dcff54edb5
Not sure why this had been missing. Precedence is slightly higher than `||`, matching the precedence order we have for bitwise operators.
47 lines
1.5 KiB
Text
47 lines
1.5 KiB
Text
import Std.Tactic.BVDecide
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-- two hard problems from: https://github.com/leanprover/LNSym/pull/85
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notation:50 x " >>>ᵤ " y => BitVec.ushiftRight x y
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def popcount32_spec_rec (i : Nat) (x : BitVec 32) : (BitVec 32) :=
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match i with
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| 0 => 0#32
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| i' + 1 =>
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let bit_idx := BitVec.extractLsb i' i' x
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let bv_idx := (BitVec.zeroExtend 32 bit_idx)
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(bv_idx + (popcount32_spec_rec i' x))
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def popcount32_spec (x : BitVec 32) : BitVec 32 :=
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popcount32_spec_rec 32 x
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def popcount32_impl (x : BitVec 32) : BitVec 32 :=
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let x' := x - ((x >>>ᵤ 1) &&& 0x55555555#32)
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let x'' := (x' &&& 0x33333333#32) + ((x' >>>ᵤ 2) &&& 0x33333333#32)
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((x'' + (x'' >>>ᵤ 4) &&& 0x0f0f0f0f#32) * 0x01010101#32) >>>ᵤ 24
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theorem popcount32_correct (x : BitVec 32) :
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(popcount32_spec x) = (popcount32_impl x) := by
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dsimp only [popcount32_spec_rec, popcount32_spec, popcount32_impl]
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bv_decide
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def parity32_spec_rec (i : Nat) (x : BitVec 32) : Bool :=
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match i with
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| 0 => false
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| i' + 1 =>
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let bit_idx := BitVec.getLsbD x i'
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bit_idx ^^ (parity32_spec_rec i' x)
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def parity32_spec (x : BitVec 32) : Bool :=
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parity32_spec_rec 32 x
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def parity32_impl (x : BitVec 32) : BitVec 32 :=
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let x1 := x ^^^ (x >>> 16)
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let x2 := x1 ^^^ (x1 >>> 8)
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let x3 := x2 ^^^ (x2 >>> 4)
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let x4 := x3 &&& 0x0000000f#32
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(0x00006996#32 >>> x4) &&& 1#32
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theorem parity32_correct (x : BitVec 32) :
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(parity32_spec x) = ((parity32_impl x).getLsbD 0) := by
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dsimp only [parity32_spec, parity32_impl, parity32_spec_rec]
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bv_decide
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