{- Copyright (C) 2009 John Millikin <jmillikin@gmail.com>
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
module Data.Binary.IEEE754 (
-- * Parsing
parseFloatBE, parseFloatLE
,getFloat16be, getFloat16le
,getFloat32be, getFloat32le
,getFloat64be, getFloat64le
,getFloat
-- * Serializing
,putFloat32be, putFloat32le
,putFloat64be, putFloat64le
,putFloat
-- * Parser implementation
,exponentWidth
,bitSlice
,splitRawIEEE754
,unbias
,mergeFloat
-- * Serializer implementation
,bias
,encodeIntBE, encodeIntLE
,floatToMerged
,mergeFloatBits
,floatComponents
-- * Useful type aliases
,Exponent
,Fraction
,BitCount
,ByteCount
) where
import Data.Bits ((.&.), (.|.), shiftL, shiftR, Bits)
import Data.Word (Word8)
import Data.List (foldl')
import qualified Data.ByteString as B
import Data.Binary.Get (Get, getByteString)
import Data.Binary.Put (Put, putByteString)
---------------------------------------------------------------------
-- |Parse a big-endian byte list into a floating-point value.
parseFloatBE :: (RealFloat a) => [Word8] -> a
parseFloatBE = parseFloat
-- |Parse a little-endian byte list into a floating-point value.
parseFloatLE :: (RealFloat a) => [Word8] -> a
parseFloatLE = parseFloat . reverse
getFloat16be :: Get Float
getFloat16be = getFloat (ByteCount 2) parseFloatBE
getFloat16le :: Get Float
getFloat16le = getFloat (ByteCount 2) parseFloatLE
getFloat32be :: Get Float
getFloat32be = getFloat (ByteCount 4) parseFloatBE
getFloat32le :: Get Float
getFloat32le = getFloat (ByteCount 4) parseFloatLE
getFloat64be :: Get Double
getFloat64be = getFloat (ByteCount 8) parseFloatBE
getFloat64le :: Get Double
getFloat64le = getFloat (ByteCount 8) parseFloatLE
-- |Parse a floating-point value of the given width (in bytes) from within
-- a Get monad.
getFloat :: (RealFloat a) => ByteCount -> ([Word8] -> a) -> Get a
getFloat (ByteCount width) parser = do
bytes <- getByteString width
(return . parser . B.unpack) bytes
---------------------------------------------------------------------
putFloat32be :: Float -> Put
putFloat32be x = putFloat (ByteCount 4) encodeIntBE x
putFloat32le :: Float -> Put
putFloat32le x = putFloat (ByteCount 4) encodeIntLE x
putFloat64be :: Double -> Put
putFloat64be x = putFloat (ByteCount 8) encodeIntBE x
putFloat64le :: Double -> Put
putFloat64le x = putFloat (ByteCount 8) encodeIntLE x
putFloat :: (RealFloat a) => ByteCount -> (ByteCount -> Integer -> [Word8]) -> a -> Put
putFloat width f v = putByteString $ B.pack words'
where words' = f width (floatToMerged width v)
floatComponents :: (RealFloat a) => ByteCount -> a -> (Bool, Fraction, Exponent)
floatComponents width v =
case (dFraction, dExponent, biasedE) of
(0, 0, _) -> (sign, 0, 0)
(_, _, 0) -> (sign, truncatedFraction + 1, 0)
_ -> (sign, truncatedFraction, biasedE)
where dFraction = Fraction $ fst (decodeFloat v)
dExponent = Exponent $ snd (decodeFloat v)
eWidth = exponentWidth (bitCount width)
fWidth = (bitCount width) - eWidth - 1 -- 1 for sign bit
biasedE = bias (dExponent + (fromIntegral fWidth)) eWidth
absFraction = abs dFraction
-- Weird check is for detecting -0.0
sign = (1.0 / v) < 0.0
-- Fraction needs to be truncated, depending on the exponent
truncatedFraction = absFraction - (1 `bitShiftL` fWidth)
floatToMerged :: (RealFloat a) => ByteCount -> a -> Integer
floatToMerged width v = mergeFloatBits' (floatComponents width v)
where mergeFloatBits' (s, f, e) = mergeFloatBits fWidth eWidth s f e
eWidth = exponentWidth (bitCount width)
fWidth = (bitCount width) - eWidth - 1 -- 1 for sign bit
mergeFloatBits :: BitCount -> BitCount -> Bool -> Fraction -> Exponent -> Integer
mergeFloatBits fWidth eWidth s f e = shiftedSign .|. shiftedFrac .|. shiftedExp
where sBit = (if s then 1 else 0) :: Integer
shiftedSign = (sBit `bitShiftL` (fWidth + eWidth)) :: Integer
shiftedExp = ((fromIntegral e) `bitShiftL` fWidth) :: Integer
shiftedFrac = fromIntegral f
-- |Encode an integer to a list of words, in big-endian format
encodeIntBE :: ByteCount -> Integer -> [Word8]
encodeIntBE 0 _ = []
encodeIntBE width x = (encodeIntBE (width - 1) (x `shiftR` 8)) ++ [step]
where step = (fromIntegral x) .&. 0xFF
-- |Encode an integer to a list of words, in little-endian format
encodeIntLE :: ByteCount -> Integer -> [Word8]
encodeIntLE width x = reverse (encodeIntBE width x)
bias :: Exponent -> BitCount -> Exponent
bias e eWidth = e - (1 - (2 `iExp` (eWidth - 1)))
---------------------------------------------------------------------
parseFloat :: (RealFloat a) => [Word8] -> a
parseFloat bs = merge' (splitRawIEEE754 bs)
where merge' (sign, e, f) = encode' (mergeFloat e f width) * signFactor sign
encode' (f, e) = encodeFloat f e
signFactor s = if s then (-1) else 1
width = bitsInWord8 bs
-- |Considering a byte list as a sequence of bits, slice it from start
-- inclusive to end exclusive, and return the resulting bit sequence as an
-- integer
bitSlice :: [Word8] -> BitCount -> BitCount -> Integer
bitSlice bs = sliceInt (foldl' step 0 bs) bitCount'
where step acc w = (shiftL acc 8) + (fromIntegral w)
bitCount' = bitsInWord8 bs
-- |Slice a single integer by start and end bit location
sliceInt :: Integer -> BitCount -> BitCount -> BitCount -> Integer
sliceInt x xBitCount s e = fromIntegral $ (x .&. startMask) `bitShiftR` (xBitCount - e)
where startMask = n1Bits (xBitCount - s)
n1Bits n = (2 `iExp` n) - 1
-- |Split a raw bit array into (sign, exponent, fraction) components. These
-- components have not been processed (unbiased, added significant bit,
-- etc).
splitRawIEEE754 :: [Word8] -> (Bool, Exponent, Fraction)
splitRawIEEE754 bs = (sign, exp', frac)
where sign = (head bs .&. 0x80) == 0x80
exp' = Exponent (fromIntegral $ bitSlice bs 1 (1 + w))
frac = Fraction (bitSlice bs (1 + w) (bitsInWord8 bs))
w = exponentWidth $ bitsInWord8 bs
-- |Unbias an exponent
unbias :: Exponent -> BitCount -> Exponent
unbias e eWidth = e + 1 - (2 `iExp` (eWidth - 1))
-- |Parse values into a form suitable for encodeFloat
-- sign exponent fraction width-in-bits -> fraction, exponent
mergeFloat :: Exponent -> Fraction -> BitCount -> (Integer, Int)
-- Zero
mergeFloat 0 0 _ = (0, 0)
mergeFloat e f width
-- Infinity / NaN (TODO)
| e == eMax = error "Infinity/NaN not supported"
| otherwise = case e of
-- Denormalized
0 -> (fromIntegral f, (fromIntegral unbiasedE + 1) - (fromIntegral fWidth))
-- Normalized
_ -> (fromIntegral f + (1 `bitShiftL` fWidth), (fromIntegral unbiasedE) - (fromIntegral fWidth))
where eWidth = exponentWidth width
fWidth = width - eWidth - 1
eMax = (2 `iExp` eWidth) - 1
unbiasedE = unbias e (eWidth)
---------------------------------------------------------------------
-- |Calculate the proper size of the exponent field, in bits, given the
-- size of the full structure.
exponentWidth :: BitCount -> BitCount
exponentWidth k
| k == 16 = 5
| k == 32 = 8
| k `mod` 32 == 0 = ceiling (4 * (logBase 2 (fromIntegral k))) - 13
| otherwise = error "Invalid length of floating-point value"
-- |Integral exponent
iExp :: (Integral a, Integral b, Integral c) => a -> b -> c
iExp b e = floor $ (fromIntegral b) ** (fromIntegral e)
newtype Exponent = Exponent Int
deriving (Show, Eq, Num, Ord, Real, Enum, Integral, Bits)
newtype Fraction = Fraction Integer
deriving (Show, Eq, Num, Ord, Real, Enum, Integral, Bits)
newtype BitCount = BitCount Int
deriving (Show, Eq, Num, Ord, Real, Enum, Integral)
newtype ByteCount = ByteCount Int
deriving (Show, Eq, Num, Ord, Real, Enum, Integral)
bitCount :: ByteCount -> BitCount
bitCount (ByteCount x) = BitCount (x * 8)
bitsInWord8 :: [Word8] -> BitCount
bitsInWord8 ws = bitCount (ByteCount (length ws))
bitShiftL :: (Bits a) => a -> BitCount -> a
bitShiftL x (BitCount n) = shiftL x n
bitShiftR :: (Bits a) => a -> BitCount -> a
bitShiftR x (BitCount n) = shiftR x n