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feat: add BitVec.(toInt, toFin)_rotate(Left, Right) (#7616)

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This PR introduces `BitVec.(toInt, toFin)_rotate(Left, Right)`,
completing the API for `BitVec.rotate(Left, Right)`
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Luisa Cicolini 2025-03-24 08:51:54 +00:00 • committed by GitHub
parent 7c41aad194
commit 5fa0e50440
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18
src/Init/Data/BitVec/Lemmas.lean
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@ -4015,6 +4015,16 @@ theorem toNat_rotateLeft {x : BitVec w} {r : Nat} :
(x.rotateLeft r).toNat = (x.toNat <<< (r % w)) % (2^w) ||| x.toNat >>> (w - r % w) := by
simp only [rotateLeft_def, toNat_shiftLeft, toNat_ushiftRight, toNat_or]
theorem toInt_rotateLeft {x : BitVec w} {r : Nat} :
(x.rotateLeft r).toInt =
((x <<< (r % w)).toNat ||| (x >>> (w - r % w)).toNat : Int).bmod (2 ^ w) := by
simp [rotateLeft_def, toInt_shiftLeft, toInt_ushiftRight, toInt_or]
theorem toFin_rotateLeft {x : BitVec w} {r : Nat} :
(x.rotateLeft r).toFin =
Fin.ofNat' (2 ^ w) (x.toNat <<< (r % w)) ||| x.toFin / Fin.ofNat' (2 ^ w) (2 ^ (w - r % w)) := by
simp [rotateLeft_def, toFin_shiftLeft, toFin_ushiftRight, toFin_or]
/-! ## Rotate Right -/
/-- `rotateRight` is defined in terms of left and right shifts. -/
@ -4161,6 +4171,14 @@ theorem toNat_rotateRight {x : BitVec w} {r : Nat} :
(x.rotateRight r).toNat = (x.toNat >>> (r % w)) ||| x.toNat <<< (w - r % w) % (2^w) := by
simp only [rotateRight_def, toNat_shiftLeft, toNat_ushiftRight, toNat_or]
theorem toInt_rotateRight {x : BitVec w} {r : Nat} :
(x.rotateRight r).toInt = ((x >>> (r % w)).toNat ||| (x <<< (w - r % w)).toNat : Int).bmod (2 ^ w) := by
simp [rotateRight_def, toInt_shiftLeft, toInt_ushiftRight, toInt_or]
theorem toFin_rotateRight {x : BitVec w} {r : Nat} :
(x.rotateRight r).toFin = x.toFin / Fin.ofNat' (2 ^ w) (2 ^ (r % w)) ||| Fin.ofNat' (2 ^ w) (x.toNat <<< (w - r % w)) := by
simp [rotateRight_def, toFin_shiftLeft, toFin_ushiftRight, toFin_or]
/- ## twoPow -/
theorem twoPow_eq (w : Nat) (i : Nat) : twoPow w i = 1#w <<< i := by