more nat bitwise ops
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@ -9,6 +9,11 @@ import Syntax.PreorderReasoning
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%default total
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infixl 8 `shiftL`, `shiftR`
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infixl 7 .&.
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infixl 6 `xor`
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infixl 5 .|.
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public export
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data LTE' : Nat -> Nat -> Type where
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@ -119,3 +124,86 @@ spread mask subj = go 1 (halfRec mask) subj 0 where
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go bit (HalfRecOdd _ rec) subj res = case half subj of
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HalfOdd subj => go (bit + bit) rec subj (res + bit)
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HalfEven subj => go (bit + bit) rec subj res
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public export
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data BitwiseRec : Nat -> Nat -> Type where
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BwDone : BitwiseRec 0 0
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Bw00 : (m, n : Nat) -> Lazy (BitwiseRec m n) ->
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BitwiseRec (m + m) (n + n)
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Bw01 : (m, n : Nat) -> Lazy (BitwiseRec m n) ->
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BitwiseRec (m + m) (S (n + n))
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Bw10 : (m, n : Nat) -> Lazy (BitwiseRec m n) ->
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BitwiseRec (S (m + m)) (n + n)
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Bw11 : (m, n : Nat) -> Lazy (BitwiseRec m n) ->
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BitwiseRec (S (m + m)) (S (n + n))
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export
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bitwiseRec : (m, n : Nat) -> BitwiseRec m n
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bitwiseRec m n = go (halfRec m) (halfRec n) where
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go : forall m, n. HalfRec m -> HalfRec n -> BitwiseRec m n
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go HalfRecZ HalfRecZ = BwDone
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go HalfRecZ (HalfRecEven n nr) = Bw00 0 n $ go HalfRecZ nr
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go HalfRecZ (HalfRecOdd n nr) = Bw01 0 n $ go HalfRecZ nr
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go (HalfRecEven m mr) HalfRecZ = Bw00 m 0 $ go mr HalfRecZ
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go (HalfRecEven m mr) (HalfRecEven n nr) = Bw00 m n $ go mr nr
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go (HalfRecEven m mr) (HalfRecOdd n nr) = Bw01 m n $ go mr nr
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go (HalfRecOdd m mr) HalfRecZ = Bw10 m 0 $ go mr HalfRecZ
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go (HalfRecOdd m mr) (HalfRecEven n nr) = Bw10 m n $ go mr nr
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go (HalfRecOdd m mr) (HalfRecOdd n nr) = Bw11 m n $ go mr nr
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export
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bitwise : (Bool -> Bool -> Bool) -> Nat -> Nat -> Nat
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bitwise f m n = go 1 (bitwiseRec m n) 0 where
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one : Bool -> Bool -> Nat -> Nat -> Nat
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one p q bit res = if f p q then bit + res else res
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go : forall m, n. Nat -> BitwiseRec m n -> Nat -> Nat
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go bit BwDone res = res
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go bit (Bw00 m n rec) res = go (bit + bit) rec $ one False False bit res
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go bit (Bw01 m n rec) res = go (bit + bit) rec $ one False True bit res
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go bit (Bw10 m n rec) res = go (bit + bit) rec $ one True False bit res
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go bit (Bw11 m n rec) res = go (bit + bit) rec $ one True True bit res
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export
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(.&.) : Nat -> Nat -> Nat
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(.&.) = bitwise $ \p, q => p && q
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private %foreign "scheme:blodwen-and"
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primAnd : Nat -> Nat -> Nat
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%transform "NatExtra.(.&.)" NatExtra.(.&.) m n = primAnd m n
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export
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(.|.) : Nat -> Nat -> Nat
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(.|.) = bitwise $ \p, q => p || q
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private %foreign "scheme:blodwen-or"
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primOr : Nat -> Nat -> Nat
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%transform "NatExtra.(.|.)" NatExtra.(.|.) m n = primOr m n
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export
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xor : Nat -> Nat -> Nat
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xor = bitwise (/=)
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private %foreign "scheme:blodwen-xor"
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primXor : Nat -> Nat -> Nat
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%transform "NatExtra.xor" NatExtra.xor m n = primXor m n
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export
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shiftL : Nat -> Nat -> Nat
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shiftL n 0 = n
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shiftL n (S i) = shiftL (n + n) i
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private %foreign "scheme:blodwen-shl"
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primShiftL : Nat -> Nat -> Nat
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%transform "NatExtra.shiftL" NatExtra.shiftL n i = primShiftL n i
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export
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shiftR : Nat -> Nat -> Nat
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shiftR n 0 = n
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shiftR n (S i) = shiftL (floorHalf n) i
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private %foreign "scheme:blodwen-shr"
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primShiftR : Nat -> Nat -> Nat
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%transform "NatExtra.shiftR" NatExtra.shiftR n i = primShiftR n i
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