Re: [PATCH] random_normal function

On Mon, 9 Jan 2023 at 23:38, Tom Lane <tgl(at)sss(dot)pgh(dot)pa(dot)us> wrote:
>
> I tried this on some 32-bit big-endian hardware (NetBSD on macppc)
> to verify my thesis that the results of random() are now machine
> independent. That part works, but the random_normal() tests didn't;

Ah yes, I wondered about that.

> I saw low-order-bit differences from the results on x86_64 Linux.
> Presumably, that's because one or more of sqrt()/log()/sin() are
> rounding off a bit differently there. v2 attached deals with this by
> backing off to "extra_float_digits = 0" for that test.

Makes sense.

I double-checked the one-in-a-billion claim, and it looks about right
for each test.

The one I wasn't sure about was the chance of duplicates for
random_normal(). Analysing it more closely, it actually has a smaller
chance of duplicates, since the difference between 2 standard normal
distributions is another normal distribution with a standard deviation
of sqrt(2), and so the probability of a pair of random_normal()'s
being the same is about 2*sqrt(pi) ~ 3.5449 times lower than for
random(). So you can call random_normal() around 5600 times (rather
than 3000 times) before having a 1e-9 chance of duplicates. So, as
with the random() duplicates test, the probability of failure with
just 1000 values should be well below 1e-9. Intuitively, that was
always going to be true, but I wanted to know the details.

The rest looks good to me, except there's a random non-ASCII character
instead of a hyphen in "Kolmogorov-Smirnov" (because I copy-pasted the
name from some random website).

Regards,
Dean