Conversion from Gibibits per second to Pebioctets per second

Information about the Gibibit per second (Gibit/s)

The gibibit per second is a unit of data transfer rate equal to 1,073,741,824 bits per second. Its symbol is Gibit/s. It is the binary counterpart of the gigabit per second, and the two now differ by 7.4 per cent, which is enough to matter in any engineering specification.

The unit belongs to the inside of a machine rather than to the network. Memory buses, processor interconnects and the links between chips on the same board all move a power-of-two number of bits per clock cycle, so their throughput is naturally expressed with a binary prefix. A bus sixty-four bits wide clocked at a given frequency delivers a rate that is a binary multiple of that frequency.

Networking, by contrast, is decimal all the way down. Gigabit Ethernet carries exactly one thousand million bits per second, not 1,073,741,824, and the symbol rate on the wire is chosen to make that so. Confusing the two overstates a link's capacity by seven per cent, which in a capacity plan is the difference between adequate and insufficient.

In octets a gibibit per second is 134,217,728, or 128 mebioctets per second. That is close to the throughput of a fast mechanical hard drive and well below a modern solid-state drive, so it sits at the point where storage and internal buses meet and where matching their rates becomes a design question.

Benchmark tools are the commonest place to see the unit written correctly. A memory bandwidth test that allocates buffers in powers of two and measures how long they take to traverse naturally reports in gibibits or gibioctets per second, and a well-written tool says so explicitly rather than rounding to the decimal unit.

The reason to insist on the distinction here rather than lower down the scale is arithmetic. At the kibibit the gap was 2.4 per cent and could be ignored; here it is nearly a thirteenth, and it grows by a further 2.4 per cent at every step above. Getting into the habit at this level costs nothing and avoids compounding errors later.

One gibibit per second equals 1,073,741,824 bits per second, 134,217,728 octets per second, or about 1.074 gigabits 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.