Note: From skimming your readme it is worth noting that log1p _is_ in base now (alongside expm1, log1pexp, and log1mexp). We added them all a couple of years back as a result of the very thread linked in your README.

You need to `import Numeric` to see them, though.

Switching to more accurate functions for doubles and floats for asinh, atanh, etc. to exploit this sort of functionality at least seems to make a lot of sense.

That can be done locally without any user API impact as the current definitions aren't supplied as defaults, merely as pointwise implementations instance by instance. Things will just become more accurate.

In that same spirit, we can probably crib a better version for complex numbers from somewhere as well, as it follows the same general simplistic formula right now, even if it can't be plugged directly into the equations you've given. For that matter, the log1p definition we're using for complex numbers was the best I could come up with, but there may well be a more accurate version you can find down in the mines of libm or another math library written by real analysts.

    log1p x@(a :+ b)
      | abs a < 0.5 && abs b < 0.5
      , u <- 2*a + a*a + b*b = log1p (u/(1 + sqrt(u+1))) :+ atan2 (1 + a) b
      | otherwise = log (1 + x)

So, here's a +1 from the libraries committee side towards improving the situation.

From there, it's a small matter of implementation.

Here's where I'd usually get Ben involved. Hi Ben!

-Edward

On Sat, Jun 2, 2018 at 1:23 AM, Matt Peddie <mpeddie@gmail.com> wrote:

Hi devs,

I tried to use asinh :: Double -> Double and discovered that it's
inaccurate compared to my system library (GNU libm), even returning
-Infinity in place of finite values in the neighborhood of -22 for
large negative arguments. `atanh` is also inaccurate compared to the
system library. I wrote up a more detailed description of the problem
including plots in the README file at
https://github.com/peddie/ghc-inverse-hyperbolic -- this repository is
package that can help you examine the error for yourself or generate
the plots, and it also contains accurate pure-Haskell translations of
the system library's implementation for these functions. What's the
next step to fixing this in GHC?

Cheers

Matt Peddie
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