[Haskell-beginners] Printing the bits of an Int|Double

[Stephen Tetley]

Hello M Xyz

Here's a module[1] that seems to work for single precision floats -
you might want to do some checking of random numbers with toAndFro
(there's plenty of room for errors).

The print functions is printBin uses showIntAtBase which doesn't pad
with leading zeros, you might want to add them.


Best wishes

Stephen

[1] I wrote it a while ago but checking this morning it had some
nefarious bugs in.

module PrintIeeeFloat where

import Data.Bits
import Data.Char
import Data.Word
import Numeric


const_B :: Int
const_B = 127


printBin :: (Fractional a,Ord a) => a -> ShowS
printBin a =
    f s . showChar ' ' . f t . showChar ' ' . f u . showChar ' ' . f v
  where
    f = showIntAtBase 2 (chr . (48+))
    (s,t,u,v) = packIEEESingle a

toAndFro :: (Fractional a, Ord a) => a -> a
toAndFro a = let (s,t,u,v) = packIEEESingle a in unpackIEEESingle s t u v

unpackIEEESingle :: Fractional a => Word8 -> Word8 -> Word8 -> Word8 -> a
unpackIEEESingle b24_31 b16_23 b8_15 b0_7 =  sign $ fract * (2 ^^ expo)
  where
    sign  = if b24_31 `testBit` 7 then negate else id

    expo  = exponent' b24_31 b16_23

    fract = fraction b16_23 b8_15 b0_7


exponent' :: Word8  -> Word8 -> Int
exponent' a b = (a' `shiftL` 1) + (b' `shiftR` 7) - 127
  where
    a' = fromIntegral $ (a .&. 0x7f)
    b' = fromIntegral $ (b .&. 0x80)


fraction :: Fractional a => Word8 -> Word8 -> Word8 -> a
fraction b16_24 b8_15 b0_7 = 1.0 + ((fromIntegral frac) / (2 ^^ 23))
  where
   frac :: Int
   frac = (shiftL16 (b16_24 .&. 0x7f)) + (shiftL8 b8_15) + fromIntegral b0_7



packIEEESingle :: (Fractional a,Ord a) => a -> (Word8,Word8,Word8,Word8)
packIEEESingle a = (flipSign b24_31, exp_part+mant_part, b8_15, b0_7)
  where
    k     = findPosExpo $ abs a
    e     = k + const_B
    halfa = (abs a) / (2 ^^ fromIntegral k)
    f     = expand $ halfa - 1

    (b24_31, exp_part)          = expoWords e
    (mant_part,b8_15, b0_7)     = mantWords f

    flipSign = if a > 0 then id else (`setBit` 7)


findPosExpo :: (Fractional a, Ord a) => a -> Int
findPosExpo r | r <= 0    = 0
              | otherwise = step r 1
  where
    step r' k | r <= fromIntegral 2 ^^ k = k-1
              | otherwise                = step r' (k+1)


expand :: (Fractional a, Ord a) => a -> Word32
expand n = (`shiftR` 9) $ step n 0 id
  where
    step x ix f | x <= 0    = f (0::Word32)
                | otherwise = let y = 1 / (2 ^^ (ix+1))
                              in if x >= y
                                 then step (x-y) (ix+1) (f . (`setBit` (31-ix)))
                                 else step x (ix+1) f



-- 7 bits left, 1 bit right
expoWords :: Int -> (Word8,Word8)
expoWords n = (left, right)
  where
    right = if n `testBit` 0 then 128 else 0
    left  = fromIntegral $ n `shiftR` 1


mantWords :: Word32 -> (Word8,Word8,Word8)
mantWords x = (a,b,c)
  where
    c = fromIntegral $ x .&. 0xff
    b = fromIntegral $ (`shiftR` 8)  $ x .&. 0xff00
    a = fromIntegral $ (`shiftR` 16) $ x .&. 0xff0000

shiftL8 :: (Bits b, Integral b) => Word8 -> b
shiftL8 = (`shiftL` 8) . fromIntegral


shiftL16 :: (Bits b, Integral b) => Word8 -> b
shiftL16 = (`shiftL` 16) . fromIntegral


shiftL24 :: (Bits b, Integral b) => Word8 -> b
shiftL24 = (`shiftL` 24) . fromIntegral


w32be :: Word8 -> Word8 -> Word8 -> Word8 -> Word32
w32be a b c d = (shiftL24 a) + (shiftL16 b) + (shiftL8 c) + fromIntegral d



2009/12/11 M Xyz <functionallyharmonious at yahoo.com>
>
> I've been trying to play around with binary data, but I haven't made much progress
> trying to print the bits of a Double. With help from #haskell I've made it this far:
>
> -- Printing the bits of an Int
> main = do putStrLn $ showIntAtBase 2 (chr . (48+)) z ""
>
> -- 103 = 1100111, after bit shifting 11001
> z = shiftR (103 :: Int64) 2
>
> This is as far as I got with Doubles:
>
> import Data.Binary.IEEE754
> import qualified Data.ByteString.Lazy as BS
> main = do BS.putStrLn $ runPut $ putFloat64be 4.123
>
> Instead of playing with ByteStrings, is there just a way to fill an Int64 with the bits of a Double (Similar to Java's long = Double.doubleToLongBits(double))?
>
>
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