Re: Infinity vs Error for division by zero

On Fri, Mar 1, 2019 at 12:59 PM Andrew Gierth <andrew(at)tao11(dot)riddles(dot)org(dot)uk>
wrote:

> >>>>> "Matt" == Matt Pulver <mpulver(at)unitytechgroup(dot)com> writes:
>
> Matt> ERROR: division by zero
>
> Matt> Question: If Infinity and NaN are supported, then why throw an
> Matt> exception here, instead of returning Infinity?
>
> Spec says so:
>
> 4) The dyadic arithmetic operators <plus sign>, <minus sign>,
> <asterisk>, and <solidus> (+, -, *, and /, respectively) specify
> addition, subtraction, multiplication, and division, respectively.
> If the value of a divisor is zero, then an exception condition is
> raised: data exception -- division by zero.

Thank you, that is what I was looking for. In case anyone else is looking
for source documentation on the standard, there is a link from
https://en.wikipedia.org/wiki/SQL:2003#Documentation_availability to a zip
file of the SQL 2003 draft http://www.wiscorp.com/sql_2003_standard.zip
where one can confirm this (page 242 of 5WD-02-Foundation-2003-09.pdf).

On Fri, Mar 1, 2019 at 2:26 PM David G. Johnston <david(dot)g(dot)johnston(at)gmail(dot)com>
wrote:

> On Friday, March 1, 2019, Chapman Flack <chap(at)anastigmatix(dot)net> wrote:
>
>>
>> But if someone wanted to write a user-defined division function or
>> operator that would return Inf for (anything > 0) / 0 and for
>> (anything < 0) / -0, and -Inf for (anything < 0) / 0 and for
>> (anything > 0) / -0, and NaN for (either zero) / (either zero), I think
>> that function or operator would be fully in keeping with IEEE 754.
>>
>
> Upon further reading you are correct - IEEE 754 has chosen to treat n/0
> differently for n=0 and n<>0 cases. I'm sure they have their reasons but
> within the scope of this database, and the core arithmetic functions it
> provides, those distinctions don't seeming meaningful and having to add
> query logic to deal with both cases would just be annoying. I don't use,
> or have time for the distraction, to understand why such a decision was
> made and how it could be useful. Going from an exception to NaN makes
> sense to me, going instead to infinity - outside of limit expressions which
> aren't applicable here - does not.
>
> For my part in the queries I have that encounter divide-by-zero I end up
> transforming the result to zero which is considerably easier to
> present/absorb along side other valid fractions in a table or chart.
>

In heavy financial/scientific calculations with tables of data, using inf
and nan are very useful, much more so than alternatives such as throwing an
exception (which row(s) included the error?), or replacing them with NULL
or 0. There are many intermediate values where using inf makes sense and
results in finite outcomes at the appropriate limit: atan(1.0/0)=pi/2,
erf(1.0/0)=1, exp(-1.0/0)=0, etc.

In contrast, nan represents a mathematically indeterminate form, in which
the appropriate limit could not be ascertained. E.g. 0.0/0, inf-inf,
0.0*inf, etc. In many applications, I would much rather see calculations
carried out via IEEE 754 all the way to the end, with nans and infs, which
provides much more useful diagnostic information than an exception that
doesn't return any rows at all. As Andres Freund pointed out, it is also
more expensive to do the intermediate checks. Just let IEEE 754 do its
thing! (More directed at the SQL standard than to PostgreSQL.)

Best regards,
Matt