Conversion from Tebioctets per second to Pebioctets per second

Information about the Tebioctet per second (Tio/s)

The tebioctet per second is a unit of data transfer rate equal to 1,024 gibioctets per second, or two to the fortieth power octets per second. Its symbol is Tio/s. It is the binary counterpart of the teraoctet per second, and the two differ by 10 per cent.

Nothing outside a large machine moves data this quickly. The rate describes the memory bandwidth of an accelerator with stacked memory, the internal fabric of a high-end processor package, or the aggregate throughput of a parallel filesystem spread across thousands of drives. All of these are built from binary structures, and their totals are binary quantities divided by time.

High-performance computing is where the unit is written most often. A supercomputer's storage system is specified by how many tebioctets per second it can deliver to the compute nodes, because that number determines how quickly a simulation can save its state and resume. A machine that computes quickly but writes slowly spends its time waiting.

The ten per cent difference from the decimal unit is significant in that context. A filesystem procured to deliver 10 teraoctets per second and one delivering 10 tebioctets per second differ by a whole teraoctet per second, which in a facility of that size represents a substantial fraction of the hardware budget.

In bits a tebioctet per second is 8 tebibits per second, and in decimal terms about 1.1 teraoctets per second. Expressing the same rate four different ways is routine at this level, because the storage industry, the memory industry, the network industry and the standards bodies each prefer a different one.

For everyday comparison, a tebioctet per second would fill a large consumer hard drive in about twenty seconds. No external interface carries this; the figure describes movement between components inside a single system, where the wires are short and there are very many of them running in parallel.

Graphics processors have brought the rate within reach of a single component. A stack of high-bandwidth memory bonded directly to the processor die delivers well over a tebioctet per second to the chip that uses it, and a card carrying several such stacks passes a few. That bandwidth, rather than raw arithmetic speed, is what limits the training of large models: the arithmetic units sit idle unless the memory can keep them fed. The same reasoning explains why supercomputer designers spend as much effort on the paths between memory and processor as on the processors themselves, and why the rate is quoted in binary units when the memory it describes is addressed in powers of two.

One tebioctet per second equals 1,024 gibioctets per second, 1,099,511,627,776 octets per second, or about 1.100 teraoctets per second.

Information about the Pebioctet per second (Pio/s)

The pebioctet per second is a unit of data transfer rate equal to 1,024 tebioctets per second, or two to the fiftieth power octets per second. Its symbol is Pio/s. It is the binary counterpart of the petaoctet per second, and the two differ by 12.6 per cent.

The rate exists only as a total. The aggregate memory bandwidth of a whole supercomputer, or the summed capacity of the network fabric joining its cabinets, reaches this range, and both are sums over tens of thousands of components, each of which moves a few hundred gibioctets per second on its own.

Whether such a total means anything depends on the calculation being run. A problem that divides so that each node works mostly on its own data can use the full aggregate. A problem where every node must constantly consult every other cannot, and the machine's effective bandwidth falls to what the slowest shared path allows. Most of the art of parallel programming lies in getting problems into the first category.

In octets a pebioctet per second is 1,125,899,906,842,624, and in decimal terms about 1.126 petaoctets per second. The 12.6 per cent difference is the accumulated effect of five multiplications by 1.024, and it is now large enough that no report can leave the convention unstated without introducing real uncertainty.

The unit also appears in descriptions of parallel filesystems at the largest facilities, where a storage system spread across tens of thousands of drives delivers a few pebioctets per second to a compute cluster. That number determines how quickly the machine can checkpoint its state, which in turn determines how much work is lost when a component fails — and in a machine of that size, something is always failing.

For a converter the requirement is simply that the arithmetic be exact and the label preserved. Multiplying by 1,024 five times is not difficult; silently substituting the decimal prefix is the error to avoid.

One pebioctet per second equals 1,024 tebioctets per second, 1,125,899,906,842,624 octets per second, or about 1.126 petaoctets per second.