List: General Discussion « Previous MessageNext Message » From: Thomas Lenherr Date: February 25 2005 4:07pm Subject: Re: modulo operation View as plain text
```Hi Jigal, Hi Peter,

first of all: it's true, the wikipedia-site is not contradicting the
mysql-implementation, it seems i didn't read it too carefully...

The guy who "invented" the modulo-operation was G.F. Gauss in his book
"Disquisitiones Arithmeticae" which was published in 1801.
His definition is documented here:
http://en.wikipedia.org/wiki/Modular_arithmetic (section congruence
relation).

He defined the equivalence operation "modulo" as following:
"We call two integers a, b congruent modulo n if their difference is
divisible by n, or equivalently: if they leave the same remainder when
divided by n. "

This sentence seems to be the source of your different opinion:
The difference of a and b is always >= 0 therefore their difference mod
n would always be a positive integer.
The second part defines the relation in slightly other way, using the
remainder. As pointed out by the table pasted by Peter "remainder" and
"modulo" is not always exactly the same, but if the remainder by any
chance can be negative, the following line is not more always working
for example in an if-statement:

a mod n == b mod n

because if exactly one of a and b is negative so are the remainders (if
they're not multiples of n), ex:

-3 mod 2 != 1 mod 2, as -3 mod 2 == -1

but abs(-3 - 1) mod 2 == abs(-4) mod 2 == 4 mod 2 == 0

Thomas

Jigal van Hemert wrote:
> From: "Peter Brawley"
>
>
>>There are various interpretations of modulo. It's not simply
>>"remainder", eg see the discussion at
>>http://mathforum.org/library/drmath/view/52343.html including this chart
>
>
> The article at wikipedia already mentioned multiple interpretations.
>
> My point was that while Thomas wrote that modulo in MySQL was flawed and
> question was not contradicting the MySQL implementation at all.
>
>
>>>From: "Thomas Lenherr"
>>>
>>>>(For the exact definition see
>>>>http://en.wikipedia.org/wiki/Modulo_operation )
>
>
> It is strange for mathematical operations/functions to depend upon
> "interpretation" or "implementation". If there is anything in this world
> that is properly defined, it must be mathematics.
>
> Maybe Thomas (or you) can file a bugreport with the suggestion to add a
> mathematically correct modulo function; I don't think the current modulo
> function/operator should be altered, since this might break a lot of queries
> out there!
>
> Regards, Jigal.
>
>
```