| Arithmetic {base} | R Documentation |
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 to such, or other objects for which methods have been written. |
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.
%% and x %/% y can be used for non-integer y,
e.g. 1 %/% 0.2, but the results are subject to representation
error and so may be platform-dependent. Because the IEC 60059
representation of 0.2 is a binary fraction slightly larger than
0.2, the answer to 1 %/% 0.2 should be 4 but
most platforms give 5.
Users are sometimes surprised by the value returned, for example why
(-8)^(1/3) is 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.
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 of %% is NA_integer_ or
NaN (depending on the typeof of the
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
/ and ^ 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, 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.
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).
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
zero: 1/x is Inf or -Inf depending on the sign of
zero x.
** 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 Deprecated but
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.
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
sqrt for miscellaneous and Special for special
mathematical functions.
Syntax for operator precedence.
%*% for matrix multiplication.
x <- -1:12 x + 1 2 * x + 3 x %% 2 #-- is periodic x %/% 5