Add exponential ranges

[chris-martin]

Closes #37

[chris-martin]

The outcome seems right, but my math could probably use a double-check here. I seem to be struggling to recall my high school algebra today.

[jacobstanley]

Maybe we could change this to:

scaleExponentialFrac :: RealFrac a => Size -> a -> a -> a
scaleExponentialFrac sz0 z n =
  let
    sz =
      clamp 0 99 sz0

    p :: Double
    p =
      realToFrac (abs (n - z) + 1) ** (realToFrac sz / 99)

    diff =
      (realToFrac p - 1) * signum (n - z)
  in
    if sz == 99 then
      z + n
    else
      z + diff

That way it's using floating point for less of the calculation, and it will work for Rational too, even if it's not ideal.

[chris-martin]

I'm still doubting whether it's desirable to have Rational exponential ranges, because "shrinking" sort of loses its human relevance if the numerators and denominators are always huge numbers regardless of the size parameter.

> scaleExponentialFrac 80 (0 :: Rational) (100 :: Rational)
5721500312938077 % 140737488355328

> scaleExponentialFrac 2 (0 :: Rational) (100 :: Rational)
440089068475887 % 4503599627370496

If I were to really need this, I think rather have to write realToFrac <$> Range.exponentialFloat 0 (2^64) to acknowledge that I'm generating messy arbitrarily-precise ratios.

But... hmmm, maybe we could do better. Given that there's a fixed number of outputs from sizes 0 to 99, Maybe there's a clever way to reduce the ratios to a precision that is contextually appropriate?

[jacobstanley]

I should get a chance to look at this tonight

[chris-martin]

Some notes on the design:

• The way I'm doing the calculation involves a non-integral exponent, so I had to use floating-point arithmetic.
• The Integral functions are just based on the Floating functions, with a rounding step at the end.
• I didn't include Fractional exponential ranges; I'm not sure whether there is a reasonable way to do that.

[jacobstanley]

These examples should probably have x instead of 0 because those things are true for all x

[jacobstanley]

I think this is better than what we have, so I'm going to rebase and merge it, we can always improve the algorithm in the future. No sense bikeshedding over Rational imo.

[jacobstanley]

Rebase and merged fca1700