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<pre>Network Working Group H. Kennedy
Request for Comments: 3091 University of Michigan
Category: Informational 1 April 2001
<span class="h1">Pi Digit Generation Protocol</span>
Status of this Memo
This memo provides information for the Internet community. It does
not specify an Internet standard of any kind. Distribution of this
memo is unlimited.
Copyright Notice
Copyright (C) The Internet Society (2001). All Rights Reserved.
Abstract
This memo defines a protocol to provide the Pi digit generation
service (PIgen) used between clients and servers on host computers.
Introduction
This protocol is intended to provide the Pi digit generation service
(PIgen), and be used between clients and servers on host computers.
Typically the clients are on workstation hosts lacking local Pi
support, and the servers are more capable machines with greater Pi
calculation capabilities. The essential tradeoff is the use of
network resources and time instead of local computational cycles.
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in <a href="./rfc2119">RFC 2119</a> [<a href="./rfc2119" title=""Key words for use in RFCs to Indicate Requirement Levels"">RFC2119</a>].
Note
All digits supplied by implementations of this service are ASCII
[<a href="#ref-US-ASCII">US-ASCII</a>] representations of decimal (base 10) numbers following the
decimal point in values or approximations of Pi. There MUST be an
implied decimal value of 3 (three) preceding the values provided by
the service defined by this protocol.
<span class="h2"><a class="selflink" id="section-1" href="#section-1">1</a>. TCP Based Digit Generator Service</span>
One REQUIRED PIgen service is defined as a stateless TCP service. A
server listens on TCP port 314159. Once a connection is established
the server sends a stream of data, one digit of Pi at at time,
<span class="grey">Kennedy Informational [Page 1]</span></pre>
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<span class="grey"><a href="./rfc3091">RFC 3091</a> Pi Digit Generation Protocol 1 April 2001</span>
starting with the most significant digit following the decimal point.
Any incoming data MUST be discarded. This continues until the client
closes the connection.
The data flow over the connection is limited by the normal TCP flow
control mechanisms, so there is no concern about the server sending
data faster than the client can process it.
Servers MAY use any appropriate method of Pi digit generation to
provide this service, including (but not limited to) table lookup
[<a href="#ref-DIGITS">DIGITS</a>], numerical calculation [<a href="#ref-FIBPI">FIBPI</a>,<a href="#ref-PIFFT">PIFFT</a>] and statistical
sampling [<a href="#ref-MCM">MCM</a>]. However, the method chosen SHOULD provide a precise
value for the digits of Pi generated.
Implementors of PIgen MUST provide this service to be conditionally
compliant with this RFC.
<span class="h3"><a class="selflink" id="section-1.1" href="#section-1.1">1.1</a>. Approximate Service</span>
An OPTIONAL PIgen service is defined as a stateless TCP service. A
server listens on TCP port 220007. Once a connection is established
the server sends a stream of data, one digit of the rational number
22/7 at a time, starting with the most significant digit following
the decimal point. Any incoming data MUST be discarded. This
continues until the client closes the connection.
<span class="h2"><a class="selflink" id="section-2" href="#section-2">2</a>. UDP Based Digit Generator Service</span>
An OPTIONAL PIgen service is defined as a stateless UDP service. A
server listens on UDP port 314159. When a datagram requesting a
specific digit of Pi is received, an answering datagram is sent
containing the value of the requested digit of Pi according to the
format defined in sections <a href="#section-2.1.1">2.1.1</a>. and 2.1.2.
The requested digit value MAY be determined by any appropriate method
of Pi digit generation. RECOMMENDED methods include table lookup
[<a href="#ref-DIGITS">DIGITS</a>], or numerical calculation [<a href="#ref-BBPPA">BBPPA</a>].
<span class="h3"><a class="selflink" id="section-2.1" href="#section-2.1">2.1</a>. Packet Format</span>
The datagram-based components of the PIgen protocol suite all share
the following UDP data payload formats (defined in the ABNF of <a href="./rfc2234">RFC</a>
<a href="./rfc2234">2234</a> [<a href="./rfc2234" title=""Augmented BNF for Syntax Specifications: ABNF"">RFC2234</a>]).
<span class="grey">Kennedy Informational [Page 2]</span></pre>
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<span class="grey"><a href="./rfc3091">RFC 3091</a> Pi Digit Generation Protocol 1 April 2001</span>
<span class="h4"><a class="selflink" id="section-2.1.1" href="#section-2.1.1">2.1.1</a>. Request Payload Format</span>
request = nth_digit
nth_digit = 1*DIGIT ; specifying the n-th digit following the
; decimal point
<span class="h4"><a class="selflink" id="section-2.1.2" href="#section-2.1.2">2.1.2</a>. Reply Payload Format</span>
reply = nth_digit ":" DIGIT ; where DIGIT is the value of the n-th
; digit following the decimal
; point
<span class="h3"><a class="selflink" id="section-2.2" href="#section-2.2">2.2</a>. Approximate Service</span>
An OPTIONAL PIgen service is defined as a stateless UDP service. A
server listens on UDP port 220007. When a datagram requesting a
specific digit of the rational number 22/7 is received, an answering
datagram is sent containing the value of the requested digit of 22/7
according to the format defined in sections <a href="#section-2.1.1">2.1.1</a>. and 2.1.2.
<span class="h2"><a class="selflink" id="section-3" href="#section-3">3</a>. IP Multicast Based Digit Generator Service</span>
An OPTIONAL PIgen service is defined as a stateless UDP service. A
random distribution of digits of Pi are sent using the payload format
described in <a href="#section-2.1.2">section 2.1.2</a>. to the IP multicast group
314.159.265.359.
There is no request structure. If a server implementing this
component of the protocol suite joins the PIgen multicast group and
does not detect a server providing digits within 30 seconds, it MAY
elect to become the PIgen multicast provider.
The PIgen multicast provider generates a random distribution of the
digits of Pi and sends them out to the multicast group. PIgen
multicast clients build up a coherent value of Pi by listening to the
multicast group over time.
The randomly selected digit value MAY be determined by any
appropriate method of Pi digit generation. RECOMMENDED methods
include table lookup [<a href="#ref-DIGITS">DIGITS</a>], or numerical calculation [<a href="#ref-BBPPA">BBPPA</a>]. To
ensure an adequately random distribution, a proper random number
generator should be used, see [<a href="#ref-RANDOM">RANDOM</a>] for some examples.
<span class="grey">Kennedy Informational [Page 3]</span></pre>
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<span class="grey"><a href="./rfc3091">RFC 3091</a> Pi Digit Generation Protocol 1 April 2001</span>
<span class="h2"><a class="selflink" id="section-4" href="#section-4">4</a>. Service Discovery</span>
Clients SHOULD discover PIgen servers via the DNS SRV algorithm
[<a href="./rfc2782" title=""A DNS RR for specifying the location of services (DNS SRV)"">RFC2782</a>]. The service used is "pigen" and the protocols used are
"tcp" and "udp". Approximate services (sections <a href="#section-1.1">1.1</a>. and 2.2.)
should be discovered using a service of "pigem". This allows for
central administration of addressing, fallback for failed relays and
collectors, and static load balancing.
<span class="h2"><a class="selflink" id="section-5" href="#section-5">5</a>. Security Considerations</span>
As almost every secure Internet protocol requires a highly accurate
value of Pi in order to function correctly, it is imperative that
clients only use a trusted PIgen server. The imminent collapse of
the Internet is assured if this guideline is not strictly followed.
<span class="h2"><a class="selflink" id="section-6" href="#section-6">6</a>. References</span>
[<a id="ref-RFC2119">RFC2119</a>] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", <a href="https://www.rfc-editor.org/bcp/bcp14">BCP 14</a>, <a href="./rfc2119">RFC 2119</a>, March 1997.
[<a id="ref-US-ASCII">US-ASCII</a>] Coded Character Set--7-Bit American Standard Code for
Information Interchange, ANSI X3.4-1986.
[<a id="ref-DIGITS">DIGITS</a>] <a href="ftp://pi.super-computing.org/pub/pi">ftp://pi.super-computing.org/pub/pi</a>
[<a id="ref-FIBPI">FIBPI</a>] Pi and the Fibonacci Numbers
<a href="http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibpi.html">http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/</a>
<a href="http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibpi.html">fibpi.html</a>
[<a id="ref-PIFFT">PIFFT</a>] Pi Calculation based on FFT and AGM <a href="http://momonga.t.u-tokyo.ac.jp/~ooura/pi_fft.html">http://momonga.t.u-</a>
<a href="http://momonga.t.u-tokyo.ac.jp/~ooura/pi_fft.html">tokyo.ac.jp/~ooura/pi_fft.html</a>
[<a id="ref-MCM">MCM</a>] The Monte Carlo Method
<a href="http://www.daimi.aau.dk/~u951581/pi/MonteCarlo/pimc.html">http://www.daimi.aau.dk/~u951581/pi/MonteCarlo/pimc.html</a>
[<a id="ref-BBPPA">BBPPA</a>] Bailey-Borwien-Plouffe Pi Algorithm
<a href="http://www.mathsoft.com/asolve/plouffe/plouffe.html">http://www.mathsoft.com/asolve/plouffe/plouffe.html</a>
[<a id="ref-RFC2234">RFC2234</a>] Crocker, D. and P. Overell, "Augmented BNF for Syntax
Specifications: ABNF", <a href="./rfc2234">RFC 2234</a>, November 1997.
[<a id="ref-RANDOM">RANDOM</a>] Randomness for Crypto <a href="http://www.cs.berkeley.edu/~daw/rnd/">http://www.cs.berkeley.edu/~daw/rnd/</a>
[<a id="ref-RFC2782">RFC2782</a>] Gulbrandsen, A., Vixie, P. and L. Esibov, "A DNS RR for
specifying the location of services (DNS SRV)", <a href="./rfc2782">RFC 2782</a>,
February 2000.
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<span class="grey"><a href="./rfc3091">RFC 3091</a> Pi Digit Generation Protocol 1 April 2001</span>
[<a id="ref-CHARGEN">CHARGEN</a>] Postel, J., "Character Generation Protocol", STD 22, <a href="./rfc864">RFC</a>
<a href="./rfc864">864</a>, May 1983.
<span class="h2"><a class="selflink" id="section-7" href="#section-7">7</a>. Author's Address</span>
Hugh Kennedy
University of Michigan
2281 Bonisteel Blvd.
Ann Arbor, MI 48109-2099
USA
EMail: kennedyh@engin.umich.edu
<span class="grey">Kennedy Informational [Page 5]</span></pre>
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<span class="grey"><a href="./rfc3091">RFC 3091</a> Pi Digit Generation Protocol 1 April 2001</span>
Full Copyright Statement
Copyright (C) The Internet Society (2001). All Rights Reserved.
This document and translations of it may be copied and furnished to
others, and derivative works that comment on or otherwise explain it
or assist in its implementation may be prepared, copied, published
and distributed, in whole or in part, without restriction of any
kind, provided that the above copyright notice and this paragraph are
included on all such copies and derivative works. However, this
document itself may not be modified in any way, such as by removing
the copyright notice or references to the Internet Society or other
Internet organizations, except as needed for the purpose of
developing Internet standards in which case the procedures for
copyrights defined in the Internet Standards process must be
followed, or as required to translate it into languages other than
English.
The limited permissions granted above are perpetual and will not be
revoked by the Internet Society or its successors or assigns.
This document and the information contained herein is provided on an
"AS IS" basis and THE INTERNET SOCIETY AND THE INTERNET ENGINEERING
TASK FORCE DISCLAIMS ALL WARRANTIES, EXPRESS OR IMPLIED, INCLUDING
BUT NOT LIMITED TO ANY WARRANTY THAT THE USE OF THE INFORMATION
HEREIN WILL NOT INFRINGE ANY RIGHTS OR ANY IMPLIED WARRANTIES OF
MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.
Acknowledgement
Funding for the RFC Editor function is currently provided by the
Internet Society.
Kennedy Informational [Page 6]
</pre>
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