Remainder after division

Find the remainder after division for a vector of integers and the divisor `3`

.

a = 1:5; b = 3; r = rem(a,b)

`r = `*1×5*
1 2 0 1 2

Find the remainder after division for a set of integers including both positive and negative values. Note that nonzero results have the same sign as the dividend.

a = [-4 -1 7 9]; b = 3; r = rem(a,b)

`r = `*1×4*
-1 -1 1 0

Find the remainder after division for several angles using a divisor of `2*pi`

. When possible, `rem`

attempts to produce exact integer results by compensating for floating-point round-off effects.

theta = [0.0 3.5 5.9 6.2 9.0 4*pi]; b = 2*pi; r = rem(theta,b)

`r = `*1×6*
0 3.5000 5.9000 6.2000 2.7168 0

`a`

— Dividendscalar | vector | matrix | multidimensional array

Dividend, specified as a scalar, vector, matrix, or multidimensional
array. `a`

must be a real-valued array of any numerical
type. Numeric inputs `a`

and `b`

must
either be the same size or have sizes that are compatible (for example, `a`

is
an `M`

-by-`N`

matrix and `b`

is
a scalar or `1`

-by-`N`

row vector).
For more information, see Compatible Array Sizes for Basic Operations.

If `a`

and `b`

are duration
arrays, then they must be the same size unless one is a scalar. If
one input is a duration array, the other input can be a duration array
or a numeric array. In this context, `rem`

treats
numeric values as a number of standard 24-hour days.

If one input has an integer data type, then the other input
must be of the same integer data type or be a scalar `double`

.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

| `logical`

| `duration`

| `char`

`b`

— Divisorscalar | vector | matrix | multidimensional array

Divisor, specified as a scalar, vector, matrix, or multidimensional
array. `b`

must be a real-valued array of any numerical
type. Numeric inputs `a`

and `b`

must
either be the same size or have sizes that are compatible (for example, `a`

is
an `M`

-by-`N`

matrix and `b`

is
a scalar or `1`

-by-`N`

row vector).
For more information, see Compatible Array Sizes for Basic Operations.

If `a`

and `b`

are duration
arrays, then they must be the same size unless one is a scalar. If
one input is a duration array, the other input can be a duration array
or a numeric array. In this context, `rem`

treats
numeric values as a number of standard 24-hour days.

If one input has an integer data type, then the other input
must be of the same integer data type or be a scalar `double`

.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

| `logical`

| `duration`

| `char`

The concept of remainder after division is
not uniquely defined, and the two functions `mod`

and `rem`

each
compute a different variation. The `mod`

function
produces a result that is either zero or has the same sign as the
divisor. The `rem`

function produces a result that
is either zero or has the same sign as the dividend.

Another difference is the convention when the divisor is zero.
The `mod`

function follows the convention that `mod(a,0)`

returns `a`

,
whereas the `rem`

function follows the convention
that `rem(a,0)`

returns `NaN`

.

Both variants have their uses. For example, in signal processing,
the `mod`

function is useful in the context of
periodic signals because its output is periodic (with period equal
to the divisor).

Calculate with arrays that have more rows than fit in memory.

This function fully supports tall arrays. For more information, see Tall Arrays.

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

Generated code performs the arithmetic using the output class. Results might not match MATLAB

^{®}due to differences in rounding errors.If one of the inputs has type

`int64`

or`uint64`

, then both inputs must have the same type.

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

64-bit integers are not supported.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

A modified version of this example exists on your system. Do you want to open this version instead?

You clicked a link that corresponds to this MATLAB command:

Run the command by entering it in the MATLAB Command Window. Web browsers do not support MATLAB commands.

Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .

Select web siteYou can also select a web site from the following list:

Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.

- América Latina (Español)
- Canada (English)
- United States (English)

- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)

- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom (English)