# Implementation details

This section contains technical information about internals of the code.

## Random number generator

Often subgrid models require random numbers, for this purpose SWIFT has a random number generator. The random number generator of SWIFT is based on a combination of the standard rand_r and erand48 random number generators. Since for some applications in cosmology we want to be able to sample random numbers with a probability lower than $$10^{-8}$$, we could not simply use the 32-bit rand_r due to its cut-off and spacing of around $$2^{-32} \approx 2 \times 10^{-10}$$. For the erand48 algorithm with 48 bits the spacing and cutoff are significantly smaller and around $$2^{-48} \approx 3.5 \times 10^{-15}$$, so this is very suitable for our applications.

### Reproducible random numbers

In our simulations we want to be able to reproduce the exact same random numbers if we do exactly the same simulation twice. Because of this we want to seed the random number generator in a reproducible way. In order to do this we seed with the particle ID of the current particle and the current integer simulation time.

To produce several different types of random numbers we have an additional argument called the type of random number which is basically the nth random number for the specified seed, which is added to the particle ID, thus providing a distinct state per random number type.

If the user wishes to run a simulation with a different set of random number, an option during the configuration (--with-random-seed=INT) is available. This option simply flip some bits in the initial number composed of the ID and the current simulation time through the binary operator XOR.

### Implementation

Our random number generator packs the particle ID (plus the random number type) and the current simulation time as two 64-bit values, plus a constant 16-bit value, into a 144-bit buffer. This buffer is treated as an array of 9 uint16 values.

In a first pass we initialize the seed to 0 and run through the 9 uint16 values, xor-ing them with the seed and calling rand_r on the seed to advance it. Using rand_r with the thus-generated seed, we generate a sequence of 9 16-bit values and xor them with the original 144-bit buffer.

The 9 bytes of this modified buffer are then used for three passes of erand48, xor-ing the state in the same way as before. erand48 is then called one final time with the last state, producing a random double-precision value with a 48-bit mantissa.

### What to do if we break the random number generator?

The most likely case is that the RNG is not strong enough for our application, in this case we could simply do multiple passes of both shuffling the state and generating the final value from the state. This increases the computational cost but will make the random number generator stronger.

An other case is that we need probabilities that are lower than $$1 \times 10^{-17}$$, in this case we simply cannot use our random number generator and for example need to generate two random numbers in order to probe these low probabilities.

## Generating new unique IDs

When spawning new particles (not converting them) for star formation or other similar processes, the code needs to create new unique particle IDs. This is implemented in the file space_unique_id.c and can be switched on/off in the star formation file star_formation_struct.h by setting the variable star_formation_need_unique_id to 1 or 0.

The generation of new IDs is done by computing the maximal ID present in the initial condition (across all particle types) and then attributing two batches of new, unused IDs to each MPI rank. The size of each batch is computed in the same way as the count of extra particles in order to ensure that we will have enough available IDs between two tree rebuilds (where the extra particles are regenerated).

When a new ID is requested, the next available ID in the first batch is returned. If the last available ID in the first batch is requested, we switch to the next batch of IDs and flag it for regeneration at the next rebuild time. If the second batch is also fully used, the code will exit with an error message 1. At each tree-rebuild steps, the ranks will request a new batch if required and make sure the batches are unique across all MPI ranks.

As we are using the maximal ID from the ICs, nothing can be done against the user providing the maximal integer possible as an ID (that can for instance be the case in some of the EAGLE ICs as the ID encode their Lagrangian position on a Peano-Hilbert curve).

1

Thanks to the size of the fresh ID batches, the code should run out of extra particles before reaching this point and triggered a new rebuild if this is allowed by the star formation scheme.