On 06 Jun 2000 02:00:13 -0500, Dave Thomas <Dave / thomases.com> wrote:
>
>In (say) Python, the modulus operator (%) is actually a remainder
>function too; Python arranges the quotient of integer division so that
>the remainder equals the modulo.
>
>In Ruby, % is a true modulo operator, and a.remainder(b) is used to
>get the remainder.
>
>                         Ruby                   Python
>   a     b  |   a/b   a%b  a.remainder(b) |    a/b      a%b
>============|=============================|=================
>  13     4  |    3     1       1          |     3        1   
>  13    -4  |   -3    -3       1          |    -4       -3
> -13     4  |   -3     3      -1          |    -4        3
> -13    -4  |    3    -1      -1          |     3       -1

Another perspective on this is that of Forth, where we talk about doing
either floored division (where the quotient is rounded to minus infinity) or
symmetric division (where the quotient is rounded to zero). In floored
division the remainder = the modulus; in symmetric division it may not.
Either way, the invariant qb+r=a is preserved.

Yet another way to look at it is forcing either the quotient or the
remainder to have the same sign as the divisor.

So the suggestion that there are two division operations as well as two
remainders is correct.

ANSI Forth has both, because both are widely used (and one was mandated by
the Forth-79 standard, and the other by the Forth-83 standard). Most people
find symmetric division more intuitive, but floored division is
mathematically more symmetric...

-- 
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