File format and basic information

The parameter file uses a format similar to the YAML format but reduced to only the elements required for the SWIFT parameters. Options are given by a name followed by a column and the value of the parameter:

ICs:        santa_barbara.hdf5
dt_max:     1.5
shift:      [2., 4., 5.]

Comments can be inserted anywhere and start with a hash:

# Description of the physics
viscosity_alpha:     2.0
dt_max:              1.5     # seconds

A typical SWIFT parameter file is split into multiple sections that may or may not be present depending on the different configuration options. The sections start with a label and can contain any number of parameters:

Cosmology:    # Planck13
  Omega_m:        0.307
  Omega_lambda:   0.693
  Omega_b:        0.0455
  h:              0.6777
  a_begin:        0.0078125     # z = 127

The options can be integer values, floating point numbers, characters or strings. If SWIFT expects a number and string is given, an error will be raised. The code can also read an array of values:

shift:  [2., 4., 5.]

Some options in the parameter file are optional and when not provided, SWIFT will run with the default value. However, if a compulsory parameter is missing an error will be raised at start-up.

Finally, SWIFT outputs two YAML files at the start of a run. The first one used_parameters.yml contains all the parameters that were used for this run, including all the optional parameters left unspecified with their default values. This file can be used to start an exact copy of the run. The second file, unused_parameters.yml contains all the values that were not read from the parameter file. This can be used to simplify the parameter file or check that nothing important was ignored (for instance because the code is not configured to use some options).

The rest of this page describes all the SWIFT parameters, split by section. A list of all the possible parameters is kept in the file examples/parameter_examples.yml.

Meta Data

The MetaData section contains basic information about the simulation. It currently only contains one parameter: run_name. This is a string of characters describing the simulation. It is written to the snapshots’ headers.

Internal Unit System

The InternalUnitSystem section describes the units used internally by the code. This is the system of units in which all the equations are solved. All physical constants are converted to this system and if the ICs use a different system (see the snapshots’ Optional Components section of the documentation) the particle quantities will be converted when read in.

The system of units is described using the value of the 5 basic units of any system with respect to the CGS system. Instead of using a unit of time we use a unit of velocity as this is more intuitive. Users hence need to provide:

  • a unit of length: UnitLength_in_cgs,
  • a unit of mass: UnitMass_in_cgs,
  • a unit of velocity UnitVelocity_in_cgs,
  • a unit of electric current UnitCurrent_in_cgs,
  • a unit of temperature UnitTemp_in_cgs.

All these need to be expressed with respect to their cgs counter-part (i.e. \(cm\), \(g\), \(cm/s\), \(A\) and \(K\)). Recall that there are no h-factors in any of SWIFT’s quantities; we, for instance, use \(cm\) and not \(cm/h\).

For instance to use the commonly adopted system of 10^10 Msun as a unit for mass, mega-parsec as a unit of length and km/s as a unit of speed, we would use:

# Common unit system for cosmo sims
InternalUnitSystem:
  UnitMass_in_cgs:     1.98848e43    # 10^10 M_sun in grams
  UnitLength_in_cgs:   3.08567758e24 # 1 Mpc in centimeters
  UnitVelocity_in_cgs: 1e5           # 1 km/s in centimeters per second
  UnitCurrent_in_cgs:  1             # 1 Ampere
  UnitTemp_in_cgs:     1             # 1 Kelvin

Note that there are currently no variables in any of the SWIFT physics schemes that make use of the unit of electric current. There is also no incentive to use anything else than Kelvin but that makes the whole system consistent with any possible unit system.

If one is interested in using the more humorous FFF unit system one would use

# FFF unit system
InternalUnitSystem:
  UnitMass_in_cgs:     40823.3133  # 1 Firkin (fir) in grams
  UnitLength_in_cgs:   20116.8     # 1 Furlong (fur) in cm
  UnitVelocity_in_cgs: 0.01663095  # 1 Furlong (fur) per Fortnight (ftn) in cm/s
  UnitCurrent_in_cgs:  1           # 1 Ampere
  UnitTemp_in_cgs:     1           # 1 Kelvin

The value of the physical constants in this system is left as an exercise for the reader [1].

Cosmology

When running a cosmological simulation, the section Cosmology sets the values of the cosmological model. The expanded \(\Lambda\rm{CDM}\) parameters governing the background evolution of the Universe need to be specified here. These are:

  • The reduced Hubble constant: \(h\): h,
  • The matter density parameter \(\Omega_m\): Omega_m,
  • The cosmological constant density parameter \(\Omega_\Lambda\): Omega_lambda,
  • The baryon density parameter \(\Omega_b\): Omega_b,
  • The radiation density parameter \(\Omega_r\): Omega_r.

The last parameter can be omitted and will default to \(\Omega_r = 0\). Note that SWIFT will verify on start-up that the matter content of the initial conditions matches the cosmology specified in this section.

This section also specifies the start and end of the simulation expressed in terms of scale-factors. The two parameters are:

  • Initial scale-factor: a_begin,
  • Final scale-factor: a_end.

Two additional optional parameters can be used to change the equation of state of dark energy \(w(a)\). We use the evolution law \(w(a) = w_0 + w_a (1 - a)\). The two parameters in the YAML file are:

  • The \(z=0\) dark energy equation of state parameter \(w_0\): w_0
  • The dark energy equation of state evolution parameter \(w_a\): w_a

If unspecified these parameters default to the default \(\Lambda\rm{CDM}\) values of \(w_0 = -1\) and \(w_a = 0\).

For a Planck+13 cosmological model (ignoring radiation density as is commonly done) and running from \(z=127\) to \(z=0\), one would hence use the following parameters:

Cosmology:
  a_begin:        0.0078125     # z = 127
  a_end:          1.0           # z = 0
  h:              0.6777
  Omega_m:        0.307
  Omega_lambda:   0.693
  Omega_b:        0.0482519
  Omega_r:        0.            # (Optional)
  w_0:            -1.0          # (Optional)
  w_a:            0.            # (Optional)

When running a non-cosmological simulation (i.e. without the -c run-time flag) this section of the YAML file is entirely ignored.

Gravity

The behaviour of the self-gravity solver can be modified by the parameters provided in the Gravity section. The theory document puts these parameters into the context of the equations being solved. We give a brief overview here.

  • The Plummer-equivalent co-moving softening length used for all dark matter particles \(\epsilon_{\rm com,DM}\): comoving_DM_softening,
  • The Plummer-equivalent co-moving softening length used for all baryon particles (gas, stars, BHs) \(\epsilon_{\rm com,bar}\): comoving_baryon_softening,
  • The Plummer-equivalent maximal physical softening length used for all dark matter particles \(\epsilon_{\rm max,DM}\): max_physical_DM_softening,
  • The Plummer-equivalent maximal physical softening length used for all baryon particles (gas, stars, BHs) \(\epsilon_{\rm max,bar}\): max_physical_baryon_softening,

At any redshift \(z\), the Plummer-equivalent softening length used by the code will be \(\epsilon=\min(\epsilon_{max}, \frac{\epsilon_{com}}{z+1})\). The same calculation is performed independently for the dark matter and baryon particles. All the softening quantities are expressed in internal units. Calculations that only involve DM or baryons can leave the unused quantities out of the parameter file. For non-cosmological runs, only the physical softening lengths need to be supplied.

In case of zoom simulations, the softening of the additional, more massive, background particles is specified via the parameter softening_ratio_background. Since these particles will typically have different masses to degrade the resolution away from the zoom-in region, the particles won’t have a single softening value. Instead, we specify the fraction of the mean inter-particle separation to use. The code will then derive the softening length of each particle assuming the mean density of the Universe. That is \(\epsilon_{\rm background} = f\sqrt[3]{\frac{m}{\Omega_m\rho_{\rm crit}}}\), where \(f\) is the user-defined value (typically of order 0.05).

The accuracy of the gravity calculation is governed by the following four parameters:

  • The multipole acceptance criterion: MAC
  • The fixed opening angle used in the geometric MAC \(\theta_{\rm cr}\): theta_cr,
  • The accuracy criterion used in the adaptive MAC: \(\epsilon_{\rm fmm}\): epsilon_fmm,
  • The time-step size pre-factor \(\eta\): eta,

The first three parameters govern the way the Fast-Multipole method tree-walk is done (see the theory documents for full details). The MAC parameter can take two values: adaptive or geometric. In the first case, the tree recursion decision is based on the estimated accelerations that a given tree node will produce, trying to recurse to levels where the fractional contribution of the accelerations to the cell is less than \(\epsilon_{\rm fmm}\). In the second case, a fixed Barnes-Hut-like opening angle \(\theta_{\rm cr}\) is used.

The time-step of a given particle is given by \(\Delta t = \sqrt{2\eta\epsilon_i/|\overrightarrow{a}_i|}\), where \(\overrightarrow{a}_i\) is the particle’s acceleration and \(\epsilon_i\) its (spline) softening length. Power et al. (2003) recommend using \(\eta=0.025\).

The last tree-related parameters are:

  • The tree rebuild frequency: rebuild_frequency.
  • Whether or not to use the approximate gravity from the FMM tree below the softening scale: use_tree_below_softening (default: 0)
  • Whether or not the truncated force estimator in the adaptive tree-walk considers the exponential mesh-related cut-off: allow_truncation_in_MAC (default: 0)

The tree rebuild frequency is an optional parameter defaulting to \(0.01\). It is used to trigger the re-construction of the tree every time a fraction of the particles have been integrated (kicked) forward in time. The other two parameters default to good all-around choices. See the theory documentation about their exact effects.

Simulations using periodic boundary conditions use additional parameters for the Particle-Mesh part of the calculation. The last five are optional:

  • The number cells along each axis of the mesh \(N\): mesh_side_length,
  • The mesh smoothing scale in units of the mesh cell-size \(a_{\rm smooth}\): a_smooth (default: 1.25),
  • The scale above which the short-range forces are assumed to be 0 (in units of the mesh cell-size multiplied by \(a_{\rm smooth}\)) \(r_{\rm cut,max}\): r_cut_max (default: 4.5),
  • The scale below which the short-range forces are assumed to be exactly Newtonian (in units of the mesh cell-size multiplied by \(a_{\rm smooth}\)) \(r_{\rm cut,min}\): r_cut_min (default: 0.1),

For most runs, the default values can be used. Only the number of cells along each axis needs to be specified. The remaining three values are best described in the context of the full set of equations in the theory documents.

As a summary, here are the values used for the EAGLE \(100^3~{\rm Mpc}^3\) simulation:

# Parameters for the self-gravity scheme for the EAGLE-100 box
Gravity:
  eta:                    0.025
  MAC:                    adaptive
  theta_cr:               0.6
  epsilon_fmm:            0.001
  mesh_side_length:       512
  comoving_DM_softening:         0.0026994  # 0.7 proper kpc at z=2.8.
  max_physical_DM_softening:     0.0007     # 0.7 proper kpc
  comoving_baryon_softening:     0.0026994  # 0.7 proper kpc at z=2.8.
  max_physical_baryon_softening: 0.0007     # 0.7 proper kpc
  rebuild_frequency:      0.01   # Default optional value
  a_smooth:          1.25        # Default optional value
  r_cut_max:         4.5         # Default optional value
  r_cut_min:         0.1         # Default optional value
  use_tree_below_softening: 0    # Default optional value
  allow_truncation_in_MAC:  0    # Default optional value

SPH

The SPH section is used to set parameters that describe the SPH calculations. There are some scheme-specific values that are detailed in the Hydrodynamics Schemes section. The common parameters are detailed below.

In all cases, users have to specify two values:

  • The smoothing length in terms of mean inter-particle separation: resolution_eta
  • The CFL condition that enters the time-step calculation: CFL_condition

These quantities are dimensionless. The first, resolution_eta, specifies how smooth the simulation should be, and is used here instead of the number of neighbours to smooth over as this also takes into account non-uniform particle distributions. A value of 1.2348 gives approximately 48 neighbours in 3D with the cubic spline kernel. More information on the choices behind these parameters can be found in Dehnen & Aly 2012.

The second quantity, the CFL condition, specifies how accurate the time integration should be and enters as a pre-factor into the hydrodynamics time-step calculation. This factor should be strictly bounded by 0 and 1, and typically takes a value of 0.1 for SPH calculations.

The next set of parameters deal with the calculation of the smoothing lengths directly and are all optional:

  • Whether to use or not the mass-weighted definition of the SPH number of neighbours: use_mass_weighted_num_ngb (Default: 0)
  • The (relative) tolerance to converge smoothing lengths within: h_tolerance (Default: 1e-4)
  • The maximal smoothing length in internal units: h_max (Default: FLT_MAX)
  • The minimal allowed smoothing length in terms of the gravitational softening: h_min_ratio (Default: 0.0, i.e. no minimum)
  • The maximal (relative) allowed change in volume over one time-step: max_volume_change (Default: 1.4)
  • The maximal number of iterations allowed to converge the smoothing lengths: max_ghost_iterations (Default: 30)

These parameters all set the accuracy of the smoothing lengths in various ways. The first one specified what definition of the local number density of particles to use. By default, we use

\[n_i = \sum_j W(\|\mathbf{r}_i - \mathbf{r}_j\|, h_i)\]

but switching on the use_mass_weighted_num_ngb flag changes the defintion to:

\[n_i = \frac{\rho_i}{m_i}\]

where the density has been computed in the traditional SPH way (i.e. \(\rho_i = \sum_j m_j W(\|\mathbf{r}_i - \mathbf{r}_j\|, h_i)\)). Note that in the case where all the particles in the simulation have the same mass, the two definitions lead to the same number density value.

We dot not recommend using this alternative neighbour number definition in production runs. It is mainly provided for backward compatibility with earlier simulations.

The second one, the relative tolerance for the smoothing length, specifies the convergence criteria for the smoothing length when using the Newton-Raphson scheme. This works with the maximal number of iterations, max_ghost_iterations (so called because the smoothing length calculation occurs in the ghost task), to ensure that the values of the smoothing lengths are consistent with the local number density. We solve:

\[(\eta \gamma)^{n_D} = n_i\]

with \(\gamma\) the ratio of smoothing length to kernel support (this is fixed for a given kernel shape), \(n_D\) the number of spatial dimensions, \(\eta\) the value of resolution_eta, and \(n_i\) the local number density. We adapt the value of the smoothing length, \(h\), to be consistent with the number density.

The maximal smoothing length, by default, is set to FLT_MAX, and if set prevents the smoothing length from going beyond h_max (in internal units) during the run, irrespective of the above equation. The minimal smoothing length is set in terms of the gravitational softening, h_min_ratio, to prevent the smoothing length from going below this value in dense environments. This will lead to smoothing over more particles than specified by \(\eta\).

The optional parameter particle_splitting (Default: 0) activates the splitting of overly massive particles into 2. By switching this on, the code will loop over all the particles at every tree rebuild and split the particles with a mass above a fixed threshold into two copies that are slightly shifted (by a randomly orientated vector of norm \(0.2h\)). Their masses and other relevant particle-carried quantities are then halved. The mass threshold for splitting is set by the parameter particle_splitting_mass_threshold which is specified using the internal unit system. The IDs of the newly created particles can be either drawn randomly by setting the parameter generate_random_ids (Default: 0) to \(1\). When this is activated, there is no check that the newly generated IDs do not clash with any other pre-existing particle. If this option is set to \(0\) (the default setting) then the new IDs are created in increasing order from the maximal pre-existing value in the simulation, hence preventing any clash.

The final set of parameters in this section determine the initial and minimum temperatures of the particles.

  • The initial temperature of all particles: initial_temperature (Default: InternalEnergy from the initial conditions)
  • The minimal temperature of any particle: minimal_temperature (Default: 0)
  • The mass fraction of hydrogen used to set the initial temperature: H_mass_fraction (Default: 0.755)
  • The ionization temperature (from neutral to ionized) for primordial gas, again used in this conversion: H_ionization_temperature (Default: 1e4)

These parameters, if not present, are set to the default values. The initial temperature is used, along with the hydrogen mass fraction and ionization temperature, to set the initial internal energy per unit mass (or entropy per unit mass) of the particles.

Throughout the run, if the temperature of a particle drops below minimal_temperature, the particle has energy added to it such that it remains at that temperature. The run is not terminated prematurely. The temperatures specified in this section are in internal units.

The full section to start a typical cosmological run would be:

SPH:
  resolution_eta:                     1.2
  CFL_condition:                      0.1
  h_tolerance:                        1e-4
  h_min_ratio:                        0.1
  h_max:                              1.    # U_L
  initial_temperature:                273   # U_T
  minimal_temperature:                100   # U_T
  H_mass_fraction:                    0.755
  H_ionization_temperature:           1e4   # U_T
  particle_splitting:                 1
  particle_splitting_mass_threshold:  5e-3  # U_M

Stars

The Stars section is used to set parameters that describe the Stars calculations when doing feedback or enrichment. Note that if stars only act gravitationally (i.e. SWIFT is run without --feedback) no parameters in this section are used.

The first four parameters are related to the neighbour search:

  • The (relative) tolerance to converge smoothing lengths within: h_tolerance (Default: same as SPH scheme)
  • The maximal smoothing length in internal units: h_max (Default: same as SPH scheme)
  • The minimal allowed smoothing length in terms of the gravitational softening: h_min_ratio (Default: same as SPH scheme)
  • The maximal (relative) allowed change in volume over one time-step: max_volume_change (Default: same as SPH scheme)

These four parameters are optional and will default to their SPH equivalent if left unspecified. That is the value specified by the user in that section or the default SPH value if left unspecified there as well.

The next four parameters govern the time-step size choices for star particles. By default star particles get their time-step sizes set solely by the condition based on gravity. Additional criteria can be applied by setting some of the following parameters (the actual time-step size is then the minimum of this criterion and of the gravity criterion):

  • Time-step size for young stars in Mega-years: max_timestep_young_Myr (Default: FLT_MAX)
  • Time-step size for old stars in Mega-years: max_timestep_old_Myr (Default: FLT_MAX)
  • Age transition from young to old in Mega-years: timestep_age_threshold_Myr (Default: FLT_MAX)
  • Age above which no time-step limit is applied in Mega-years: timestep_age_threshold_unlimited_Myr (Default: 0)

Star particles with ages above the unlimited threshold only use the gravity condition. Star particles with ages below that limit use either the young or old time-step sizes based on their ages. These parameters effectively allow for three different age brackets with the last age bracket imposing no time-step length.

The remaining parameters can be used to overwrite the birth time (or scale-factor), birth density and birth temperatures (if these quantities exist) of the stars that were read from the ICs. This can be useful to start a simulation with stars already of a given age or with specific (uniform and non-0) properties at birth. The parameters are:

  • Whether or not to overwrite all the birth times: overwrite_birth_time (Default: 0)
  • The value to use: birth_time
  • Whether or not to overwrite all the birth densities: overwrite_birth_density (Default: 0)
  • The value to use: birth_density
  • Whether or not to overwrite all the birth temperatures: overwrite_birth_temperature (Default: 0)
  • The value to use: birth_temperature

Note that if the birth time is set to -1 then the stars will never enter any feedback or enrichment loop. When these values are not specified, SWIFT will start and use the birth times specified in the ICs. If no values are given in the ICs, the stars’ birth times will be zeroed, which can cause issues depending on the type of run performed.

Time Integration

The TimeIntegration section is used to set some general parameters related to time integration. In all cases, users have to provide a minimal and maximal time-step size:

  • Maximal time-step size: dt_max
  • Minimal time-step size: dt_min

These quantities are expressed in internal units. All particles will have their time-step limited by the maximal value on top of all the other criteria that may apply to them (gravity acceleration, Courant condition, etc.). If a particle demands a time-step size smaller than the minimum, SWIFT will abort with an error message. This is a safe-guard against simulations that would never complete due to the number of steps to run being too large. Note that in cosmological runs, the meaning of these variables changes slightly. They do not correspond to differences in time but in logarithm of the scale-factor. For these runs, the simulation progresses in jumps of \(\Delta\log(a)\). dt_max is then the maximally allowed change in \(\Delta\log(a)\) allowed for any particle in the simulation. This behaviour mimics the variables of the smae name in the Gadget code.

When running a non-cosmological simulation, the user also has to provide the time of the start and the time of the end of the simulation:

  • Start time: time_begin
  • End time: time_end

Both are expressed in internal units. The start time is typically set to 0 but SWIFT can handle any value here. For cosmological runs, these values are ignored and the start- and end-points of the runs are specified by the start and end scale-factors in the cosmology section of the parameter file.

Additionally, when running a cosmological volume, advanced users can specify the value of the dimensionless pre-factor entering the time-step condition linked with the motion of particles with respect to the background expansion and mesh size. See the theory document for the exact equations. Note that we explicitly ignore the Header/Time attribute in initial conditions files, and only read the start and end times or scale factors from the parameter file.

  • Dimensionless pre-factor of the maximal allowed displacement: max_dt_RMS_factor (default: 0.25)

This value rarely needs altering. See the theory documents for its precise meaning.

A full time-step section for a non-cosmological run would be:

TimeIntegration:
  time_begin:   0    # Start time in internal units.
  time_end:     10.  # End time in internal units.
  dt_max:       1e-2
  dt_min:       1e-6

Whilst for a cosmological run, one would need:

TimeIntegration:
  dt_max:            1e-4
  dt_min:            1e-10
  max_dt_RMS_factor: 0.25     # Default optional value

Initial Conditions

The InitialConditions section of the parameter file contains all the options related to the initial conditions. The main two parameters are

  • The name of the initial conditions file: file_name,
  • Whether the problem uses periodic boundary conditions or not: periodic.

The file path is relative to where the code is being executed. These parameters can be complemented by some optional values to drive some specific behaviour of the code.

  • Whether to generate gas particles from the DM particles: generate_gas_in_ics (default: 0),
  • Whether to activate an additional clean-up of the SPH smoothing lengths: cleanup_smoothing_lengths (default: 0)

The procedure used to generate gas particles from the DM ones is outlined in the theory documents and is too long for a full description here. The cleaning of the smoothing lengths is an expensive operation but can be necessary in the cases where the initial conditions are of poor quality and the values of the smoothing lengths are far from the values they should have.

When starting from initial conditions created for Gadget, some additional flags can be used to convert the values from h-full to h-free and remove the additional \(\sqrt{a}\) in the velocities:

  • Whether to re-scale all the fields to remove powers of h from the quantities: cleanup_h_factors (default: 0),
  • Whether to re-scale the velocities to remove the \(\sqrt{a}\) assumed by Gadget : cleanup_velocity_factors (default: 0).

The h-factors are self-consistently removed according to their units and this is applied to all the quantities irrespective of particle types. The correct power of h is always calculated for each quantity.

Finally, SWIFT also offers these options:

  • A factor to re-scale all the smoothing-lengths by a fixed amount: smoothing_length_scaling (default: 1.),
  • A shift to apply to all the particles: shift (default: [0.0,0.0,0.0]),
  • Whether to replicate the box along each axis: replicate (default: 1).
  • Whether to re-map the IDs to the range [0, N] and hence discard the original IDs from the IC file: remap_ids (default: 0).

The shift is expressed in internal units. The option to replicate the box is especially useful for weak-scaling tests. When set to an integer >1, the box size is multiplied by this integer along each axis and the particles are duplicated and shifted such as to create exact copies of the simulation volume.

The remapping of IDs is especially useful in combination with the option to generate increasing IDs when splitting gas particles as it allows for the creation of a compact range of IDs beyond which the new IDs generated by splitting can be safely drawn from. Note that, when remap_ids is switched on the ICs do not need to contain a ParticleIDs field.

The full section to start a DM+hydro run from Gadget DM-only ICs would be:

InitialConditions:
  file_name:  my_ics.hdf5
  periodic:                    1
  cleanup_h_factors:           1
  cleanup_velocity_factors:    1
  generate_gas_in_ics:         1
  cleanup_smoothing_lengths:   1

Physical Constants

For some idealised test it can be useful to overwrite the value of some physical constants; in particular the value of the gravitational constant. SWIFT offers an optional parameter to overwrite the value of \(G_N\).

PhysicalConstants:
  G:   1

Note that this set \(G\) to the specified value in the internal system of units. Setting a value of 1 when using the system of units (10^10 Msun, Mpc, km/s) will mean that \(G_N=1\) in these units [2] instead of the normal value \(G_N=43.00927\).

This option is only used for specific tests and debugging. This entire section of the YAML file can typically be left out. More constants may be handled in the same way in future versions.

Snapshots

The Snapshots section of the parameter file contains all the options related to the dump of simulation outputs in the form of HDF5 Snapshots. The main parameter is the base name that will be used for all the outputs in the run:

  • The base name of the HDF5 snapshots: basename.

This name will then be appended by an under-score and 4 digits followed by .hdf5 (e.g. base_name_1234.hdf5). The 4 digits are used to label the different outputs, starting at 0000. In the default setup the digits simply increase by one for each snapshot. However, if the optional parameter int_time_label_on is switched on, then we use 6 digits and these will the physical time of the simulation rounded to the nearest integer (e.g. base_name_001234.hdf5) [3].

The time of the first snapshot is controlled by the two following options:

  • Time of the first snapshot (non-cosmological runs): time_first,
  • Scale-factor of the first snapshot (cosmological runs): scale_factor_first.

One of those two parameters has to be provided depending on the type of run. In the case of non-cosmological runs, the time of the first snapshot is expressed in the internal units of time. Users also have to provide the difference in time (or scale-factor) between consecutive outputs:

  • Time difference between consecutive outputs: delta_time.

In non-cosmological runs this is also expressed in internal units. For cosmological runs, this value is multiplied to obtain the scale-factor of the next snapshot. This implies that the outputs are equally spaced in \(\log(a)\) (See Output List to have snapshots not regularly spaced in time).

The location and naming of the snapshots is altered by the following options:

  • Directory in which to write snapshots: subdir. (default: empty string).

If this is set then the full path to the snapshot files will be generated by taking this value and appending a slash and then the snapshot file name described above - e.g. subdir/base_name_1234.hdf5. The directory is created if necessary. Any VELOCIraptor output produced by the run is also written to this directory.

When running the code with structure finding activated, it is often useful to have a structure catalog written at the same simulation time as the snapshots. To activate this, the following parameter can be switched on:

  • Run VELOCIraptor every time a snapshot is dumped: invoke_stf (default: 0).

This produces catalogs using the options specified for the stand-alone VELOCIraptor outputs (see the section Structure finding (VELOCIraptor)) but with a base name and output number that matches the snapshot name (e.g. stf_base_name_1234.hdf5) irrespective of the name specified in the section dedicated to VELOCIraptor. Note that the invocation of VELOCIraptor at every dump is done additionally to the stand-alone dumps that can be specified in the corresponding section of the YAML parameter file. When running with _more_ calls to VELOCIraptor than snapshots, gaps between snapshot numbers will be created to accommodate for the intervening VELOCIraptor-only catalogs.

When running over MPI, users have the option to split the snapshot over more than one file. This can be useful if the parallel-io on a given system is slow but has the drawback of producing many files per time slice. This is activated by setting the parameter:

  • Distributed snapshots over MPI: distributed (default: 0).

This option has no effect when running the non-MPI version of the code. Note also that unlike other codes, SWIFT does not let the users chose the number of individual files over which a snapshot is distributed. This is set by the number of MPI ranks used in a given run. The individual files of snapshot 1234 will have the name base_name_1234.x.hdf5 where when running on N MPI ranks, x runs from 0 to N-1.

Users can optionally specify the level of compression used by the HDF5 library using the parameter:

  • GZIP compression level of the HDF5 arrays: compression (default: 0).

The default level of 0 implies no compression and values have to be in the range \([0-9]\). This integer is passed to the i/o library and used for the loss-less GZIP compression algorithm. The compression is applied to all the fields in the snapshots. Higher values imply higher compression but also more time spent deflating and inflating the data. When compression is switched on the SHUFFLE filter is also applied to get higher compression rates. Note that up until HDF5 1.10.x this option is not available when using the MPI-parallel version of the i/o routines.

Finally, it is possible to specify a different system of units for the snapshots than the one that was used internally by SWIFT. The format is identical to the one described above (See the Internal Unit System section) and read:

  • a unit of length: UnitLength_in_cgs (default: InternalUnitSystem:UnitLength_in_cgs),
  • a unit of mass: UnitMass_in_cgs (default: InternalUnitSystem:UnitMass_in_cgs),
  • a unit of velocity UnitVelocity_in_cgs (default: InternalUnitSystem:UnitVelocity_in_cgs),
  • a unit of electric current UnitCurrent_in_cgs (default: InternalUnitSystem:UnitCurrent_in_cgs),
  • a unit of temperature UnitTemp_in_cgs (default: InternalUnitSystem:UnitTemp_in_cgs).

When unspecified, these all take the same value as assumed by the internal system of units. These are rarely used but can offer a practical alternative to converting data in the post-processing of the simulations.

For a standard cosmological run with structure finding activated, the full section would be:

Snapshots:
  basename:            output
  scale_factor_first:  0.02    # z = 49
  delta_time:          1.02
  invoke_stf:          1

Showing all the parameters for a basic non-cosmological hydro test-case, one would have:

Snapshots:
  basename:            sedov
  subdir:              snapshots
  time_first:          0.01
  delta_time:          0.005
  invoke_stf:          0
  int_time_label_on:   0
  compression:         3
  distributed:         1
  UnitLength_in_cgs:   1.  # Use cm in outputs
  UnitMass_in_cgs:     1.  # Use grams in outputs
  UnitVelocity_in_cgs: 1.  # Use cm/s in outputs
  UnitCurrent_in_cgs:  1.  # Use Ampere in outputs
  UnitTemp_in_cgs:     1.  # Use Kelvin in outputs

Some additional specific options for the snapshot outputs are described in the following pages:

Line-of-sight outputs

The LineOfSight section of the parameter file contains all the options related to the dump of simulation outputs in the form of HDF5 Line-of-sights outputs data to be processed by the SpecWizard tool (See Theuns et al. 1998, Tepper-Garcia et al. 2011). The parameters are:

LineOfSight:
  basename:            los
  scale_factor_first:  0.02    # Only used when running in cosmological mode
  delta_time:          1.02
  time_first:          0.01    # Only used when running in non-cosmological mode
  output_list_on:      0       # Overwrite the regular output times with a list of output times
  num_along_x:         0
  num_along_y:         0
  num_along_z:         100
  allowed_los_range_x: [0, 100.]   # Range along the x-axis where LoS along Y or Z are allowed
  allowed_los_range_y: [0, 100.]   # Range along the y-axis where LoS along X or Z are allowed
  allowed_los_range_z: [0, 100.]   # Range along the z-axis where LoS along X or Y are allowed
  range_when_shooting_down_x: 100. # Range along the x-axis of LoS along x
  range_when_shooting_down_y: 100. # Range along the y-axis of LoS along y
  range_when_shooting_down_z: 100. # Range along the z-axis of LoS along z

Equation of State (EoS)

The EoS section contains options for the equations of state. Multiple EoS can be used for Planetary Simulations, see Planetary Equations of State for more information.

To enable one or multiple of these EoS, the corresponding planetary_use_*: flag(s) must be set to 1 in the parameter file for a simulation, along with the path to any table files, which are provided with the planetary_*_table_file: parameters. This currently means that all EoS within each base type are prepared at once, which we intend to simplify in the future.

The data files for the tabulated EoS can be downloaded using the examples/EoSTables/get_eos_tables.sh script.

For the (non-planetary) isothermal EoS, the isothermal_internal_energy: parameter sets the thermal energy per unit mass.

EoS:
  isothermal_internal_energy: 20.26784  # Thermal energy per unit mass for the case of isothermal equation of state (in internal units).

  planetary_use_Til:    1   # (Optional) Whether to prepare the Tillotson EoS
  planetary_use_HM80:   0   # (Optional) Whether to prepare the Hubbard & MacFarlane (1980) EoS
  planetary_use_SESAME: 0   # (Optional) Whether to prepare the SESAME EoS
  planetary_use_ANEOS:  0   # (Optional) Whether to prepare the ANEOS EoS
                            # (Optional) Table file paths
  planetary_HM80_HHe_table_file:            ./EoSTables/HM80_HHe.txt
  planetary_HM80_ice_table_file:            ./EoSTables/HM80_ice.txt
  planetary_HM80_rock_table_file:           ./EoSTables/HM80_rock.txt
  planetary_SESAME_iron_table_file:         ./EoSTables/SESAME_iron_2140.txt
  planetary_SESAME_basalt_table_file:       ./EoSTables/SESAME_basalt_7530.txt
  planetary_SESAME_water_table_file:        ./EoSTables/SESAME_water_7154.txt
  planetary_SS08_water_table_file:          ./EoSTables/SS08_water.txt
  planetary_ANEOS_forsterite_table_file:    ./EoSTables/ANEOS_forsterite_S19.txt
  planetary_ANEOS_iron_table_file:          ./EoSTables/ANEOS_iron_S20.txt
  planetary_ANEOS_Fe85Si15_table_file:      ./EoSTables/ANEOS_Fe85Si15_S20.txt

Friends-Of-Friends (FOF)

The parameters are described separately on the page Friends-Of-Friends Parameters within the more general Friends-Of-Friends (FOF) Halo Finder description.

Statistics

Some additional specific options for the statistics outputs are described in the following page:

  • Output List (to have statistics outputs not evenly spaced in time).

Restarts

SWIFT can write check-pointing files and restart from them. The behaviour of this mechanism is driven by the options in the Restarts section of the YAML parameter file. All the parameters are optional but default to values that ensure a reasonable behaviour.

  • Whether or not to enable the dump of restart files: enable (default: 1).

This parameter acts a master-switch for the check-pointing capabilities. All the other options require the enable parameter to be set to 1.

  • Whether or not to save a copy of the previous set of check-pointing files: save (default: 1),
  • Whether or not to dump a set of restart file on regular exit: onexit (default: 0),
  • The wall-clock time in hours between two sets of restart files: delta_hours (default: 5.0).

Note that there is no buffer time added to the delta_hours value. If the system’s batch queue run time limit is set to 5 hours, the user must specify a smaller value to allow for enough time to safely dump the check-point files.

  • The sub-directory in which to store the restart files: subdir (default: restart),
  • The basename of the restart files: basename (default: swift)

If the directory does not exist, SWIFT will create it. When resuming a run, SWIFT, will look for files with the name provided in the sub-directory specified here. The files themselves are named basename_000001.rst where the basename is replaced by the user-specified name and the 6-digits number corresponds to the MPI-rank. SWIFT writes one file per MPI rank. If the save option has been activated, the previous set of restart files will be named basename_000000.rst.prev.

SWIFT can also be stopped by creating an empty file called stop in the directory where the restart files are written (i.e. the directory speicified by the parameter subdir). This will make SWIFT dump a fresh set of restart file (irrespective of the specified delta_time between dumps) and exit cleanly. One parameter governs this behaviour:

  • Number of steps between two checks for the presence of a stop file: stop_steps (default: 100).

The default value is chosen such that SWIFT does not need to poll the file-system to often, which can take a significant amount of time on distributed systems. For runs where the small time-steps take a much larger amount of time, a smaller value is recommended to allow for a finer control over when the code can be stopped.

Finally, SWIFT can automatically stop after a specified amount of wall-clock time. The code can also run a command when exiting in this fashion, which can be used, for instance, to interact with the batch queue system:

  • Maximal wall-clock run time in hours: max_run_time (default: 24.0),
  • Whether or not to run a command on exit: resubmit_on_exit (default: 0),
  • The command to run on exit: resubmit_command (default: ./resub.sh).

Note that no check is performed on the validity of the command to run. SWIFT simply calls system() with the user-specified command.

To run SWIFT, dumping check-pointing files every 6 hours and running for 24 hours after which a shell command will be run, one would use:

Restarts:
  enable:             1
  save:               1          # Keep copies
  onexit:             0
  subdir:             restart    # Sub-directory of the directory where SWIFT is run
  basename:           swift
  delta_hours:        5.0
  stop_steps:         100
  max_run_time:       24.0       # In hours
  resubmit_on_exit:   1
  resubmit_command:   ./resub.sh

Scheduler

The Scheduler section contains various parameters that control how the cell tree is configured and defines some values for the related tasks. In general these should be considered as tuning parameters, both for speed and memory use.

nr_queues: 0

Defines the number of task queues used. These are normally set to one per thread and should be at least that number.

A number of parameters decide how the cell tree will be split into sub-cells, according to the number of particles and their expected interaction count, and the type of interaction. These are:

cell_max_size:             8000000
cell_sub_size_pair_hydro:  256000000
cell_sub_size_self_hydro:  32000
cell_sub_size_pair_grav:   256000000
cell_sub_size_self_grav:   32000
cell_sub_size_pair_stars:  256000000
cell_sub_size_self_stars:  32000
cell_split_size:           400

when possible cells that exceed these constraints will be split into a further level of sub-cells. So for instance a sub-cell should not contain more than 400 particles (this number defines the scale of most N*N interactions).

To control the number of self-gravity tasks we have the parameter:

cell_subdepth_diff_grav:   4

which stops these from being done at the scale of the leaf cells, of which there can be a large number. In this case cells with gravity tasks must be at least 4 levels above the leaf cells (when possible).

To control the depth at which the ghost tasks are placed, there are two parameters (one for the gas, one for the stars). These specify the maximum number of particles allowed in such a task before splitting into finer ones. A similar parameter exists for the cooling tasks, which can be useful to tweak for models in which the cooling operations are expensive. These three parameters are:

engine_max_parts_per_ghost:    1000
engine_max_sparts_per_ghost:   1000
engine_max_parts_per_cooling: 10000

Extra space is required when particles are created in the system (to the time of the next rebuild). These are controlled by:

cell_extra_parts:          0
cell_extra_gparts:         0
cell_extra_sparts:         400

The number of top-level cells is controlled by the parameter:

max_top_level_cells:       12

this is the number per dimension, we will have 12x12x12 cells. There must be at least 3 top-level cells per dimension.

The number of top-level cells should be set so that the number of particles per cell is not too large, this is particularly important when using MPI as this defines the maximum size of cell exchange and also the size of non-local cells (these are used for cell interactions with local cells), which can have a large influence on memory use. Best advice for this is to at least scale for additional nodes.

The memory used for holding the task and task-link lists needs to be pre-allocated, but cannot be pre-calculated, so we have the two parameters:

tasks_per_cell:            0.0
links_per_tasks:           10

which are guesses at the mean numbers of tasks per cell and number of links per task. The tasks_per_cell value will be conservatively guessed when set to 0.0, but you will be able to save memory by setting a value. The way to get a better estimate is to run SWIFT with verbose reporting on (`--verbose=1`) and check for the lines that report the `per cell` or with MPI maximum per cell` values. This number can vary as the balance between MPI ranks does, so it is probably best to leave some head room.

If these are exceeded you should get an obvious error message.

Finally the parameter:

mpi_message_limit:         4096

Defines the size (in bytes) below which MPI communication will be sent using non-buffered calls. These should have lower latency, but how that works or is honoured is an implementation question.

Domain Decomposition:

This section determines how the top-level cells are distributed between the ranks of an MPI run. An ideal decomposition should result in each rank having a similar amount of work to do, so that all the ranks complete at the same time. Achieving a good balance requires that SWIFT is compiled with either the ParMETIS or METIS libraries. ParMETIS is an MPI version of METIS, so is preferred for performance reasons.

When we use ParMETIS/METIS the top-level cells of the volume are considered as a graph, with a cell at each vertex and edges that connect the vertices to all the neighbouring cells (so we have 26 edges connected to each vertex). Decomposing such a graph into domains is known as partitioning, so in SWIFT we refer to domain decomposition as partitioning.

This graph of cells can have weights associated with the vertices and the edges. These weights are then used to guide the partitioning, seeking to balance the total weight of the vertices and minimize the weights of the edges that are cut by the domain boundaries (known as the edgecut). We can consider the edge weights as a proxy for the exchange of data between cells, so minimizing this reduces communication.

The Initial Partition:

When SWIFT first starts it reads the initial conditions and then does an initial distribution of the top-level cells. At this time the only information available is the cell structure and, by geometry, the particles each cell should contain. The type of partitioning attempted is controlled by the:

DomainDecomposition:
  initial_type:

parameter. Which can have the values memory, edgememory, region, grid or vectorized:

  • edgememory

This is the default if METIS or ParMETIS is available. It performs a partition based on the memory use of all the particles in each cell. The total memory per cell is used to weight the cell vertex and all the associated edges. This attempts to equalize the memory used by all the ranks but with some consideration given to the need to not cut dense regions (by also minimizing the edge cut). How successful this attempt is depends on the granularity of cells and particles and the number of ranks, clearly if most of the particles are in one cell, or a small region of the volume, balance is impossible or difficult. Having more top-level cells makes it easier to calculate a good distribution (but this comes at the cost of greater overheads).

  • memory

This is like edgememory, but doesn’t include any edge weights, it should balance the particle memory use per rank more exactly (but note effects like the numbers of cells per rank will also have an effect, as that changes the need for foreign cells).

  • region

The one other METIS/ParMETIS option is “region”. This attempts to assign equal numbers of cells to each rank, with the surface area of the regions minimised.

If ParMETIS and METIS are not available two other options are possible, but will give a poorer partition:

  • grid

Split the cells into a number of axis aligned regions. The number of splits per axis is controlled by the:

initial_grid

parameter. It takes an array of three values. The product of these values must equal the number of MPI ranks. If not set a suitable default will be used.

  • vectorized

Allocate the cells on the basis of proximity to a set of seed positions. The seed positions are picked every nranks along a vectorized cell list (1D representation). This is guaranteed to give an initial partition for all cases when the number of cells is greater equal to the number of MPI ranks, so can be used if the others fail. Don’t use this.

If ParMETIS and METIS are not available then only an initial partition will be performed. So the balance will be compromised by the quality of the initial partition.

Repartitioning:

When ParMETIS or METIS is available we can consider adjusting the balance during the run, so we can improve from the initial partition and also track changes in the run that require a different balance. The initial partition is usually not optimal as although it may have balanced the distribution of particles it has not taken account of the fact that different particles types require differing amounts of processing and we have not considered that we also need to do work requiring communication between cells. This latter point is important as we are running an MPI job, as inter-cell communication may be very expensive.

There are a number of possible repartition strategies which are defined using the:

DomainDecomposition:
  repartition_type:

parameter. The possible values for this are none, fullcosts, edgecosts, memory, timecosts.

  • none

Rather obviously, don’t repartition. You are happy to run with the initial partition.

  • fullcosts

Use computation weights derived from the running tasks for the vertex and edge weights. This is the default.

  • edgecosts

Only use computation weights derived from the running tasks for the edge weights.

  • memory

Repeat the initial partition with the current particle positions re-balancing the memory use.

  • timecosts

Only use computation weights derived from the running tasks for the vertex weights and the expected time the particles will interact in the cells as the edge weights. Using time as the edge weight has the effect of keeping very active cells on single MPI ranks, so can reduce MPI communication.

The computation weights are actually the measured times, in CPU ticks, that tasks associated with a cell take. So these automatically reflect the relative cost of the different task types (SPH, self-gravity etc.), and other factors like how well they run on the current hardware and are optimized by the compiler used, but this means that we have a constraint on how often we can consider repartitioning, namely when all (or nearly all) the tasks of the system have been invoked in a step. To control this we have the:

minfrac:     0.9

parameter. Which defines the minimum fraction of all the particles in the simulation that must have been actively updated in the last step, before repartitioning is considered.

That then leaves the question of when a run is considered to be out of balance and should benefit from a repartition. That is controlled by the:

trigger:          0.05

parameter. This value is the CPU time difference between MPI ranks, as a fraction, if less than this value a repartition will not be done. Repartitioning can be expensive not just in CPU time, but also because large numbers of particles can be exchanged between MPI ranks, so is best avoided.

If you are using ParMETIS there additional ways that you can tune the repartition process.

METIS only offers the ability to create a partition from a graph, which means that each solution is independent of those that have already been made, that can make the exchange of particles very large (although SWIFT attempts to minimize this), however, using ParMETIS we can use the existing partition to inform the new partition, this has two algorithms that are controlled using:

adaptive:         1

which means use adaptive repartition, otherwise simple refinement. The adaptive algorithm is further controlled by the:

itr:              100

parameter, which defines the ratio of inter node communication time to data redistribution time, in the range 0.00001 to 10000000.0. Lower values give less data movement during redistributions. The best choice for these can only be determined by experimentation (the gains are usually small, so not really recommended).

Finally we have the parameter:

usemetis:         0

Forces the use of the METIS API, probably only useful for developers.

Fixed cost repartitioning:

So far we have assumed that repartitioning will only happen after a step that meets the minfrac: and trigger: criteria, but we may want to repartition at some arbitrary steps, and indeed do better than the initial partition earlier in the run. This can be done using fixed cost repartitioning.

Fixed costs are output during each repartition step into the file partition_fixed_costs.h, this should be created by a test run of your full simulation (with possibly with a smaller volume, but all the physics enabled). This file can then be used to replace the same file found in the src/ directory and SWIFT should then be recompiled. Once you have that, you can use the parameter:

use_fixed_costs:  1

to control whether they are used or not. If enabled these will be used to repartition after the second step, which will generally give as good a repartition immediately as you get at the first unforced repartition.

Also once these have been enabled you can change the trigger value to numbers greater than 2, and repartitioning will be forced every trigger steps. This latter option is probably only useful for developers, but tuning the second step to use fixed costs can give some improvements.

Structure finding (VELOCIraptor)

This section describes the behaviour of the on-the-fly structure finding using the VELOCIraptor library (see VELOCIraptor Interface). The section is named StructureFinding and also governs the behaviour of the structure finding code when invoked at snapshots dumping time via the parameter Snapshots:invoke_stf.

The main parameters are:

  • The VELOCIraptor parameter file to use for the run: config_file_name,
  • The directory in which the structure catalogs will be written: basename.

Both these parameters must always be specified when running SWIFT with on-the-fly calls to the structure finding code. In particular, when only running VELOCIraptor when snapshots are written, nothing more is necessary and one would use:

Snapshots:
  invoke_stf:        1                              # We want VELOCIraptor to be called when snapshots are dumped.
  # ...
  # Rest of the snapshots properties

StructureFinding:
  config_file_name:  my_stf_configuration_file.cfg  # See the VELOCIraptor manual for the content of this file.
  basename:          ./haloes/                      # Write the catalogs in this sub-directory

If one additionally want to call VELOCIraptor at times not linked with snapshots, the additional parameters need to be supplied.

The time of the first call is controlled by the two following options:

  • Time of the first call to VELOCIraptor (non-cosmological runs): time_first,
  • Scale-factor of the first call to VELOCIraptor (cosmological runs): scale_factor_first.

One of those two parameters has to be provided depending on the type of run. In the case of non-cosmological runs, the time of the first call is expressed in the internal units of time. Users also have to provide the difference in time (or scale-factor) between consecutive outputs:

  • Time difference between consecutive outputs: delta_time.

In non-cosmological runs this is also expressed in internal units. For cosmological runs, this value is multiplied to obtain the scale-factor of the next call. This implies that the outputs are equally spaced in \(\log(a)\) (See Output List to have calls not regularly spaced in time).

Since VELOCIraptor produces many small output files when running with MPI, it can be useful to make a separate directory for each output time:

  • Base name of directory created for each VELOCIraptor output: subdir_per_output (default: empty string).

If this is set then a new directory is created each time VELOCIraptor is run. The directory name will be subdir_per_output followed by the same output number used in the filenames. Note that this directory is relative to the subdir parameter from the Snapshots section if that is set.

By default this is an empty string, which means that all VELOCIraptor outputs will be written to a single directory.

Showing all the parameters for a basic cosmologica test-case, one would have:

StructureFinding:
 config_file_name:     my_stf_configuration_file.cfg  # See the VELOCIraptor manual for the content of this file.
 basename:             haloes                         # Base name for VELOCIraptor output files
 subdir_per_output:    stf                            # Make a stf_XXXX subdirectory for each output
 scale_factor_first:   0.1                            # Scale-factor of the first output
 delta_time:           1.1                            # Delta log-a between outputs

Gravity Force Checks

By default, when the code is configured with --enable-gravity-force-checks, the “exact” forces of all active gparts are computed during each timestep.

To give a bit more control over this, you can select to only perform the exact force computation during the timesteps that all gparts are active, and/or only at the timesteps when a snapshot is being dumped, i.e.,

ForceChecks:
  only_when_all_active:   1    # Only compute exact forces during timesteps when all gparts are active.
  only_at_snapshots:      1    # Only compute exact forces during timesteps when a snapshot is being dumped.

If only_when_all_active:1 and only_at_snapshots:1 are enabled together, and all the gparts are not active during the timestep of the snapshot dump, the exact forces computation is performed on the first timestep at which all the gparts are active after that snapshot output timestep.


[1]The thorough reader (or overly keen SWIFT tester) would find that the speed of light is \(c=1.8026\times10^{12}\,\rm{fur}\,\rm{ftn}^{-1}\), Newton’s constant becomes \(G_N=4.896735\times10^{-4}~\rm{fur}^3\,\rm{fir}^{-1}\,\rm{ftn}^{-2}\) and Planck’s constant turns into \(h=4.851453\times 10^{-34}~\rm{fur}^2\,\rm{fir}\,\rm{ftn}^{-1}\).
[2]which would translate into a constant \(G_N=1.5517771\times10^{-9}~cm^{3}\,g^{-1}\,s^{-2}\) if expressed in the CGS system.
[3]This feature only makes sense for non-cosmological runs for which the internal time unit is such that when rounded to the nearest integer a sensible number is obtained. A use-case for this feature would be to compare runs over the same physical time but with different numbers of snapshots. Snapshots at a given time would always have the same set of digits irrespective of the number of snapshots produced before.