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# Will the mean year-over-year growth rate of the sum of teraflops in the TOP500 decline each 3-year period from 2025 to 2034?

In the seven decades since the invention of the point-contact transistor at Bell Labs, relentless progress in the development of semiconductor devices — Moore’s law — has been achieved despite regular warnings from industry observers about impending limits.

For the last three decades, the microelectronic industry has benefited enormously from the MOSFET miniaturisation. The shrinking of transistors to dimensions below 100 nm enables hundreds of millions transistors to be placed on a single chip. However, it is well-known that the currently most commonly used semiconductor device design method that has dominated for the past two-three decades, planar CMOS, runs into serious issues at the microscopic scale.

One of these issue arises from practical limits related to 'leak' current at small gate lengths (Thompson et al, 2006). This leakage current wastes power, raises the temperature and, if excessive, can cause the device to fail. Leakage becomes a serious problem when insulating barriers within transistors approach thicknesses of 3 nanometres or so (currently, in 2019, some transistors are ~ 5nm thick). Below that, leakage increases exponentially, rendering the device pretty near useless.

Additionally, a thermodynamical effect effect, the increasing of thermal fluctuations (Johnson-Nyquist noise), may result in increasingly many false bit occurences on the density of transistors on a chip (Kish, 2002).

To continue along at the exponential pace of performance progress, manufacturers have added more processors to each chip. For example, modern CPUs have between two and 32 cores, with most processors containing four to eight. In practice, exploiting eight cores means that a problem has to be broken down into eight pieces — which for many algorithms is difficult to impossible. In fact, Amdahl's law predicts that the theoretical speedup of even the most parallelizable program is limited to at most 20 times.

The sum of teraflops of the all 500 supercomputers in the TOP500 experienced an a geometric mean of 68.9% year-over-year growth since the first TOP500 publication in July of 1993. This growth rate amounts to a doubling time in total computational power of the top 500 supercomputers of roughly 16 months.

Progress in compute seemed to have peaked in the three year period ending in 2008 at an average of 128.85% year-over-year growth. The weakest growth was in the three year period ending in 2014, at an average of only 30.45%.

**Will the mean year-over-year growth rate of the sum of teraFLOPS in the TOP500 decline each 3-year period from 2025 to 2034?**

**Resolution**

The question resolves positively if the geometric mean of the year-over-year (yoy) growth rate (in %) of the sum of performance experienced over each three year period, from 2025 to 2034, is lower than the next. That is, it resolves positively, if:

geometric mean(growth rate from 2025 to 2028) > geometric mean(growth rate from 2028 to 2031) > geometric mean(growth rate from 2031 to 2034).

Performance here means performance on the High Performance Linpack (HPL) benchmark of the all 500 supercomputers in the TOP500, in teraFLOPS at Rmax (i.e. the maximal LINPACK performance achieved).

As the TOP500 publishes two lists each year, to maximally use all available information, a three-year period shall have six yoy growth rates: the yoy growth rate from:

- Jul year 0 to Jul year 1
- Nov year 0 to Nov year 1
- Jul year 1 to Jul year 2
- Nov year 1 to Nov year 2
- Jul year 2 to Jul year 3
- Nov year 2 to Nov year 3

For example, the three year period starting in 2025 ending in 2028 will have the following six growth rates:

- Jul 2025 to Jul 2026
- Nov 2025 to Nov 2026
- Jul 2026 to Jul 2027
- Nov 2026 to Nov 2027
- Jul 2027 to Jul 2028
- Nov 2027 to Nov 2028

The geometric mean is used, as opposed to the more common arithmetic mean, because this is appropriate for growth that multiplies over time.

**Data**

Historical data can be found here. Please make a copy by clicking "file" and then "make a copy" if you wish to edit it. If you make useful additions to the dataset, please share the file in the comments.

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