# Arbitrary floating-point types

Since DFTK is completely generic in the floating-point type in its routines, there is no reason to perform the computation using double-precision arithmetic (i.e.`Float64`

). Other floating-point types such as `Float32`

(single precision) are readily supported as well. On top of that we already reported^{[HLC2020]} calculations in DFTK using elevated precision from DoubleFloats.jl or interval arithmetic using IntervalArithmetic.jl. In this example, however, we will concentrate on single-precision computations with `Float32`

.

The setup of such a reduced-precision calculation is basically identical to the regular case, since Julia automatically compiles all routines of DFTK at the precision, which is used for the lattice vectors. Apart from setting up the model with an explicit cast of the lattice vectors to `Float32`

, there is thus no change in user code required:

```
using DFTK
# Setup silicon lattice
a = 10.263141334305942 # lattice constant in Bohr
lattice = a / 2 .* [[0 1 1.]; [1 0 1.]; [1 1 0.]]
Si = ElementPsp(:Si; psp=load_psp("hgh/lda/Si-q4"))
atoms = [Si, Si]
positions = [ones(3)/8, -ones(3)/8]
# Cast to Float32, setup model and basis
model = model_LDA(lattice, atoms, positions)
basis = PlaneWaveBasis(convert(Model{Float32}, model), Ecut=7, kgrid=[4, 4, 4])
# Run the SCF
scfres = self_consistent_field(basis, tol=1e-3);
```

```
n Energy log10(ΔE) log10(Δρ) Diag Δtime
--- --------------- --------- --------- ---- ------
1 -7.900509834290 -0.70 4.5 71.7ms
2 -7.905005931854 -2.35 -1.52 1.0 45.2ms
3 -7.905178546906 -3.76 -2.52 1.1 47.1ms
4 -7.905211448669 -4.48 -2.84 2.8 62.8ms
5 -7.905211925507 -6.32 -2.99 1.1 46.7ms
6 -7.905212402344 -6.32 -4.63 1.0 44.9ms
```

To check the calculation has really run in Float32, we check the energies and density are expressed in this floating-point type:

`scfres.energies`

```
Energy breakdown (in Ha):
Kinetic 3.1021390
AtomicLocal -2.1988561
AtomicNonlocal 1.7295821
Ewald -8.3978958
PspCorrection -0.2946220
Hartree 0.5530639
Xc -2.3986232
total -7.905212402344
```

`eltype(scfres.energies.total)`

`Float32`

`eltype(scfres.ρ)`

`Float32`

For more unusual floating-point types (like IntervalArithmetic or DoubleFloats), which are not directly supported in the standard `LinearAlgebra`

and `FFTW`

libraries one additional step is required: One needs to explicitly enable the generic versions of standard linear-algebra operations like `cholesky`

or `qr`

or standard `fft`

operations, which DFTK requires. THis is done by loading the `GenericLinearAlgebra`

package in the user script (i.e. just add ad `using GenericLinearAlgebra`

next to your `using DFTK`

call).

- HLC2020M. F. Herbst, A. Levitt, E. Cancès.
*A posteriori error estimation for the non-self-consistent Kohn-Sham equations*ArXiv 2004.13549