mod
Remainder after division (modulo operation)
Syntax
Description
Examples
Remainder After Division of Scalar
Remainder After Division of Vector
Find the remainder after division for a vector of integers and the divisor3
.
a = 1:5; m = 3; b = mod(a,m)
b =1×51 2 0 1 2
Remainder After Division for Positive and Negative Values
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 =1×42 2 1 0
Remainder After Division for Negative Divisor
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 =1×4-1 -1 -2 0
Remainder After Division for Floating-Point Values
Find the remainder after division for several angles using a modulus of2*pi
. Note thatmod
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 =1×60 3.5000 5.9000 6.2000 2.7168 0
Input Arguments
a
—Dividend
scalar|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. Inputsa
andm
must either be the same size or have sizes that are compatible (for example,a
is anM
-by-N
matrix andm
is a scalar or1
-by-N
row vector). For more information, seeCompatible Array Sizes for Basic Operations.
Ifa
is aduration
array andm
is a numeric array, then the values inm
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 scalardouble
.
Data Types:single
|double
|int8
|int16
|int32
|int64
|uint8
|uint16
|uint32
|uint64
|logical
|duration
|char
m
—Divisor
scalar|vector|matrix|multidimensional array
Divisor, specified as a scalar, vector, matrix, or multidimensional array.m
must be a real-valued array of any numerical type. Inputsa
andm
must either be the same size or have sizes that are compatible (for example,a
is anM
-by-N
matrix andm
is a scalar or1
-by-N
row vector). For more information, seeCompatible Array Sizes for Basic Operations.
Ifm
is aduration
array anda
is a numeric array, then the values ina
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 scalardouble
.
Data Types:single
|double
|int8
|int16
|int32
|int64
|uint8
|uint16
|uint32
|uint64
|logical
|duration
|char
More About
Differences Between mod and rem
The concept of remainder after division is not uniquely defined, and the two functionsmod
andrem
each compute a different variation. Themod
function produces a result that is either zero or has the same sign as the divisor. Therem
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. Themod
函数遵循convention thatmod(a,0)
returnsa
, whereas therem
函数遵循convention thatrem(a,0)
returnsNaN
.
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).
Congruence Relationships
Themod
function is useful for congruence relationships:a
andb
are congruent (mod m) if and only ifmod(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
Tall Arrays
Calculate with arrays that have more rows than fit in memory.
This function fully supports tall arrays. For more information, seeTall Arrays.
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
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
oruint64
, both inputs must have the same type.
Thread-Based Environment
Run code in the background using MATLAB®backgroundPool
or accelerate code with Parallel Computing Toolbox™ThreadPool
.
This function fully supports thread-based environments. For more information, seeRun MATLAB Functions in Thread-Based Environment.
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
Usage notes and limitations:
64-bit integers are not supported.
更多的在formation, seeRun MATLAB Functions on a GPU(Parallel Computing Toolbox).
Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.
This function fully supports distributed arrays. For more information, seeRun MATLAB Functions with Distributed Arrays(Parallel Computing Toolbox).
Version History
See Also
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