mod - Remainder after division (modulo operation) - MATLAB (original) (raw)

Remainder after division (modulo operation)

Syntax

Description

b = mod([a](#btvg3sl-1-a),[m](#btvg3sl-1-m)) returns the remainder after division of a by m, wherea 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 thatmod(a,0) returns a.

example

Examples

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

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

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)

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)

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 4pi]; m = 2pi; b = mod(theta,m)

b = 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, multidimensional array, table, or timetable. a must be a real-valued array of any numerical type. Inputsa and m must either be the same size or have sizes that are compatible (for example, a is anM-by-N matrix and m is a scalar or1-by-N row vector). For more information, see Compatible Array Sizes for Basic Operations.

If a is a duration array and m is a numeric array, then the values in m 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.

Divisor, specified as a scalar, vector, matrix, multidimensional array, table, or timetable. m must be a real-valued array of any numerical type. Inputsa and m must either be the same size or have sizes that are compatible (for example, a is anM-by-N matrix and m is a scalar or1-by-N row vector). For more information, see Compatible Array Sizes for Basic Operations.

If m 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.

More About

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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 thatrem(a,0) returns NaN.

Both variants have their uses. For example, in signal processing, themod function is useful in the context of periodic signals because its output is periodic (with period equal to the divisor).

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).

References

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

Extended Capabilities

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

Usage notes and limitations:

Arithmetic is performed 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, both inputs must have the same type.

The mod function fully supports GPU arrays. To run the function on a GPU, specify the input data as a gpuArray (Parallel Computing Toolbox). For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced before R2006a

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The mod function can calculate on all variables within a table or timetable without indexing to access those variables. All variables must have data types that support the calculation. For more information, see Direct Calculations on Tables and Timetables.