Gather-scatter (vector addressing)
Gather-scatter is a type of memory addressing that often arises when addressing vectors in sparse linear algebra operations. It is the vector-equivalent of register indirect addressing, with gather involving indexed reads and scatter indexed writes. Vector processors (and some SIMD units in CPUs) have hardware support for gather-scatter operations, providing instructions such as Load Vector Indexed for gather and Store Vector Indexed for scatter.
Definitions
Gather
A sparsely-populated vector holding non-empty elements can be represented by two densely-populated vectors of length ; containing the non-empty elements of , and giving the index in where 's element is located. The gather of into , denoted , assigns with having already been calculated.[1] A C implementation is
for (i=0; i<N; ++i)
x[i] = y[idx[i]];
Scatter
The sparse scatter, denoted is the reverse operation. It copies the values of into the corresponding locations in the sparsely-populated vector , i.e. .
for (i=0; i<N; ++i)
y[idx[i]] = x[i];