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mod

Remainder after division (modulo operation)

Syntax

Description

example

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

Examples

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Compute 23 modulo 5.

b = mod(23,5)
b =

     3

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

a = 1:5;
m = 3;
b = mod(a,m)
b =

     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 are always positive if the divisor is positive.

a = [-4 -1 7 9];
m = 3;
b = mod(a,m)
b =

     2     2     1     0

Find the remainder after division by a negative divisor for a set of integers including both positive and negative values. Note that nonzero results are always negative if the divisor is negative.

a = [-4 -1 7 9];
m = -3;
b = mod(a,m)
b =

    -1    -1    -2     0

Find the remainder after division for several angles using a modulus of 2*pi. Note that mod attempts to compensate for floating-point round-off effects to produce exact integer results when possible.

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

         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. Numeric inputs a and m must either be the same size or have sizes that are compatible (for example, a is an M-by-N matrix and m is a scalar or 1-by-N row vector). For more information, see Compatible Array Sizes for Basic Operations.

If a and m 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, mod 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 | duration | char

Divisor, specified as a scalar, vector, matrix, or multidimensional array. m must be a real-valued array of any numerical type. Numeric inputs a and m must either be the same size or have sizes that are compatible (for example, a is an M-by-N matrix and m is a scalar or 1-by-N row vector). For more information, see Compatible Array Sizes for Basic Operations.

If a and m 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, mod 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 | duration | char

More About

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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).

Congruence Relationships

The mod function is useful for congruence relationships: a and b are congruent (mod m) if and only if mod(a,m) == mod(b,m). For example, 23 and 13 are congruent (mod 5).

Tall Array Support

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

References

[1] Knuth, Donald E. The Art of Computer Programming. Vol. 1. Addison Wesley, 1997 pp.39–40.

See Also

Introduced before R2006a

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