# rem

Remainder after division

## Description

example

r = rem(a,b) returns the remainder after division of a by b, where a is the dividend and b is the divisor. This function is often called the remainder operation, which can be expressed as r = a - b.*fix(a./b). The rem function follows the convention that rem(a,0) is NaN.

## Examples

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Compute the remainder after dividing 5 into 23.

a = 23;
b = 5;
r = rem(a,b)
r = 3

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

## Input Arguments

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Dividend, specified as a scalar, vector, matrix, or multidimensional array. a must be a real-valued array of any numerical type. 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 is a duration array and b is a numeric array, then the values in b are treated as numbers of 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

Divisor, specified as a scalar, vector, matrix, or multidimensional array. b must be a real-valued array of any numerical type. 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 b is a duration array and a is a numeric array, then the values in a are treated as numbers of 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

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### Differences Between mod and rem

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).

## Version History

Introduced before R2006a