The concept of transprecision computing

For many years, computing systems rely on guaranteed numerical
precision of each step in complex computations. Moore's law sustains
exponential improvements in the semiconductor industry over several
decades for building computing infrastructure, from tiny Internet-of-
Things nodes, over personal smartphones, laptops or workstations, up
to large high performance computing (HPC) computing server centers.
With the paradigm of the "power wall", achievable improvements
start to saturate. To that end, the concept of transprecision computing
emerged, where existing over-conservative "precis" computing
assumptions are relaxed and replaced with more flexible and efficient
policies to gain performance.

Unfortunately, it is non-straight forward to adopt and integrate
general transprecision concepts into the variety of today's computing
infrastructure. The main challenge consists of leveraging domainspecific
knowledge and provide full solutions covering from physical
foundations over circuit-level up through the full software stack to the
application level.

This work focuses on how transprecision concepts improve general
computing. We identify and elaborate the standard number representations,
especially the one defined in the IEEE 754 floating-point
standard, as the enabler of low precision computing. We developed
lightweight libraries that allow integrating transprecision concepts
into algorithms. Finally, we focus on building automatized workflows
for specific problems, where the solution space is enlarged by multiple
orders of magnitude due to the various configurations of low precision.
We demonstrate how heuristic optimization strategies applied on top
of transprecision computing find near to optimal configurations of
approximated kernels in a short time.