The 'Bailey-Borwein-Plouffe' (BBP) algorithm for {pi} is based on the BBP formula for {pi}, which was discovered in 1995 and published in 1996 [3]: {pi} = {summation}{sub k=0}{sup {infinity}} 1/16{sup k} (4/8k+1 - 2/8k+4 - 1/8k+5 - 1/8k+6). This formula as it stands permits {pi} to be computed fairly rapidly to any given precision (although it is not as efficient for that purpose as some other formulas that are now known [4, pg. 108-112]). But its remarkable property is that it permits one to calculate (after a fairly simple manipulation) hexadecimal or binary digits of {pi} beginning at an arbitrary ...
continued below
Publisher Info:
Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA (United States)
Place of Publication:
Berkeley, California
Provided By
UNT Libraries Government Documents Department
Serving as both a federal and a state depository library, the UNT Libraries Government Documents Department maintains millions of items in a variety of formats. The department is a member of the FDLP Content Partnerships Program and an Affiliated Archive of the National Archives.
Descriptive information to help identify this report.
Follow the links below to find similar items on the Digital Library.
Description
The 'Bailey-Borwein-Plouffe' (BBP) algorithm for {pi} is based on the BBP formula for {pi}, which was discovered in 1995 and published in 1996 [3]: {pi} = {summation}{sub k=0}{sup {infinity}} 1/16{sup k} (4/8k+1 - 2/8k+4 - 1/8k+5 - 1/8k+6). This formula as it stands permits {pi} to be computed fairly rapidly to any given precision (although it is not as efficient for that purpose as some other formulas that are now known [4, pg. 108-112]). But its remarkable property is that it permits one to calculate (after a fairly simple manipulation) hexadecimal or binary digits of {pi} beginning at an arbitrary starting position. For example, ten hexadecimal digits {pi} beginning at position one million can be computed in only five seconds on a 2006-era personal computer. The formula itself was found by a computer program, and almost certainly constitutes the first instance of a computer program finding a significant new formula for {pi}. It turns out that the existence of this formula has implications for the long-standing unsolved question of whether {pi} is normal to commonly used number bases (a real number x is said to be b-normal if every m-long string of digits in the base-b expansion appears, in the limit, with frequency b{sup -m}). Extending this line of reasoning recently yielded a proof of normality for class of explicit real numbers (although not yet including {pi}) [4, pg. 148-156].
This report is part of the following collection of related materials.
Office of Scientific & Technical Information Technical Reports
Reports, articles and other documents harvested from the Office of Scientific and Technical Information.
Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.
Bailey, David H.The BBP Algorithm for Pi,
report,
September 17, 2006;
Berkeley, California.
(digital.library.unt.edu/ark:/67531/metadc1013585/:
accessed April 21, 2018),
University of North Texas Libraries, Digital Library, digital.library.unt.edu;
crediting UNT Libraries Government Documents Department.