These unary and binary operators perform arithmetic on numeric or complex vectors (or objects which can be coerced to them).
+ x - x 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 to such, or other objects for which methods have been written.
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
x ^ y should also give the proper limit result when
either (numeric) argument is infinite (one of
Objects such as arrays or time-series can be operated on this way provided they are conformable.
For double arguments,
%% can be subject to catastrophic loss of
x is much larger than
y, and a warning is
given if this is detected.
x %/% y can be used for non-integer
1 %/% 0.2, but the results are subject to representation
error and so may be platform-dependent. Because the IEC 60059
0.2 is a binary fraction slightly larger than
0.2, the answer to
1 %/% 0.2 should be
most platforms give
Users are sometimes surprised by the value returned, for example why
NaN. For double inputs, R makes
use of IEC 60559 arithmetic on all platforms, together with the C
system function pow for the
^ operator. The relevant
standards define the result in many corner cases. In particular, the
result in the example above is mandated by the C99 standard. On many
Unix-alike systems the command
man pow gives details of the
values in a large number of corner cases.
Arithmetic on type double in R is supposed to be done in round to nearest, ties to even mode, but this does depend on the compiler and FPU being set up correctly.
-return a numeric or complex vector. All attributes (including class) are preserved if there is no coercion: logical
xis coerced to integer and names, dims and dimnames are preserved.The binary operators return vectors containing the result of the element by element operations. If involving a zero-length vector the result has length zero. Otherwise, the elements of shorter vectors are recycled as necessary (with a
warningwhen they are recycled only fractionally). The operators are
/for division and
x mod yand
%/%indicates integer division. It is guaranteed that
x == (x %% y) + y * ( x %/% y )(up to rounding error) unless
y == 0where the result of
NaN(depending on the
typeofof the arguments), and for non-finite arguments.If either argument is complex the result will be complex, otherwise if one or both arguments are numeric, the result will be numeric. If both arguments are of type integer, the type of the result of
^is numeric and for the other operators it is integer (with overflow, which occurs at $+/- (2^31 - 1)$, returned as
NA_integer_with a warning).The rules for determining the attributes of the result are rather complicated. Most attributes are taken from the longer argument. Names will be copied from the first if it is the same length as the answer, otherwise from the second if that is. If the arguments are the same length, attributes will be copied from both, with those of the first argument taking precedence when the same attribute is present in both arguments. For time series, these operations are allowed only if the series are compatible, when the class and
tspattribute 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.
All logical operations involving a zero-length vector have a zero-length result.
The binary operators are sometimes called as functions as
`&`(x, y): see the description of how
argument-matching is done in
** is translated in the parser to
^, but this was
undocumented for many years. It appears as an index entry in Becker
et al (1988), pointing to the help for
is not actually mentioned on that page. Even though it had been
deprecated in S for 20 years, it was still accepted in R in 2008.
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) (with
e2 missing for a unary operator).
R is dependent on OS services (and they on FPUs) for floating-point
arithmetic. On all current R platforms IEC 60559 (also known as IEEE
754) arithmetic is used, but some things in those standards are
optional. In particular, the support for denormal numbers
(those outside the range given by
.Machine) may differ
between platforms and even between calculations on a single platform. Another potential issue is signed zeroes: on IEC 60659 platforms there
are two zeroes with internal representations differing by sign. Where
possible R treats them as the same, but for example direct output
from C code often does not do so and may output -0.0 (and on
Windows whether it does so or not depends on the version of Windows).
One place in R where the difference might be seen is in division by
-Inf depending on the sign of
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.
D. Goldberg (1991) What Every Computer Scientist Should Know about Floating-Point Arithmetic ACM Computing Surveys, 23(1). Postscript version available at http://www.validlab.com/goldberg/paper.ps Extended PDF version at http://www.validlab.com/goldberg/paper.pdf
Syntax for operator precedence.
%*% for matrix multiplication.
x <- -1:12 x + 1 2 * x + 3 x %% 2 #-- is periodic x %/% 5