Of these, probably the least bad is #3, even though it might require a few rounds of experimentation to find the best extra_float_digits setting to use. I'll go try it without any roundoff, just to see what the raw results look like ...
Yeah, that seems like a reasonable thing to try.
I'm amazed that jacana's asinh() returned -0 for an input of +0. I'm not aware of any implementation that does that. I'd be quite interested to know what it returned for an input like 1e-20. If that returned any variety of zero, I'd say that it's worse than useless. Another interesting test case would be whether or not it satisfies asinh(-x) = -asinh(x) for a variety of different values of x, because that's something that commonly breaks down badly with naive implementations.
It's not unreasonable to expect these functions to be accurate to within the last 1 or 2 digits, so testing with extra_float_digits or whatever seems reasonable, but I think a wider variety of test inputs is required.
I also wonder if we should be doing what we do for the regular trig functions and explicitly handle special cases like Inf and NaN to ensure POSIX compatibility on all platforms.
