mirror of
https://github.com/idris-lang/Idris2.git
synced 2024-12-18 16:51:51 +03:00
208 lines
6.2 KiB
Idris
208 lines
6.2 KiB
Idris
module Data.Bits
|
|
|
|
import Data.DPair
|
|
import public Data.Nat
|
|
|
|
%default total
|
|
|
|
infixl 8 `shiftL`, `shiftR`
|
|
infixl 7 .&.
|
|
infixl 6 `xor`
|
|
infixl 5 .|.
|
|
|
|
||| Utility for using bitwise operations at compile
|
|
||| time.
|
|
|||
|
|
||| ```idris example
|
|
||| the Bits8 13 `shiftL` fromNat 3
|
|
||| ```
|
|
export
|
|
fromNat : (k : Nat)
|
|
-> {n : Nat}
|
|
-> {auto 0 prf : lt k n === True}
|
|
-> Subset Nat (`LT` n)
|
|
fromNat k = Element k (ltReflectsLT k n prf)
|
|
|
|
--------------------------------------------------------------------------------
|
|
-- Interface Bits
|
|
--------------------------------------------------------------------------------
|
|
|
|
||| The `Bits` interface defines bitwise operations over integral types.
|
|
public export
|
|
interface Bits a where
|
|
0 Index : Type
|
|
|
|
||| Bitwise "and"
|
|
(.&.) : a -> a -> a
|
|
|
|
||| Bitwise "or"
|
|
(.|.) : a -> a -> a
|
|
|
|
||| Bitwise "xor".
|
|
xor : a -> a -> a
|
|
|
|
||| Shift the argument left by the specified number of bits.
|
|
shiftL : a -> Index -> a
|
|
|
|
||| Shift the argument right by the specified number of bits.
|
|
shiftR : a -> Index -> a
|
|
|
|
||| Sets the `i`-th bit.
|
|
bit : (i : Index) -> a
|
|
|
|
||| The value with all bits unset.
|
|
zeroBits : a
|
|
|
|
||| Returns the bitwise complement of a value.
|
|
complement : a -> a
|
|
|
|
||| The value with all bits set..
|
|
oneBits : a
|
|
oneBits = complement zeroBits
|
|
|
|
||| `complementBit x i` is the same as `xor x (bit i)`.
|
|
complementBit : (x : a) -> (i : Index) -> a
|
|
complementBit x i = x `xor` bit i
|
|
|
|
||| `clearBit x i` is the same as `x .&. complement (bit i)`
|
|
clearBit : (x : a) -> (i : Index) -> a
|
|
clearBit x i = x `xor` (bit i .&. x)
|
|
|
|
||| Tests, whether the i-th bit is set in the given value.
|
|
testBit : a -> Index -> Bool
|
|
|
|
||| Sets the i-th bit of a value.
|
|
setBit : a -> (i : Index) -> a
|
|
setBit x i = x .|. bit i
|
|
|
|
public export %inline
|
|
Bits Bits8 where
|
|
Index = Subset Nat (`LT` 8)
|
|
(.&.) = prim__and_Bits8
|
|
(.|.) = prim__or_Bits8
|
|
xor = prim__xor_Bits8
|
|
bit = (1 `shiftL`)
|
|
zeroBits = 0
|
|
testBit x i = (x .&. bit i) /= 0
|
|
shiftR x = prim__shr_Bits8 x . fromInteger . cast . fst
|
|
shiftL x = prim__shl_Bits8 x . fromInteger . cast . fst
|
|
complement = xor 0xff
|
|
oneBits = 0xff
|
|
|
|
public export %inline
|
|
Bits Bits16 where
|
|
Index = Subset Nat (`LT` 16)
|
|
(.&.) = prim__and_Bits16
|
|
(.|.) = prim__or_Bits16
|
|
xor = prim__xor_Bits16
|
|
bit = (1 `shiftL`)
|
|
zeroBits = 0
|
|
testBit x i = (x .&. bit i) /= 0
|
|
shiftR x = prim__shr_Bits16 x . fromInteger . cast . fst
|
|
shiftL x = prim__shl_Bits16 x . fromInteger . cast . fst
|
|
complement = xor 0xffff
|
|
oneBits = 0xffff
|
|
|
|
public export %inline
|
|
Bits Bits32 where
|
|
Index = Subset Nat (`LT` 32)
|
|
(.&.) = prim__and_Bits32
|
|
(.|.) = prim__or_Bits32
|
|
xor = prim__xor_Bits32
|
|
bit = (1 `shiftL`)
|
|
zeroBits = 0
|
|
testBit x i = (x .&. bit i) /= 0
|
|
shiftR x = prim__shr_Bits32 x . fromInteger . cast . fst
|
|
shiftL x = prim__shl_Bits32 x . fromInteger . cast . fst
|
|
complement = xor 0xffffffff
|
|
oneBits = 0xffffffff
|
|
|
|
public export %inline
|
|
Bits Int where
|
|
Index = Subset Nat (`LT` 64)
|
|
(.&.) = prim__and_Int
|
|
(.|.) = prim__or_Int
|
|
xor = prim__xor_Int
|
|
bit = (1 `shiftL`)
|
|
zeroBits = 0
|
|
testBit x i = (x .&. bit i) /= 0
|
|
shiftR x = prim__shr_Int x . cast . fst
|
|
shiftL x = prim__shl_Int x . cast . fst
|
|
complement = xor (-1)
|
|
oneBits = (-1)
|
|
|
|
--------------------------------------------------------------------------------
|
|
-- FiniteBits
|
|
--------------------------------------------------------------------------------
|
|
|
|
public export
|
|
interface Bits a => FiniteBits a where
|
|
||| Return the number of bits in values of type `t`.
|
|
bitSize : Nat
|
|
|
|
||| Properly correlates `bitSize` and `Index`.
|
|
bitsToIndex : Subset Nat (`LT` bitSize) -> Index {a}
|
|
|
|
||| Return the number of set bits in the argument. This number is
|
|
||| known as the population count or the Hamming weight.
|
|
popCount : a -> Nat
|
|
|
|
public export %inline
|
|
FiniteBits Bits8 where
|
|
bitSize = 8
|
|
bitsToIndex = id
|
|
|
|
popCount x0 =
|
|
-- see https://stackoverflow.com/questions/109023/how-to-count-the-number-of-set-bits-in-a-32-bit-integer
|
|
let x1 = (x0 .&. 0x55) + ((x0 `shiftR` fromNat 1) .&. 0x55)
|
|
x2 = (x1 .&. 0x33) + ((x1 `shiftR` fromNat 2) .&. 0x33)
|
|
x3 = ((x2 + (x2 `shiftR` fromNat 4)) .&. 0x0F)
|
|
in fromInteger $ cast x3
|
|
|
|
public export %inline
|
|
FiniteBits Bits16 where
|
|
bitSize = 16
|
|
bitsToIndex = id
|
|
|
|
popCount x0 =
|
|
-- see https://stackoverflow.com/questions/109023/how-to-count-the-number-of-set-bits-in-a-32-bit-integer
|
|
let x1 = (x0 .&. 0x5555) + ((x0 `shiftR` fromNat 1) .&. 0x5555)
|
|
x2 = (x1 .&. 0x3333) + ((x1 `shiftR` fromNat 2) .&. 0x3333)
|
|
x3 = ((x2 + (x2 `shiftR` fromNat 4)) .&. 0x0F0F)
|
|
x4 = (x3 * 0x0101) `shiftR` fromNat 8
|
|
in fromInteger $ cast x4
|
|
|
|
public export %inline
|
|
FiniteBits Bits32 where
|
|
bitSize = 32
|
|
bitsToIndex = id
|
|
|
|
popCount x0 =
|
|
-- see https://stackoverflow.com/questions/109023/how-to-count-the-number-of-set-bits-in-a-32-bit-integer
|
|
let x1 = (x0 .&. 0x55555555) + ((x0 `shiftR` fromNat 1) .&. 0x55555555)
|
|
x2 = (x1 .&. 0x33333333) + ((x1 `shiftR` fromNat 2) .&. 0x33333333)
|
|
x3 = ((x2 + (x2 `shiftR` fromNat 4)) .&. 0x0F0F0F0F)
|
|
x4 = (x3 * 0x01010101) `shiftR` fromNat 24
|
|
in fromInteger $ cast x4
|
|
|
|
public export %inline
|
|
FiniteBits Int where
|
|
bitSize = 64
|
|
bitsToIndex = id
|
|
|
|
popCount x =
|
|
-- see https://stackoverflow.com/questions/109023/how-to-count-the-number-of-set-bits-in-a-32-bit-integer
|
|
-- We have to treat negative numbers separately in order to
|
|
-- prevent overflows in the first addition.
|
|
-- The top bit is therefore cleared and 1 is added in the end
|
|
-- in case of a negative number
|
|
let x0 = x `clearBit` fromNat 63
|
|
x1 = (x0 .&. 0x5555555555555555)
|
|
+ ((x0 `shiftR` fromNat 1) .&. 0x5555555555555555)
|
|
x2 = (x1 .&. 0x3333333333333333)
|
|
+ ((x1 `shiftR` fromNat 2) .&. 0x3333333333333333)
|
|
x3 = ((x2 + (x2 `shiftR` fromNat 4)) .&. 0x0F0F0F0F0F0F0F0F)
|
|
x4 = (x3 * 0x0101010101010101) `shiftR` fromNat 56
|
|
x5 = if x < 0 then x4 + 1 else x4
|
|
in fromInteger $ cast x5
|