PIgen: Pi Digit Generation Protocol

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,
   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]).

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.

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.

   [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

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