# [R] Integer division

Richard O'Keefe r@oknz @end|ng |rom gm@||@com
Tue Dec 20 03:01:38 CET 2022

```The Fortran '08 standard says <<
One operand of type integer may be divided by another operand of type
integer. Although the mathematical
quotient of two integers is not necessarily an integer, Table 7.2 specifies
that an expression involving the division
operator with two operands of type integer is interpreted as an expression
of type integer. The result of such an
operation is the integer closest to the mathematical quotient and between
zero and the mathematical quotient
inclusively. >>
Another way to say this is that integer division in
Fortran TRUNCATES towards zero.  It does not round and
never has.

C carefully left the behaviour of integer division (/)
unspecified, but introduced the div(,) function with the
same effect as Fortran (/).  Later versions of the C
standard tightened this up, and the C17 standard reads <<
The result of the / operator is the quotient from the division of the first
operand by the second; the
result of the % operator is the remainder. In both operations, if the value
of the second operand is
zero, the behavior is undefined.
When integers are divided, the result of the / operator is the algebraic
quotient with any fractional
part discarded. 107) If the quotient a/b is representable, the expression
(a/b)*b + a%b shall equal a ;
otherwise, the behavior of both a/b and a%b is undefined.>>

That is, C17 TRUNCATES the result of division towards
zero.  I don't know of any C compiler that rounds,
certainly gcc does not.

The Java 15 Language Specification says
<< Integer division rounds toward 0. >>
which also specified truncating division.

The help for ?"%/%" does not say what the result is.
Or if it does, I can't find it.  Either way, this is
a defect in the documentation.  It needs to be spelled
out very clearly.
R version 4.2.2 Patched (2022-11-10 r83330) -- "Innocent and Trusting"
> c(-8,8) %/% 3
[1] -3  2
so we deduce that R *neither* rounds *not* truncates,
but returns the floor of the quotient.
It is widely argued that flooring division is more
generally useful than rounding or truncating division,

On Tue, 20 Dec 2022 at 02:51, Göran Broström <gb using ehar.se> wrote:

> I have a long vector x with five-digit codes where the first digit of
> each is of special interest, so I extracted them through
>
>  > y <- x %/% 10000
>
> but to my surprise y contained the value -1 in some places. It turned
> out that x contains -1 as a symbol for 'missing value' so in effect I
> found that
>
>  > -1 %/% 10000 == -1
>
> Had to check the help page for "%/%", and the first relevant comment I
> found was:
>
> "Users are sometimes surprised by the value returned".
>
> No surprise there. Further down:
>
> ‘%%’ indicates ‘x mod y’ (“x modulo y”) and ‘%/%’ indicates
>       integer division.  It is guaranteed that
>
>       ‘ x == (x %% y) + y * (x %/% y) ’ (up to rounding error)
>
> I did expect  (a %/% b) to return round(a / b), like gfortran and gcc,
> but instead I get floor(a / b) in R. What is the reason for these
> different definitions? And shouldn't R's definition be documented?
>
> Thanks, Göran
>
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