In this talk, we show how to control the numerical quality
of half precision computations using stochastic arithmetic. The CADNA
library that is used to estimate rounding errors and detect numerical
instabilities in floating-point codes has been improved and extended to
support half precision. A performance gain up to a factor 20 has been
observed wrt accuracy estimate in arbitrary precision. Furthermore,
we present how to generate codes mixing half, single, and double precision
with a requested accuracy on results providing a user-defined numerical
quality of the code. Control of robustness and floating-point auto-tuning
taking into account half precision have been successfully performed on
various numerical simulations, in particular a control application.