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|
-----------------------------------------------------------------------------
-- |
-- Module : Data.SBV.Core.Sized
-- Copyright : (c) Levent Erkok
-- License : BSD3
-- Maintainer: erkokl@gmail.com
-- Stability : experimental
--
-- Type-level sized bit-vectors. Thanks to Ben Blaxill for providing an
-- initial implementation of this idea.
-----------------------------------------------------------------------------
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeApplications #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE UndecidableInstances #-}
{-# OPTIONS_GHC -Wall -Werror #-}
module Data.SBV.Core.Sized (
-- * Type-sized unsigned bit-vectors
SWord, WordN, sWord, sWord_, sWords
-- * Type-sized signed bit-vectors
, SInt, IntN, sInt, sInt_, sInts
-- * Bit-vector operations
, bvExtract, (#), zeroExtend, signExtend, bvDrop, bvTake
) where
import Data.Bits
import Data.Maybe (fromJust)
import Data.Proxy (Proxy(..))
import GHC.TypeLits
import Data.SBV.Core.Data
import Data.SBV.Core.Kind
import Data.SBV.Core.Model
import Data.SBV.Core.Operations
import Data.SBV.Core.Symbolic
import Data.SBV.SMT.SMT
import Test.QuickCheck(Arbitrary(..))
-- | An unsigned bit-vector carrying its size info
newtype WordN (n :: Nat) = WordN Integer deriving (Eq, Ord)
-- | A symbolic unsigned bit-vector carrying its size info
type SWord (n :: Nat) = SBV (WordN n)
-- | Show instance for 'WordN'
instance Show (WordN n) where
show (WordN v) = show v
-- | 'WordN' has a kind
instance (KnownNat n, BVIsNonZero n) => HasKind (WordN n) where
kindOf _ = KBounded False (intOfProxy (Proxy @n))
-- | 'SymVal' instance for 'WordN'
instance (KnownNat n, BVIsNonZero n) => SymVal (WordN n) where
literal x = genLiteral (kindOf x) x
mkSymVal = genMkSymVar (kindOf (undefined :: WordN n))
fromCV = genFromCV
-- | A signed bit-vector carrying its size info
newtype IntN (n :: Nat) = IntN Integer deriving (Eq, Ord)
-- | A symbolic signed bit-vector carrying its size info
type SInt (n :: Nat) = SBV (IntN n)
-- | Show instance for 'IntN'
instance Show (IntN n) where
show (IntN v) = show v
-- | 'IntN' has a kind
instance (KnownNat n, BVIsNonZero n) => HasKind (IntN n) where
kindOf _ = KBounded True (intOfProxy (Proxy @n))
-- | 'SymVal' instance for 'IntN'
instance (KnownNat n, BVIsNonZero n) => SymVal (IntN n) where
literal x = genLiteral (kindOf x) x
mkSymVal = genMkSymVar (kindOf (undefined :: IntN n))
fromCV = genFromCV
-- Lift a unary operation via SVal
lift1 :: (KnownNat n, BVIsNonZero n, HasKind (bv n), Integral (bv n), Show (bv n)) => String -> (SVal -> SVal) -> bv n -> bv n
lift1 nm op x = uc $ op (c x)
where k = kindOf x
c = SVal k . Left . normCV . CV k . CInteger . toInteger
uc (SVal _ (Left (CV _ (CInteger v)))) = fromInteger v
uc r = error $ "Impossible happened while lifting " ++ show nm ++ " over " ++ show (k, x, r)
-- Lift a binary operation via SVal
lift2 :: (KnownNat n, BVIsNonZero n, HasKind (bv n), Integral (bv n), Show (bv n)) => String -> (SVal -> SVal -> SVal) -> bv n -> bv n -> bv n
lift2 nm op x y = uc $ c x `op` c y
where k = kindOf x
c = SVal k . Left . normCV . CV k . CInteger . toInteger
uc (SVal _ (Left (CV _ (CInteger v)))) = fromInteger v
uc r = error $ "Impossible happened while lifting " ++ show nm ++ " over " ++ show (k, x, y, r)
-- Lift a binary operation via SVal where second argument is an Int
lift2I :: (KnownNat n, BVIsNonZero n, HasKind (bv n), Integral (bv n), Show (bv n)) => String -> (SVal -> Int -> SVal) -> bv n -> Int -> bv n
lift2I nm op x i = uc $ c x `op` i
where k = kindOf x
c = SVal k . Left . normCV . CV k . CInteger . toInteger
uc (SVal _ (Left (CV _ (CInteger v)))) = fromInteger v
uc r = error $ "Impossible happened while lifting " ++ show nm ++ " over " ++ show (k, x, i, r)
-- Lift a binary operation via SVal where second argument is an Int and returning a Bool
lift2IB :: (KnownNat n, BVIsNonZero n, HasKind (bv n), Integral (bv n), Show (bv n)) => String -> (SVal -> Int -> SVal) -> bv n -> Int -> Bool
lift2IB nm op x i = uc $ c x `op` i
where k = kindOf x
c = SVal k . Left . normCV . CV k . CInteger . toInteger
uc (SVal _ (Left v)) = cvToBool v
uc r = error $ "Impossible happened while lifting " ++ show nm ++ " over " ++ show (k, x, i, r)
-- | 'Bounded' instance for 'WordN'
instance (KnownNat n, BVIsNonZero n) => Bounded (WordN n) where
minBound = WordN 0
maxBound = let sz = intOfProxy (Proxy @n) in WordN $ 2 ^ sz - 1
-- | 'Bounded' instance for 'IntN'
instance (KnownNat n, BVIsNonZero n) => Bounded (IntN n) where
minBound = let sz1 = intOfProxy (Proxy @n) - 1 in IntN $ - (2 ^ sz1)
maxBound = let sz1 = intOfProxy (Proxy @n) - 1 in IntN $ 2 ^ sz1 - 1
-- | 'Num' instance for 'WordN'
instance (KnownNat n, BVIsNonZero n) => Num (WordN n) where
(+) = lift2 "(+)" svPlus
(-) = lift2 "(*)" svMinus
(*) = lift2 "(*)" svTimes
negate = lift1 "signum" svUNeg
abs = lift1 "abs" svAbs
signum = WordN . signum . toInteger
fromInteger = WordN . fromJust . svAsInteger . svInteger (kindOf (undefined :: WordN n))
-- | 'Num' instance for 'IntN'
instance (KnownNat n, BVIsNonZero n) => Num (IntN n) where
(+) = lift2 "(+)" svPlus
(-) = lift2 "(*)" svMinus
(*) = lift2 "(*)" svTimes
negate = lift1 "signum" svUNeg
abs = lift1 "abs" svAbs
signum = IntN . signum . toInteger
fromInteger = IntN . fromJust . svAsInteger . svInteger (kindOf (undefined :: IntN n))
-- | 'Enum' instance for 'WordN'
instance (KnownNat n, BVIsNonZero n) => Enum (WordN n) where
toEnum = fromInteger . toInteger
fromEnum = fromIntegral . toInteger
-- | 'Enum' instance for 'IntN'
instance (KnownNat n, BVIsNonZero n) => Enum (IntN n) where
toEnum = fromInteger . toInteger
fromEnum = fromIntegral . toInteger
-- | 'Real' instance for 'WordN'
instance (KnownNat n, BVIsNonZero n) => Real (WordN n) where
toRational (WordN x) = toRational x
-- | 'Real' instance for 'IntN'
instance (KnownNat n, BVIsNonZero n) => Real (IntN n) where
toRational (IntN x) = toRational x
-- | 'Integral' instance for 'WordN'
instance (KnownNat n, BVIsNonZero n) => Integral (WordN n) where
toInteger (WordN x) = x
quotRem (WordN x) (WordN y) = let (q, r) = quotRem x y in (WordN q, WordN r)
-- | 'Integral' instance for 'IntN'
instance (KnownNat n, BVIsNonZero n) => Integral (IntN n) where
toInteger (IntN x) = x
quotRem (IntN x) (IntN y) = let (q, r) = quotRem x y in (IntN q, IntN r)
-- 'Bits' instance for 'WordN'
instance (KnownNat n, BVIsNonZero n) => Bits (WordN n) where
(.&.) = lift2 "(.&.)" svAnd
(.|.) = lift2 "(.|.)" svOr
xor = lift2 "xor" svXOr
complement = lift1 "complement" svNot
shiftL = lift2I "shiftL" svShl
shiftR = lift2I "shiftR" svShr
rotateL = lift2I "rotateL" svRol
rotateR = lift2I "rotateR" svRor
testBit = lift2IB "svTestBit" svTestBit
bitSizeMaybe = Just . const (intOfProxy (Proxy @n))
bitSize _ = intOfProxy (Proxy @n)
isSigned = hasSign . kindOf
bit i = 1 `shiftL` i
popCount = fromIntegral . popCount . toInteger
-- 'Bits' instance for 'IntN'
instance (KnownNat n, BVIsNonZero n) => Bits (IntN n) where
(.&.) = lift2 "(.&.)" svAnd
(.|.) = lift2 "(.|.)" svOr
xor = lift2 "xor" svXOr
complement = lift1 "complement" svNot
shiftL = lift2I "shiftL" svShl
shiftR = lift2I "shiftR" svShr
rotateL = lift2I "rotateL" svRol
rotateR = lift2I "rotateR" svRor
testBit = lift2IB "svTestBit" svTestBit
bitSizeMaybe = Just . const (intOfProxy (Proxy @n))
bitSize _ = intOfProxy (Proxy @n)
isSigned = hasSign . kindOf
bit i = 1 `shiftL` i
popCount = fromIntegral . popCount . toInteger
-- | 'SIntegral' instance for 'WordN'
instance (KnownNat n, BVIsNonZero n) => SIntegral (WordN n)
-- | 'SIntegral' instance for 'IntN'
instance (KnownNat n, BVIsNonZero n) => SIntegral (IntN n)
-- | 'SDivisible' instance for 'WordN'
instance (KnownNat n, BVIsNonZero n) => SDivisible (WordN n) where
sQuotRem x 0 = (0, x)
sQuotRem x y = x `quotRem` y
sDivMod x 0 = (0, x)
sDivMod x y = x `divMod` y
-- | 'SDivisible' instance for 'IntN'
instance (KnownNat n, BVIsNonZero n) => SDivisible (IntN n) where
sQuotRem x 0 = (0, x)
sQuotRem x y = x `quotRem` y
sDivMod x 0 = (0, x)
sDivMod x y = x `divMod` y
-- | 'SDivisible' instance for 'SWord'
instance (KnownNat n, BVIsNonZero n) => SDivisible (SWord n) where
sQuotRem = liftQRem
sDivMod = liftDMod
-- | 'SDivisible' instance for 'SInt'
instance (KnownNat n, BVIsNonZero n) => SDivisible (SInt n) where
sQuotRem = liftQRem
sDivMod = liftDMod
-- | 'SFiniteBits' instance for 'WordN'
instance (KnownNat n, BVIsNonZero n) => SFiniteBits (WordN n) where
sFiniteBitSize _ = intOfProxy (Proxy @n)
-- | 'SFiniteBits' instance for 'IntN'
instance (KnownNat n, BVIsNonZero n) => SFiniteBits (IntN n) where
sFiniteBitSize _ = intOfProxy (Proxy @n)
-- | Constructing models for 'WordN'
instance (KnownNat n, BVIsNonZero n) => SatModel (WordN n) where
parseCVs = genParse (kindOf (undefined :: WordN n))
-- | Constructing models for 'IntN'
instance (KnownNat n, BVIsNonZero n) => SatModel (IntN n) where
parseCVs = genParse (kindOf (undefined :: IntN n))
-- | Optimizing 'WordN'
instance (KnownNat n, BVIsNonZero n) => Metric (WordN n)
-- | Optimizing 'IntN'
instance (KnownNat n, BVIsNonZero n) => Metric (IntN n) where
type MetricSpace (IntN n) = WordN n
toMetricSpace x = sFromIntegral x + 2 ^ (intOfProxy (Proxy @n) - 1)
fromMetricSpace x = sFromIntegral x - 2 ^ (intOfProxy (Proxy @n) - 1)
-- | Generalization of 'Data.SBV.sWord'
sWord :: (KnownNat n, BVIsNonZero n) => MonadSymbolic m => String -> m (SWord n)
sWord = symbolic
-- | Generalization of 'Data.SBV.sWord_'
sWord_ :: (KnownNat n, BVIsNonZero n) => MonadSymbolic m => m (SWord n)
sWord_ = free_
-- | Generalization of 'Data.SBV.sWord64s'
sWords :: (KnownNat n, BVIsNonZero n) => MonadSymbolic m => [String] -> m [SWord n]
sWords = symbolics
-- | Generalization of 'Data.SBV.sInt'
sInt :: (KnownNat n, BVIsNonZero n) => MonadSymbolic m => String -> m (SInt n)
sInt = symbolic
-- | Generalization of 'Data.SBV.sInt_'
sInt_ :: (KnownNat n, BVIsNonZero n) => MonadSymbolic m => m (SInt n)
sInt_ = free_
-- | Generalization of 'Data.SBV.sInts'
sInts :: (KnownNat n, BVIsNonZero n) => MonadSymbolic m => [String] -> m [SInt n]
sInts = symbolics
-- | Extract a portion of bits to form a smaller bit-vector.
bvExtract :: forall i j n bv proxy. ( KnownNat n, BVIsNonZero n, SymVal (bv n)
, KnownNat i
, KnownNat j
, i + 1 <= n
, j <= i
, BVIsNonZero (i - j + 1)
) => proxy i -- ^ @i@: Start position, numbered from @n-1@ to @0@
-> proxy j -- ^ @j@: End position, numbered from @n-1@ to @0@, @j <= i@ must hold
-> SBV (bv n) -- ^ Input bit vector of size @n@
-> SBV (bv (i - j + 1)) -- ^ Output is of size @i - j + 1@
bvExtract start end = SBV . svExtract i j . unSBV
where i = fromIntegral (natVal start)
j = fromIntegral (natVal end)
-- | Join two bitvectors.
(#) :: ( KnownNat n, BVIsNonZero n, SymVal (bv n)
, KnownNat m, BVIsNonZero m, SymVal (bv m)
) => SBV (bv n) -- ^ First input, of size @n@, becomes the left side
-> SBV (bv m) -- ^ Second input, of size @m@, becomes the right side
-> SBV (bv (n + m)) -- ^ Concatenation, of size @n+m@
n # m = SBV $ svJoin (unSBV n) (unSBV m)
infixr 5 #
-- | Zero extend a bit-vector.
zeroExtend :: forall n m bv. ( KnownNat n, BVIsNonZero n, SymVal (bv n)
, KnownNat m, BVIsNonZero m, SymVal (bv m)
, n + 1 <= m
, SIntegral (bv (m - n))
, BVIsNonZero (m - n)
) => SBV (bv n) -- ^ Input, of size @n@
-> SBV (bv m) -- ^ Output, of size @m@. @n < m@ must hold
zeroExtend n = SBV $ svZeroExtend i (unSBV n)
where nv = intOfProxy (Proxy @n)
mv = intOfProxy (Proxy @m)
i = fromIntegral (mv - nv)
-- | Sign extend a bit-vector.
signExtend :: forall n m bv. ( KnownNat n, BVIsNonZero n, SymVal (bv n)
, KnownNat m, BVIsNonZero m, SymVal (bv m)
, n + 1 <= m
, SFiniteBits (bv n)
, SIntegral (bv (m - n))
, BVIsNonZero (m - n)
) => SBV (bv n) -- ^ Input, of size @n@
-> SBV (bv m) -- ^ Output, of size @m@. @n < m@ must hold
signExtend n = SBV $ svSignExtend i (unSBV n)
where nv = intOfProxy (Proxy @n)
mv = intOfProxy (Proxy @m)
i = fromIntegral (mv - nv)
-- | Drop bits from the top of a bit-vector.
bvDrop :: forall i n m bv proxy. ( KnownNat n, BVIsNonZero n
, KnownNat i
, i + 1 <= n
, i + m - n <= 0
, BVIsNonZero (n - i)
) => proxy i -- ^ @i@: Number of bits to drop. @i < n@ must hold.
-> SBV (bv n) -- ^ Input, of size @n@
-> SBV (bv m) -- ^ Output, of size @m@. @m = n - i@ holds.
bvDrop i = SBV . svExtract start 0 . unSBV
where nv = intOfProxy (Proxy @n)
start = nv - fromIntegral (natVal i) - 1
-- | Take bits from the top of a bit-vector.
bvTake :: forall i n bv proxy. ( KnownNat n, BVIsNonZero n
, KnownNat i, BVIsNonZero i
, i <= n
) => proxy i -- ^ @i@: Number of bits to take. @0 < i <= n@ must hold.
-> SBV (bv n) -- ^ Input, of size @n@
-> SBV (bv i) -- ^ Output, of size @i@
bvTake i = SBV . svExtract start end . unSBV
where nv = intOfProxy (Proxy @n)
start = nv - 1
end = start - fromIntegral (natVal i) + 1
-- | Quickcheck instance for WordN
instance KnownNat n => Arbitrary (WordN n) where
arbitrary = (WordN . norm . abs) `fmap` arbitrary
where sz = intOfProxy (Proxy @n)
norm v | sz == 0 = 0
| True = v .&. (((1 :: Integer) `shiftL` sz) - 1)
-- | Quickcheck instance for IntN
instance KnownNat n => Arbitrary (IntN n) where
arbitrary = (IntN . norm) `fmap` arbitrary
where sz = intOfProxy (Proxy @n)
norm v | sz == 0 = 0
| True = let rg = 2 ^ (sz - 1)
in case divMod v rg of
(a, b) | even a -> b
(_, b) -> b - rg
|
