Remainder after division (modulo operation)
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
a — DividendDividend, specified as a scalar, vector, matrix, or multidimensional array.
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
m — DivisorDivisor, specified as a scalar, vector, matrix, or multidimensional array.
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
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).
[1] Knuth, Donald E. The Art of Computer Programming. Vol. 1. Addison Wesley, 1997 pp.39–40.
This 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.
Usage notes and limitations:
64-bit integers are not supported.
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).
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