clash-prelude-0.10.13: src/CLaSH/Sized/Internal/Unsigned.hs
{-|
Copyright : (C) 2013-2016, University of Twente
License : BSD2 (see the file LICENSE)
Maintainer : Christiaan Baaij <christiaan.baaij@gmail.com>
-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE DeriveDataTypeable #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE MagicHash #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TemplateHaskell #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE UndecidableInstances #-}
{-# LANGUAGE Unsafe #-}
{-# OPTIONS_HADDOCK show-extensions #-}
module CLaSH.Sized.Internal.Unsigned
( -- * Datatypes
Unsigned (..)
-- * Accessors
-- ** Length information
, size#
-- * Type classes
-- ** BitConvert
, pack#
, unpack#
-- ** 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#
-- ** Resize
, resize#
)
where
import Control.DeepSeq (NFData (..))
import Control.Lens (Index, Ixed (..), IxValue)
import Data.Bits (Bits (..), FiniteBits (..))
import Data.Data (Data)
import Data.Default (Default (..))
import Data.Proxy (Proxy (..))
import Text.Read (Read (..), ReadPrec)
import GHC.TypeLits (KnownNat, Nat, type (+), natVal)
import Language.Haskell.TH (TypeQ, appT, conT, litT, numTyLit, sigE)
import Language.Haskell.TH.Syntax (Lift(..))
import Test.QuickCheck.Arbitrary (Arbitrary (..), CoArbitrary (..),
arbitraryBoundedIntegral,
coarbitraryIntegral)
import CLaSH.Class.BitPack (BitPack (..))
import CLaSH.Class.Num (ExtendingNum (..), SaturatingNum (..),
SaturationMode (..))
import CLaSH.Class.Resize (Resize (..))
import CLaSH.Prelude.BitIndex ((!), msb, replaceBit, split)
import CLaSH.Prelude.BitReduction (reduceOr)
import CLaSH.Promoted.Ord (Max)
import CLaSH.Sized.Internal.BitVector (BitVector (BV), Bit, high, low)
import qualified CLaSH.Sized.Internal.BitVector as BV
-- | Arbitrary-width unsigned integer represented by @n@ bits
--
-- Given @n@ bits, an 'Unsigned' @n@ number has a range of: [0 .. 2^@n@-1]
--
-- __NB__: The 'Num' operators perform @wrap-around@ on overflow. If you want
-- saturation on overflow, check out the 'SaturatingNum' class.
--
-- >>> maxBound :: Unsigned 3
-- 7
-- >>> minBound :: Unsigned 3
-- 0
-- >>> read (show (maxBound :: Unsigned 3)) :: Unsigned 3
-- 7
-- >>> 1 + 2 :: Unsigned 3
-- 3
-- >>> 2 + 6 :: Unsigned 3
-- 0
-- >>> 1 - 3 :: Unsigned 3
-- 6
-- >>> 2 * 3 :: Unsigned 3
-- 6
-- >>> 2 * 4 :: Unsigned 3
-- 0
-- >>> (2 :: Unsigned 3) `times` (4 :: Unsigned 3) :: Unsigned 6
-- 8
-- >>> (2 :: Unsigned 3) `plus` (6 :: Unsigned 3) :: Unsigned 4
-- 8
-- >>> satPlus SatSymmetric 2 6 :: Unsigned 3
-- 7
-- >>> satMin SatSymmetric 2 3 :: Unsigned 3
-- 0
newtype Unsigned (n :: Nat) =
-- | The constructor, 'U', and the field, 'unsafeToInteger', are not
-- synthesisable.
U { unsafeToInteger :: Integer }
deriving Data
{-# NOINLINE size# #-}
size# :: KnownNat n => Unsigned n -> Int
size# u = fromInteger (natVal u)
instance NFData (Unsigned n) where
rnf (U i) = rnf i `seq` ()
{-# NOINLINE rnf #-}
-- NOINLINE is needed so that CLaSH doesn't trip on the "Unsigned ~# Integer"
-- coercion
instance Show (Unsigned n) where
show (U i) = show i
{-# NOINLINE show #-}
-- | None of the 'Read' class' methods are synthesisable.
instance KnownNat n => Read (Unsigned n) where
readPrec = fromIntegral <$> (readPrec :: ReadPrec Word)
instance BitPack (Unsigned n) where
type BitSize (Unsigned n) = n
pack = pack#
unpack = unpack#
{-# NOINLINE pack# #-}
pack# :: Unsigned n -> BitVector n
pack# (U i) = BV i
{-# NOINLINE unpack# #-}
unpack# :: BitVector n -> Unsigned n
unpack# (BV i) = U i
instance Eq (Unsigned n) where
(==) = eq#
(/=) = neq#
{-# NOINLINE eq# #-}
eq# :: Unsigned n -> Unsigned n -> Bool
eq# (U v1) (U v2) = v1 == v2
{-# NOINLINE neq# #-}
neq# :: Unsigned n -> Unsigned n -> Bool
neq# (U v1) (U v2) = v1 /= v2
instance Ord (Unsigned n) where
(<) = lt#
(>=) = ge#
(>) = gt#
(<=) = le#
lt#,ge#,gt#,le# :: Unsigned n -> Unsigned n -> Bool
{-# NOINLINE lt# #-}
lt# (U n) (U m) = n < m
{-# NOINLINE ge# #-}
ge# (U n) (U m) = n >= m
{-# NOINLINE gt# #-}
gt# (U n) (U m) = n > m
{-# NOINLINE le# #-}
le# (U n) (U m) = n <= m
-- | The functions: 'enumFrom', 'enumFromThen', 'enumFromTo', and
-- 'enumFromThenTo', are not synthesisable.
instance KnownNat n => Enum (Unsigned 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# :: Unsigned n -> [Unsigned n]
enumFromThen# :: Unsigned n -> Unsigned n -> [Unsigned n]
enumFromTo# :: Unsigned n -> Unsigned n -> [Unsigned n]
enumFromThenTo# :: Unsigned n -> Unsigned n -> Unsigned n -> [Unsigned n]
enumFrom# x = map U [unsafeToInteger x ..]
enumFromThen# x y = map U [unsafeToInteger x, unsafeToInteger y ..]
enumFromTo# x y = map U [unsafeToInteger x .. unsafeToInteger y]
enumFromThenTo# x1 x2 y = map U [unsafeToInteger x1, unsafeToInteger x2 .. unsafeToInteger y]
instance KnownNat n => Bounded (Unsigned n) where
minBound = minBound#
maxBound = maxBound#
{-# NOINLINE minBound# #-}
minBound# :: Unsigned n
minBound# = U 0
{-# NOINLINE maxBound# #-}
maxBound# :: KnownNat n => Unsigned n
maxBound# = let res = U ((2 ^ natVal res) - 1) in res
instance KnownNat n => Num (Unsigned n) where
(+) = (+#)
(-) = (-#)
(*) = (*#)
negate = negate#
abs = id
signum bv = resize# (unpack# (reduceOr bv))
fromInteger = fromInteger#
(+#),(-#),(*#) :: KnownNat n => Unsigned n -> Unsigned n -> Unsigned n
{-# NOINLINE (+#) #-}
(+#) (U i) (U j) = fromInteger_INLINE (i + j)
{-# NOINLINE (-#) #-}
(-#) (U i) (U j) = fromInteger_INLINE (i - j)
{-# NOINLINE (*#) #-}
(*#) (U i) (U j) = fromInteger_INLINE (i * j)
{-# NOINLINE negate# #-}
negate# :: KnownNat n => Unsigned n -> Unsigned n
negate# u@(U i) = sz `seq` U (sz - i)
where
sz = 2 ^ natVal u
{-# NOINLINE fromInteger# #-}
fromInteger# :: KnownNat n => Integer -> Unsigned n
fromInteger# = fromInteger_INLINE
{-# INLINE fromInteger_INLINE #-}
fromInteger_INLINE :: forall n . KnownNat n => Integer -> Unsigned n
fromInteger_INLINE i = sz `seq` U (i `mod` (shiftL 1 sz))
where
sz = fromInteger (natVal (Proxy :: Proxy n))
instance (KnownNat (1 + Max m n), KnownNat (m + n)) =>
ExtendingNum (Unsigned m) (Unsigned n) where
type AResult (Unsigned m) (Unsigned n) = Unsigned (1 + Max m n)
plus = plus#
minus = minus#
type MResult (Unsigned m) (Unsigned n) = Unsigned (m + n)
times = times#
plus#, minus# :: KnownNat (1 + Max m n) => Unsigned m -> Unsigned n
-> Unsigned (1 + Max m n)
{-# NOINLINE plus# #-}
plus# (U a) (U b) = fromInteger_INLINE (a + b)
{-# NOINLINE minus# #-}
minus# (U a) (U b) = fromInteger_INLINE (a - b)
{-# NOINLINE times# #-}
times# :: KnownNat (m + n) => Unsigned m -> Unsigned n -> Unsigned (m + n)
times# (U a) (U b) = fromInteger_INLINE (a * b)
instance KnownNat n => Real (Unsigned n) where
toRational = toRational . toInteger#
instance KnownNat n => Integral (Unsigned 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# :: Unsigned n -> Unsigned n -> Unsigned n
{-# NOINLINE quot# #-}
quot# (U i) (U j) = U (i `quot` j)
{-# NOINLINE rem# #-}
rem# (U i) (U j) = U (i `rem` j)
{-# NOINLINE toInteger# #-}
toInteger# :: Unsigned n -> Integer
toInteger# (U i) = i
instance (KnownNat n, KnownNat (n + 1), KnownNat (n + 2)) => Bits (Unsigned n) where
(.&.) = and#
(.|.) = or#
xor = xor#
complement = complement#
zeroBits = 0
bit i = replaceBit i high 0
setBit v i = replaceBit i high v
clearBit v i = replaceBit i low v
complementBit v i = replaceBit i (BV.complement# (v ! i)) v
testBit v i = 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 u = popCount (pack# u)
{-# NOINLINE and# #-}
and# :: Unsigned n -> Unsigned n -> Unsigned n
and# (U v1) (U v2) = U (v1 .&. v2)
{-# NOINLINE or# #-}
or# :: Unsigned n -> Unsigned n -> Unsigned n
or# (U v1) (U v2) = U (v1 .|. v2)
{-# NOINLINE xor# #-}
xor# :: Unsigned n -> Unsigned n -> Unsigned n
xor# (U v1) (U v2) = U (v1 `xor` v2)
{-# NOINLINE complement# #-}
complement# :: KnownNat n => Unsigned n -> Unsigned n
complement# (U i) = fromInteger_INLINE (complement i)
shiftL#, shiftR#, rotateL#, rotateR# :: KnownNat n => Unsigned n -> Int
-> Unsigned n
{-# NOINLINE shiftL# #-}
shiftL# (U v) i
| i < 0 = error
$ "'shiftL undefined for negative number: " ++ show i
| otherwise = fromInteger_INLINE (shiftL v i)
{-# NOINLINE shiftR# #-}
shiftR# (U v) i
| i < 0 = error
$ "'shiftR undefined for negative number: " ++ show i
| otherwise = fromInteger_INLINE (shiftR v i)
{-# NOINLINE rotateL# #-}
rotateL# _ b | b < 0 = error "'shiftL undefined for negative numbers"
rotateL# bv@(U 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@(U 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)
instance (KnownNat n, KnownNat (n + 1), KnownNat (n + 2)) => FiniteBits (Unsigned n) where
finiteBitSize = size#
instance Resize Unsigned where
resize = resize#
zeroExtend = resize#
signExtend = resize#
truncateB = resize#
{-# NOINLINE resize# #-}
resize# :: KnownNat m => Unsigned n -> Unsigned m
resize# (U i) = fromInteger_INLINE i
instance Default (Unsigned n) where
def = minBound#
instance KnownNat n => Lift (Unsigned n) where
lift u@(U i) = sigE [| fromInteger# i |] (decUnsigned (natVal u))
{-# NOINLINE lift #-}
decUnsigned :: Integer -> TypeQ
decUnsigned n = appT (conT ''Unsigned) (litT $ numTyLit n)
instance (KnownNat n, KnownNat (1 + n), KnownNat (n + n)) =>
SaturatingNum (Unsigned n) where
satPlus SatWrap a b = a +# b
satPlus w a b = case msb r of
0 -> resize# r
_ -> case w of
SatZero -> minBound#
_ -> maxBound#
where
r = plus# a b
satMin SatWrap a b = a -# b
satMin _ a b = case msb r of
0 -> resize# r
_ -> minBound#
where
r = minus# a b
satMult SatWrap a b = a *# b
satMult w a b = case rL of
0 -> unpack# rR
_ -> case w of
SatZero -> minBound#
_ -> maxBound#
where
r = times# a b
(rL,rR) = split r
instance KnownNat n => Arbitrary (Unsigned n) where
arbitrary = arbitraryBoundedIntegral
shrink = BV.shrinkSizedUnsigned
instance KnownNat n => CoArbitrary (Unsigned n) where
coarbitrary = coarbitraryIntegral
type instance Index (Unsigned n) = Int
type instance IxValue (Unsigned n) = Bit
instance KnownNat n => Ixed (Unsigned n) where
ix i f s = unpack# <$> BV.replaceBit# (pack# s) i
<$> f (BV.index# (pack# s) i)