7c62881a95
This PR adds short-circuit support to bv_decide to accelerate multiplications with shared coefficients. In particular, `a * x = b * x` can be extended to `a = b v (a * x = b * x)`. The latter is faster if `a = b` is true, as `a = b` may be evaluated without considering the multiplication circuit. On the other hand, we require the multiplication circuit, as `a * x = b * x -> a = b` is not always true due to two's complement wrapping. We support multiplications through acNF, which takes into account shared terms across equality canonicalizing `a * (b * c1) = a * (b * c2)` to `(a * b) * c1 = (a * b) * c2`. As a result, the non-shared terms are lifted to the top such that canonical rewrites for binary multiplication with shared terms on the left/right are sufficient. We add an option `bv_decide +shortCircuit` which controls this feature (currently disabled by default). --------- Co-authored-by: Siddharth Bhat <siddu.druid@gmail.com> Co-authored-by: Henrik Böving <hargonix@gmail.com>
24 lines
991 B
Text
24 lines
991 B
Text
import Std.Tactic.BVDecide
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theorem remAnd_a_thm (x : _root_.BitVec 32) :
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x + x.sdiv 8#32 * 4294967288#32 &&& 1#32 = x &&& 1#32 := by
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bv_decide
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theorem test21_thm (x : _root_.BitVec 8) :
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x.sshiftRight 7 &&& 1#8 = x >>> 7 := by
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bv_decide
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theorem bitvec_AndOrXor_1683_2 : ∀ (a b : BitVec 64), (b ≤ a) || (a != b) = true := by
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intros; bv_decide
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theorem short_circuit_mul_right (x x_1 : BitVec 32) (h : ¬x_1 &&& 4096#32 == 0#32) :
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(x ||| 4096#32) * (x ||| 4096#32) = (x ||| x_1 &&& 4096#32) * (x ||| 4096#32) := by
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bv_decide +shortCircuit
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theorem short_circuit_mul_left (x x_1 : BitVec 32) (h : ¬x_1 &&& 4096#32 == 0#32) :
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(x ||| 4096#32) * (x ||| 4096#32) = (x ||| 4096#32) * (x ||| x_1 &&& 4096#32) := by
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bv_decide +shortCircuit
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theorem short_circuit_triple_mul (x x_1 x_2 : BitVec 32) (h : ¬x_2 &&& 4096#32 == 0#32) :
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(x_1 ||| 4096#32) * x * (x_1 ||| 4096#32) = (x_1 ||| x_2 &&& 4096#32) * x * (x_1 ||| 4096#32) := by
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bv_decide +acNf +shortCircuit
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