clash-prelude-0.99: src/Clash/Sized/Internal/BitVector.hs
{-|
Copyright : (C) 2013-2016, University of Twente,
2016 , Myrtle Software Ltd
License : BSD2 (see the file LICENSE)
Maintainer : Christiaan Baaij <christiaan.baaij@gmail.com>
-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE DeriveDataTypeable #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE MagicHash #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TemplateHaskell #-}
{-# LANGUAGE TypeApplications #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE UndecidableInstances #-}
{-# LANGUAGE Unsafe #-}
{-# OPTIONS_GHC -fplugin GHC.TypeLits.KnownNat.Solver #-}
{-# OPTIONS_GHC -fplugin GHC.TypeLits.Normalise #-}
{-# OPTIONS_HADDOCK show-extensions not-home #-}
module Clash.Sized.Internal.BitVector
( -- * Bit
Bit (..)
-- ** Construction
, high
, low
-- ** Type classes
-- *** Eq
, eq##
, neq##
-- *** Ord
, lt##
, ge##
, gt##
, le##
-- *** Num
, fromInteger##
-- *** Bits
, and##
, or##
, xor##
, complement##
-- *** BitPack
, pack#
, unpack#
-- * BitVector
, BitVector (..)
-- ** Accessors
, size#
, maxIndex#
-- ** Construction
, bLit
-- ** Concatenation
, (++#)
-- ** Reduction
, reduceAnd#
, reduceOr#
, reduceXor#
-- ** Indexing
, index#
, replaceBit#
, setSlice#
, slice#
, split#
, msb#
, lsb#
-- ** Type classes
-- **** Eq
, eq#
, neq#
-- *** Ord
, lt#
, ge#
, gt#
, le#
-- *** Enum (not synthesisable)
, enumFrom#
, enumFromThen#
, enumFromTo#
, enumFromThenTo#
-- *** Bounded
, minBound#
, maxBound#
-- *** Num
, (+#)
, (-#)
, (*#)
, negate#
, fromInteger#
-- *** ExtendingNum
, plus#
, minus#
, times#
-- *** Integral
, quot#
, rem#
, toInteger#
-- *** Bits
, and#
, or#
, xor#
, complement#
, shiftL#
, shiftR#
, rotateL#
, rotateR#
, popCountBV
-- *** FiniteBits
, countLeadingZerosBV
, countTrailingZerosBV
-- *** Resize
, resize#
-- *** QuickCheck
, shrinkSizedUnsigned
)
where
import Control.DeepSeq (NFData (..))
import Control.Lens (Index, Ixed (..), IxValue)
import Data.Bits (Bits (..), FiniteBits (..))
import Data.Char (digitToInt)
import Data.Data (Data)
import Data.Default (Default (..))
import Data.Maybe (listToMaybe)
import Data.Proxy (Proxy (..))
import GHC.Integer (smallInteger)
import GHC.Prim (dataToTag#)
import GHC.TypeLits (KnownNat, Nat, type (+), type (-), natVal)
import GHC.TypeLits.Extra (Max)
import Language.Haskell.TH (Q, TExp, TypeQ, appT, conT, litT, numTyLit, sigE)
import Language.Haskell.TH.Syntax (Lift(..))
import Numeric (readInt)
import Test.QuickCheck.Arbitrary (Arbitrary (..), CoArbitrary (..),
arbitraryBoundedIntegral,
coarbitraryIntegral, shrinkIntegral)
import Clash.Class.Num (ExtendingNum (..), SaturatingNum (..),
SaturationMode (..))
import Clash.Class.Resize (Resize (..))
import Clash.Promoted.Nat (SNat, snatToInteger, snatToNum)
import Clash.XException (ShowX (..), showsPrecXWith)
import {-# SOURCE #-} qualified Clash.Sized.Vector as V
import {-# SOURCE #-} qualified Clash.Sized.Internal.Index as I
{- $setup
>>> :set -XTemplateHaskell
>>> :set -XBinaryLiterals
-}
-- * Type definitions
-- | A vector of bits.
--
-- * Bit indices are descending
-- * 'Num' instance performs /unsigned/ arithmetic.
newtype BitVector (n :: Nat) =
-- | The constructor, 'BV', and the field, 'unsafeToInteger', are not
-- synthesisable.
BV { unsafeToInteger :: Integer}
deriving (Data)
-- * Bit
-- | Bit
newtype Bit =
-- | The constructor, 'Bit', and the field, 'unsafeToInteger#', are not
-- synthesisable.
Bit { unsafeToInteger# :: Integer}
deriving (Data)
-- * Constructions
-- ** Initialisation
{-# NOINLINE high #-}
-- | logic '1'
high :: Bit
high = Bit 1
{-# NOINLINE low #-}
-- | logic '0'
low :: Bit
low = Bit 0
-- ** Instances
instance NFData Bit where
rnf (Bit i) = rnf i `seq` ()
{-# NOINLINE rnf #-}
instance Show Bit where
show (Bit b) =
case b of
0 -> "0"
_ -> "1"
instance ShowX Bit where
showsPrecX = showsPrecXWith showsPrec
instance Lift Bit where
lift (Bit i) = if i == 0 then [| low |] else [| high |]
{-# NOINLINE lift #-}
instance Eq Bit where
(==) = eq##
(/=) = neq##
eq## :: Bit -> Bit -> Bool
eq## (Bit b1) (Bit b2) = b1 == b2
{-# NOINLINE eq## #-}
neq## :: Bit -> Bit -> Bool
neq## (Bit b1) (Bit b2) = b1 == b2
{-# NOINLINE neq## #-}
instance Ord Bit where
(<) = lt##
(<=) = le##
(>) = gt##
(>=) = ge##
lt##,ge##,gt##,le## :: Bit -> Bit -> Bool
lt## (Bit n) (Bit m) = n < m
{-# NOINLINE lt## #-}
ge## (Bit n) (Bit m) = n >= m
{-# NOINLINE ge## #-}
gt## (Bit n) (Bit m) = n > m
{-# NOINLINE gt## #-}
le## (Bit n) (Bit m) = n <= m
{-# NOINLINE le## #-}
instance Enum Bit where
toEnum = fromInteger## . toInteger
fromEnum b = if eq## b low then 0 else 1
instance Bounded Bit where
minBound = low
maxBound = high
instance Default Bit where
def = low
instance Num Bit where
(+) = xor##
(-) = xor##
(*) = and##
negate = complement##
abs = id
signum b = b
fromInteger = fromInteger##
fromInteger## :: Integer -> Bit
fromInteger## i = Bit (i `mod` 2)
{-# NOINLINE fromInteger## #-}
instance Real Bit where
toRational b = if eq## b low then 0 else 1
instance Integral Bit where
quot a _ = a
rem _ _ = low
div a _ = a
mod _ _ = low
quotRem n _ = (n,low)
divMod n _ = (n,low)
toInteger b = if eq## b low then 0 else 1
instance Bits Bit where
(.&.) = and##
(.|.) = or##
xor = xor##
complement = complement##
zeroBits = low
bit i = if i == 0 then high else low
setBit _ i = if i == 0 then high else low
clearBit _ i = if i == 0 then low else high
complementBit b i = if i == 0 then complement## b else b
testBit b i = if i == 0 then eq## b high else False
bitSizeMaybe _ = Just 1
bitSize _ = 1
isSigned _ = False
shiftL b i = if i == 0 then b else low
shiftR b i = if i == 0 then b else low
rotateL b _ = b
rotateR b _ = b
popCount b = if eq## b low then 0 else 1
instance FiniteBits Bit where
finiteBitSize _ = 1
countLeadingZeros b = if eq## b low then 1 else 0
countTrailingZeros b = if eq## b low then 1 else 0
and##, or##, xor## :: Bit -> Bit -> Bit
and## (Bit v1) (Bit v2) = Bit (v1 .&. v2)
{-# NOINLINE and## #-}
or## (Bit v1) (Bit v2) = Bit (v1 .|. v2)
{-# NOINLINE or## #-}
xor## (Bit v1) (Bit v2) = Bit (v1 `xor` v2)
{-# NOINLINE xor## #-}
complement## :: Bit -> Bit
complement## (Bit 0) = Bit 1
complement## _ = Bit 0
{-# NOINLINE complement## #-}
-- *** BitPack
pack# :: Bit -> BitVector 1
pack# (Bit b) = BV b
{-# NOINLINE pack# #-}
unpack# :: BitVector 1 -> Bit
unpack# (BV b) = Bit b
{-# NOINLINE unpack# #-}
-- * Instances
instance NFData (BitVector n) where
rnf (BV i) = rnf i `seq` ()
{-# NOINLINE rnf #-}
-- NOINLINE is needed so that Clash doesn't trip on the "BitVector ~# Integer"
-- coercion
instance KnownNat n => Show (BitVector n) where
show bv@(BV i) = reverse . underScore . reverse $ showBV (natVal bv) i []
where
showBV 0 _ s = s
showBV n v s = let (a,b) = divMod v 2
in case b of
1 -> showBV (n - 1) a ('1':s)
_ -> showBV (n - 1) a ('0':s)
underScore xs = case splitAt 5 xs of
([a,b,c,d,e],rest) -> [a,b,c,d,'_'] ++ underScore (e:rest)
(rest,_) -> rest
{-# NOINLINE show #-}
instance KnownNat n => ShowX (BitVector n) where
showsPrecX = showsPrecXWith showsPrec
-- | Create a binary literal
--
-- >>> $$(bLit "1001") :: BitVector 4
-- 1001
-- >>> $$(bLit "1001") :: BitVector 3
-- 001
--
-- __NB__: You can also just write:
--
-- >>> 0b1001 :: BitVector 4
-- 1001
--
-- The advantage of 'bLit' is that you can use computations to create the
-- string literal:
--
-- >>> import qualified Data.List as List
-- >>> $$(bLit (List.replicate 4 '1')) :: BitVector 4
-- 1111
bLit :: KnownNat n => String -> Q (TExp (BitVector n))
bLit s = [|| fromInteger# i' ||]
where
i :: Maybe Integer
i = fmap fst . listToMaybe . (readInt 2 (`elem` "01") digitToInt) $ filter (/= '_') s
i' :: Integer
i' = case i of
Just j -> j
_ -> error "Failed to parse: " s
instance Eq (BitVector n) where
(==) = eq#
(/=) = neq#
{-# NOINLINE eq# #-}
eq# :: BitVector n -> BitVector n -> Bool
eq# (BV v1) (BV v2) = v1 == v2
{-# NOINLINE neq# #-}
neq# :: BitVector n -> BitVector n -> Bool
neq# (BV v1) (BV v2) = v1 /= v2
instance Ord (BitVector n) where
(<) = lt#
(>=) = ge#
(>) = gt#
(<=) = le#
lt#,ge#,gt#,le# :: BitVector n -> BitVector n -> Bool
{-# NOINLINE lt# #-}
lt# (BV n) (BV m) = n < m
{-# NOINLINE ge# #-}
ge# (BV n) (BV m) = n >= m
{-# NOINLINE gt# #-}
gt# (BV n) (BV m) = n > m
{-# NOINLINE le# #-}
le# (BV n) (BV m) = n <= m
-- | The functions: 'enumFrom', 'enumFromThen', 'enumFromTo', and
-- 'enumFromThenTo', are not synthesisable.
instance KnownNat n => Enum (BitVector n) where
succ = (+# fromInteger# 1)
pred = (-# fromInteger# 1)
toEnum = fromInteger# . toInteger
fromEnum = fromEnum . toInteger#
enumFrom = enumFrom#
enumFromThen = enumFromThen#
enumFromTo = enumFromTo#
enumFromThenTo = enumFromThenTo#
{-# NOINLINE enumFrom# #-}
{-# NOINLINE enumFromThen# #-}
{-# NOINLINE enumFromTo# #-}
{-# NOINLINE enumFromThenTo# #-}
enumFrom# :: KnownNat n => BitVector n -> [BitVector n]
enumFromThen# :: KnownNat n => BitVector n -> BitVector n -> [BitVector n]
enumFromTo# :: BitVector n -> BitVector n -> [BitVector n]
enumFromThenTo# :: BitVector n -> BitVector n -> BitVector n -> [BitVector n]
enumFrom# x = map fromInteger_INLINE [unsafeToInteger x ..]
enumFromThen# x y = map fromInteger_INLINE [unsafeToInteger x, unsafeToInteger y ..]
enumFromTo# x y = map BV [unsafeToInteger x .. unsafeToInteger y]
enumFromThenTo# x1 x2 y = map BV [unsafeToInteger x1, unsafeToInteger x2 .. unsafeToInteger y]
instance KnownNat n => Bounded (BitVector n) where
minBound = minBound#
maxBound = maxBound#
{-# NOINLINE minBound# #-}
minBound# :: BitVector n
minBound# = BV 0
{-# NOINLINE maxBound# #-}
maxBound# :: forall n . KnownNat n => BitVector n
maxBound# = let m = 1 `shiftL` fromInteger (natVal (Proxy @n))
in BV (m-1)
instance KnownNat n => Num (BitVector n) where
(+) = (+#)
(-) = (-#)
(*) = (*#)
negate = negate#
abs = id
signum bv = resize# (pack# (reduceOr# bv))
fromInteger = fromInteger#
(+#),(-#),(*#) :: forall n . KnownNat n => BitVector n -> BitVector n -> BitVector n
{-# NOINLINE (+#) #-}
(+#) (BV i) (BV j) = let m = 1 `shiftL` fromInteger (natVal (Proxy @n))
z = i + j
in if z >= m then BV (z - m) else BV z
{-# NOINLINE (-#) #-}
(-#) (BV i) (BV j) = let m = 1 `shiftL` fromInteger (natVal (Proxy @n))
z = i - j
in if z < 0 then BV (m + z) else BV z
{-# NOINLINE (*#) #-}
(*#) (BV i) (BV j) = fromInteger_INLINE (i * j)
{-# NOINLINE negate# #-}
negate# :: forall n . KnownNat n => BitVector n -> BitVector n
negate# (BV 0) = BV 0
negate# (BV i) = BV (sz - i)
where
sz = 1 `shiftL` fromInteger (natVal (Proxy @n))
{-# NOINLINE fromInteger# #-}
fromInteger# :: KnownNat n => Integer -> BitVector n
fromInteger# = fromInteger_INLINE
{-# INLINE fromInteger_INLINE #-}
fromInteger_INLINE :: forall n . KnownNat n => Integer -> BitVector n
fromInteger_INLINE i = sz `seq` BV (i `mod` sz)
where
sz = 1 `shiftL` fromInteger (natVal (Proxy @n))
instance (KnownNat m, KnownNat n) => ExtendingNum (BitVector m) (BitVector n) where
type AResult (BitVector m) (BitVector n) = BitVector (Max m n + 1)
plus = plus#
minus = minus#
type MResult (BitVector m) (BitVector n) = BitVector (m + n)
times = times#
{-# NOINLINE plus# #-}
plus# :: BitVector m -> BitVector n -> BitVector (Max m n + 1)
plus# (BV a) (BV b) = BV (a + b)
{-# NOINLINE minus# #-}
minus# :: forall m n . (KnownNat m, KnownNat n) => BitVector m -> BitVector n
-> BitVector (Max m n + 1)
minus# (BV a) (BV b) =
let sz = fromInteger (natVal (Proxy @(Max m n + 1)))
mask = 1 `shiftL` sz
z = a - b
in if z < 0 then BV (mask + z) else BV z
{-# NOINLINE times# #-}
times# :: BitVector m -> BitVector n -> BitVector (m + n)
times# (BV a) (BV b) = BV (a * b)
instance KnownNat n => Real (BitVector n) where
toRational = toRational . toInteger#
instance KnownNat n => Integral (BitVector n) where
quot = quot#
rem = rem#
div = quot#
mod = rem#
quotRem n d = (n `quot#` d,n `rem#` d)
divMod n d = (n `quot#` d,n `rem#` d)
toInteger = toInteger#
quot#,rem# :: BitVector n -> BitVector n -> BitVector n
{-# NOINLINE quot# #-}
quot# (BV i) (BV j) = BV (i `quot` j)
{-# NOINLINE rem# #-}
rem# (BV i) (BV j) = BV (i `rem` j)
{-# NOINLINE toInteger# #-}
toInteger# :: BitVector n -> Integer
toInteger# (BV i) = i
instance KnownNat n => Bits (BitVector n) where
(.&.) = and#
(.|.) = or#
xor = xor#
complement = complement#
zeroBits = 0
bit i = replaceBit# 0 i high
setBit v i = replaceBit# v i high
clearBit v i = replaceBit# v i low
complementBit v i = replaceBit# v i (complement## (index# v i))
testBit v i = eq## (index# v i) high
bitSizeMaybe v = Just (size# v)
bitSize = size#
isSigned _ = False
shiftL v i = shiftL# v i
shiftR v i = shiftR# v i
rotateL v i = rotateL# v i
rotateR v i = rotateR# v i
popCount bv = fromInteger (I.toInteger# (popCountBV (bv ++# (0 :: BitVector 1))))
instance KnownNat n => FiniteBits (BitVector n) where
finiteBitSize = size#
countLeadingZeros = fromInteger . I.toInteger# . countLeadingZerosBV
countTrailingZeros = fromInteger . I.toInteger# . countTrailingZerosBV
countLeadingZerosBV :: KnownNat n => BitVector n -> I.Index (n+1)
countLeadingZerosBV = V.foldr (\l r -> if eq## l low then 1 + r else 0) 0 . V.bv2v
{-# INLINE countLeadingZerosBV #-}
countTrailingZerosBV :: KnownNat n => BitVector n -> I.Index (n+1)
countTrailingZerosBV = V.foldl (\l r -> if eq## r low then 1 + l else 0) 0 . V.bv2v
{-# INLINE countTrailingZerosBV #-}
{-# NOINLINE reduceAnd# #-}
reduceAnd# :: KnownNat n => BitVector n -> Bit
reduceAnd# bv@(BV i) = Bit (smallInteger (dataToTag# check))
where
check = i == maxI
sz = natVal bv
maxI = (2 ^ sz) - 1
{-# NOINLINE reduceOr# #-}
reduceOr# :: BitVector n -> Bit
reduceOr# (BV i) = Bit (smallInteger (dataToTag# check))
where
check = i /= 0
{-# NOINLINE reduceXor# #-}
reduceXor# :: BitVector n -> Bit
reduceXor# (BV i) = Bit (toInteger (popCount i `mod` 2))
instance Default (BitVector n) where
def = minBound#
-- * Accessors
-- ** Length information
{-# NOINLINE size# #-}
size# :: KnownNat n => BitVector n -> Int
size# bv = fromInteger (natVal bv)
{-# NOINLINE maxIndex# #-}
maxIndex# :: KnownNat n => BitVector n -> Int
maxIndex# bv = fromInteger (natVal bv) - 1
-- ** Indexing
{-# NOINLINE index# #-}
index# :: KnownNat n => BitVector n -> Int -> Bit
index# bv@(BV v) i
| i >= 0 && i < sz = Bit (smallInteger
(dataToTag#
(testBit v i)))
| otherwise = err
where
sz = fromInteger (natVal bv)
err = error $ concat [ "(!): "
, show i
, " is out of range ["
, show (sz - 1)
, "..0]"
]
{-# NOINLINE msb# #-}
-- | MSB
msb# :: forall n . KnownNat n => BitVector n -> Bit
msb# (BV v)
= let i = fromInteger (natVal (Proxy @n) - 1)
in Bit (smallInteger (dataToTag# (testBit v i)))
{-# NOINLINE lsb# #-}
-- | LSB
lsb# :: BitVector n -> Bit
lsb# (BV v) = Bit (smallInteger (dataToTag# (testBit v 0)))
{-# NOINLINE slice# #-}
slice# :: BitVector (m + 1 + i) -> SNat m -> SNat n -> BitVector (m + 1 - n)
slice# (BV i) m n = BV (shiftR (i .&. mask) n')
where
m' = snatToInteger m
n' = snatToNum n
mask = 2 ^ (m' + 1) - 1
-- * Constructions
-- ** Concatenation
{-# NOINLINE (++#) #-}
-- | Concatenate two 'BitVector's
(++#) :: KnownNat m => BitVector n -> BitVector m -> BitVector (n + m)
(BV v1) ++# bv2@(BV v2) = BV (v1' + v2)
where
v1' = shiftL v1 (fromInteger (natVal bv2))
-- * Modifying BitVectors
{-# NOINLINE replaceBit# #-}
replaceBit# :: KnownNat n => BitVector n -> Int -> Bit -> BitVector n
replaceBit# bv@(BV v) i (Bit b)
| i >= 0 && i < sz = BV (if b == 1 then setBit v i else clearBit v i)
| otherwise = err
where
sz = fromInteger (natVal bv)
err = error $ concat [ "replaceBit: "
, show i
, " is out of range ["
, show (sz - 1)
, "..0]"
]
{-# NOINLINE setSlice# #-}
setSlice# :: BitVector (m + 1 + i) -> SNat m -> SNat n -> BitVector (m + 1 - n)
-> BitVector (m + 1 + i)
setSlice# (BV i) m n (BV j) = BV ((i .&. mask) .|. j')
where
m' = snatToInteger m
n' = snatToInteger n
j' = shiftL j (fromInteger n')
mask = complement ((2 ^ (m' + 1) - 1) `xor` (2 ^ n' - 1))
{-# NOINLINE split# #-}
split# :: forall n m . KnownNat n
=> BitVector (m + n) -> (BitVector m, BitVector n)
split# (BV i) = (BV l, BV r)
where
n = fromInteger (natVal (Proxy @n))
mask = 1 `shiftL` n
-- The code below is faster than:
-- > (l,r) = i `divMod` mask
r = i `mod` mask
l = i `shiftR` n
and#, or#, xor# :: BitVector n -> BitVector n -> BitVector n
{-# NOINLINE and# #-}
and# (BV v1) (BV v2) = BV (v1 .&. v2)
{-# NOINLINE or# #-}
or# (BV v1) (BV v2) = BV (v1 .|. v2)
{-# NOINLINE xor# #-}
xor# (BV v1) (BV v2) = BV (v1 `xor` v2)
{-# NOINLINE complement# #-}
complement# :: KnownNat n => BitVector n -> BitVector n
complement# (BV v1) = fromInteger_INLINE (complement v1)
shiftL#, shiftR#, rotateL#, rotateR#
:: KnownNat n => BitVector n -> Int -> BitVector n
{-# NOINLINE shiftL# #-}
shiftL# (BV v) i
| i < 0 = error
$ "'shiftL undefined for negative number: " ++ show i
| otherwise = fromInteger_INLINE (shiftL v i)
{-# NOINLINE shiftR# #-}
shiftR# (BV v) i
| i < 0 = error
$ "'shiftR undefined for negative number: " ++ show i
| otherwise = BV (shiftR v i)
{-# NOINLINE rotateL# #-}
rotateL# _ b | b < 0 = error "'shiftL undefined for negative numbers"
rotateL# bv@(BV n) b = fromInteger_INLINE (l .|. r)
where
l = shiftL n b'
r = shiftR n b''
b' = b `mod` sz
b'' = sz - b'
sz = fromInteger (natVal bv)
{-# NOINLINE rotateR# #-}
rotateR# _ b | b < 0 = error "'shiftR undefined for negative numbers"
rotateR# bv@(BV n) b = fromInteger_INLINE (l .|. r)
where
l = shiftR n b'
r = shiftL n b''
b' = b `mod` sz
b'' = sz - b'
sz = fromInteger (natVal bv)
popCountBV :: forall n . KnownNat n => BitVector (n+1) -> I.Index (n+2)
popCountBV bv =
let v = V.bv2v bv
in sum (V.map (fromIntegral . pack#) v)
{-# INLINE popCountBV #-}
instance Resize BitVector where
resize = resize#
zeroExtend = extend
signExtend = \bv -> (if msb# bv == low then id else complement) 0 ++# bv
truncateB = resize#
{-# NOINLINE resize# #-}
resize# :: forall n m . KnownNat m => BitVector n -> BitVector m
resize# (BV i) = let m = 1 `shiftL` fromInteger (natVal (Proxy @m))
in if i >= m then fromInteger_INLINE i else BV i
instance KnownNat n => Lift (BitVector n) where
lift bv@(BV i) = sigE [| fromInteger# i |] (decBitVector (natVal bv))
{-# NOINLINE lift #-}
decBitVector :: Integer -> TypeQ
decBitVector n = appT (conT ''BitVector) (litT $ numTyLit n)
instance KnownNat n => SaturatingNum (BitVector n) where
satPlus SatWrap a b = a +# b
satPlus SatZero a b =
let r = plus# a b
in if msb# r == low
then resize# r
else minBound#
satPlus _ a b =
let r = plus# a b
in if msb# r == low
then resize# r
else maxBound#
satMin SatWrap a b = a -# b
satMin _ a b =
let r = minus# a b
in if msb# r == low
then resize# r
else minBound#
satMult SatWrap a b = a *# b
satMult SatZero a b =
let r = times# a b
(rL,rR) = split# r
in case rL of
0 -> rR
_ -> minBound#
satMult _ a b =
let r = times# a b
(rL,rR) = split# r
in case rL of
0 -> rR
_ -> maxBound#
instance KnownNat n => Arbitrary (BitVector n) where
arbitrary = arbitraryBoundedIntegral
shrink = shrinkSizedUnsigned
-- | 'shrink' for sized unsigned types
shrinkSizedUnsigned :: (KnownNat n, Integral (p n)) => p n -> [p n]
shrinkSizedUnsigned x | natVal x < 2 = case toInteger x of
1 -> [0]
_ -> []
-- 'shrinkIntegral' uses "`quot` 2", which for sized types
-- less than 2 bits wide results in a division by zero.
--
-- See: https://github.com/clash-lang/clash-compiler/issues/153
| otherwise = shrinkIntegral x
{-# INLINE shrinkSizedUnsigned #-}
instance KnownNat n => CoArbitrary (BitVector n) where
coarbitrary = coarbitraryIntegral
type instance Index (BitVector n) = Int
type instance IxValue (BitVector n) = Bit
instance KnownNat n => Ixed (BitVector n) where
ix i f bv = replaceBit# bv i <$> f (index# bv i)