Copyright	(c) 2012-2016 Iago Abal (c) 2012-2013 HASLab & University of Minho
License	BSD3
Maintainer	Iago Abal <mail@iagoabal.eu>
Safe Haskell	None
Language	Haskell98

Data.BitVector

Contents

Bit-vectors
Creation
Test
Comparison
Indexing
Arithmetic
List-like operations
Bitwise operations
Conversion
Pretty-printing

Description

Bit-vector arithmetic inspired by SMT-LIB http://smt-lib.org/ and Cryptol http://cryptol.net/.

Bit-vectors are represented as a pair size and value, where sizes are of type Int and values are Integer.

Bit-vectors are interpreted as unsigned integers (i.e. natural numbers) except for some specific signed operations.
Most operations are in some way size-polymorphic and, if required, will perform padding to adjust the size of input bit-vectors.

For documentation purposes we will write [n]k to denote a bit-vector of size n representing the natural number k.

Synopsis

type BitVector = BV
data BV
size :: BV -> Int
width :: BV -> Int
nat :: BV -> Integer
uint :: BV -> Integer
int :: BV -> Integer
nil :: BV
bitVec :: Integral a => Int -> a -> BV
bitVecs :: Integral a => Int -> [a] -> [BV]
ones :: Int -> BV
zeros :: Int -> BV
isNat :: BV -> Bool
isPos :: BV -> Bool
(==.) :: BV -> BV -> Bool
(/=.) :: BV -> BV -> Bool
(<.) :: BV -> BV -> Bool
(<=.) :: BV -> BV -> Bool
(>.) :: BV -> BV -> Bool
(>=.) :: BV -> BV -> Bool
slt :: BV -> BV -> Bool
sle :: BV -> BV -> Bool
sgt :: BV -> BV -> Bool
sge :: BV -> BV -> Bool
(@.) :: Integral ix => BV -> ix -> Bool
index :: Integral ix => ix -> BV -> Bool
(@@) :: Integral ix => BV -> (ix, ix) -> BV
extract :: Integral ix => ix -> ix -> BV -> BV
(@:) :: Integral ix => BV -> [ix] -> BV
(!.) :: Integral ix => BV -> ix -> Bool
least :: Integral ix => ix -> BV -> BV
most :: Integral ix => ix -> BV -> BV
msb :: BV -> Bool
lsb :: BV -> Bool
msb1 :: BV -> Int
lsb1 :: BV -> Int
signumI :: Integral a => BV -> a
pow :: Integral exp => BV -> exp -> BV
sdiv :: BV -> BV -> BV
srem :: BV -> BV -> BV
smod :: BV -> BV -> BV
lg2 :: BV -> BV
(#) :: BV -> BV -> BV
cat :: BV -> BV -> BV
append :: BV -> BV -> BV
concat :: [BV] -> BV
zeroExtend :: Integral size => size -> BV -> BV
signExtend :: Integral size => size -> BV -> BV
foldl :: (a -> Bool -> a) -> a -> BV -> a
foldl_ :: (a -> Bool -> a) -> a -> BV -> a
foldr :: (Bool -> a -> a) -> a -> BV -> a
foldr_ :: (Bool -> a -> a) -> a -> BV -> a
reverse :: BV -> BV
reverse_ :: BV -> BV
replicate :: Integral size => size -> BV -> BV
replicate_ :: Integral size => size -> BV -> BV
and :: [BV] -> BV
and_ :: [BV] -> BV
or :: [BV] -> BV
or_ :: [BV] -> BV
split :: Integral times => times -> BV -> [BV]
group :: Integral size => size -> BV -> [BV]
group_ :: Integral size => size -> BV -> [BV]
join :: [BV] -> BV
class Eq a => Bits a where
- (.&.) :: a -> a -> a
- (.|.) :: a -> a -> a
- xor :: a -> a -> a
- complement :: a -> a
- shift :: a -> Int -> a
- rotate :: a -> Int -> a
- zeroBits :: a
- bit :: Int -> a
- setBit :: a -> Int -> a
- clearBit :: a -> Int -> a
- complementBit :: a -> Int -> a
- testBit :: a -> Int -> Bool
- bitSizeMaybe :: a -> Maybe Int
- bitSize :: a -> Int
- isSigned :: a -> Bool
- shiftL :: a -> Int -> a
- unsafeShiftL :: a -> Int -> a
- shiftR :: a -> Int -> a
- unsafeShiftR :: a -> Int -> a
- rotateL :: a -> Int -> a
- rotateR :: a -> Int -> a
- popCount :: a -> Int
bitDefault :: (Bits a, Num a) => Int -> a
popCountDefault :: (Bits a, Num a) => a -> Int
testBitDefault :: (Bits a, Num a) => a -> Int -> Bool
toIntegralSized :: (Integral a, Integral b, Bits a, Bits b) => a -> Maybe b
(!<<.) :: Bits a => a -> Int -> a
(!>>.) :: Bits a => a -> Int -> a
(.<<.) :: Bits a => a -> Int -> a
(.>>.) :: Bits a => a -> Int -> a
(.^.) :: Bits a => a -> a -> a
oneBits :: FiniteBits a => a
class Bits b => FiniteBits b where
- finiteBitSize :: b -> Int
- countLeadingZeros :: b -> Int
- countTrailingZeros :: b -> Int
newtype And a = And {
- getAnd :: a
}
newtype Iff a = Iff {
- getIff :: a
}
newtype Ior a = Ior {
- getIor :: a
}
newtype Xor a = Xor {
- getXor :: a
}
not :: BV -> BV
not_ :: BV -> BV
nand :: BV -> BV -> BV
nor :: BV -> BV -> BV
xnor :: BV -> BV -> BV
(<<.) :: BV -> BV -> BV
shl :: BV -> BV -> BV
(>>.) :: BV -> BV -> BV
shr :: BV -> BV -> BV
ashr :: BV -> BV -> BV
(<<<.) :: BV -> BV -> BV
rol :: BV -> BV -> BV
(>>>.) :: BV -> BV -> BV
ror :: BV -> BV -> BV
fromBool :: Bool -> BV
fromBits :: [Bool] -> BV
toBits :: BV -> [Bool]
showBin :: BV -> String
showOct :: BV -> String
showHex :: BV -> String

Bit-vectors

type BitVector = BV Source #

An alias for BV.

data BV Source #

Big-endian pseudo size-polymorphic bit-vectors.

Instances

Instances details

Monoid BV Source #
Instance details Defined in Data.BitVector Methods mempty :: BV mappend :: BV -> BV -> BV mconcat :: [BV] -> BV
Semigroup BV Source #
Instance details Defined in Data.BitVector Methods (<>) :: BV -> BV -> BV sconcat :: NonEmpty BV -> BV stimes :: Integral b => b -> BV -> BV
Bits BV Source #
Instance details Defined in Data.BitVector Methods (.&.) :: BV -> BV -> BV # (.\|.) :: BV -> BV -> BV # xor :: BV -> BV -> BV # complement :: BV -> BV # shift :: BV -> Int -> BV # rotate :: BV -> Int -> BV # zeroBits :: BV # bit :: Int -> BV # setBit :: BV -> Int -> BV # clearBit :: BV -> Int -> BV # complementBit :: BV -> Int -> BV # testBit :: BV -> Int -> Bool # bitSizeMaybe :: BV -> Maybe Int # bitSize :: BV -> Int # isSigned :: BV -> Bool # shiftL :: BV -> Int -> BV # unsafeShiftL :: BV -> Int -> BV # shiftR :: BV -> Int -> BV # unsafeShiftR :: BV -> Int -> BV # rotateL :: BV -> Int -> BV # rotateR :: BV -> Int -> BV # popCount :: BV -> Int #
Data BV Source #
Instance details Defined in Data.BitVector Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> BV -> c BV gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c BV toConstr :: BV -> Constr dataTypeOf :: BV -> DataType dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c BV) dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c BV) gmapT :: (forall b. Data b => b -> b) -> BV -> BV gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> BV -> r gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> BV -> r gmapQ :: (forall d. Data d => d -> u) -> BV -> [u] gmapQi :: Int -> (forall d. Data d => d -> u) -> BV -> u gmapM :: Monad m => (forall d. Data d => d -> m d) -> BV -> m BV gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> BV -> m BV gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> BV -> m BV
Enum BV Source #
Instance details Defined in Data.BitVector Methods succ :: BV -> BV pred :: BV -> BV toEnum :: Int -> BV fromEnum :: BV -> Int enumFrom :: BV -> [BV] enumFromThen :: BV -> BV -> [BV] enumFromTo :: BV -> BV -> [BV] enumFromThenTo :: BV -> BV -> BV -> [BV]
Num BV Source #
Instance details Defined in Data.BitVector Methods (+) :: BV -> BV -> BV (-) :: BV -> BV -> BV (*) :: BV -> BV -> BV negate :: BV -> BV abs :: BV -> BV signum :: BV -> BV fromInteger :: Integer -> BV
Read BV Source #
Instance details Defined in Data.BitVector Methods readsPrec :: Int -> ReadS BV readList :: ReadS [BV] readPrec :: ReadPrec BV readListPrec :: ReadPrec [BV]
Integral BV Source #
Instance details Defined in Data.BitVector Methods quot :: BV -> BV -> BV rem :: BV -> BV -> BV div :: BV -> BV -> BV mod :: BV -> BV -> BV quotRem :: BV -> BV -> (BV, BV) divMod :: BV -> BV -> (BV, BV) toInteger :: BV -> Integer
Real BV Source #
Instance details Defined in Data.BitVector Methods toRational :: BV -> Rational
Show BV Source #
Instance details Defined in Data.BitVector Methods showsPrec :: Int -> BV -> ShowS show :: BV -> String showList :: [BV] -> ShowS
Eq BV Source #
Instance details Defined in Data.BitVector Methods (==) :: BV -> BV -> Bool (/=) :: BV -> BV -> Bool
Ord BV Source #
Instance details Defined in Data.BitVector Methods compare :: BV -> BV -> Ordering (<) :: BV -> BV -> Bool (<=) :: BV -> BV -> Bool (>) :: BV -> BV -> Bool (>=) :: BV -> BV -> Bool max :: BV -> BV -> BV min :: BV -> BV -> BV

size :: BV -> Int Source #

The size of a bit-vector.

width :: BV -> Int Source #

An alias for size.

nat :: BV -> Integer Source #

The value of a bit-vector, as a natural number.

uint :: BV -> Integer Source #

An alias for nat.

int :: BV -> Integer Source #

2's complement value of a bit-vector.

>>> int [2]3
-1

>>> int [4]12
-4

Creation

nil :: BV Source #

The empty bit-vector, ie. [0]0.

bitVec :: Integral a => Int -> a -> BV Source #

Create a bit-vector given a size and an integer value.

>>> bitVec 4 3
[4]3

This function also handles negative values.

>>> bitVec 4 (-1)
[4]15

bitVecs :: Integral a => Int -> [a] -> [BV] Source #

List of bit-vector literals of the same size

When a list of integer literals is interpreted as a list of bit-vectors, fromInteger is applied to each element invidually:

>>> [1,3,5] :: [BV]
[ [1]1, [2]3, [3]5 ]

Sometimes we want to specify a list of bit-vectors literals of the same size, and for that we can use bitVects:

>>> bitVecs 3 [1,3,5]
[ [3]1, [3]3, [3]5 ]

ones :: Int -> BV Source #

Create a mask of ones.

zeros :: Int -> BV Source #

Create a mask of zeros.

Test

isNat :: BV -> Bool Source #

Test if the signed value of a bit-vector is a natural number.

isPos :: BV -> Bool Source #

Test if the signed value of a bit-vector is a positive number.

Comparison

(==.) :: BV -> BV -> Bool infix 4 Source #

Fixed-size equality.

In contrast with ==, which is size-polymorphic, this equality requires both bit-vectors to be of equal size.

>>> [n]k ==. [m]k
False

>>> [n]k ==. [n]k
True

(/=.) :: BV -> BV -> Bool infix 4 Source #

Fixed-size inequality.

The negated version of ==..

(<.) :: BV -> BV -> Bool infix 4 Source #

Fixed-size less-than.

(<=.) :: BV -> BV -> Bool infix 4 Source #

Fixed-size less-than-or-equals.

(>.) :: BV -> BV -> Bool infix 4 Source #

Fixed-size greater-than.

(>=.) :: BV -> BV -> Bool infix 4 Source #

Fixed-size greater-than-or-equals.

slt :: BV -> BV -> Bool infix 4 Source #

Fixed-size signed less-than.

sle :: BV -> BV -> Bool infix 4 Source #

Fixed-size signed less-than-or-equals.

sgt :: BV -> BV -> Bool infix 4 Source #

Fixed-size signed greater-than.

sge :: BV -> BV -> Bool infix 4 Source #

Fixed-size signed greater-than-or-equals.

Indexing

(@.) :: Integral ix => BV -> ix -> Bool infixl 9 Source #

Bit indexing.

u @. i stands for the i-th bit of u.

>>> [4]2 @. 0
False

>>> [4]2 @. 1
True

index :: Integral ix => ix -> BV -> Bool Source #

index i a == a @. i

(@@) :: Integral ix => BV -> (ix, ix) -> BV infixl 9 Source #

Bit-string extraction.

u @@ (j,i) == fromBits (map (u @.) [j,j-1..i])

>>> [4]7 @@ (3,1)
[3]3

extract :: Integral ix => ix -> ix -> BV -> BV Source #

extract j i a == a @@ (j,i)

(@:) :: Integral ix => BV -> [ix] -> BV infixl 9 Source #

Bit list indexing.

u @: is ==. fromBits $ List.map (u @.) is

(!.) :: Integral ix => BV -> ix -> Bool infixl 9 Source #

Reverse bit-indexing.

Index starting from the most significant bit.

u !. i == u @. (size u - i - 1)

>>> [3]3 !. 0
False

least :: Integral ix => ix -> BV -> BV Source #

Take least significant bits.

least m u == u @@ (m-1,0)

most :: Integral ix => ix -> BV -> BV Source #

Take most significant bits.

most m u == u @@ (n-1,n-m)

msb :: BV -> Bool Source #

Most significant bit.

msb u == u !. 0

lsb :: BV -> Bool Source #

Least significant bit.

lsb u == u @. 0

msb1 :: BV -> Int Source #

Most significant 1-bit.

Pre: input must be non-zero.

>>> msb1 [4]2
1

>>> msb1 [4]4
2

lsb1 :: BV -> Int Source #

Least significant 1-bit.

Pre: input must be non-zero.

>>> msb1 [4]3
0

>>> msb1 [4]6
1

Arithmetic

signumI :: Integral a => BV -> a Source #

Bit-vector signum as an Integral.

pow :: Integral exp => BV -> exp -> BV Source #

Bit-vector exponentiation.

pow [n]k e computes k raised to e modulo n.

This is faster than Haskell's (^) operator because it performs modulo division just once. Besides, a^0 == [1]0 !!!

sdiv :: BV -> BV -> BV Source #

2's complement signed division.

srem :: BV -> BV -> BV Source #

2's complement signed remainder (sign follows dividend).

smod :: BV -> BV -> BV Source #

2's complement signed remainder (sign follows divisor).

lg2 :: BV -> BV Source #

Ceiling logarithm base 2.

Pre: input bit-vector must be non-zero.

List-like operations

(#) :: BV -> BV -> BV infixr 5 Source #

Concatenation of two bit-vectors.

cat :: BV -> BV -> BV Source #

Deprecated: Use (#) or append instead

Concatenation of two bit-vectors.

append :: BV -> BV -> BV Source #

Concatenation of two bit-vectors.

concat :: [BV] -> BV Source #

An alias for join.

zeroExtend :: Integral size => size -> BV -> BV Source #

Logical extension.

>>> zeroExtend 3 [1]1
[4]1

signExtend :: Integral size => size -> BV -> BV Source #

Arithmetic extension.

>>> signExtend 2 [2]1
[4]1

>>> signExtend 2 [2]3
[4]15

foldl :: (a -> Bool -> a) -> a -> BV -> a Source #

foldl f z (fromBits [un, ..., u1, u0]) == ((((z `f` un) `f` ...) `f` u1) `f` u0)

foldl f e = fromBits . foldl f e . toBits

foldl_ :: (a -> Bool -> a) -> a -> BV -> a Source #

Deprecated: Use corresponding versions without underscore

foldl f z (fromBits [un, ..., u1, u0]) == ((((z `f` un) `f` ...) `f` u1) `f` u0)

foldl f e = fromBits . foldl f e . toBits

foldr :: (Bool -> a -> a) -> a -> BV -> a Source #

foldr f z (fromBits [un, ..., u1, u0]) == un `f` (... `f` (u1 `f` (u0 `f` z)))

foldr f e = fromBits . foldr f e . toBits

foldr_ :: (Bool -> a -> a) -> a -> BV -> a Source #

Deprecated: Use corresponding versions without underscore

foldr f z (fromBits [un, ..., u1, u0]) == un `f` (... `f` (u1 `f` (u0 `f` z)))

foldr f e = fromBits . foldr f e . toBits

reverse :: BV -> BV Source #

reverse == fromBits . reverse . toBits

reverse_ :: BV -> BV Source #

Deprecated: Use corresponding versions without underscore

reverse == fromBits . reverse . toBits

replicate :: Integral size => size -> BV -> BV Source #

Pre: if replicate_ n u then n > 0 must hold.

replicate_ n == fromBits . concat . replicate n . toBits

replicate_ :: Integral size => size -> BV -> BV Source #

Deprecated: Use corresponding versions without underscore

Pre: if replicate_ n u then n > 0 must hold.

replicate_ n == fromBits . concat . replicate n . toBits

and :: [BV] -> BV Source #

Conjunction.

Essentially, and == foldr1 (.&.).

Returns [1]1 if the input list is empty.

and_ :: [BV] -> BV Source #

Deprecated: Use corresponding versions without underscore

Conjunction.

Essentially, and == foldr1 (.&.).

Returns [1]1 if the input list is empty.

or :: [BV] -> BV Source #

Disjunction.

Essentially, or == foldr1 (.|.).

Returns [1]0 if the input list is empty.

or_ :: [BV] -> BV Source #

Deprecated: Use corresponding versions without underscore

Disjunction.

Essentially, or == foldr1 (.|.).

Returns [1]0 if the input list is empty.

split :: Integral times => times -> BV -> [BV] Source #

Split a bit-vector k times.

>>> split 3 [4]15
[[2]0,[2]3,[2]3]

group :: Integral size => size -> BV -> [BV] Source #

Split a bit-vector into n-wide pieces.

>>> group 3 [4]15
[[3]1,[3]7]

group_ :: Integral size => size -> BV -> [BV] Source #

Deprecated: Use corresponding versions without underscore

Split a bit-vector into n-wide pieces.

>>> group 3 [4]15
[[3]1,[3]7]

join :: [BV] -> BV Source #

Concatenate a (possibly empty) list of bit-vectors.

>>> join [[2]3,[2]2]
[4]14

Bitwise operations

class Eq a => Bits a where #

Minimal complete definition

(.&.), (.|.), xor, complement, (shift | shiftL, shiftR), (rotate | rotateL, rotateR), bitSize, bitSizeMaybe, isSigned, testBit, bit, popCount

Methods

(.&.) :: a -> a -> a #

(.|.) :: a -> a -> a #

xor :: a -> a -> a #

complement :: a -> a #

shift :: a -> Int -> a #

rotate :: a -> Int -> a #

zeroBits :: a #

bit :: Int -> a #

setBit :: a -> Int -> a #

clearBit :: a -> Int -> a #

complementBit :: a -> Int -> a #

testBit :: a -> Int -> Bool #

bitSizeMaybe :: a -> Maybe Int #

bitSize :: a -> Int #

isSigned :: a -> Bool #

shiftL :: a -> Int -> a #

unsafeShiftL :: a -> Int -> a #

shiftR :: a -> Int -> a #

unsafeShiftR :: a -> Int -> a #

rotateL :: a -> Int -> a #

rotateR :: a -> Int -> a #

popCount :: a -> Int #

Instances

Instances details

Bits BV Source #
Instance details Defined in Data.BitVector Methods (.&.) :: BV -> BV -> BV # (.\|.) :: BV -> BV -> BV # xor :: BV -> BV -> BV # complement :: BV -> BV # shift :: BV -> Int -> BV # rotate :: BV -> Int -> BV # zeroBits :: BV # bit :: Int -> BV # setBit :: BV -> Int -> BV # clearBit :: BV -> Int -> BV # complementBit :: BV -> Int -> BV # testBit :: BV -> Int -> Bool # bitSizeMaybe :: BV -> Maybe Int # bitSize :: BV -> Int # isSigned :: BV -> Bool # shiftL :: BV -> Int -> BV # unsafeShiftL :: BV -> Int -> BV # shiftR :: BV -> Int -> BV # unsafeShiftR :: BV -> Int -> BV # rotateL :: BV -> Int -> BV # rotateR :: BV -> Int -> BV # popCount :: BV -> Int #
Bits Integer
Instance details Defined in GHC.Internal.Bits Methods (.&.) :: Integer -> Integer -> Integer # (.\|.) :: Integer -> Integer -> Integer # xor :: Integer -> Integer -> Integer # complement :: Integer -> Integer # shift :: Integer -> Int -> Integer # rotate :: Integer -> Int -> Integer # zeroBits :: Integer # bit :: Int -> Integer # setBit :: Integer -> Int -> Integer # clearBit :: Integer -> Int -> Integer # complementBit :: Integer -> Int -> Integer # testBit :: Integer -> Int -> Bool # bitSizeMaybe :: Integer -> Maybe Int # bitSize :: Integer -> Int # isSigned :: Integer -> Bool # shiftL :: Integer -> Int -> Integer # unsafeShiftL :: Integer -> Int -> Integer # shiftR :: Integer -> Int -> Integer # unsafeShiftR :: Integer -> Int -> Integer # rotateL :: Integer -> Int -> Integer # rotateR :: Integer -> Int -> Integer # popCount :: Integer -> Int #
Bits Natural
Instance details Defined in GHC.Internal.Bits Methods (.&.) :: Natural -> Natural -> Natural # (.\|.) :: Natural -> Natural -> Natural # xor :: Natural -> Natural -> Natural # complement :: Natural -> Natural # shift :: Natural -> Int -> Natural # rotate :: Natural -> Int -> Natural # zeroBits :: Natural # bit :: Int -> Natural # setBit :: Natural -> Int -> Natural # clearBit :: Natural -> Int -> Natural # complementBit :: Natural -> Int -> Natural # testBit :: Natural -> Int -> Bool # bitSizeMaybe :: Natural -> Maybe Int # bitSize :: Natural -> Int # isSigned :: Natural -> Bool # shiftL :: Natural -> Int -> Natural # unsafeShiftL :: Natural -> Int -> Natural # shiftR :: Natural -> Int -> Natural # unsafeShiftR :: Natural -> Int -> Natural # rotateL :: Natural -> Int -> Natural # rotateR :: Natural -> Int -> Natural # popCount :: Natural -> Int #
Bits Bool
Instance details Defined in GHC.Internal.Bits Methods (.&.) :: Bool -> Bool -> Bool # (.\|.) :: Bool -> Bool -> Bool # xor :: Bool -> Bool -> Bool # complement :: Bool -> Bool # shift :: Bool -> Int -> Bool # rotate :: Bool -> Int -> Bool # zeroBits :: Bool # bit :: Int -> Bool # setBit :: Bool -> Int -> Bool # clearBit :: Bool -> Int -> Bool # complementBit :: Bool -> Int -> Bool # testBit :: Bool -> Int -> Bool # bitSizeMaybe :: Bool -> Maybe Int # bitSize :: Bool -> Int # isSigned :: Bool -> Bool # shiftL :: Bool -> Int -> Bool # unsafeShiftL :: Bool -> Int -> Bool # shiftR :: Bool -> Int -> Bool # unsafeShiftR :: Bool -> Int -> Bool # rotateL :: Bool -> Int -> Bool # rotateR :: Bool -> Int -> Bool # popCount :: Bool -> Int #
Bits Int
Instance details Defined in GHC.Internal.Bits Methods (.&.) :: Int -> Int -> Int # (.\|.) :: Int -> Int -> Int # xor :: Int -> Int -> Int # complement :: Int -> Int # shift :: Int -> Int -> Int # rotate :: Int -> Int -> Int # zeroBits :: Int # bit :: Int -> Int # setBit :: Int -> Int -> Int # clearBit :: Int -> Int -> Int # complementBit :: Int -> Int -> Int # testBit :: Int -> Int -> Bool # bitSizeMaybe :: Int -> Maybe Int # bitSize :: Int -> Int # isSigned :: Int -> Bool # shiftL :: Int -> Int -> Int # unsafeShiftL :: Int -> Int -> Int # shiftR :: Int -> Int -> Int # unsafeShiftR :: Int -> Int -> Int # rotateL :: Int -> Int -> Int # rotateR :: Int -> Int -> Int # popCount :: Int -> Int #
Bits Word
Instance details Defined in GHC.Internal.Bits Methods (.&.) :: Word -> Word -> Word # (.\|.) :: Word -> Word -> Word # xor :: Word -> Word -> Word # complement :: Word -> Word # shift :: Word -> Int -> Word # rotate :: Word -> Int -> Word # zeroBits :: Word # bit :: Int -> Word # setBit :: Word -> Int -> Word # clearBit :: Word -> Int -> Word # complementBit :: Word -> Int -> Word # testBit :: Word -> Int -> Bool # bitSizeMaybe :: Word -> Maybe Int # bitSize :: Word -> Int # isSigned :: Word -> Bool # shiftL :: Word -> Int -> Word # unsafeShiftL :: Word -> Int -> Word # shiftR :: Word -> Int -> Word # unsafeShiftR :: Word -> Int -> Word # rotateL :: Word -> Int -> Word # rotateR :: Word -> Int -> Word # popCount :: Word -> Int #
Bits a => Bits (And a)
Instance details Defined in GHC.Internal.Data.Bits Methods (.&.) :: And a -> And a -> And a # (.\|.) :: And a -> And a -> And a # xor :: And a -> And a -> And a # complement :: And a -> And a # shift :: And a -> Int -> And a # rotate :: And a -> Int -> And a # zeroBits :: And a # bit :: Int -> And a # setBit :: And a -> Int -> And a # clearBit :: And a -> Int -> And a # complementBit :: And a -> Int -> And a # testBit :: And a -> Int -> Bool # bitSizeMaybe :: And a -> Maybe Int # bitSize :: And a -> Int # isSigned :: And a -> Bool # shiftL :: And a -> Int -> And a # unsafeShiftL :: And a -> Int -> And a # shiftR :: And a -> Int -> And a # unsafeShiftR :: And a -> Int -> And a # rotateL :: And a -> Int -> And a # rotateR :: And a -> Int -> And a # popCount :: And a -> Int #
Bits a => Bits (Iff a)
Instance details Defined in GHC.Internal.Data.Bits Methods (.&.) :: Iff a -> Iff a -> Iff a # (.\|.) :: Iff a -> Iff a -> Iff a # xor :: Iff a -> Iff a -> Iff a # complement :: Iff a -> Iff a # shift :: Iff a -> Int -> Iff a # rotate :: Iff a -> Int -> Iff a # zeroBits :: Iff a # bit :: Int -> Iff a # setBit :: Iff a -> Int -> Iff a # clearBit :: Iff a -> Int -> Iff a # complementBit :: Iff a -> Int -> Iff a # testBit :: Iff a -> Int -> Bool # bitSizeMaybe :: Iff a -> Maybe Int # bitSize :: Iff a -> Int # isSigned :: Iff a -> Bool # shiftL :: Iff a -> Int -> Iff a # unsafeShiftL :: Iff a -> Int -> Iff a # shiftR :: Iff a -> Int -> Iff a # unsafeShiftR :: Iff a -> Int -> Iff a # rotateL :: Iff a -> Int -> Iff a # rotateR :: Iff a -> Int -> Iff a # popCount :: Iff a -> Int #
Bits a => Bits (Ior a)
Instance details Defined in GHC.Internal.Data.Bits Methods (.&.) :: Ior a -> Ior a -> Ior a # (.\|.) :: Ior a -> Ior a -> Ior a # xor :: Ior a -> Ior a -> Ior a # complement :: Ior a -> Ior a # shift :: Ior a -> Int -> Ior a # rotate :: Ior a -> Int -> Ior a # zeroBits :: Ior a # bit :: Int -> Ior a # setBit :: Ior a -> Int -> Ior a # clearBit :: Ior a -> Int -> Ior a # complementBit :: Ior a -> Int -> Ior a # testBit :: Ior a -> Int -> Bool # bitSizeMaybe :: Ior a -> Maybe Int # bitSize :: Ior a -> Int # isSigned :: Ior a -> Bool # shiftL :: Ior a -> Int -> Ior a # unsafeShiftL :: Ior a -> Int -> Ior a # shiftR :: Ior a -> Int -> Ior a # unsafeShiftR :: Ior a -> Int -> Ior a # rotateL :: Ior a -> Int -> Ior a # rotateR :: Ior a -> Int -> Ior a # popCount :: Ior a -> Int #
Bits a => Bits (Xor a)
Instance details Defined in GHC.Internal.Data.Bits Methods (.&.) :: Xor a -> Xor a -> Xor a # (.\|.) :: Xor a -> Xor a -> Xor a # xor :: Xor a -> Xor a -> Xor a # complement :: Xor a -> Xor a # shift :: Xor a -> Int -> Xor a # rotate :: Xor a -> Int -> Xor a # zeroBits :: Xor a # bit :: Int -> Xor a # setBit :: Xor a -> Int -> Xor a # clearBit :: Xor a -> Int -> Xor a # complementBit :: Xor a -> Int -> Xor a # testBit :: Xor a -> Int -> Bool # bitSizeMaybe :: Xor a -> Maybe Int # bitSize :: Xor a -> Int # isSigned :: Xor a -> Bool # shiftL :: Xor a -> Int -> Xor a # unsafeShiftL :: Xor a -> Int -> Xor a # shiftR :: Xor a -> Int -> Xor a # unsafeShiftR :: Xor a -> Int -> Xor a # rotateL :: Xor a -> Int -> Xor a # rotateR :: Xor a -> Int -> Xor a # popCount :: Xor a -> Int #
Bits a => Bits (Down a)
Instance details Defined in GHC.Internal.Data.Ord Methods (.&.) :: Down a -> Down a -> Down a # (.\|.) :: Down a -> Down a -> Down a # xor :: Down a -> Down a -> Down a # complement :: Down a -> Down a # shift :: Down a -> Int -> Down a # rotate :: Down a -> Int -> Down a # zeroBits :: Down a # bit :: Int -> Down a # setBit :: Down a -> Int -> Down a # clearBit :: Down a -> Int -> Down a # complementBit :: Down a -> Int -> Down a # testBit :: Down a -> Int -> Bool # bitSizeMaybe :: Down a -> Maybe Int # bitSize :: Down a -> Int # isSigned :: Down a -> Bool # shiftL :: Down a -> Int -> Down a # unsafeShiftL :: Down a -> Int -> Down a # shiftR :: Down a -> Int -> Down a # unsafeShiftR :: Down a -> Int -> Down a # rotateL :: Down a -> Int -> Down a # rotateR :: Down a -> Int -> Down a # popCount :: Down a -> Int #

bitDefault :: (Bits a, Num a) => Int -> a #

popCountDefault :: (Bits a, Num a) => a -> Int #

testBitDefault :: (Bits a, Num a) => a -> Int -> Bool #

toIntegralSized :: (Integral a, Integral b, Bits a, Bits b) => a -> Maybe b #

(!<<.) :: Bits a => a -> Int -> a #

(!>>.) :: Bits a => a -> Int -> a #

(.<<.) :: Bits a => a -> Int -> a #

(.>>.) :: Bits a => a -> Int -> a #

(.^.) :: Bits a => a -> a -> a #

oneBits :: FiniteBits a => a #

class Bits b => FiniteBits b where #

Minimal complete definition

finiteBitSize

Methods

finiteBitSize :: b -> Int #

countLeadingZeros :: b -> Int #

countTrailingZeros :: b -> Int #

Instances

Instances details

FiniteBits Bool
Instance details Defined in GHC.Internal.Bits Methods finiteBitSize :: Bool -> Int # countLeadingZeros :: Bool -> Int # countTrailingZeros :: Bool -> Int #
FiniteBits Int
Instance details Defined in GHC.Internal.Bits Methods finiteBitSize :: Int -> Int # countLeadingZeros :: Int -> Int # countTrailingZeros :: Int -> Int #
FiniteBits Word
Instance details Defined in GHC.Internal.Bits Methods finiteBitSize :: Word -> Int # countLeadingZeros :: Word -> Int # countTrailingZeros :: Word -> Int #
FiniteBits a => FiniteBits (And a)
Instance details Defined in GHC.Internal.Data.Bits Methods finiteBitSize :: And a -> Int # countLeadingZeros :: And a -> Int # countTrailingZeros :: And a -> Int #
FiniteBits a => FiniteBits (Iff a)
Instance details Defined in GHC.Internal.Data.Bits Methods finiteBitSize :: Iff a -> Int # countLeadingZeros :: Iff a -> Int # countTrailingZeros :: Iff a -> Int #
FiniteBits a => FiniteBits (Ior a)
Instance details Defined in GHC.Internal.Data.Bits Methods finiteBitSize :: Ior a -> Int # countLeadingZeros :: Ior a -> Int # countTrailingZeros :: Ior a -> Int #
FiniteBits a => FiniteBits (Xor a)
Instance details Defined in GHC.Internal.Data.Bits Methods finiteBitSize :: Xor a -> Int # countLeadingZeros :: Xor a -> Int # countTrailingZeros :: Xor a -> Int #
FiniteBits a => FiniteBits (Down a)
Instance details Defined in GHC.Internal.Data.Ord Methods finiteBitSize :: Down a -> Int # countLeadingZeros :: Down a -> Int # countTrailingZeros :: Down a -> Int #

newtype And a #

Constructors

And
Fields getAnd :: a

Instances

Instances details

FiniteBits a => Monoid (And a)
Instance details Defined in GHC.Internal.Data.Bits Methods mempty :: And a mappend :: And a -> And a -> And a mconcat :: [And a] -> And a
Bits a => Semigroup (And a)
Instance details Defined in GHC.Internal.Data.Bits Methods (<>) :: And a -> And a -> And a sconcat :: NonEmpty (And a) -> And a stimes :: Integral b => b -> And a -> And a
Bits a => Bits (And a)
Instance details Defined in GHC.Internal.Data.Bits Methods (.&.) :: And a -> And a -> And a # (.\|.) :: And a -> And a -> And a # xor :: And a -> And a -> And a # complement :: And a -> And a # shift :: And a -> Int -> And a # rotate :: And a -> Int -> And a # zeroBits :: And a # bit :: Int -> And a # setBit :: And a -> Int -> And a # clearBit :: And a -> Int -> And a # complementBit :: And a -> Int -> And a # testBit :: And a -> Int -> Bool # bitSizeMaybe :: And a -> Maybe Int # bitSize :: And a -> Int # isSigned :: And a -> Bool # shiftL :: And a -> Int -> And a # unsafeShiftL :: And a -> Int -> And a # shiftR :: And a -> Int -> And a # unsafeShiftR :: And a -> Int -> And a # rotateL :: And a -> Int -> And a # rotateR :: And a -> Int -> And a # popCount :: And a -> Int #
FiniteBits a => FiniteBits (And a)
Instance details Defined in GHC.Internal.Data.Bits Methods finiteBitSize :: And a -> Int # countLeadingZeros :: And a -> Int # countTrailingZeros :: And a -> Int #
Bounded a => Bounded (And a)
Instance details Defined in GHC.Internal.Data.Bits Methods minBound :: And a maxBound :: And a
Enum a => Enum (And a)
Instance details Defined in GHC.Internal.Data.Bits Methods succ :: And a -> And a pred :: And a -> And a toEnum :: Int -> And a fromEnum :: And a -> Int enumFrom :: And a -> [And a] enumFromThen :: And a -> And a -> [And a] enumFromTo :: And a -> And a -> [And a] enumFromThenTo :: And a -> And a -> And a -> [And a]
Read a => Read (And a)
Instance details Defined in GHC.Internal.Data.Bits Methods readsPrec :: Int -> ReadS (And a) readList :: ReadS [And a] readPrec :: ReadPrec (And a) readListPrec :: ReadPrec [And a]
Show a => Show (And a)
Instance details Defined in GHC.Internal.Data.Bits Methods showsPrec :: Int -> And a -> ShowS show :: And a -> String showList :: [And a] -> ShowS
Eq a => Eq (And a)
Instance details Defined in GHC.Internal.Data.Bits Methods (==) :: And a -> And a -> Bool (/=) :: And a -> And a -> Bool

newtype Iff a #

Constructors

Iff
Fields getIff :: a

Instances

Instances details

FiniteBits a => Monoid (Iff a)
Instance details Defined in GHC.Internal.Data.Bits Methods mempty :: Iff a mappend :: Iff a -> Iff a -> Iff a mconcat :: [Iff a] -> Iff a
FiniteBits a => Semigroup (Iff a)
Instance details Defined in GHC.Internal.Data.Bits Methods (<>) :: Iff a -> Iff a -> Iff a sconcat :: NonEmpty (Iff a) -> Iff a stimes :: Integral b => b -> Iff a -> Iff a
Bits a => Bits (Iff a)
Instance details Defined in GHC.Internal.Data.Bits Methods (.&.) :: Iff a -> Iff a -> Iff a # (.\|.) :: Iff a -> Iff a -> Iff a # xor :: Iff a -> Iff a -> Iff a # complement :: Iff a -> Iff a # shift :: Iff a -> Int -> Iff a # rotate :: Iff a -> Int -> Iff a # zeroBits :: Iff a # bit :: Int -> Iff a # setBit :: Iff a -> Int -> Iff a # clearBit :: Iff a -> Int -> Iff a # complementBit :: Iff a -> Int -> Iff a # testBit :: Iff a -> Int -> Bool # bitSizeMaybe :: Iff a -> Maybe Int # bitSize :: Iff a -> Int # isSigned :: Iff a -> Bool # shiftL :: Iff a -> Int -> Iff a # unsafeShiftL :: Iff a -> Int -> Iff a # shiftR :: Iff a -> Int -> Iff a # unsafeShiftR :: Iff a -> Int -> Iff a # rotateL :: Iff a -> Int -> Iff a # rotateR :: Iff a -> Int -> Iff a # popCount :: Iff a -> Int #
FiniteBits a => FiniteBits (Iff a)
Instance details Defined in GHC.Internal.Data.Bits Methods finiteBitSize :: Iff a -> Int # countLeadingZeros :: Iff a -> Int # countTrailingZeros :: Iff a -> Int #
Bounded a => Bounded (Iff a)
Instance details Defined in GHC.Internal.Data.Bits Methods minBound :: Iff a maxBound :: Iff a
Enum a => Enum (Iff a)
Instance details Defined in GHC.Internal.Data.Bits Methods succ :: Iff a -> Iff a pred :: Iff a -> Iff a toEnum :: Int -> Iff a fromEnum :: Iff a -> Int enumFrom :: Iff a -> [Iff a] enumFromThen :: Iff a -> Iff a -> [Iff a] enumFromTo :: Iff a -> Iff a -> [Iff a] enumFromThenTo :: Iff a -> Iff a -> Iff a -> [Iff a]
Read a => Read (Iff a)
Instance details Defined in GHC.Internal.Data.Bits Methods readsPrec :: Int -> ReadS (Iff a) readList :: ReadS [Iff a] readPrec :: ReadPrec (Iff a) readListPrec :: ReadPrec [Iff a]
Show a => Show (Iff a)
Instance details Defined in GHC.Internal.Data.Bits Methods showsPrec :: Int -> Iff a -> ShowS show :: Iff a -> String showList :: [Iff a] -> ShowS
Eq a => Eq (Iff a)
Instance details Defined in GHC.Internal.Data.Bits Methods (==) :: Iff a -> Iff a -> Bool (/=) :: Iff a -> Iff a -> Bool

newtype Ior a #

Constructors

Ior
Fields getIor :: a

Instances

Instances details

Bits a => Monoid (Ior a)
Instance details Defined in GHC.Internal.Data.Bits Methods mempty :: Ior a mappend :: Ior a -> Ior a -> Ior a mconcat :: [Ior a] -> Ior a
Bits a => Semigroup (Ior a)
Instance details Defined in GHC.Internal.Data.Bits Methods (<>) :: Ior a -> Ior a -> Ior a sconcat :: NonEmpty (Ior a) -> Ior a stimes :: Integral b => b -> Ior a -> Ior a
Bits a => Bits (Ior a)
Instance details Defined in GHC.Internal.Data.Bits Methods (.&.) :: Ior a -> Ior a -> Ior a # (.\|.) :: Ior a -> Ior a -> Ior a # xor :: Ior a -> Ior a -> Ior a # complement :: Ior a -> Ior a # shift :: Ior a -> Int -> Ior a # rotate :: Ior a -> Int -> Ior a # zeroBits :: Ior a # bit :: Int -> Ior a # setBit :: Ior a -> Int -> Ior a # clearBit :: Ior a -> Int -> Ior a # complementBit :: Ior a -> Int -> Ior a # testBit :: Ior a -> Int -> Bool # bitSizeMaybe :: Ior a -> Maybe Int # bitSize :: Ior a -> Int # isSigned :: Ior a -> Bool # shiftL :: Ior a -> Int -> Ior a # unsafeShiftL :: Ior a -> Int -> Ior a # shiftR :: Ior a -> Int -> Ior a # unsafeShiftR :: Ior a -> Int -> Ior a # rotateL :: Ior a -> Int -> Ior a # rotateR :: Ior a -> Int -> Ior a # popCount :: Ior a -> Int #
FiniteBits a => FiniteBits (Ior a)
Instance details Defined in GHC.Internal.Data.Bits Methods finiteBitSize :: Ior a -> Int # countLeadingZeros :: Ior a -> Int # countTrailingZeros :: Ior a -> Int #
Bounded a => Bounded (Ior a)
Instance details Defined in GHC.Internal.Data.Bits Methods minBound :: Ior a maxBound :: Ior a
Enum a => Enum (Ior a)
Instance details Defined in GHC.Internal.Data.Bits Methods succ :: Ior a -> Ior a pred :: Ior a -> Ior a toEnum :: Int -> Ior a fromEnum :: Ior a -> Int enumFrom :: Ior a -> [Ior a] enumFromThen :: Ior a -> Ior a -> [Ior a] enumFromTo :: Ior a -> Ior a -> [Ior a] enumFromThenTo :: Ior a -> Ior a -> Ior a -> [Ior a]
Read a => Read (Ior a)
Instance details Defined in GHC.Internal.Data.Bits Methods readsPrec :: Int -> ReadS (Ior a) readList :: ReadS [Ior a] readPrec :: ReadPrec (Ior a) readListPrec :: ReadPrec [Ior a]
Show a => Show (Ior a)
Instance details Defined in GHC.Internal.Data.Bits Methods showsPrec :: Int -> Ior a -> ShowS show :: Ior a -> String showList :: [Ior a] -> ShowS
Eq a => Eq (Ior a)
Instance details Defined in GHC.Internal.Data.Bits Methods (==) :: Ior a -> Ior a -> Bool (/=) :: Ior a -> Ior a -> Bool

newtype Xor a #

Constructors

Xor
Fields getXor :: a

Instances

Instances details

Bits a => Monoid (Xor a)
Instance details Defined in GHC.Internal.Data.Bits Methods mempty :: Xor a mappend :: Xor a -> Xor a -> Xor a mconcat :: [Xor a] -> Xor a
Bits a => Semigroup (Xor a)
Instance details Defined in GHC.Internal.Data.Bits Methods (<>) :: Xor a -> Xor a -> Xor a sconcat :: NonEmpty (Xor a) -> Xor a stimes :: Integral b => b -> Xor a -> Xor a
Bits a => Bits (Xor a)
Instance details Defined in GHC.Internal.Data.Bits Methods (.&.) :: Xor a -> Xor a -> Xor a # (.\|.) :: Xor a -> Xor a -> Xor a # xor :: Xor a -> Xor a -> Xor a # complement :: Xor a -> Xor a # shift :: Xor a -> Int -> Xor a # rotate :: Xor a -> Int -> Xor a # zeroBits :: Xor a # bit :: Int -> Xor a # setBit :: Xor a -> Int -> Xor a # clearBit :: Xor a -> Int -> Xor a # complementBit :: Xor a -> Int -> Xor a # testBit :: Xor a -> Int -> Bool # bitSizeMaybe :: Xor a -> Maybe Int # bitSize :: Xor a -> Int # isSigned :: Xor a -> Bool # shiftL :: Xor a -> Int -> Xor a # unsafeShiftL :: Xor a -> Int -> Xor a # shiftR :: Xor a -> Int -> Xor a # unsafeShiftR :: Xor a -> Int -> Xor a # rotateL :: Xor a -> Int -> Xor a # rotateR :: Xor a -> Int -> Xor a # popCount :: Xor a -> Int #
FiniteBits a => FiniteBits (Xor a)
Instance details Defined in GHC.Internal.Data.Bits Methods finiteBitSize :: Xor a -> Int # countLeadingZeros :: Xor a -> Int # countTrailingZeros :: Xor a -> Int #
Bounded a => Bounded (Xor a)
Instance details Defined in GHC.Internal.Data.Bits Methods minBound :: Xor a maxBound :: Xor a
Enum a => Enum (Xor a)
Instance details Defined in GHC.Internal.Data.Bits Methods succ :: Xor a -> Xor a pred :: Xor a -> Xor a toEnum :: Int -> Xor a fromEnum :: Xor a -> Int enumFrom :: Xor a -> [Xor a] enumFromThen :: Xor a -> Xor a -> [Xor a] enumFromTo :: Xor a -> Xor a -> [Xor a] enumFromThenTo :: Xor a -> Xor a -> Xor a -> [Xor a]
Read a => Read (Xor a)
Instance details Defined in GHC.Internal.Data.Bits Methods readsPrec :: Int -> ReadS (Xor a) readList :: ReadS [Xor a] readPrec :: ReadPrec (Xor a) readListPrec :: ReadPrec [Xor a]
Show a => Show (Xor a)
Instance details Defined in GHC.Internal.Data.Bits Methods showsPrec :: Int -> Xor a -> ShowS show :: Xor a -> String showList :: [Xor a] -> ShowS
Eq a => Eq (Xor a)
Instance details Defined in GHC.Internal.Data.Bits Methods (==) :: Xor a -> Xor a -> Bool (/=) :: Xor a -> Xor a -> Bool

not :: BV -> BV Source #

An alias for complement.

not_ :: BV -> BV Source #

Deprecated: Use corresponding versions without underscore

An alias for complement.

nand :: BV -> BV -> BV Source #

Negated .&..

nor :: BV -> BV -> BV Source #

Negated .|..

xnor :: BV -> BV -> BV Source #

Negated xor.

(<<.) :: BV -> BV -> BV infixl 8 Source #

Left shift.

shl :: BV -> BV -> BV infixl 8 Source #

Left shift.

(>>.) :: BV -> BV -> BV infixl 8 Source #

Logical right shift.

shr :: BV -> BV -> BV infixl 8 Source #

Logical right shift.

ashr :: BV -> BV -> BV infixl 8 Source #

Arithmetic right shift

(<<<.) :: BV -> BV -> BV infixl 8 Source #

Rotate left.

rol :: BV -> BV -> BV infixl 8 Source #

Rotate left.

(>>>.) :: BV -> BV -> BV infixl 8 Source #

Rotate right.

ror :: BV -> BV -> BV infixl 8 Source #

Rotate right.

Conversion

fromBool :: Bool -> BV Source #

Create a bit-vector from a single bit.

fromBits :: [Bool] -> BV Source #

Create a bit-vector from a big-endian list of bits.

>>> fromBits [False, False, True]
[3]1

toBits :: BV -> [Bool] Source #

Create a big-endian list of bits from a bit-vector.

>>> toBits [4]11
[True, False, True, True]

Pretty-printing

showBin :: BV -> String Source #

Show a bit-vector in binary form.

showOct :: BV -> String Source #

Show a bit-vector in octal form.

showHex :: BV -> String Source #

Show a bit-vector in hexadecimal form.