mod
Remainder after division (modulo operation)
Syntax
Description
Examples
Find the remainder after division for a vector of integers and the divisor 3
.
a = 1:5; m = 3; b = mod(a,m)
b = 1×5
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 are always positive if the divisor is positive.
a = [-4 -1 7 9]; m = 3; b = mod(a,m)
b = 1×4
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 = 1×4
-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 = 1×6
0 3.5000 5.9000 6.2000 2.7168 0
Input Arguments
Dividend, specified as a scalar, vector, matrix, multidimensional array, table, or
timetable. a
must be a real-valued array of any numerical type. 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
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
.
Data Types: single
| double
| int8
| int16
| int32
| int64
| uint8
| uint16
| uint32
| uint64
| logical
| duration
| char
| table
| timetable
Divisor, specified as a scalar, vector, matrix, multidimensional array, table, or
timetable. m
must be a real-valued array of any numerical type. 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 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
.
Data Types: single
| double
| int8
| int16
| int32
| int64
| uint8
| uint16
| uint32
| uint64
| logical
| duration
| char
| table
| timetable
More About
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).
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
The
mod
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
oruint64
, both inputs must have the same type.
This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.
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).
This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).
Version History
Introduced before R2006aThe 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.
See Also
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