How to extract dyadic fraction from float

Question

Now, floating and double-precision numbers, although they can approximate any sort of number (although the same could be said integers, floats are just more precise), they are represented as binary decimals internally. For example, one tenth would be approximated

0.00011001100110011... (... only goes to computers precision, not infinity)

Now, any number in binary with finite bits as something called a dyadic fraction representation in mathematics (has nothing to do with p-adic). This means you represent it as a fraction, where the denominator is a power of 2. For example, let's say our computer approximates one tenth as 0.00011. The dyadic fraction for that is 3/32 or 3/(2^5), which is close to one tenth. Now for my technical question. What would be the simplest way to extract the dyadic fraction from a floating number.

Irrelevant Note: If you are wondering why I would want to do this, it is because I am creating a surreal number library in Haskell. Dyadic fractions are easily translated into Surreal numbers, which is why it is convenient that binary is easily translated into dyadic, (I'll sure have trouble with the rational numbers though.)

Answer 1

The decodeFloat function seems useful for this. Technically, you should also check that floatRadix is 2, but as far I can see this is always the case in GHC.

Just be careful since it does not simplify mantissa and exponent. Here, if I evaluate decodeFloat (1.0 :: Double) I get an exponent of -52 and a mantissa of 2^52 which is not what I expected.

Also, toRational seems to generate a dyadic fraction. I am not sure this is always the case, though.