Arithmetic package:base R
These binary operators perform arithmetic on numeric or complex
vectors (or objects which can be coerced to them).
x + y
x - y
x * y
x / y
x ^ y
x %% y
x %/% y
x, y: numeric or complex vectors or objects which can be coerced
such, or other objects for which methods have been
The binary arithmetic operators are generic functions: methods
be written for them individually or via the 'Ops' group generic
function. (See 'Ops' for how dispatch is computed.)
If applied to arrays the result will be an array if this is
sensible (for example it will not if the recycling rule has
Logical vectors will be coerced to integer or numeric vectors,
'FALSE' having value zero and 'TRUE' having value one.
'1 ^ y' and 'y ^ 0' are '1', _always_. 'x ^ y' should also
the proper limit result when either argument is infinite (i.e.,
Objects such as arrays or time-series can be operated on this
provided they are conformable.
For real arguments, '%%' can be subject to catastrophic loss of
accuracy if 'x' is much larger than 'y', and a warning is given
this is detected.
These operators return vectors containing the result of the
element by element operations. The elements of shorter vectors
are recycled as necessary (with a 'warning' when they are
only _fractionally_). The operators are '+' for addition, '-'
subtraction, '*' for multiplication, '/' for division and '^'
'%%' indicates 'x mod y' and '%/%' indicates integer division.
is guaranteed that 'x == (x %% y) + y * ( x %/% y )' (up to
rounding error) unless 'y == 0' where the result is
or 'NaN' (depending on the 'typeof' of the arguments). See
http://en.wikipedia.org/wiki/Modulo_operation> for the
If either argument is complex the result will be complex, and
one or both arguments are numeric, the result will be numeric.
both arguments are integer, the result of '/' and '^' is
and of the other operators integer (with overflow returned as
with a warning).
The rules for determining the attributes of the result are
complicated. Most attributes are taken from the longer
the first if they are of the same length. Names will be copied
from the first if it is the same length as the answer,
from the second if that is. For time series, these operations
allowed only if the series are compatible, when the class and
'tsp' attribute of whichever is a time series (the same, if
are) are used. For arrays (and an array result) the dimensions
and dimnames are taken from first argument if it is an array,
otherwise the second.
These operators are members of the S4 'Arith' group generic,
so methods can be written for them individually as well as for
group generic (or the 'Ops' group generic), with arguments
'**' is translated in the parser to '^', but this was
for many years. It appears as an index entry in Becker _et al_
(1988), pointing to the help for 'Deprecated' but is not
mentioned on that page. Even though it has been deprecated in
for 20 years, it is still accepted.
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) _The New
Language_. Wadsworth & Brooks/Cole.
'sqrt' for miscellaneous and 'Special' for special mathematical
'Syntax' for operator precedence.
'%*%' for matrix multiplication.
x <- -1:12
x + 1
2 * x + 3
x %% 2 #-- is periodic
x %/% 5