# R: Arithmetic Operators

Arithmetic {base} | R Documentation

## Arithmetic Operators

### Description

These binary operators perform arithmetic on numeric or complex vectors (or objects which can be coerced to them).

### Usage

    x + y
    x - y
    x * y
    x / y
    x ^ y
    x %% y
    x %/% y

### Arguments

`x, y` | numeric or complex vectors or objects which can be coerced to such, or other objects for which methods have been written.

### Details

The binary arithmetic operators are generic functions: methods can 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 been invoked).

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 give the proper limit result when either argument is infinite (i.e., `+- Inf`).

Objects such as arrays or time-series can be operated on this way 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 if this is detected.

### Value

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 recycled only fractionally). The operators are `+` for addition, `-` for subtraction, `*` for multiplication, `/` for division and `^` for exponentiation.
`%%` indicates `x mod y` and `%/%` indicates integer division. It is guaranteed that `x == (x %% y) + y * ( x %/% y )` (up to rounding error) unless `y == 0` where the result is `NA_integer_` or `NaN` (depending on the `typeof` of the arguments). See http://en.wikipedia.org/wiki/Modulo_operation for the rationale.
If either argument is complex the result will be complex, and if one or both arguments are numeric, the result will be numeric. If both arguments are integer, the result of `/` and `^` is numeric and of the other operators integer (with overflow returned as `NA` with a warning).
The rules for determining the attributes of the result are rather complicated. Most attributes are taken from the longer argument, 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, otherwise from the second if that is. For time series, these operations are allowed only if the series are compatible, when the class and `tsp` attribute of whichever is a time series (the same, if both 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.

### S4 methods

These operators are members of the S4 `Arith` group generic, and so methods can be written for them individually as well as for the group generic (or the `Ops` group generic), with arguments `c(e1, e2)`.

### References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.

### See Also

`sqrt` for miscellaneous and `Special` for special mathematical functions.

`Syntax` for operator precedence.

`%*%` for matrix multiplication.

### Examples

    x <- -1:12
    x + 1
    2 * x + 3
    x %% 2 #-- is periodic
    x %/% 5

[Package base version 2.6.0 Index]