Section: Scientific Foundations

Technology

The traditional arithmetic operators are small, low-level, close-to-the-silicon hardware building bricks, and it is therefore important to anticipate the evolutions of the technology to address the new challenges these evolutions will bring.

It is well known now that Moore's law is no longer what it used to be. It continues to bring more transistors on a chip with each new generation, but the speed of these transistors no longer increases, and their power consumption no longer decreases. With more integration come also more reliability issues.

These are the driving forces behind the shift to multicore processors, and to coarser and more complex processing units in these processors: single-instruction, multiple data (SIMD) instructions, fused multiply-and-add, and soon dot-product operations. It also led to the emergence of new massively parallel computing devices such as graphical processing units (GPU) and field-programmable gate arrays (FPGAs). Both are increasingly being used for general purpose computing.

In the shift to massively parallel multicores and GPUs, the real challenge is how to program them. With respect to computer arithmetic, the main problem is the control of numerical precision: the order of the elementary operations is changed in a parallel execution, and will very often not even be deterministic if the main objective is performance. Assessing or guaranteeing numerical quality in the face of this uncertainty is an open problem, all the more as SIMD units and limited data bandwidth encourage the use of mixed precision where possible.

Concerning FPGAs, their programming model is that of a digital circuit which may be application-specific, and even change in the lifetime of an application. The challenge here is to design arithmetic operators that exploit this reconfigurability, which is their main strength. Whereas processor operators have to be as general-purpose as possible, in an FPGA an operator can be designed specifically for a given application's context. A related challenge is to convince application designers that they should use these operators, which may be radically different from those they are used to see in processors. The C-to-hardware community addresses this challenge by hiding the FPGA behind a classical C programming model. This raises the arithmetic problem of automatically extracting from a piece of C code a fragment that is suitable for implementation as an application-specific operator in an FPGA.

In traditional circuit design, power consumption is no longer a concern only for embedded, battery-powered applications: heat dissipation is now the main issue limiting the frequency of high-performance processors. The nature of power consumption is also changing: it used to be caused mostly by the active switching transistors, but leakage power is now as much of a concern. All this impacts the design of operators, but also their use: the energy-per-computation metric will become more and more important and will orient algorithmic choices, for instance inviting us to reassess the benefits of pre-computing values.

Finally, the industry is preparing to address, within a decade or two, the end of silicon-based Moore's law. In addition to the physical limits (it is believed so far that we need at least one atom to build a transistor), the raising cost of fabrication plants at each generation has led to increasing concentration in fewer and fewer foundries. There will therefore be an economic limit when the number of foundries is down to one. Silicon replacement alternative are emerging in laboratories, without a clear winner yet. When these alternatives reach the integrated circuit, they may be expected to drastically change the rules by which arithmetic operators are designed.