Section: Scientific Foundations

Applications

Whether its purpose is to design better operators or to make the best use of existing ones, computer arithmetic is strongly connected to applications. Some application domains are particularly in demand for high-quality arithmetic: high-performance computing (HPC) for floating-point, accounting for decimal, digital signal processing (DSP) for fixed-point, embedded systems for application-specific operators, cryptography for finite fields. Each domain comes with its specific constraints and quality metric. For example, cryptography has a specific need of resistance to attacks that impact the design of the operators themselves: a good operator for cryptography should have electromagnetic emissions and power consumption patterns independent of the data it manipulates. Another example is very large-scale HPC, which in some cases is reaching the limits of the accuracy provided by the prevalent double-precision floating-point arithmetic.

The regional (Rhône-Alpes) context is especially strong in embedded systems, with the Minalogic Competitivity Centre, major players such as STMicroelectronics, CEA and Inria, and strong startups such as Kalray. This is also true at the European level, with the HiPEAC European network of excellence. This network addresses hardware issues, but also software and compiler issues.

Indeed, the bridge between the application and the underlying hardware arithmetic is usually the compiler. Therefore, more and more arithmetic expertise should be integrated within the compiler. This goes on par with the current trend to automate arithmetic core generation. In the long term, working at the compiler level opens optimization perspective beyond what compilers traditionally perform, for instance ad-hoc generation and optimization in context of application-specific functional cores.

However, much of computer arithmetic research still focuses on the implementation of standard computing cores (such as elementary functions, linear algebra operators, or DSP filters), although this implementation is more and more automated as illustrated by projects such as ATLAS, Spiral, FFTW, and others.

Cryptography is an active field of research where there is a strong demand for efficient arithmetic operators. Practical schemes such as hash functions, public-key encryption and digital signatures may be used in constrained environments, leading to interesting arithmetic problems. Common examples are long integer arithmetic (RSA) and arithmetic of algebraic curves and finite fields of medium sizes (elliptic curve cryptography, including pairing-based cryptography), and small finite fields (code-based cryptography and lattice-based cryptography).