{-# OPTIONS -fno-implicit-prelude #-}
-----------------------------------------------------------------------------
-- |
-- Module : Data.Bits
-- Copyright : (c) The University of Glasgow 2001
-- License : BSD-style (see the file libraries/base/LICENSE)
--
-- Maintainer : libraries@haskell.org
-- Stability : experimental
-- Portability : portable
--
-- This module defines bitwise operations for signed and unsigned
-- integers. Instances of the class 'Bits' for the 'Int' and
-- 'Integer' types are available from this module, and instances for
-- explicitly sized integral types are available from the
-- "Data.Int" and "Data.Word" modules.
--
-----------------------------------------------------------------------------
module Data.Bits (
Bits(
(.&.), (.|.), xor, -- :: a -> a -> a
complement, -- :: a -> a
shift, -- :: a -> Int -> a
rotate, -- :: a -> Int -> a
bit, -- :: Int -> a
setBit, -- :: a -> Int -> a
clearBit, -- :: a -> Int -> a
complementBit, -- :: a -> Int -> a
testBit, -- :: a -> Int -> Bool
bitSize, -- :: a -> Int
isSigned, -- :: a -> Bool
shiftL, shiftR, -- :: a -> Int -> a
rotateL, rotateR -- :: a -> Int -> a
)
-- instance Bits Int
-- instance Bits Integer
) where
-- Defines the @Bits@ class containing bit-based operations.
-- See library document for details on the semantics of the
-- individual operations.
import Hugs.Bits
infixl 8 `shift`, `rotate`, `shiftL`, `shiftR`, `rotateL`, `rotateR`
infixl 7 .&.
infixl 6 `xor`
infixl 5 .|.
{-|
The 'Bits' class defines bitwise operations over integral types.
* Bits are numbered from 0 with bit 0 being the least
significant bit.
-}
class Num a => Bits a where
-- | Bitwise \"and\"
(.&.) :: a -> a -> a
-- | Bitwise \"or\"
(.|.) :: a -> a -> a
-- | Bitwise \"xor\"
xor :: a -> a -> a
{-| Reverse all the bits in the argument -}
complement :: a -> a
{-| Shift the argument left by the specified number of bits.
Right shifts (signed) are specified by giving a negative value.
An instance can define either this unified 'shift' or 'shiftL' and
'shiftR', depending on which is more convenient for the type in
question. -}
shift :: a -> Int -> a
x `shift` i | i<0 = x `shiftR` (-i)
| i==0 = x
| i>0 = x `shiftL` i
{-| Rotate the argument left by the specified number of bits.
Right rotates are specified by giving a negative value.
For unbounded types like 'Integer', 'rotate' is equivalent to 'shift'.
An instance can define either this unified 'rotate' or 'rotateL' and
'rotateR', depending on which is more convenient for the type in
question. -}
rotate :: a -> Int -> a
x `rotate` i | i<0 = x `rotateR` (-i)
| i==0 = x
| i>0 = x `rotateL` i
{-
-- Rotation can be implemented in terms of two shifts, but care is
-- needed for negative values. This suggested implementation assumes
-- 2's-complement arithmetic. It is commented out because it would
-- require an extra context (Ord a) on the signature of 'rotate'.
x `rotate` i | i<0 && isSigned x && x<0
= let left = i+bitSize x in
((x `shift` i) .&. complement ((-1) `shift` left))
.|. (x `shift` left)
| i<0 = (x `shift` i) .|. (x `shift` (i+bitSize x))
| i==0 = x
| i>0 = (x `shift` i) .|. (x `shift` (i-bitSize x))
-}
-- | @bit i@ is a value with the @i@th bit set
bit :: Int -> a
-- | @x \`setBit\` i@ is the same as @x .|. bit i@
setBit :: a -> Int -> a
-- | @x \`clearBit\` i@ is the same as @x .&. complement (bit i)@
clearBit :: a -> Int -> a
-- | @x \`complementBit\` i@ is the same as @x \`xor\` bit i@
complementBit :: a -> Int -> a
-- | Return 'True' if the @n@th bit of the argument is 1
testBit :: a -> Int -> Bool
{-| Return the number of bits in the type of the argument. The actual
value of the argument is ignored. The function 'bitSize' is
undefined for types that do not have a fixed bitsize, like 'Integer'.
-}
bitSize :: a -> Int
{-| Return 'True' if the argument is a signed type. The actual
value of the argument is ignored -}
isSigned :: a -> Bool
bit i = 1 `shiftL` i
x `setBit` i = x .|. bit i
x `clearBit` i = x .&. complement (bit i)
x `complementBit` i = x `xor` bit i
x `testBit` i = (x .&. bit i) /= 0
{-| Shift the argument left by the specified number of bits
(which must be non-negative).
An instance can define either this and 'shiftR' or the unified
'shift', depending on which is more convenient for the type in
question. -}
shiftL :: a -> Int -> a
x `shiftL` i = x `shift` i
{-| Shift the argument right (signed) by the specified number of bits
(which must be non-negative).
An instance can define either this and 'shiftL' or the unified
'shift', depending on which is more convenient for the type in
question. -}
shiftR :: a -> Int -> a
x `shiftR` i = x `shift` (-i)
{-| Rotate the argument left by the specified number of bits
(which must be non-negative).
An instance can define either this and 'rotateR' or the unified
'rotate', depending on which is more convenient for the type in
question. -}
rotateL :: a -> Int -> a
x `rotateL` i = x `rotate` i
{-| Rotate the argument right by the specified number of bits
(which must be non-negative).
An instance can define either this and 'rotateL' or the unified
'rotate', depending on which is more convenient for the type in
question. -}
rotateR :: a -> Int -> a
x `rotateR` i = x `rotate` (-i)
instance Bits Int where
(.&.) = primAndInt
(.|.) = primOrInt
xor = primXorInt
complement = primComplementInt
shift = primShiftInt
bit = primBitInt
testBit = primTestInt
bitSize _ = 4*8
x `rotate` i
| i<0 && x<0 = let left = i+bitSize x in
((x `shift` i) .&. complement ((-1) `shift` left))
.|. (x `shift` left)
| i<0 = (x `shift` i) .|. (x `shift` (i+bitSize x))
| i==0 = x
| i>0 = (x `shift` i) .|. (x `shift` (i-bitSize x))
isSigned _ = True
instance Bits Integer where
-- reduce bitwise binary operations to special cases we can handle
x .&. y | x<0 && y<0 = complement (complement x `posOr` complement y)
| otherwise = x `posAnd` y
x .|. y | x<0 || y<0 = complement (complement x `posAnd` complement y)
| otherwise = x `posOr` y
x `xor` y | x<0 && y<0 = complement x `posXOr` complement y
| x<0 = complement (complement x `posXOr` y)
| y<0 = complement (x `posXOr` complement y)
| otherwise = x `posXOr` y
-- assuming infinite 2's-complement arithmetic
complement a = -1 - a
shift x i | i >= 0 = x * 2^i
| otherwise = x `div` 2^(-i)
rotate x i = shift x i -- since an Integer never wraps around
bitSize _ = error "Data.Bits.bitSize(Integer)"
isSigned _ = True
-- Crude implementation of bitwise operations on Integers: convert them
-- to finite lists of Ints (least significant first), zip and convert
-- back again.
-- posAnd requires at least one argument non-negative
-- posOr and posXOr require both arguments non-negative
posAnd, posOr, posXOr :: Integer -> Integer -> Integer
posAnd x y = fromInts $ zipWith (.&.) (toInts x) (toInts y)
posOr x y = fromInts $ longZipWith (.|.) (toInts x) (toInts y)
posXOr x y = fromInts $ longZipWith xor (toInts x) (toInts y)
longZipWith :: (a -> a -> a) -> [a] -> [a] -> [a]
longZipWith f xs [] = xs
longZipWith f [] ys = ys
longZipWith f (x:xs) (y:ys) = f x y:longZipWith f xs ys
toInts :: Integer -> [Int]
toInts n
| n == 0 = []
| otherwise = mkInt (n `mod` numInts):toInts (n `div` numInts)
where mkInt n | n > toInteger(maxBound::Int) = fromInteger (n-numInts)
| otherwise = fromInteger n
fromInts :: [Int] -> Integer
fromInts = foldr catInt 0
where catInt d n = (if d<0 then n+1 else n)*numInts + toInteger d
numInts = toInteger (maxBound::Int) - toInteger (minBound::Int) + 1
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