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rfc:rfc3091

Network Working Group H. Kennedy Request for Comments: 3091 University of Michigan Category: Informational 1 April 2001

                    Pi Digit Generation Protocol

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 RFC 2119 [RFC2119].

Note

 All digits supplied by implementations of this service are ASCII
 [US-ASCII] 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.

1. TCP Based Digit Generator Service

 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,

Kennedy Informational [Page 1] RFC 3091 Pi Digit Generation Protocol 1 April 2001

 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
 [DIGITS], numerical calculation [FIBPI,PIFFT] and statistical
 sampling [MCM].  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.

1.1. Approximate Service

 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.

2. UDP Based Digit Generator Service

 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 2.1.1. and 2.1.2.
 The requested digit value MAY be determined by any appropriate method
 of Pi digit generation.  RECOMMENDED methods include table lookup
 [DIGITS], or numerical calculation [BBPPA].

2.1. Packet Format

 The datagram-based components of the PIgen protocol suite all share
 the following UDP data payload formats (defined in the ABNF of RFC
 2234 [RFC2234]).

Kennedy Informational [Page 2] RFC 3091 Pi Digit Generation Protocol 1 April 2001

2.1.1. Request Payload Format

 request   = nth_digit
 nth_digit = 1*DIGIT  ; specifying the n-th digit following the
                      ; decimal point

2.1.2. Reply Payload Format

 reply  = nth_digit ":" DIGIT ; where DIGIT is the value of the n-th
                              ; digit following the decimal
                              ; point

2.2. Approximate Service

 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 2.1.1. and 2.1.2.

3. IP Multicast Based Digit Generator Service

 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 section 2.1.2. 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 [DIGITS], or numerical calculation [BBPPA].  To
 ensure an adequately random distribution, a proper random number
 generator should be used, see [RANDOM] for some examples.

Kennedy Informational [Page 3] RFC 3091 Pi Digit Generation Protocol 1 April 2001

4. Service Discovery

 Clients SHOULD discover PIgen servers via the DNS SRV algorithm
 [RFC2782].  The service used is "pigen" and the protocols used are
 "tcp" and "udp".  Approximate services (sections 1.1. 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.

5. Security Considerations

 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.

6. References

 [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
            Requirement Levels", BCP 14, RFC 2119, March 1997.
 [US-ASCII] Coded Character Set--7-Bit American Standard Code for
            Information Interchange, ANSI X3.4-1986.
 [DIGITS]   ftp://pi.super-computing.org/pub/pi
 [FIBPI]    Pi and the Fibonacci Numbers
            http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/
            fibpi.html
 [PIFFT]    Pi Calculation based on FFT and AGM http://momonga.t.u-
            tokyo.ac.jp/~ooura/pi_fft.html
 [MCM]      The Monte Carlo Method
            http://www.daimi.aau.dk/~u951581/pi/MonteCarlo/pimc.html
 [BBPPA]    Bailey-Borwien-Plouffe Pi Algorithm
            http://www.mathsoft.com/asolve/plouffe/plouffe.html
 [RFC2234]  Crocker, D. and P. Overell, "Augmented BNF for Syntax
            Specifications: ABNF", RFC 2234, November 1997.
 [RANDOM]   Randomness for Crypto http://www.cs.berkeley.edu/~daw/rnd/
 [RFC2782]  Gulbrandsen, A., Vixie, P. and L. Esibov, "A DNS RR for
            specifying the location of services (DNS SRV)", RFC 2782,
            February 2000.

Kennedy Informational [Page 4] RFC 3091 Pi Digit Generation Protocol 1 April 2001

 [CHARGEN]  Postel, J., "Character Generation Protocol", STD 22, RFC
            864, May 1983.

7. Author's Address

 Hugh Kennedy
 University of Michigan
 2281 Bonisteel Blvd.
 Ann Arbor, MI 48109-2099
 USA
 EMail: kennedyh@engin.umich.edu

Kennedy Informational [Page 5] RFC 3091 Pi Digit Generation Protocol 1 April 2001

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]

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