# modulo

remainder modulo m with the left operand sign

# pmodulo

positive euclidian remainder modulo m

## Calling Sequence

    i = modulo(n,m)

    i = pmodulo(n,m)

## Arguments

m, n

  Scalar, vector, matrix or hypermatrix of encoded integers, reals or polynomials (Hypermatrix is not supported for polynomials). `m` and `n` must have the same type. If they are of integer type, they may be of distinct encoding length (for instance int8 and int16). If none of them is scalar, they must have the same sizes.

i

  Scalar, vector, matrix or hypermatrix of same type (and inttype) as `n`. `i` takes the sizes of the bigger `m` or`n`.

## Description

`modulo` computes `i = n (modulo m)` i.e. remainder of `n` divided by `m`.

`i = n - m .* int (n ./ m)`. Here the answer may be negative if `n` or `m` are negative.

`pmodulo` computes `i = n - |m| .* floor (n ./ |m|)`, the answer is positive or zero.

If `m` contains at least one 0 value, `modulo(x,m)` and `pmodulo(x,m)` will perform a division by zero. If `m` is of real type, this exception will be processed according to the `ieee()` mode. For encoded integers, it will always yield an error.

## Examples

    n = [1,2,10,15];
    m = [2,2,3,5];
    modulo(n,m)

    modulo(-3, 9)
    modulo(10, -4)

    pmodulo(-3, 9)
    pmodulo(10, -6)
    pmodulo(-10, -6)

    // Encoded integers
    modulo( int8(-13), int16(-7))
    pmodulo(int8(-13), int16(-7))
    modulo( int8(-13), int16([-7 5]))
    pmodulo(int8(-13), int16([-7 5]))
    modulo( int8([-13 8]), int16(-7))
    pmodulo(int8([-13 8]), int16(-7))
    modulo( int8([-13 8]), int16([-7 5]))
    pmodulo(int8([-13 8]), int16([-7 5]))

    // Hypermatrices
    m = grand(2,2,2,"uin",-100,100)
    n = grand(2,2,2,"uin",-10 ,10);
    n(n==0) = 1
    modulo(m, 5)
    pmodulo(m,5)
    modulo(51, n)
    pmodulo(51,n)
    modulo(m, n)
    pmodulo(m,n)

    // Polynomials
    modulo( %z^2+1, %z)
    pmodulo(%z^2+1, %z)

## See also

- unwrap
- ieee

## History

5.5.0
Extension to encoded integers and to hypermatrices of encoded integers or reals.