Abstract
The intrinsic computational efficiency (ICE) of silicon defines the upper limit of the amount of computation within a given technology and power envelope. The effective computational efficiency (ECE) and the effective computational density (ECD) of silicon, by taking computation, memory and communication into account, offer a more realistic upper bound for computation of a given technology. Among other factors, they consider how distributed the memory is, how much area is occupied by computation, memory and interconnect, and the geometric properties of 3-D stacked technology with through silicon vias (TSV) as vertical links. We use ECE and ECD to study the limits of performance under different memory distribution constraints of various 2-D and 3-D topologies, in current and future technology nodes. Among other results, our model shows that in a 35 nm technology a 16 stack 3-D system can, as a theoretical upper limit, obtain 3.4 times the performance of a 2-D system (8.8 Tera OPS vs 2.6 TOPS) at 70% reduced frequency (2.1 vs 3.7 GHz) on 1/8 the total area (50 vs 400 mm2).
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Notes
- 1.
Again, this is a simplification, because there are fewer operators but they are pipelined. In effect, 8 operations can be completed per cycle in the best case, motivating the number 8 that we use in this example.
- 2.
This figure depends less on architectural choices, but more on how information is coded, protected and compressed. Although a simplification, it is important to note that the same assumption is used for all architectures and the relative comparisons and main trends are not sensitive to the chosen value for switching activity.
- 3.
We assume registers and small register files close to the operators. Reading and writing of registers is not considered as memory access.
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Jantsch, A., Grange, M., Pamunuwa, D. (2011). The Promises and Limitations of 3-D Integration. In: Sheibanyrad, A., Pétrot, F., Jantsch, A. (eds) 3D Integration for NoC-based SoC Architectures. Integrated Circuits and Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7618-5_2
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