[Tutor] The remainder %

[Karl Pflästerer]

On  3 Jun 2003, Bob Gailer <- bgailer@alum.rpi.edu wrote:

> In math modulo is NOT the same as remainder. At least the explanation
> says "remainder". Modulo and remainder have the same values when the
> left argument is >= 0, and different values for < 0. Example:
> n   n modulo 3  n % 3
> 3           0            0
> 2           2            2
> 1           1            1
> 0           0            0
> -1          2            1
> -2          1            2
> -3          0            0

Some time ago I had nearly the same discussion (the subject was: how
exactly is modulo in math defined); it turned out that there is no
definition for modulo which returnes *one* number. Modulo describes
something which in german is called `Restklasse' (residue class).

So it's up to the implementor of the function in the particular language
how he defines modulo.

> The only programming language I know that "got is right" is APL. There
> the function is named modulo and it DOES modulo. Most other languages
> call it modulo and it does remainder.

I am sure that Common Lisp does it `right' and I think Ada also (modulo
the multiple possibilities to define modulo :-))

$ clisp
[1]> 
(format t
        "+5 modulo +3 = ~A ~@
         +5 modulo -3 = ~A ~@
         -5 modulo +3 = ~A ~@
         -5 modulo -3 = ~A ~2%~@
         +5 reminder +3 = ~A ~@
         +5 reminder -3 = ~A ~@
         -5 reminder +3 = ~A ~@
         -5 reminder -3 = ~A"
        (mod 5 3) (mod 5 -3) (mod -5 3) (mod -5 -3)
        (rem 5 3) (rem 5 -3) (rem -5 3) (rem -5 -3))
+5 modulo +3 = 2 
+5 modulo -3 = -1 
-5 modulo +3 = 1 
-5 modulo -3 = -2 


+5 reminder +3 = 2 
+5 reminder -3 = 2 
-5 reminder +3 = -2 
-5 reminder -3 = -2
NIL
[2]> 


Python uses the same definition for modulo as Common Lisp.

bye
   Karl
-- 
"Lisp is worth learning for the profound enlightenment experience you
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