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
) where
import Data.Bits ((.&.), (.|.), shiftL, shiftR)
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 2 parseFloatBE
getFloat16le :: Get Float
getFloat16le = getFloat 2 parseFloatLE
getFloat32be :: Get Float
getFloat32be = getFloat 4 parseFloatBE
getFloat32le :: Get Float
getFloat32le = getFloat 4 parseFloatLE
getFloat64be :: Get Double
getFloat64be = getFloat 8 parseFloatBE
getFloat64le :: Get Double
getFloat64le = getFloat 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 width parser = do
bytes <- getByteString width
(return . parser . B.unpack) bytes
---------------------------------------------------------------------
putFloat32be :: (RealFloat a) => a -> Put
putFloat32be = putFloat 4 encodeIntBE
putFloat32le :: (RealFloat a) => a -> Put
putFloat32le = putFloat 4 encodeIntLE
putFloat64be :: (RealFloat a) => a -> Put
putFloat64be = putFloat 8 encodeIntBE
putFloat64le :: (RealFloat a) => a -> Put
putFloat64le = putFloat 8 encodeIntLE
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)
otherwise -> (sign, truncatedFraction, biasedE)
where dFraction = fst (decodeFloat v)
dExponent = snd (decodeFloat v)
eWidth = exponentWidth (width * 8)
fWidth = (width * 8) - eWidth - 1 -- 1 for sign bit
biasedE = bias (dExponent + 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 `shiftL` 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 (width * 8)
fWidth = (width * 8) - 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 `shiftL` (fWidth + eWidth)) :: Integer
shiftedExp = ((fromIntegral e) `shiftL` fWidth) :: Integer
shiftedFrac = f
-- |Encode an integer to a list of words, in big-endian format
encodeIntBE :: ByteCount -> Integer -> [Word8]
encodeIntBE 0 x = []
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 :: (Integral a, Integral b) => a -> b -> a
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 = length bs * 8
-- |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 = ((length bs) * 8)
-- |Slice a single integer by start and end bit location
sliceInt :: Integer -> BitCount -> BitCount -> BitCount -> Integer
sliceInt x xBitCount s e = fromIntegral $ (x .&. startMask) `shiftR` (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 = fromIntegral $ bitSlice bs 1 (1 + w)
frac = bitSlice bs (1 + w) (length bs * 8)
w = exponentWidth $ length bs * 8
-- |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 -> (f, (-fWidth) + (unbiasedE + 1))
-- Normalized
_ -> (f + (1 `shiftL` fWidth), (-fWidth) + unbiasedE)
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 * (log2 k)) - 13
| otherwise = error "Invalid length of floating-point value"
-- |Base-2 log of an integer
log2 = (logBase 2) . fromIntegral
-- |Integral exponent
iExp b e = floor $ (fromIntegral b) ** (fromIntegral e)
type Exponent = Int
type Fraction = Integer
type BitCount = Int
type ByteCount = Int