Now that we have random_normal(), it seems like it would be useful to
add the error functions erf() and erfc(), which I think are
potentially useful to the people who will find random_normal() useful,
and possibly others.
An immediate use for erf() is that it allows us to do a
Kolmogorov-Smirnov test for random_normal(), similar to the one for
random().
Both of these functions are defined in POSIX and C99, so in theory
they should be available on all platforms. If that turns out not to be
the case, then there's a commonly used implementation (e.g., see [1]),
which we could include. I played around with that (replacing the
direct bit manipulation stuff with frexp()/ldexp(), see pg_erf.c
attached), and it appeared to be accurate to +/-1 ULP across the full
range of inputs. Hopefully we won't need that though.
I tested this on a couple of different platforms and found I needed to
reduce extra_float_digits to -1 to get the regression tests to pass
consistently, due to rounding errors. It wouldn't surprise me if that
needs to be reduced further, though perhaps it's not necessary to have
so many tests (I included one test value from each branch, while
testing the hand-rolled implementation).
Regards,
Dean
[1] https://github.com/lsds/musl/blob/master/src/math/erf.c