Are Real(4) U,V,W coordinates sufficient ?

A peculiar case are the U,V,W coordinates. With very long baselines (20 km with ALMA) and short wavelengths (0.3 mm), one is tempted to say that U,V,W should be Real(8), as absolute baseline lengths are measured (and defined by the ultimate antenna stability) to a fraction of wavelength, say 40 $\mu$m for example. 40 $\mu$m/ 20 km equals $2\,10^{-9}$ which exceeds the precision of Real(4) numbers by 2 decimals...

So in principle, Real(4) are insufficient. But this is only true if a full astrometric calibration is required. GILDAS UV tables are intended for imaging purposes only, although this should include self-calibration.

Real(4) precision will only limit the field of view for a given angular resolution. The phase error due to a (relative) numerical precision $\delta$ is given by

$$\Delta \phi = 2 \pi u \delta \Delta X = 2\pi \frac{B}{\lambda} \delta \Delta X$$ (2)

so to obtain for example less than 0.1 radian (6 degree), we must have

$$\Delta X \le \frac{0.1 \lambda} {2 \pi B \delta}$$ (3)

Plugging extreme numbers ( $\delta = 10^{-7}$, $B = 20$ km, $\lambda = 0.3$ mm) we obtain $\Delta X \le 2.4\,10^{-3}$ radian, or $0.13^\circ$, which is quite a wide field of view.

So, the Real(4) precision do not allow to perform normal calibration (phase calibrators being in general more than a (few) degree(s) away), but is quite sufficient for even wide field imaging and self-calibration.