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 and
is computed using b = a - m.*floor(a./m). The mod function
follows the convention that mod(a,0) returns a.

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.

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.

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)

a — Dividendscalar | 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. Inputs a and m must be
the same size unless one is a scalar. A scalar value expands to be
the same size as the other array.

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.

m — Divisorscalar | 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. Inputs a and m must be
the same size unless one is a scalar. A scalar value expands to be
the same size as the other array.

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.

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.