module Data.Binary.IEEE754 (
parseFloatBE, parseFloatLE
,getFloat16be, getFloat16le
,getFloat32be, getFloat32le
,getFloat64be, getFloat64le
,getFloat
,putFloat32be, putFloat32le
,putFloat64be, putFloat64le
,putFloat
,exponentWidth
,bitSlice
,splitRawIEEE754
,unbias
,mergeFloat
,bias
,encodeIntBE, encodeIntLE
,floatToMerged
,mergeFloatBits
,floatComponents
,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)
parseFloatBE :: (RealFloat a) => [Word8] -> a
parseFloatBE = parseFloat
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
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
biasedE = bias (dExponent + fWidth) eWidth
absFraction = abs dFraction
sign = (1.0 / v) < 0.0
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
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
encodeIntBE :: ByteCount -> Integer -> [Word8]
encodeIntBE 0 x = []
encodeIntBE width x = (encodeIntBE (width 1) (x `shiftR` 8)) ++ [step]
where step = (fromIntegral x) .&. 0xFF
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
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)
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
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 :: Exponent -> BitCount -> Exponent
unbias e eWidth = e + 1 (2 `iExp` (eWidth 1))
mergeFloat :: Exponent -> Fraction -> BitCount -> (Integer, Int)
mergeFloat 0 0 _ = (0, 0)
mergeFloat e f width
| e == eMax = error "Infinity/NaN not supported"
| otherwise = case e of
0 -> (f, (fWidth) + (unbiasedE + 1))
_ -> (f + (1 `shiftL` fWidth), (fWidth) + unbiasedE)
where eWidth = exponentWidth width
fWidth = width eWidth 1
eMax = (2 `iExp` eWidth) 1
unbiasedE = unbias e (eWidth)
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"
log2 = (logBase 2) . fromIntegral
iExp b e = floor $ (fromIntegral b) ** (fromIntegral e)
type Exponent = Int
type Fraction = Integer
type BitCount = Int
type ByteCount = Int