PiHex was a
distributed computing
A distributed system is a system whose components are located on different computer network, networked computers, which communicate and coordinate their actions by message passing, passing messages to one another from any system. Distributed com ...
project
A project is any undertaking, carried out individually or collaboratively and possibly involving research or design, that is carefully planned to achieve a particular goal.
An alternative view sees a project managerially as a sequence of even ...
organized by
Colin Percival
Colin A. Percival (born 1980) is a Canadian computer scientist and computer security researcher. He completed his undergraduate education at Simon Fraser University and a doctorate at the University of Oxford. While at university he joined the F ...
to calculate specific
bit
The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represente ...
s of
. 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 BBP may refer to:
Science
*Bailey–Borwein–Plouffe formula, a formula for computing the ''n''th binary digit of pi
* Baseband processor, a device in a network interface that manages all the radio functions
* Benzyl butyl phthalate, a plastici ...
.
History
To calculate the five trillionth digit (and the following seventy-six digits) took 13,500 CPU hours, using 25 computers from 6 different countries. The forty trillionth digit required 84,500 CPU hours and 126 computers from 18 different countries. The highest calculation, the one quadrillionth digit, took 1.2 million CPU hours and 1,734 computers from 56 different 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 ever attempted 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 , which compute results in
base 10
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numer ...
, PiHex computed in
base 2 (bits), because Bellard's formula and the BBP formula could only be used to compute in base 2 at the time.
The final bit strings for each of the three calculations resulted as such:
* Binary digits of 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
0111 1001 0000 1011 0101 1011 0101 1001 0111 1001
* Binary digits of 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
0001 0111 0101 1001 0011 1110 0000
* Binary digits of 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
1011 0110 1100 0001 1101 0011
Therefore, the least significant known bit of is 1 at position 1,000,000,000,000,060 (one quadrillion and sixty) or
.
References
Pi-related software
Distributed computing projects
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