Vector arguments of VM mathematical functions are passed in one-dimensional arrays with unit vector increment. It means that a vector of length n is passed contiguously in an array a whose values are defined as
a(1), a(2), ..., a(n)
To accommodate for arrays with other increments, or more complicated indexing, VM contains auxiliary pack/unpack functions that gather the array elements into a contiguous vector and then scatter them after the computation is complete.
Generally, if the vector elements are stored in a one-dimensional array a as
a(m0), a(m1), ..., a(mn-1)
and need to be regrouped into an array y as
y(k0), y(k1), ..., y(kn-1),
VM pack/unpack functions can use one of the following indexing methods:
Positive Increment Indexing
kj = incy * j, mj = inca * j, j = 1 ,..., n
Constraint: incy > 0 and inca > 0.
For example, setting incy = 1 specifies gathering array elements into a contiguous vector.
This method is similar to that used in BLAS, with the exception that negative and zero increments are not permitted.
Index Vector Indexing
kj = iy(j), mj = ia(j), j = 1 ,..., n,
where ia and iy are arrays of length n that contain index vectors for the input and output arrays a and y, respectively.
Mask Vector Indexing
Indices kj , mj are such that:
my(kj) ≠ 0, ma(mj) ≠ 0 , j = 1,..., n,
where ma and my are arrays that contain mask vectors for the input and output arrays a and y, respectively.