PiHex
Encyclopedia
PiHex was a distributed computing
project
organized by Colin Percival to calculate specific bits
of Pi
, the greatest calculation of Pi ever successfully attempted. 1,246 contributors used idle time slices on almost two thousand computers to make its calculations. They made use of Bellard's formula
, a faster version of the BBP formula, with the algorithm
discovered by Bailey
, Borwein
, and Plouffe
in 1995.
After setting three records, calculating bits five trillion minus 3 through five trillion plus 76, forty trillion minus 3 through forty trillion plus 64, and one quadrillion minus 3 through one quadrillion plus 60 bits, the project ended on September 11, 2000.
Unlike most computations of Pi, which compute results in Base 10, PiHex computed Base 2 digits (bits); the BBP algorithm can only be used to compute Pi in Base 2.
Here are the final digit
strings for each of the three calculations:
Therefore, the least significant known bit of Pi is 1 at position 1,000,000,000,000,060 (one quadrillion sixty) or 1015+60.
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.
While the PiHex project calculated the least significant digits of Pi ever attempted in any base, second place is held by Shigeru Kondo who derived the 5 trillionth digit in base 10.
Distributed computing
Distributed computing is a field of computer science that studies distributed systems. A distributed system consists of multiple autonomous computers that communicate through a computer network. The computers interact with each other in order to achieve a common goal...
project
Project
A project in business and science is typically defined as a collaborative enterprise, frequently involving research or design, that is carefully planned to achieve a particular aim. Projects can be further defined as temporary rather than permanent social systems that are constituted by teams...
organized by Colin Percival to calculate specific bits
BITS
BITS or bits may refer to:* Plural of bit* Background Intelligent Transfer Service, a file transfer protocol* Birla Institute of Technology and Science, a technology school in Pilani, Rajasthan, India, with campuses in Goa, Hyderabad, and Dubai...
of Pi
Pi
' is a mathematical constant that is the ratio of any circle's circumference to its diameter. is approximately equal to 3.14. Many formulae in mathematics, science, and engineering involve , which makes it one of the most important mathematical constants...
, the greatest calculation of Pi ever successfully attempted. 1,246 contributors used idle time slices on almost two thousand computers to make its calculations. They made use of Bellard's formula
Bellard's formula
Bellard's formula, as used by PiHex, the now-completed distributed computing project, is used to calculate the nth digit of π in base 2. It is a faster version of the Bailey–Borwein–Plouffe formula...
, a faster version of the BBP formula, with the algorithm
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
discovered by Bailey
David H. Bailey
David Harold Bailey is a mathematician and computer scientist. He received his B.S. in mathematics from Brigham Young University in 1972 and his Ph.D. in mathematics from Stanford University in 1976...
, Borwein
Peter Borwein
Peter Benjamin Borwein is a Canadian mathematicianand a professor at Simon Fraser University. He is known as a co-discoverer of the Bailey-Borwein-Plouffe algorithm for computing π.-First interest in mathematics:...
, and Plouffe
Simon Plouffe
Simon Plouffe is a Quebec mathematician born on June 11, 1956 in Saint-Jovite, Quebec. He discovered the formula for the BBP algorithm which permits the computation of the nth binary digit of π, in 1995...
in 1995.
After setting three records, calculating bits five trillion minus 3 through five trillion plus 76, forty trillion minus 3 through forty trillion plus 64, and one quadrillion minus 3 through one quadrillion plus 60 bits, the project ended on September 11, 2000.
Unlike most computations of Pi, which compute results in Base 10, PiHex computed Base 2 digits (bits); the BBP algorithm can only be used to compute Pi in Base 2.
Here are the final digit
Digit
Digit may refer to:* Digit , one of several most distal parts of a limb—fingers, thumbs, and toes on hands and feet* Numerical digit, as used in mathematics or computer science* Hexadecimal, representing a four-bit number...
strings for each of the three calculations:
- Binary digits of Pi from five trillion minus three to five trillion seventy-six (completed August 30, 1998):
- 00000111111001000101011100110011110011000111100100001011010110110101100101111001
- Binary digits of Pi from forty trillion minus three to forty trillion sixty-four (February 9, 1999):
- 10100000111110011111111100110111000111010001011101011001001111100000
- Binary digits of Pi from one quadrillion minus three to one quadrillion sixty (September 11, 2000):
- 1110011000100001011010110000011010011100101101101100000111010011
Therefore, the least significant known bit of Pi is 1 at position 1,000,000,000,000,060 (one quadrillion sixty) or 1015+60.
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.
While the PiHex project calculated the least significant digits of Pi ever attempted in any base, second place is held by Shigeru Kondo who derived the 5 trillionth digit in base 10.