Re: Problem in

Max, just try

SELECT 1 - ( cos(radians(48.9193)) * cos(radians(48.9193)) *
cos(radians(2.5431) - radians(2.5431)) + sin(radians(48.9193)) *
sin(radians(48.9193)) ) as result;

You may find that enlightening. I did play with this for a while
yesterday (and asked people on IRC), and it seems to heavily depend
the on local systems set-up.
Seems that e.g. MacOS mojave & postgres9.6 from brew work as you
expect; someone confirmed postgres on Suse to do the right thing.
9.6.15 on Ubuntu 16.04
gives a remainder that would then make the acos fail ...

On Fri, 26 Apr 2019 at 19:24, Max Lipsky <maxlipsky(at)gmail(dot)com> wrote:
>
> Hello Tom!
>
> I think is too much for roundoff error
>
> Found funny post about it:
> https://randomascii.wordpress.com/2014/10/09/intel-underestimates-error-bounds-by-1-3-quintillion/
> http://notabs.org/fpuaccuracy/index.htm
>
>
>
> On 25 Apr 2019, at 19:56, Tom Lane <tgl(at)sss(dot)pgh(dot)pa(dot)us> wrote:
>
> Max Lipsky <maxlipsky(at)gmail(dot)com> writes:
>
> SELECT acos(
> cos(radians(48.9193))
> * cos(radians(48.9193))
> * cos(radians(2.5431) - radians(2.5431))
> + sin(radians(48.9193))
> * sin(radians(48.9193))
> ) as result;
>
>
> This returned [22003] ERROR: input is out of range
>
>
> Not too surprising, because (at least on my machine)
>
> regression=# select cos(radians(48.9193))
> regression-# * cos(radians(48.9193)) + sin(radians(48.9193))
> regression-# * sin(radians(48.9193));
> ?column?
> --------------------
> 1.0000000000000002
> (1 row)
>
> Problems of this sort are inevitable when working with finite-precision
> math.
>
> https://en.wikipedia.org/wiki/Round-off_error
>
> regards, tom lane
>
>

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