Computational Physics Lectures: How to optimize codes, from vectorization to parallelization

Contents

Number of elements that can acted upon, examples

We start with the simple scalar operations given by

for (i = 0; i < n; i++){
    a[i] = b[i] + c[i];
}

If the code is not vectorized and we have a 128-bit register to store a 32 bits floating point number, it means that we have \( 3\times 32 \) bits that are not used. For the first element we have

0	1	2	3
a[0]=	not used	not used	not used
b[0]+	not used	not used	not used
c[0]	not used	not used	not used

We have thus unused space in our SIMD registers. These registers could hold three additional integers.