computer science

PiHex

PiHex is a computer science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand PiHex rather than just read about it. In short: PiHex was a distributed computing project organized by Colin Percival to calculate specific bits of π. 1,246 contributors used idle time slices on almost two thousand computers to make its calculations. The software used for the project made use of Bellard's formula, a faster version of the BBP formula.

Key takeaways

PiHex belongs to computer science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect PiHex to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of PiHex from memory before moving on to harder problems.

Reference excerpt

PiHex was a distributed computing project organized by Colin Percival to calculate specific bits of π. 1,246 contributors used idle time slices on almost two thousand computers to make its calculations. The software used for the project made use of Bellard's formula, a faster version of the BBP formula.

History To calculate the five trillionth digit (and the following seventy-six digits) took 13,500 CPU hours, using 25 computers from 6 countries. The forty trillionth digit required 84,500 CPU hours and 126 computers from 18 countries. The highest calculation, the one quadrillionth digit, took 1.2 million CPU hours and 1,734 computers from 56 countries. Total resources: 1,885 computers donated 1.3 million CPU hours. The average computer that was used to calculate would have taken 148 years to complete the calculations alone. After setting three records, calculating the five trillionth bit, the forty trillionth bit, and the quadrillionth bit, the project ended on September 11, 2000. While the PiHex project calculated the least significant digits of π ever attempted at the time in any base, the second place is held by Peter Trueb who computed some 22+ trillion digits in 2016 and third place by houkouonchi who derived the 13.3 trillionth digit in base 10.

Algorithm Unlike most computations of π, which compute results in base 10, PiHex computed in base 2 (bits), because Bellard's formula and the BBP formula could only be used to compute π in base 2 at the time. The final bit strings for each of the three calculations resulted as such:

Binary digits of π from five trillion minus three to five trillion and seventy-six (completed August 30, 1998): 0000 0111 1110 0100 0101 0111 0011 0011 1100 1100 ^ Five trillionth bit of π 0111 1001 0000 1011 0101 1011 0101 1001 0111 1001

Binary digits of π from forty trillion minus three to forty trillion and sixty-four (February 9, 1999): 1010 0000 1111 1001 1111 1111 0011 0111 0001 1101 ^ Forty trillionth bit of π 0001 0111 0101 1001 0011 1110 0000

Binary digits of π from one quadrillion minus three to one quadrillion and sixty (September 11, 2000): 1110 0110 0010 0001 0110 1011 0000 0110 1001 1100 ^ Quadrillionth bit of π 1011 0110 1100 0001 1101 0011

References

Worked examples

Example 1 — a first encounter with PiHex

Start with the simplest possible case. Write down what PiHex claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to PiHex before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about PiHex ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of PiHex

In research: PiHex appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses PiHex in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: PiHex is common in secondary-school and first-year university syllabi. It links to neighbouring topics Distributed computing projects, Pi-related software, Software engineering stubs, so understanding it makes those chapters shorter.
In everyday life: Look for PiHex outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study PiHex in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what PiHex means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain PiHex out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is PiHex in simple terms?

Why does PiHex matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study PiHex?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on PiHex.