Generalize from double: with type family

[reubenharry]

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[turion]

Suggested change

	(Real m) ->
	Real m ->

[reubenharry]

@mknorps @idontgetoutmuch If we still want HMC, we'll need to merge/rebase this branch: it generalizes from Double in a way that allows for automatic differentiation.

[turion]

@reubenharry What is missing? Do you need any help? We're working around statistics only supporting Double right now, right?

[idontgetoutmuch]

Do we need statistics? Would mwc-random be enough? I am sure @Shimuuar would accept a PR to generalise the types e.g. here https://hackage.haskell.org/package/mwc-random-0.15.0.2/docs/System-Random-MWC-Distributions.html provided we didn't affect performance.

BTW we should also check performance before and after generalising Double to Num a (or whatever).

[turion]

mwc-random also pins the implementations of the distributions to Double.

[idontgetoutmuch]

mwc-random also pins the implementations of the distributions to Double.

I understand but I think the maintainer would be sympathetic to generalising it provided we did not impact performance.

[reubenharry]

@turion So the ad library supports the inverse error function, so we can at least currently do normal distributions without statistics. Less so for the other distributions in the MonadSample class. I don't know if we mind the sampler working in terms of Double, but if we do, we'd indeed want to request a change to mwc-random or move to something else.

[Shimuuar]

I'm not against generalization but it's kind of tricky. Some generators would be easy: exponential do not require anything beyond log. Others may be trickier. Generator for normal distribution uses ziggurat method and corresponding tables are only available for Doubles, some may use math-functions which provide only versions for Doubles as well

[turion]

Generator for normal distribution uses ziggurat method and corresponding tables are only available for Doubles

Why is that? It seems to me that the table is calculated in Haskell as well, so one could calculate several tables, possibly creating a type class for this.

[Shimuuar]

Why ziggurat? It's fast. Last time I run benchmarks (several years before random 1.2) it was only tens of percent slower than generation of Double. I didn't compare it with inversion method though.

Creating type class is possible but that's road leads to type class per distribution.