Warp wrote:

>   Answering my own question, the bit pattern for 0.3 is:
> 
> 0 01111111101 0011001100110011001100110011001100110011001100110011
> 
>   This makes be believe that 0.3 is actually not accurately representable
> with base-2 floating point numbers, and hence converting from double to
> float does lose precision, technically speaking.

test :: Double -> Bool
test x =
   let y = realToFrac x :: Float
   in  x == (realToFrac y)

 > test 0
True

 > test 1
True

 > test 0.3
False

 > test 0.1
False

 > test 0.25
True

1/10 is a recurring binary fraction. This is the source of all the 
trouble. (As you know, 10 = 2 * 5. 1/2 is no problem, 1/5 is.)

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