I think you may have misinterpreted my earlier comments. I think this is a good idea, just not always necessary if we can do thorough tests versus well-defined base cases like the lgamma from the standard library.
To really get traction on this, it should be automated to allow us to plug in two functions and a range of values and make sure all derivatives have the same value. I can help write that. It’d look something like this:
template <class F, class G>
expect_same(const ad_tolerances& tol, const F& f, const G& g,
Eigen::VectorXd x);
where the vector packs all the arguments to f or g. We cold get fancier and put in a parameter pack for x and try to use the serialization framework to reduce it to a vector to supply to our functionals.
As @martinmodrak points out,
That’s why I included tolerances.
Wouldn’t we need to write all our functions to deal with their data types? Or recode them?
I don’t get this comment. From my perspective, both @martinmodrak and @bgoodri are suggesting new, complementary tests that go beyond what we have now. If people want to put in effort making tests better, more power to them!
I don’t have any opinion about Arb vs. Mathematica in terms of coverage or accuracy. I’d never heard of Arb before @bgoodri brought it up. The problem I have is that I can’t read that Mathematica code. So the discussion we should have is whether everyone’s OK introducing one more language into the project after OCaml and C++.
But @martinmodrak, you’re the one who opened this can of worms by saying that our current tests were not best practice because they were low precision. I wasn’t offended by that, by the way—I’m totally open to having people improve things I did. That’s how we make the project better.