Vector Arguments in VML

Vector arguments of VML 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[0], a[1], ..., a[n-1] (for the C interface).

To accommodate for arrays with other increments, or more complicated indexing, VML 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],

VML pack/unpack functions can use one of the following indexing methods:

Positive Increment Indexing

kj = incy * j, mj = inca * j, j = 0 ,..., n-1

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 = 0 ,..., n-1,

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 = 0,..., n-1,

where ma and my are arrays that contain mask vectors for the input and output arrays a and y, respectively.