = 0b = p - r*2^k < 2^k // ab - a0 = 0b = p - r*2^k < 2^k
// r < 2^{N-k} // r < 2^{N-k}
// From p >= 0 we know a[N-k-1] = 0, thus:
// r < 2^{N-k-1}
// //
// Suppose q = k, p < 0 // Suppose q = k, p < 0
// p = ab // p = ab
@ -373,6 +375,10 @@ namespace polysat {
// r >= 1110 // r >= 1110
// example: // example:
// 1100 = 12 = 16 - 4 = 2^4 - 2^2 = 2^N - 2^k // 1100 = 12 = 16 - 4 = 2^4 - 2^2 = 2^N - 2^k
// ^^^ a
// p = 1ab, where b has length k, a has length N - k - 1
// r = 111a, where 111 has length k + 1
// r >= 2^N - 2^{N-k-1}
// //
// Succinct: // Succinct:
// if q = k & p >= 0 -> r*2^k + p < 2^{N-k} && r < 2^k // if q = k & p >= 0 -> r*2^k + p < 2^{N-k} && r < 2^k
@ -388,12 +394,12 @@ namespace polysat {
unsigned k = qv.val().get_unsigned(); unsigned k = qv.val().get_unsigned();
rational twoN = rational::power_of_two(N); rational twoN = rational::power_of_two(N);
rational twoK = rational::power_of_two(k); rational twoK = rational::power_of_two(k);
rational twoNk = rational::power_of_two(N - k); rational twoNk1 = rational::power_of_two(N - k - 1);
bool c1 = add_conflict(c, "q = k & 0 < k < N -> 2^k r <= p", { ~C.eq(q, k), C.ule(r * twoK, p) }); bool c1 = add_conflict(c, "q = k & 0 < k < N -> 2^k r <= p", { ~C.eq(q, k), C.ule(r * twoK, p) });
bool c2 = add_conflict(c, "q = k & 0 < k < N -> p <= 2^k*x + 2^k - 1", { ~C.eq(q, k), C.ule(p, r * twoK + twoK - 1) }); bool c2 = add_conflict(c, "q = k & 0 < k < N -> p <= 2^k*r + 2^k - 1", { ~C.eq(q, k), C.ule(p, r * twoK + twoK - 1) });
bool c3 = add_conflict(c, "p < 0 & q = k -> r >= 2^N - 2^{N-k}", { ~C.eq(q, k), ~C.slt(p, 0), C.uge(r, twoN - twoNk) }); bool c3 = add_conflict(c, "p < 0 & q = k -> r >= 2^N - 2^{N-k-1}", { ~C.eq(q, k), ~C.slt(p, 0), C.uge(r, twoN - twoNk1) });
bool c4 = add_conflict(c, "p >= 0 & q = k -> r < 2^{N-k}", { ~C.eq(q, k), C.slt(p, 0), C.ult(r, twoNk)}); bool c4 = add_conflict(c, "p >= 0 & q = k -> r < 2^{N-k-1}", { ~C.eq(q, k), C.slt(p, 0), C.ult(r, twoNk1)});
VERIFY(c1 || c2 || c3 || c4); VERIFY(c1 || c2 || c3 || c4);
} }
} }