Map/Reduce

We have now covered enough that we can use OpenMP to parallelise a map/reduce style calculation. In this case, the problem we will solve will be calculating the total interaction energy between each ion in an array of ions with a single reference ion. Passed into this function will be the reference ion, and an array of ions. The algorithm performed for each ion in the array will be;

1. Calculate the distance between the ion in the array and the reference ion.
2. Use this distance (r) to calculate the interaction energy ( 1 / r )
3. Add this interaction energy onto the total sum.

Map/reduce can be used when you have an array of data, a function you wish to apply (to map) to each item in the array, and a single value you want back that is the reduction of the results of applying the function to each item in the array. In terms of map/reduce, our algorithm would look like this;

1. Create a function that calculates and returns the interaction between a passed ion and the reference ion, e.g. calc_energy(ion)
2. Map each ion in the array against the energy function calc_energy
3. Reduce the result of each mapped function call using a sum (+)

Here are incomplete pieces of code that implement this algorithm (note that this is to provide an example of how map/reduce can be used - you don't need to complete this code);

• C
• C++
• Fortran

Note that the amount of OpenMP in these examples is very low (just 2-3 lines). This is quite common for OpenMP programs - most of the work of parallelisation is organising your code so that it can be parallelised. Once it has been organised, you then only need to add a small number of OpenMP directives.

Compile the above programs, and try running them using different numbers of threads.