[Docs] [txt|pdf] [Tracker] [WG] [Email] [Diff1] [Diff2] [Nits]

Versions: 00 01 02 03 04 05 06 07 08 09 10 11 12 13 RFC 5905

NTP WG                                                   J. Burbank, Ed.
Internet-Draft                                                   JHU/APL
Obsoletes: RFC 4330 (if approved)                         J. Martin, Ed.
Intended status: Standards Track                             Netzwert AG
Expires: April 26, 2007                                         D. Mills
                                                                 U. Del.
                                                        October 23, 2006


   Network Time Protocol Version 4 Reference and Implementation Guide
                     draft-ietf-ntp-ntpv4-proto-03

Status of this Memo

   By submitting this Internet-Draft, each author represents that any
   applicable patent or other IPR claims of which he or she is aware
   have been or will be disclosed, and any of which he or she becomes
   aware will be disclosed, in accordance with Section 6 of BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF), its areas, and its working groups.  Note that
   other groups may also distribute working documents as Internet-
   Drafts.

   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any
   time.  It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."

   The list of current Internet-Drafts can be accessed at
   http://www.ietf.org/ietf/1id-abstracts.txt.

   The list of Internet-Draft Shadow Directories can be accessed at
   http://www.ietf.org/shadow.html.

   This Internet-Draft will expire on April 26, 2007.

Copyright Notice

   Copyright (C) The Internet Society (2006).

Abstract

   The Network Time Protocol (NTP) is widely used to synchronize
   computer clocks in the Internet.  This memorandum describes Version 4
   of the NTP (NTPv4), introducing several changes from Version 3 of NTP
   (NTPv3) described in RFC 1305, including the introduction of a
   modified protocol header to accomodate Internet Protocol Version 6.



Burbank, et al.          Expires April 26, 2007                 [Page 1]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   NTPv4 also includes optional extensions to the NTPv3
   protocol,including a dynamic server discovery mechanism.


Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
     1.1.  Requirements Notation . . . . . . . . . . . . . . . . . .   4
   2.  Modes of Operation  . . . . . . . . . . . . . . . . . . . . .   4
   3.  Definitions . . . . . . . . . . . . . . . . . . . . . . . . .   6
   4.  Implementation Model  . . . . . . . . . . . . . . . . . . . .   9
   5.  Data Types  . . . . . . . . . . . . . . . . . . . . . . . . .  12
   6.  Data Structures . . . . . . . . . . . . . . . . . . . . . . .  15
     6.1.  Structure Conventions . . . . . . . . . . . . . . . . . .  16
     6.2.  Global Parameters . . . . . . . . . . . . . . . . . . . .  16
     6.3.  Packet Header Variables . . . . . . . . . . . . . . . . .  18
       6.3.1.  The Kiss-o'-Death Packet  . . . . . . . . . . . . . .  22
       6.3.2.  NTP Extension Field Format  . . . . . . . . . . . . .  23
   7.  On Wire Protocol  . . . . . . . . . . . . . . . . . . . . . .  25
   8.  Peer Process  . . . . . . . . . . . . . . . . . . . . . . . .  29
     8.1.  Peer Process Variables  . . . . . . . . . . . . . . . . .  30
     8.2.  Peer Process Operations . . . . . . . . . . . . . . . . .  32
   9.  Clock Filter Algorithm  . . . . . . . . . . . . . . . . . . .  39
   10. System Process  . . . . . . . . . . . . . . . . . . . . . . .  42
     10.1. System Process Variables  . . . . . . . . . . . . . . . .  42
     10.2. System Process Operations . . . . . . . . . . . . . . . .  43
       10.2.1. Selection Algorithm . . . . . . . . . . . . . . . . .  44
       10.2.2. Clustering Algorithm  . . . . . . . . . . . . . . . .  46
       10.2.3. Combining Algorithm . . . . . . . . . . . . . . . . .  48
       10.2.4. Clock Discipline Algorithm  . . . . . . . . . . . . .  52
     10.3. Clock Adjust Process  . . . . . . . . . . . . . . . . . .  60
   11. Poll Process  . . . . . . . . . . . . . . . . . . . . . . . .  61
     11.1. Poll Process Variables and Parameters . . . . . . . . . .  61
     11.2. Poll Process Operations . . . . . . . . . . . . . . . . .  62
   12. Security Considerations . . . . . . . . . . . . . . . . . . .  63
   13. IANA Considerations . . . . . . . . . . . . . . . . . . . . .  63
   14. Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  64
   15. References  . . . . . . . . . . . . . . . . . . . . . . . . .  64
     15.1. Normative References  . . . . . . . . . . . . . . . . . .  64
     15.2. Informative References  . . . . . . . . . . . . . . . . .  64
   Appendix A.  Code Skeleton  . . . . . . . . . . . . . . . . . . .  65
     A.1.  Global Definitions  . . . . . . . . . . . . . . . . . . .  65
     A.2.  Definitions, Constants, Parameters  . . . . . . . . . . .  65
     A.3.  Packet Data Structures  . . . . . . . . . . . . . . . . .  69
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . . 109
   Intellectual Property and Copyright Statements  . . . . . . . . . 110





Burbank, et al.          Expires April 26, 2007                 [Page 2]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


1.  Introduction

   This document is a reference and implementation guide for the Network
   Time Protocol Version 4 (NTPv4), which is widely used to synchronize
   the system clocks among a set of distributed time servers and
   clients.  This document defines the core architecture, protocol,
   state machines, data structures and algorithms.  This document
   describes NTPv4, which introduces new functionality to NTPv3 as
   described in [1], and functionality expanded from that of SNTPv4 as
   described in [2] (SNTPv4 is a subset of NTPv4).  This document
   obsoletes RFC 1305 and RFC 4330.  While certain minor changes have
   been made in some protocol header fields, these do not affect the
   interoperability between NTPv4 and previous versions.

   The NTP subnet model includes a number of widely accessible primary
   time servers synchronized by wire or radio to national standards.
   The purpose of the NTP protocol is to convey timekeeping information
   from these primary servers to secondary time servers and clients via
   both private networks and the public Internet.  Crafted algorithms
   mitigate errors that may result from network disruptions, server
   failures and possible hostile action.  Servers and clients are
   configured such that values flow from the primary servers at the root
   via branching secondary servers toward clients.

   The NTPv4 design overcomes significant shortcomings in the NTPv3
   design, corrects certain bugs and incorporates new features.  In
   particular, expanded NTP timestamp definitions encourage the use of
   floating double data types throughout any implementation.  The time
   resolution is better than one nanosecond and frequency resolution
   better than one nanosecond per second.  Additional improvements
   include a new clock discipline algorithm which is more responsive to
   system clock hardware frequency fluctuations.  Typical primary
   servers using modern machines are precise within a few tens of
   microseconds.  Typical secondary servers and clients on fast LANs are
   within a few hundred microseconds with poll intervals up to 1024
   seconds, which was the maximum with NTPv3.  With NTPv4, servers and
   clients are within a few tens of milliseconds with poll intervals up
   to 36 hours.

   The main body of this document describes only the core protocol and
   data structures necessary to interoperate between conforming
   implementations.  Additional detail is provided in the form of a
   skeleton program included as an appendix.  This program includes data
   structures and code segments for the core algorithms and in addition
   the mitigation algorithms used to enhance reliability and accuracy.
   While the skeleton and other descriptions in this document apply to a
   particular implementation, they are not intended as the only way the
   required functions can be implemented.  While the NTPv3 symmetric key



Burbank, et al.          Expires April 26, 2007                 [Page 3]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   authentication scheme described in this document carries over from
   NTPv3, the Autokey public key authentication scheme new to NTPv4 is
   described in [3].

   The NTP protocol includes the modes of operation described in Section
   2 using the data types described in Section 5 and the data structures
   in Section 6.  The implementation model described in Section 4 is
   based on a multiple-process, threaded architecture, although other
   architectures could be used as well.  The on-wire protocol described
   in Section 7 is based on a returnable-time design which depends only
   on measured clock offsets, but does not require reliable message
   delivery.  The synchronization subnet is a self-organizing,
   hierarchical, master-slave network with synchronization paths
   determined by a shortest-path spanning tree and defined metric.
   While multiple masters (primary servers) may exist, there is no
   requirement for an election protocol.

   The remaining sections of this document define the data structures
   and algorithms suitable for a fully featured NTPv4 implementation.
   Appendix A contains the code skeleton with definitions, structures
   and code segments that represent the basic structure of the reference
   implementation.

   The remainder of this document contains numerous variables and
   mathematical expressions.  Those variables take the form of Greek
   characters.  Those Greek characters are spelled out by their full
   name, with the "cap" prefix added to variables referring to the
   corresponding upper case Greek character.  For example capdelta
   refers to the uppercase Greek character, where delta refers to the
   lowercase Greek character.  Furthermore, subscripts are denoted with
   a '_' separating the variable name and the subscript.  For example
   'theta_i' refers to the variable lowercase Greek character theta with
   subscript i, or phonetically 'theta sub i.'

1.1.  Requirements Notation

   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 [4].


2.  Modes of Operation

   An NTP implementation operates as a primary server, secondary server
   or client.  A primary server is synchronized directly to a reference
   clock, such as a GPS receiver or telephone modem service.  A client
   is synchronized to one or more upstream servers, but does not provide
   synchronization to dependent clients.  A secondary server has one or



Burbank, et al.          Expires April 26, 2007                 [Page 4]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   more upstream servers and one or more downstream servers or clients.
   All servers and clients claiming full NTPv4 compliance must implement
   the entire suite of algorithms described in this document.  In order
   to maintain stability in large NTP subnets, secondary servers must be
   fully NTPv4 compliant.

   Primary servers and clients complying with a subset of NTP, called
   the Simple Network Time Protocol (SNTPv4) [2], do not need to
   implement all algorithms.  SNTP is intended for primary servers
   equipped with a single reference clock, as well as clients with a
   single upstream server and no dependent clients.  The fully developed
   NTPv4 implementation is intended for secondary servers with multiple
   upstream servers and multiple downstream servers or clients.  Other
   than these considerations, NTP and SNTP servers and clients are
   completely interoperable and can be mixed and matched in NTP subnets.

            +-------------------+--------------+-------------+
            |  Association Mode | Assoc.  Mode | Packet Mode |
            +-------------------+--------------+-------------+
            |  Symmetric Active |       1      | 1 or 2      |
            | Symmetric Passive |       2      | 1           |
            |       Client      |       3      | 4           |
            |       Server      |       4      | 3           |
            |  Broadcast Server |       5      | 5           |
            |  Broadcast Client |       6      | N/A         |
            +-------------------+--------------+-------------+

                   Table 1: Association and Packet Modes

   There are three NTP protocol variants, symmetric, client/server and
   broadcast.  Each is associated with an association mode as shown in
   Table 1.  In the client/server variant a client association sends
   mode-3 (client) packets to a server, which returns mode-4 (server)
   packets.  Servers provide synchronization to one or more clients, but
   do not accept synchronization from them.  A server can also be a
   reference clock which obtains time directly from a standard source
   such as a GPS receiver or telephone modem service.  We say that
   clients pull synchronization from servers.

   In the symmetric variant a peer operates as both a server and client
   using either a symmetric-active or symmetric-passive association.  A
   symmetric-active association sends mode-1 (symmetric-active) packets
   to a symmetric-active peer association.  Alternatively, a symmetric-
   passive association can be mobilized upon arrival of a mode-1 packet.
   That association sends mode-2 (symmetric-passive) packets and
   persists until error or timeout.  Peers both push and pull
   synchronization to and from each other.  For the purposes of this
   document, a peer operates like a client, so a reference to client



Burbank, et al.          Expires April 26, 2007                 [Page 5]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   implies peer as well.

   In the broadcast variant a broadcast server association sends
   periodic mode-5 (broadcast) packets which are received by multiple
   mode-6 (broadcast client) associations.  It is useful to provide an
   initial volley where the client operating in mode 3 exchanges several
   packets with the server in order to calibrate the propagation delay
   and to run the Autokey security protocol, after which the client
   reverts to mode 6.  We say that broadcast servers push
   synchronization to willing consumers.

   Following conventions established by the telephone industry, the
   level of each server in the hierarchy is defined by a number called
   the stratum, with the primary servers assigned stratum one and the
   secondary servers at each level assigned one greater than the
   preceding level.  As the stratum increases from one, the accuracies
   achievable degrade somewhat depending on the particular network path
   and system clock stability.  It is useful to assume that mean errors,
   and thus a metric called the synchronization distance, increase
   approximately in proportion to the stratum and measured roundtrip
   delay.  It is important to note that NTP stratum is only loosely
   modeled after telecommunications stratum.  The NTP stratum numbers
   and telecommunications stratum numbers do not correlate with one
   another.  Telecommunications stratum numbers are rigorously defined
   by international standards that are not covered within this document.

   Drawing from the experience of the telephone industry, which learned
   such lessons at considerable cost, the subnet topology should be
   organized to produce the lowest synchronization distances, but must
   never be allowed to form a loop.  In NTP the subnet topology is
   determined using a variant of the Bellman-Ford distributed routing
   algorithm, which computes the shortest-distance spanning tree rooted
   on the primary servers.  As a result of this design, the algorithm
   automatically reorganizes the subnet to produce the most accurate and
   reliable time, even when one or more primary or secondary servers or
   the network paths.


3.  Definitions

   A number of terms used throughout this document have a precise
   technical definition.  A timescale is a frame of reference where time
   is expressed as the value of a monotonic-increasing binary counter
   with an indefinite number of bits.  It counts in seconds and fraction
   with the decimal point somewhere in the middle.  The Coordinated
   Universal Time (UTC) timescale represents mean solar time as
   disseminated by national standards laboratories.  The system time is
   represented by the system clock maintained by the operating system



Burbank, et al.          Expires April 26, 2007                 [Page 6]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   kernel.  The goal of the NTP algorithms is to minimize both the time
   difference and frequency difference between UTC and the system clock.
   When these differences have been reduced below nominal tolerances,
   the system clock is said to be synchronized to UTC.

   The date of an event is the UTC time at which it takes place.  Dates
   are ephemeral values which always increase in step with reality and
   are designated with upper case T in this document.  It is convenient
   to define another timescale coincident with the running time of the
   NTP program that provides the synchronization function.  This is
   convenient in order to determine intervals for the various repetitive
   functions like poll events.  Running time is usually designated with
   lower case t.

   A timestamp T(t) represents either the UTC date or time offset from
   UTC at running time t.  Which meaning is intended should be clear
   from the context.  Let T(t) be the time offset, R(t) the frequency
   offset, D(t) the ageing rate (first derivative of R(t) with respect
   to t).  Then, if T(t_0) is the UTC time offset determined at t=t_0,
   the UTC time offset after some interval is:

   T(t+t_0) = T(t_0) + R(t_0)(t+t_0)+(1/2)*D(t_0)(t+t_0)^2 + e,

   where e is a stochastic error term discussed later in this document.
   While the D(t) term is important when characterizing precision
   oscillators, it is ordinarily neglected for computer oscillators.  In
   this document all time values are in seconds (s) and all frequency
   values are in seconds-per-second (s/s).  It is sometimes convenient
   to express frequency offsets in parts-per-million (PPM), where 1 PPM
   is equal to 1*10^(-6) seconds.

   It is important in computer timekeeping applications to assess the
   performance of the timekeeping function.  The NTP performance model
   includes four statistics which are updated each time a client makes a
   measurement with a server.  The offset theta represents the maximum
   likelihood time offset of the server clock relative to the system
   clock.  The delay del represents the roundtrip delay between the
   client and server.  The dispersion epsilon represents the maximum
   error inherent in the measurement.  It increases at a rate equal to
   the maximum disciplined system clock frequency tolerance phi,
   typically 15 PPM.  The jitter varphi, defined as the root-mean-square
   (RMS) average of the most recent time offset differences, represents
   the nominal error in estimating theta.

   While the theta, del, epsilon, and psi statistics represent
   measurements of the system clock relative to the each server clock
   separately, the NTP protocol includes mechanisms to combine the
   statistics of several servers to more accurately discipline and



Burbank, et al.          Expires April 26, 2007                 [Page 7]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   calibrate the system clock.  The system offset captheta represents
   the maximum-likelihood offset estimate for the server population.
   The system jitter vartheta represents the nominal error in estimating
   captheta.  The del and epsilon statistics are accumulated at each
   stratum level from the reference clocks to produce the root delay
   delta and root dispersion E statistics.  The synchronization distance
   gamma=E+delta/2 represents the maximum error due all causes.  The
   detailed formulations of these statistics are given later in this
   document.  They are available to the dependent applications in order
   to assess the performance of the synchronization function.









































Burbank, et al.          Expires April 26, 2007                 [Page 8]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


    0                   1                   2                   3
    0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |LI | VN  |Mode |     Strat     |     Poll      |     Prec      |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                         Root Delay                            |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                         Root Dispersion                       |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                          Reference ID                         |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                                                               |
   +                       Reference Timestamp                     +
   |                                                               |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                                                               |
   +                        Origin Timestamp                       +
   |                                                               |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                                                               |
   +                        Receive Timestamp                      +
   |                                                               |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                                                               |
   +                        Transmit Timestamp                     +
   |                                                               |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                                                               |
   +                    Extension Field 1 (Optional)               +
   |                                                               |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                                                               |
   +                    Extension Field 2 (Optional)               +
   |                                                               |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   .                                                               .
   .                          Authentication                       .
   .                       (Optional) (160 bits)                   .
   .                                                               .
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

                      Figure 1: NTPv4 Message Format


4.  Implementation Model

   Figure 1 shows two processes dedicated to each server, a peer process
   to receive messages from the server or reference clock and a poll



Burbank, et al.          Expires April 26, 2007                 [Page 9]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   process to transmit messages to the server or reference clock. .

   ..........................................................
   . Remote   ..   Peer/Poll   ..              System       .
   . Servers  ..   Processes   ..              Process      .
   .          ..               ..                           .
   .----------..-------------..--------------               .
   .|        |->|           |..|            |               .
   .|Server 1|..|Peer/Poll 1|->|            |               .
   .|        |<-|           |..|            |               ............
   .----------..-------------..|            |               .   Clock  .
                                                            .Discipline.
   .          ..       ^     ..|            |               .. Process .
   .          ..       |     ..|            |               ..         .
   .----------..-------------..|            |  |-----------|..         .
   .|        |->|           |..| Selection  |->|            ..-------- .
   .|Server 2|..|Peer/Poll 2|->|    and     |  | Combining |->| Loop | .
   .|        |<-|           |..| Clustering |  | Algorithm |..|Filter| .
   .----------..-------------..| Algorithms |->|           |.-----------
   .          ..       ^     ..|            |  |-----------|.     |
   .          ..       |     ..|            |               .     |
   .----------..-------------..|            |               .     |
   .|        |->|           |..|            |               .     |
   .|Server 3|..|Peer/Poll 3|->|            |               .     |
   .|        |<-|           |..|            |               .     |
   .----------..-------------..|------------|               .     |
   ....................^.....................................     |
                       |                                          |
                       |                                         \|/
                       |                                ...............
                       |                                .   /-----\   .
                       '----------------------------------<-| VFO |-<-.
                                                        .   \-----/   .
                                                        . Clock Adjust.
                                                        .   Process   .
                                                        ...............

                    Figure 1 NTPv4 Algorithm Interactions

                  Figure 2: NTPv4 Algorithm Interactions

   These processes operate on a common data structure called an
   association, which contains the statistics described above along with
   various other data described later.  A client sends an NTP packet to
   one or more servers and processes the replies as received.  The
   server interchanges addresses and ports, overwrites certain fields in
   the packet and returns it immediately (client/ server mode) or at
   some time later (symmetric modes).  As each NTP message is received,



Burbank, et al.          Expires April 26, 2007                [Page 10]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   the offset theta between the peer clock and the system clock is
   computed along with the associated statistics del, epsilon, and
   varphi.

   The system process includes the selection, clustering and combining
   algorithms which mitigate among the various servers and reference
   clocks to determine the most accurate and reliable candidates to
   synchronize the system clock.  The selection algorithm uses Byzantine
   principles to remote the falsetickers from the incident population,
   leaving only truechimers.  A 'truechimer' is a clock that maintains
   timekeeping accuracy to a previously published (and trusted)
   standard, while a 'falseticker' is a clock that does not maintain
   that level of timekeeping accuracy.  The clustering algorithm uses
   statistical principles to sift the most accurate truechimers leaving
   the survivors as result.  The combining algorithm develops the final
   clock offset as a statistical average of the survivors.

   The clock discipline process, which is actually part of the system
   process, includes engineered algorithms to control the time and
   frequency of the system clock, here represented as a variable
   frequency oscillator (VFO).  Timestamps struck from the VFO close the
   feedback loop which maintains the system clock time.  Associated with
   the clock discipline process is the clock adjust process, which runs
   once each second to inject a computed time offset and maintain
   constant frequency.  The RMS average of past time offset differences
   represents the nominal error or system jitter vartheta.  The RMS
   average of past frequency offset differences represents the
   oscillator frequency stability or frequency wander cappsi.

   A client sends messages to each server with a poll interval of 2^tau
   seconds, as determined by the poll exponent tau.  In NTPv4 tau ranges
   from 4 (16 s) through 17 (36 h).  The value of tau is determined by
   the clock discipline algorithm to match the loop time constant T_c =
   2^tau.  A server responds with messages at an update interval of mu
   seconds.  For stateless servers, mu = T_c, since the server responds
   immediately.  However, in symmetric modes each of two peers manages
   the time constant as a function of current system offset and system
   jitter, so may not agree with the same tau.  It is important that the
   dynamic behavior of the clock discipline algorithms be carefully
   controlled in order to maintain stability in the NTP subnet at large.
   This requires that the peers agree on a common tau equal to the
   minimum poll exponent of both peers.  The NTP protocol includes
   provisions to properly negotiate this value.

   While not shown in the figure, the implementation model includes some
   means to set and adjust the system clock.  The operating system is
   assumed to provide two functions, one to set the time directly, for
   example the Unix settimeofday() function, and another to adjust the



Burbank, et al.          Expires April 26, 2007                [Page 11]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   time in small increments advancing or retarding the time by a
   designated amount, for example the Unix adjtime()1 function
   (parentheses following a name indicate reference to a function rather
   than a simple variable).  In the intended design the clock discipline
   process uses the adjtime() function if the adjustment is less than a
   designated threshold, and the settimeofday() function if above the
   threshold.  The manner in which this is done and the value of the
   threshold is described later.


5.  Data Types

   All NTP time values are represented in twos-complement format, with
   bits numbered in big-endian (as described in Appendix A of [5])
   fashion from zero starting at the left, or high-order, position.
   There are three NTP time formats, a 128-bit date format, a 64-bit
   timestamp format and a 32-bit short format, as shown in Figure 3.
   The 128-bit date format is used where sufficient storage and word
   size are available.  It includes a 64-bit signed seconds field
   spanning 584 billion years and a 64-bit fraction field resolving .05
   attosecond (i.e. 0.5e-18).  For convenience in mapping between
   formats, the seconds field is divided into a 32-bit era field and a
   32-bit timestamp field.  Eras cannot be produced by NTP directly, nor
   is there need to do so.  When necessary, they can be derived from
   external means, such as the filesystem or dedicated hardware.


























Burbank, et al.          Expires April 26, 2007                [Page 12]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


    0                   1                   2                   3
    0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |          Seconds              |           Fraction            |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
                            NTP Short Format


    0                   1                   2                   3
    0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                            Seconds                            |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                            Fraction                           |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
                          NTP Timestamp Format


    0                   1                   2                   3
    0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                           Era Number                          |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                           Era Offset                          |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                                                               |
   |                           Fraction                            |
   |                                                               |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
                           NTP Date Format

                         Figure 3: NTP Time Format

   The 64-bit timestamp format is used in packet headers and other
   places with limited word size.  It includes a 32-bit unsigned seconds
   field spanning 136 years and a 32-bit fraction field resolving 232
   picoseconds.  The 32-bit short format is used in delay and dispersion
   header fields where the full resolution and range of the other
   formats are not justified.  It includes a 16-bit unsigned seconds
   field and a 16-bit fraction field.

   In the date format the prime epoch, or base date of era 0, is 0 h 1
   January 1900 UTC, when all bits are zero.  It should be noted that
   strictly speaking, UTC did not exist prior to 1 January 1972, but it
   is convenient to assume it has existed for all eternity, even if all
   knowledge of historic leap seconds has been lost.  Dates are relative
   to the prime epoch; values greater than zero represent times after
   that date; values less than zero represent times before it.



Burbank, et al.          Expires April 26, 2007                [Page 13]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   Timestamps are unsigned values and operations on them produce a
   result in the same or adjacent eras.  Era 0 includes dates from the
   prime epoch to some time in 2036, when the timestamp field wraps
   around and the base date for era 1 is established.  In either format
   a value of zero is a special case representing unknown or
   unsynchronized time.  Figure 4 shows a number of historic NTP dates
   together with their corresponding Modified Julian Day (MJD), NTP era
   and NTP timestamp.
   Year         MJD         NTP Era NTP Timestamp  Epoch
   1 Jan -4712  -2,400,001  -49     1,795,583,104  1st day Julian
   1 Jan -1     -679,306    -14     139,775,744    2 BCE
   1 Jan 0      -678,491    -14     171,311,744    1 BCE
   1 Jan 1      -678,575    -14     202,939,144    1 CE
   4 Oct 1582   -100,851    -3      2,873,647,488  Last day Julian
   15 Oct 1582  -100,840    -3      2,874,597,888  1st day Gregorian
   31 Dec 1899  15019       -1      4,294,880,896  Last d NTPEra-1
   1 Jan 1900   15020       0       0              First d NTPEra0
   1 Jan 1970   40,587      0       2,208,988,800  First day UNIX
   1 Jan 1972   41,317      0       2,272,060,800  First day UTC
   31 Dec 1999  51,543      0       3,155,587,200  Last d 20th Cent
   8 Feb 2036   64,731      1       63,104         1st day NTPEra1

                 Figure 4: Interesting Historic NTP Dates

   Let p be the number of significant bits in the second fraction.  The
   clock resolution is defined 2p, in seconds.  In order to minimize
   bias and help make timestamps unpredictable to an intruder, the non-
   significant bits should be set to an unbiased random bit string.  The
   clock precision is defined as the running time to read the system
   clock, in seconds.  Note that the precision defined in this way can
   be larger or smaller than the resolution.  The term rho, representing
   the precision used in this document, is the larger of the two.

   The only operation permitted with dates and timestamps is twos-
   complement subtraction, yielding a 127-bit or 63-bit signed result.
   It is critical that the first-order differences between two dates
   preserve the full 128-bit precision and the first-order differences
   between two timestamps preserve the full 64-bit precision.  However,
   the differences are ordinarily small compared to the seconds span, so
   they can be converted to floating double format for further
   processing and without compromising the precision.

   It is important to note that twos-complement arithmetic does not know
   the difference between signed and unsigned values; only the
   conditional branch instructions.  Thus, although the distinction is
   made between signed dates and unsigned timestamps, they are processed
   the same way.  A perceived hazard with 64-bit timestamp calculations
   spanning an era, such as possible in 2036, might result in incorrect



Burbank, et al.          Expires April 26, 2007                [Page 14]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   values.  In point of fact, if the client is set within 68 years of
   the server before the protocol is started, correct values are
   obtained even if the client and server are in adjacent eras.

   Some time values are represented in exponent format, including the
   precision, time constant and poll interval values.  These are in
   8-bit signed integer format in log2 (log to the base 2) seconds.

   The only operations permitted on them are increment and decrement.
   For the purpose of this document and to simplify the presentation, a
   reference to one of these state variables by name means the
   exponentiated value, e.g., the poll interval is 1024 s, while
   reference by name and exponent means the actual value, e.g., the poll
   exponent is 10.

   To convert system time in any format to NTP date and timestamp
   formats requires that the number of seconds s from the prime epoch to
   the system time be determined.  The era is the integer quotient and
   the timestamp the integer remainder as in:

   era = s / 2^(32) and timestamp = s - era*2^(32)

   which works for positive and negative dates.  To convert from NTP era
   and timestamp to system time requires the calculation

   s = era*2^(32) + timestamp

   to determine the number of seconds since the prime epoch.  Converting
   between NTP and system time can be a little messy, but beyond the
   scope of this document.  Note that the number of days in era 0 is one
   more than the number of days in most other eras and this won't happen
   again until the year 2400 in era 3.

   In the description of state variables to follow, explicit reference
   to integer type implies a 32-bit unsigned integer.  This simplifies
   bounds checks, since only the upper limit needs to be defined.
   Without explicit reference, the default type is 64-bit floating
   double.  Exceptions will be noted as necessary.


6.  Data Structures

   The NTP protocol state machines described in following sections are
   defined using state variables and flow chart fragments.  State
   variables are separated into classes according to their function in
   packet headers, peer and poll processes, the system process and the
   clock discipline process.  Packet variables represent the NTP header
   values in transmitted and received packets.  Peer and poll variables



Burbank, et al.          Expires April 26, 2007                [Page 15]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   represent the contents of the association for each server separately.
   System variables represent the state of the server as seen by its
   dependent clients.  Clock discipline variables represent the internal
   workings of the clock discipline algorithm.  Additional constant and
   variable classes are defined in Appendix A..

6.1.  Structure Conventions

   In order to distinguish between different variables of the same name
   but used in different processes, the naming convention summarized in
   Table 2 is employed.  A receive packet variable v is a member of the
   packet structure r with fully qualified name r.v.  In a similar
   manner x.v is a transmit packet variable, p.v is a peer variable, s.v
   is a system variable and c.v is a clock discipline variable.  There
   is a set of peer variables for each association; there is only one
   set of system and clock variables.  Most flow chart fragments begin
   with a statement label and end with a named go-to or exit.  A
   subroutine call includes a dummy () following the name and return at
   the end.to the point following the call.

                +------+---------------------------------+
                | Name | Description                     |
                +------+---------------------------------+
                | r.   | receive packet header variable  |
                | x.   | transmit packet header variable |
                | p.   | peer/poll variable              |
                | s.   | system variable                 |
                | c.   | clock discipline variable       |
                +------+---------------------------------+

                     Table 2: Name Prefix Conventions

6.2.  Global Parameters

   In addition to the variable classes a number of global parameters are
   defined in this document, including those shown with values in
   Figure 5














Burbank, et al.          Expires April 26, 2007                [Page 16]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   Name      Value       Description
   PORT      123         NTP port number
   VERSION   4           version number
   TOLERANCE 15e-6       frequency tolerance  (s/s)
   MINPOLL   4           minimum poll exponent (16 s)
   MAXPOLL   17          maximum poll exponent (36 h)
   MAXDISP   16          maximum dispersion (s)
   MINDISP   .005        minimum dispersion increment (s)
   MAXDIST   1           distance threshold (s)
   MAXSTRAT  16          maximum stratum number

                        Figure 5: Global Parameters

   .  While these are the only parameters needed in this document, a
   larger collection is necessary in the skeleton and larger still for
   any implementation.  Section B.1 contains those used by the skeleton
   for the mitigation algorithms, clock discipline algorithm and related
   implementation-dependent functions.  Some of these parameter values
   are cast in stone, like the NTP port number assigned by the IANA and
   the version number assigned NTPv4 itself.  Others like the frequency
   tolerance, involve an assumption about the worst case behavior of a
   system clock once synchronized and then allowed to drift when its
   sources have become unreachable.  The minimum and maximum parameters
   define the limits of state variables as described in later sections.

   While shown with fixed values in this document, some implementations
   may make them variables adjustable by configuration commands.  For
   instance, the reference implementation computes the value of
   PRECISION as log2 of the minimum time in several iterations to read
   the system clock.





















Burbank, et al.          Expires April 26, 2007                [Page 17]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   Name       Formula Description
   leap       leap    leap indicator (LI)
   version    version version number (VN)
   mode       mode    mode
   stratum    stratum stratum
   poll       poll    poll exponent
   precision rho     precision exponent
   rootdelay  delta   root delay
   rootdisp   E       root dispersion
   refid     refid    reference ID
   reftime   reftime  reference timestamp
   org       T1       origin timestamp
   rec       T2       receive timestamp
   xmt       T3       transmit timestamp
   dst       T4       destination timestamp
   keyid     keyid    key ID
   digest    digest   message digest

                     Figure 6: Packet Header Variables

6.3.  Packet Header Variables

   The most important state variables from an external point of view are
   the packet header variables described below.  The NTP packet consists
   of a number of 32-bit (4 octet) words in network byte order.  The
   packet format consists of three components, the header itself, one or
   more optional extension fields and an optional message authentication
   code (MAC).  The header component is identical to the NTPv3 header
   and previous versions.  The optional extension fields are used by the
   Autokey public key cryptographic algorithms described in [3].  The
   optional MAC is used by both Autokey and the symmetric key
   cryptographic algorithms described in the main body of this report.

   The NTP packet header follows the UDP and IP headers and the physical
   header specific to the underlying transport network.  It consists of
   a number of 32-bit (4-octet) words, although some fields use multiple
   words and others are packed in smaller fields within a word.  The NTP
   packet header shown in Appendix A has 12 words followed by optional
   extension fields and finally an optional message authentication code
   (MAC) consisting of the key identifier and message digest fields.

   The optional extension fields described in this section are used by
   the Autokey security protocol [3], which is not described here.  The
   MAC is used by both Autokey and the symmetric key authentication
   scheme described in Appendix A.  As is the convention in other
   Internet protocols, all fields are in network byte order, commonly
   called big-endian.




Burbank, et al.          Expires April 26, 2007                [Page 18]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   A list of the packet header variables is shown in Figure 6 and
   described in detail below.  The packet header fields apply to both
   transmitted (x prefix) and received packets (r prefix).  The NTP
   header is shown in Figure 7

    0                   1                   2                   3
    0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |LI | VN  |Mode |     Strat     |     Poll      |     Prec      |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                         Root Delay                            |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                         Root Dispersion                       |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                          Reference ID                         |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                                                               |
   +                       Reference Timestamp                     +
   |                                                               |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                                                               |
   +                        Origin Timestamp                       +
   |                                                               |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                                                               |
   +                        Receive Timestamp                      +
   |                                                               |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                                                               |
   +                        Transmit Timestamp                     +
   |                                                               |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                                                               |
   +                    Extension Field 1 (Optional)               +
   |                                                               |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                                                               |
   +                    Extension Field 2 (Optional)               +
   |                                                               |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   .                                                               .
   .                          Authentication                       .
   .                       (Optional) (160 bits)                   .
   .                                                               .
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

                      Figure 7: NTPv4 Message Format




Burbank, et al.          Expires April 26, 2007                [Page 19]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   , where the size of some multiple-word fields is shown in bits if not
   the default 32 bits.  The header extends from the beginning of the
   packet to the end of the Transmit Timestamp field.  The
   interpretation of the header fields is shown in the main body of this
   report.  When using the IPv4 address family these fields are
   backwards compatible with NTPv3.  When using the IPv6 address family
   on an NTPv4 server with a NTPv3 client, the Reference Identifier
   field appears to be a random value and a timing loop might not be
   detected.  The message authentication code (MAC) consists of a 32-bit
   Key Identifier followed by a 128bit Message Digest.  The message
   digest, or cryptosum, is calculated as in [6] over all header and
   optional extension fields.

   The variables are interpreted as follows:
   leap:  2-bit integer warning of an impending leap second to be
   inserted or deleted in the last minute of the current month,
   coded as follows:

       0 no warning
       1 last minute of the day has 61 seconds
       2 last minute of the day has 59 seconds
       3 alarm condition (the clock is not synchronized)

   version:
    3-bit integer representing the NTP version number, currently 4.

   mode:  3-bit integer representing the mode, with values defined
   as follows:

        0 reserved
        1 symmetric active
        2 symmetric passive
        3 client
        4 server
        5 broadcast
        6 NTP control message
        7 reserved for private use

   stratum:   8-bit integer representing the stratum, with values
   defined as follows:

        0 unspecified or invalid
        1 primary server (e.g., equipped with a GPS receiver)
        2-15 secondary server (via NTP)
        16 client-only
        17-255 undefined

   It is customary to map the stratum value 0 in received packets to



Burbank, et al.          Expires April 26, 2007                [Page 20]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   MAXSTRAT (16) in the peer variable p.stratum and to map
   p.stratum values of MAXSTRAT or greater to 0 in transmitted
   packets. This allows reference clocks, which normally appear at
   stratum 0, to be conveniently mitigated using the same algorithms
   used for external sources.

   poll: 8-bit signed integer representing the maximum interval
   between successive messages, in log2 seconds. Suggested default
   limits for minimum and maximum poll intervals are 6 and 10, '
   respectively.

   precision:  8-bit signed integer representing the precision of
   the system clock, in log2 seconds. For instance a value of -18
   corresponds to a precision of about one microsecond. The
   precision can be determined when the service first starts up as
   the minimum time of several iterations to read the system clock.

   rootdelay:  Total roundtrip delay to the reference clock, in NTP
   short format.

   rootdisp:  Total dispersion to the reference clock, in NTP short
   format.

   refid:  32-bit code identifying the particular server or
   referenceclock. The interpretation depends on the value in the
   stratum field.  For packet stratum 0 (unspecified or invalid)
   this is a four-character ASCII string, called the kiss code,
   used for debugging and monitoring purposes. For stratum 1
   (reference clock) this is a four-octet, left-justified,
   zero-padded ASCII string assigned to the radio clock. While not
   specifically enumerated in this document, the following have
   been used as ASCII identifiers:

        GOES Geosynchronous Orbit Environment Satellite
        GPS Global Position System
        PPS Generic pulse-per-second
        IRIG Inter-Range Instrumentation Group
        WWVB LF Radio WWVB Ft. Collins, CO 60 kHz
        DCF LF Radio DCF77 Mainflingen, DE 77.5 kHz
        HBG LF Radio HBG Prangins, HB 75 kHz
        MSF LF Radio MSF Rugby, UK 60 kHz
        JJY LF Radio JJY Fukushima, JP 40 kHz, Saga, JP 60 kHz
        LORC MF Radio LORAN C 100 kHz
        TDF MF Radio Allouis, FR 162 kHz
        CHU HF Radio CHU Ottawa, Ontario
        WWV HF Radio WWV Ft. Collins, CO
        WWVH HF Radio WWVH Kaui, HI
        NIST NIST telephone modem



Burbank, et al.          Expires April 26, 2007                [Page 21]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


        USNO USNO telephone modem
        PTB etc. European telephone modem

   Above stratum 1 (secondary servers and clients) this is the
   reference identifier of the server. If using the IPv4 address
   family, the identifier is the four-octet IPv4 address. If using
   the IPv6 address family, it is the first four octets of the MD5
   hash of the IPv6 address.

   reftime: Time when the system clock was last set or corrected,
   in NTP timestamp format.

   org:  Time at the client when the request departed for the
   server, in NTP timestamp format.

   rec:  Time at the server when the request arrived from the
   client, in NTP timestamp format.

   xmt:  Time at the server when the response left for the
   client, in NTP timestamp format.

   dst:  Time at the client when the reply arrived from the
   server, in NTP timestamp format. Note: This value is not
   included in a header field; it is determined upon arrival
   of the packet and made available in the packet buffer data
   structure.

   keyid: 32-bit unsigned integer used by the client and server to
   designate a secret 128-bit MD5 key. Together, the keyid and
   digest fields collectively are called message authentication
   code (MAC).

   digest: 128-bit bitstring computed by the keyed MD5 message
   digest algorithm described in Appendix A.

6.3.1.  The Kiss-o'-Death Packet

   If the Stratum field is 0, which is an 'unspecified' Stratum field
   value, the Reference Identifier field can be used to convey messages
   useful for status reporting and access control.  In NTPv4 and SNTPv4,
   packets of this kind are called Kiss-o'-Death (KoD) packets and the
   ASCII messages they convey are called kiss codes.  The KoD packets
   got their name because an early use was to tell clients to stop
   sending packets that violate server access controls.  The kiss codes
   can provide useful information for an intelligent client.  These
   codes are encoded in four-character ASCII strings left justified and
   zero filled.  The strings are designed for character displays and log
   files.  A list of the currently-defined kiss codes is given below:



Burbank, et al.          Expires April 26, 2007                [Page 22]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   +------+------------------------------------------------------------+
   | Code |                           Meaning                          |
   +------+------------------------------------------------------------+
   | ACST |         The association belongs to a unicast server        |
   | AUTH |                Server authentication failed                |
   | AUTO |                   Autokey sequence failed                  |
   | BCST |        The association belongs to a broadcast server       |
   | CRYP |    Cryptographic authentication or identification failed   |
   | DENY |               Access denied by remote server               |
   | DROP |                 Lost peer in symmetric mode                |
   | RSTR |              Access denied due to local policy             |
   | INIT |   The association has not yet synchronized for the first   |
   |      |                            time                            |
   | MCST | The association belongs to a dynamically discovered server |
   | NKEY |   No key found.  Either the key was never installed or is  |
   |      |                         not trusted                        |
   | RATE |  Rate exceeded.  The server has temporarily denied access  |
   |      |       because the client exceeded the rate threshold       |
   | RMOT |    Alteration of association from a remote host running    |
   |      |                           ntpdc.                           |
   | STEP |     A step change in system time has occurred, but the     |
   |      |           association has not yet resynchronized           |
   +------+------------------------------------------------------------+

                Figure 9: Currently-defined NTP Kiss Codes

6.3.2.  NTP Extension Field Format

   In NTPv4 one or more extension fields can be inserted after the
   header and before the MAC, which is always present when extension
   fields are present.  The extension fields can occur in any order;
   however, in some cases there is a preferred order which improves the
   protocol efficiency.

   An extension field contains a request or response message in the
   format shown in Figure 10















Burbank, et al.          Expires April 26, 2007                [Page 23]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


    0                   1                   2                   3
    0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |          Field Type           |            Length             |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                          Association ID                       |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                           Timestamp                           |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                           Filestamp                           |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                          Value Length                         |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   .                                                               .
   .                             Value                             .
   .                                                               .
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                        Signature Length                       |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   .                                                               .
   .                           Signature                           .
   .                                                               .
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                       Padding (as needed)                     |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

                   Figure 10: NTP Extension Field Format

   .  All extension fields are zero-padded to a word (4 octets)
   boundary.  The Length field covers the entire extension field,
   including the Length and Padding fields.  While the minimum field
   length is 4 words (16 octets), a maximum field length remains to be
   established.

   The RE, VN, and Code fields together form a Field Type field, a 16-
   bit integer which indicates the type of extension message contained
   within the extension field.

   The Length field is a 16-bit integer indicates the length of the
   entire extension field in octets, including the Length and Padding
   fields.

   The 32-bit Association ID field is set by clients to the value
   previously received from the server or 0 otherwise.  The server sets
   the Association ID field when sending a response as a handle for
   subsequent exchanges.  If the association ID value in a request does
   not match the association ID of any association, the server returns
   the request with the first two bits of the Field Type field set to 1.



Burbank, et al.          Expires April 26, 2007                [Page 24]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   The Timestamp and Filestamp 32-bit fields carry the seconds field of
   an NTP timestamp.  The Timestamp field establishes the signature
   epoch of the data field in the message, while the filestamp
   establishes the generation epoch of the file that ultimately produced
   the data.

   The 32-bit Value Length field indicates the length of the Value field
   in octets.  The minimum length of the Value field is 0.

   The 32-bit Value Length field indicates the length of the Value field
   in octets.  The minimum length of the Value field is 0.

   Zero padding is applied, as necessary, to extend the extension field
   to a word (4-octet) boundary.  If multiple extension fields are
   present, the last extension field is zero-padded to a double-word (8
   octet) boundary.

   The presence of the MAC and extension fields in the packet is
   determined from the length of the remaining area after the header to
   the end of the packet.  The parser initializes a pointer just after
   the header.  If the Length field is not a multiple of 4, a format
   error has occurred and the packet is discarded.  The following cases
   are possible based on the remaining length in words.
   0        The packet is not authenticated.
   1        The packet is an error report or crypto-NAK.
   2, 3, 4  The packet is discarded with a format error.
   5        The remainder of the packet is the MAC.
   >5       One or more extension fields are present.

   If an extension field is present, the parser examines the Length
   field.  If the length is less than 4 or not a multiple of 4, a format
   error has occurred and the packet is discarded; otherwise, the parser
   increments the pointer by this value.  The parser now uses the same
   rules as above to determine whether a MAC is present and/or another
   extension field.  An additional implementation dependent test is
   necessary to ensure the pointer does not stray outside the buffer
   space occupied by the packet.


7.  On Wire Protocol











Burbank, et al.          Expires April 26, 2007                [Page 25]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


              t2            t3           t6            t7
         +---------+   +---------+   +---------+   +---------+
     T1  |    0    |   |    t2   |   |   t4    |   |    t6   |
         +---------+   +---------+   +---------+   +---------+
     T2  |    0    |   |    t1   |   |   t3    |   |    t5   |  Packet
         +---------+   +---------+   +---------+   +---------+ Variables
     T3  |t2=clock |   |    t2   |   |t6=clock |   |    t6   |
         +---------+   +---------+   +---------+   +---------+
     T4  |   t1    |   |t3=clock |   |   t5    |   |t7=clock |
         +---------+   +---------+   +---------+   +---------+
                                                                Peer B
         +---------+   +---------+   +---------+   +---------+
    org  |   t1    |   |    t1   |   | T3<>t1? |   |    t5   |
         +---------+   +---------+   +---------+   +---------+   State
    rec  |   t2    |   |    t2   |   |   t6    |   |    t6   | Variables
         +---------+   +---------+   +---------+   +---------+
    xmt  |    0    |   |    t3   |   | T1<>t3? |   |    t7   |
         +---------+   +---------+   +---------+   +---------+

                   t2      t3                 t6          t7
         ---------------------------------------------------------
                  /\         \                 /\            \
                  /           \                /              \
                 /             \              /                \
                /               \/           /                 \/
         ---------------------------------------------------------
              t1                t4         t5                  t8

             t1            t4            t5             t8
         +---------+   +---------+   +---------+   +---------+
     T1  |    0    |   |    t2   |   |   t4    |   |    t6   |
         +---------+   +---------+   +---------+   +---------+
     T2  |    0    |   |    t1   |   |   t3    |   |    t5   |  Packet
         +---------+   +---------+   +---------+   +---------+ Variables
     T3  |    0    |   |t4=clock |   |   t4    |   |t8=clock |
         +---------+   +---------+   +---------+   +---------+
     T4  |t1=clock |   |    t3   |   |t5=clock |   |    t7   |
         +---------+   +---------+   +---------+   +---------+
                                                                Peer A
         +---------+   +---------+   +---------+   +---------+
    org  |    0    |   |  T3<>0? |   |   t3    |   | T3<>t3? |
         +---------+   +---------+   +---------+   +---------+   State
    rec  |    0    |   |    t4   |   |   t4    |   |    t8   | Variables
         +---------+   +---------+   +---------+   +---------+
    xmt  |   t1    |   |  T1=t1? |   |   t5    |   | T1<>t5? |
         +---------+   +---------+   +---------+   +---------+

                        Figure 12: On-Wire Protocol



Burbank, et al.          Expires April 26, 2007                [Page 26]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   The NTP on-wire protocol is the core mechanism to exchange time
   values between servers, peers and clients.  It is inherently
   resistant to lost or duplicate data packets.  Data integrity is
   provided by the IP and UDP checksums.  No flow-control or
   retransmission facilities are provided or necessary.  The protocol
   uses timestamps, either extracted from packet headers or struck from
   the system clock upon the arrival or departure of a packet.
   Timestamps are precision data and should be restruck in case of link
   level retransmission and corrected for the time to compute a MAC on
   transmit.

   NTP messages make use of two different communication modes, one to
   one and one to many, commonly referred to as unicast and broadcast.
   For the purposes of this document, the term broadcast is interpreted
   to mean any available one to many mechanism.  For IPv4 this equates
   to either IPv4 broadcast or IPv4 multicast.  For IPv6 this equates to
   IPv6 multicast.  For this purpose, IANA has allocated the IPv4
   multicast address 224.0.1.1 and the IPv6 multicast address ending
   :101, with prefix determined by scoping rules.

   The on-wire protocol uses four timestamps numbered T_1 through T_4
   and three state variables org, rec and xmt, as shown in Figure 12.
   This figure shows the most general case where each of two peers, A
   and B, independently measure the offset and delay relative to the
   other.  For purposes of illustration the individual timestamp values
   are shown in lower case with subscripts indicating the order of
   transmission and reception.

   In the figure the first packet transmitted by A containing only the
   transmit timestamp T3 with value t1.  B receives the packet at t2 and
   saves the origin timestamp T1 with value t1 in state variable org and
   the destination timestamp T4 with value t2 in state variable rec.  At
   this time or some time later B sends a packet to A containing the org
   and rec state variables in T1 and T2, respectively and in addition
   the transmit timestamp T3 with value t3, which is saved in the xmt
   state variable.  When this packet arrives at A the packet header
   variables T1, T2, T3 and destination timestamp T4 represent the four
   timestamps necessary to compute the offset and delay of B relative to
   A, as described later.

   Before the A state variables are updated, two sanity checks are
   performed in order to protect against duplicate or bogus packets.  A
   packet is a duplicate if the transmit timestamp T3 in the packet
   matches the xmt state variable.  A packet is bogus if the origin
   timestamp T1 in the packet does not match the org state variable.  In
   either of these cases the state variables are updated, but the packet
   is discarded.




Burbank, et al.          Expires April 26, 2007                [Page 27]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   The four most recent timestamps, T1 through T4, are used to compute
   the offset of B relative to A

   theta = T(B) - T(A) = 1/2*(T_2-T_1)+(T_3-T_4)

   and the roundtrip delay

   del = T(ABA)- = (T_4-T_1)-(T_3-T_2)

   Note that the quantities within parentheses are computed from 64-bit
   unsigned timestamps and result in signed values with 63 significant
   bits plus sign.  These values can represent dates from 68 years in
   the past to 68 years in the future.  However, the offset and delay
   are computed as the sum and difference of these values, which contain
   62 significant bits and two sign bits, so can represent unambiguous
   values from 34 years in the past to 34 years in the future.  In other
   words, the time of the client must be set within 34 years of the
   server before the service is started.  This is a fundamental
   limitation with 64-bit integer arithmetic..

   In implementations where floating double arithmetic is available, the
   first-order differences can be converted to floating double and the
   second-order sums and differences computed in that arithmetic.  Since
   the second-order terms are typically very small relative to the
   timestamps themselves, there is no loss in significance, yet the
   unambiguous range is increased from 34 years to 68 years.

   In some scenarios where the frequency offset between the client and
   server is relatively large and the actual propagation time small, it
   is possible that the delay computation becomes negative.  For
   instance, if the frequency difference is 100 PPM and the interval T_4
   - T_1 is 64 s, the apparent delay is -6.4 ms.  Since negative values
   are misleading in subsequent computations, the value of del should be
   clamped not less than the system precision s.precision rho defined
   below.

   The discussion above assumes the most general case where two
   symmetric peers independently measure the offsets and delays between
   them.  In the case of a stateless server, the protocol can be
   simplified.  A stateless server copies T_3 and T_4 from the client
   packet to T_1 and T_2 of the server packet and tacks on the transmit
   timestamp T_3 before sending it to the client.  Additional details
   for filling in the remaining protocol fields are given in the next
   section and in Appendix A.

   A SNTP primary server implementing the on-wire protocol has no
   upstream servers except a single reference clock In principle, it is
   indistinguishable from an NTP primary server which has the mitigation



Burbank, et al.          Expires April 26, 2007                [Page 28]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   algorithms, presumably to mitigate between multiple reference clocks.
   Upon receiving a client request, a SNTP primary server constructs and
   sends the reply packet as shown in Figure 5 below.  Note that the
   dispersion field in the packet header must be calculated in the same
   way as in the NTP case.

   A SNTP client using the on-wire protocol has a single server and no
   downstream clients.  It can operate with any subset of the NTP on-
   wire protocol, the simplest using only the transmit timestamp of the
   server packet and ignoring all other fields.  However, the additional
   complexity to implement the full on-wire protocol is minimal and is
   encouraged.


8.  Peer Process

   The peer process is called upon arrival of a server packet.  It runs
   the on-wire protocol to determine the clock offset and roundtrip
   delay and in addition computes statistics used by the system and poll
   processes.  Peer variables are instantiated in the association data
   structure when the structure is initialized and updated by arriving
   packets.  There is a peer process, poll process and association for
   each server.

   The discussion in this section covers only the variables and routines
   necessary for a conforming NTPv4 implementation.  Additional
   implementation details are in Section B.5.
























Burbank, et al.          Expires April 26, 2007                [Page 29]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


8.1.  Peer Process Variables
   Name       Formula       Description
   Configuration Variables
   srcaddr    srcaddr       source address
   srcport    srcport       source port
   dstaddr    dstaddr       destination address
   dstport    destport      destination port
   keyid      keyid         key identifier key ID
   Packet Variables
   leap       leap          leap indicator
   version    version       version number
   mode       mode          mode
   stratum    stratum       stratum
   ppoll      ppoll         peer poll exponent
   rootdelay  delta         root delay
   rootdisp   E             root dispersion
   refid     refid          reference ID
   reftime   reftime        reference timestamp
   Timestamp Variables
   t         t              epoch
   org       T1             origin timestamp
   rec       T2             receive timestamp
   xmt       T3             transmit timestamp
   Statistics Variables
   offset    theta          clock offset
   delay     del            roundtrip delay
   disp      epsilon        dispersion
   jitter    varphi         jitter

                     Figure 13: Peer Process Variables

   Figure 13 summarizes the common names, formula names and a short
   description of each peer variable, all of which have prefix p.  The
   following configuration variables are normally initialized when the
   association is mobilized, either from a configuration file or upon
   arrival of the first packet for an ephemeral association.

   p.srcadr: IP address of the remote server or reference clock.  This
   becomes the destination IP address in packets sent from this
   association.

   p.srcport: UDP port number of the server or reference clock.  This
   becomes the destination port number in packets sent from this
   association.  When operating in symmetric modes (1 and 2) this field
   must contain the NTP port number PORT (123) assigned by the IANA.  In
   other modes it can contain any number consistent with local policy.

   p.dstadr: IP address of the client.  This becomes the source IP



Burbank, et al.          Expires April 26, 2007                [Page 30]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   address in packets sent from this association.

   p.dstport: UDP port number of the client, ordinarily the NTP port
   number PORT (123) assigned by the IANA.  This becomes the source port
   number in packets sent from this association.

   p.keyid: Symmetric key ID for the 128-bit MD5 key used to generate
   and verify the MAC.  The client and server or peer can use different
   values, but they must map to the same key.

   The variables defined below are updated from the packet header as
   each packet arrives.  They are interpreted in the same way as the as
   the packet variables of the same names.
   ------------------
   |    receive     |
   ------------------
          \| /
   ------------------ no------------------
   |    format OK?  |-->| format error   |
   ------------------   ------------------
          \| /  yes
   ------------------ no------------------
   |    access OK?  |-->| access error   |
   ------------------   ------------------
          \| /  yes
   ------------------yes------------------
   |    mode = 3?   |-->| client_packet  |
   ------------------   ------------------
          \| /  no
   ------------------yes------------------
   |    auth OK?    |-->| auth error     |
   ------------------   ------------------
          \| /  yes
   ------------------
   |    match_assoc |
   ------------------

                       Figure 14: Receive Processing

   p.leap, p.version, p.mode, p.stratum, p.ppoll, p.rootdelay,
   p.rootdisp, p.refid, p.reftime

   It is convenient for later processing to convert the NTP short format
   packet values p.rootdelay and p.rootdisp to floating doubles as peer
   variables.

   The p.org, p.rec, p.xmt variables represent the timestamps computed
   by the on-wire protocol described previously.  The p.offset, p.delay,



Burbank, et al.          Expires April 26, 2007                [Page 31]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   p.disp, p.jitter variables represent the current time values and
   statistics produced by the clock filter algorithm.  The offset and
   delay are computed by the on-wire protocol; the dispersion and jitter
   are calculated as described below.  Strictly speaking, the epoch p.t
   is not a timestamp; it records the system timer upon arrival of the
   latest packet selected by the clock filter algorithm.

8.2.  Peer Process Operations

   Figure 14 shows the peer process code flow upon the arrival of a
   packet.  There is no specific method required for access control,
   although it is recommended that implementations include a match-and-
   mask scheme similar to many others now in widespread use.  Format
   checks require correct field length and alignment, acceptable version
   number (1-4) and correct extension field syntax, if present.  There
   is no specific requirement for authentication; however, if
   authentication is implemented, the symmetric key scheme described in
   Section 6 must be included among the supported.  This scheme uses the
   MD5 keyed hash algorithm Section A.2.  For the most vulnerable
   applications the Autokey public key scheme described in [3] is
   recommended.

   Next, the association table is searched for matching source address
   and source port using the find_assoc() routine in Section A.5.  The
   dispatch table near the beginning of that section is indexed by the
   packet mode and association mode (0 if no matching association) to
   determine the dispatch code and thus the case target.  The
   significant cases are FXMT, NEWPS and NEWBC.
   -----------------
   | client_packet |
   -----------------
         \ | /
   -----------------
   | copy header   |
   -----------------
         \ | /
   -----------------
   | copy T_1,T_2  |
   -----------------
         \ | /
   -----------------
   | T_3 = clock   |
   -----------------
         \ | /
   -----------------yes-----------------
   | copy header   |-->| MD5 digest    |-\
   -----------------   ----------------- |
           | no                          |



Burbank, et al.          Expires April 26, 2007                [Page 32]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


         \ | /                           |
   -----------------                     |
   | NAK digest    |                     |
   -----------------                     |
           |-----------------------------/
         \ | /
   -----------------
   | fast_xmit()   |
   -----------------
         \ | /
   -----------------
   | xmt = T_3     |
   -----------------
         \ | /
   -----------------
   | return        |
   -----------------


   Packet Variable <-- Variable
   x.leap <-- s.leap
   x.version <-- r.version
   x.mode <-- 4
   x.stratum <-- s.stratum
   x.poll <-- r.poll
   x.precision <-- s.precision
   x.rootdelay <-- s.rootdelay
   x.rootdisp <-- s.rootdisp
   x.refid <-- s.refid
   x.reftime <-- s.reftime
   x.org <-- r.xmt
   x.rec <-- r.dst
   x.xmt <-- clock
   x.keyid <-- r.keyid
   x.digest <-- md5 digest

                    Figure 15: Client Packet Processing

   FXMIT.  This is a client (mode 3) packet matching no association.
   The server constructs a server (mode 4) packet and returns it to the
   client without retaining state.  The server packet is constructed as
   in Figure 15 and the fast_xmit() routine in Section B.5.  If the
   s.rootdelay and s.rootdisp system variables are stored in floating
   double, they must be converted to NTP short format first.  Note that,
   if authentication fails, the server returns a special message called
   a crypto-NAK.  This message includes the normal NTP header data shown
   in the figure, but with a MAC consisting of four octets of zeros.
   The client is free to accept or reject the data in the message.



Burbank, et al.          Expires April 26, 2007                [Page 33]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   NEWBC.  This is a broadcast (mode 5) packet matching no association.
   The client mobilizes a client (mode 3) association as shown in the
   mobilize() and clear() routines in Section A.2.  Implementations
   supporting authentication first perform the necessary steps to run
   the Autokey or other protocol, and determine the propagation delay,
   then continues in listen-only (mode 6) to receive further packets.
   Note the distinction between a mode-6 packet, which is reserved for
   the NTP monitor and control functions, and a mode-6 association.

   NEWPS.  This is a symmetric active (1) packet matching no
   association.  The client mobilizes a symmetric passive (mode 2)
   association as shown in the mobilize() and clear() routines in
   Section A.2.  Code flow continues to the match_assoc() fragment
   described below.  In other cases the packet matches an existing
   association and code flows to the match_assoc fragment in Figure 16.
   The packet timestamps are carefully checked to avoid invalid,
   duplicate or bogus packets, as shown in the figure.  Note that a
   crypto-NAK is considered valid only if it survives these tests.
   Next, the peer variables are copied from the packet header variables
   as shown in Figure 17 and the packet() routine in Section A.5.
   Implementations must include a number of data range checks as shown
   in Table 3 and discard the packet if the ranges are exceeded;
   however, the header fields are copied even if errors occur, since
   they are necessary in symmetric modes to construct the subsequent
   poll message.


























Burbank, et al.          Expires April 26, 2007                [Page 34]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   ------------------
   | match assoc  |
   ----------------
        \ | /
   ----------------yes----------------
   | T_3 = 0?     |-->| format error |
   ----------------   ----------------
        \ | / no
   ----------------yes----------------
   | T_3 = xmt?   |-->| duplicate    |
   ----------------   ----------------
        \ | / no
   ----------------no ----------------yes
   | mode = 5?    |-->|T_1 or T2 = 0?|--\
   ----------------   ----------------  |
          | yes             \ | / no    |
        \ | /<-----\  ----------------  |
          |         \-| T_1 = xmt?   |  |
   ----------------   ----------------  |
   | auth = NAK?  |      no  \ | /<-----/
   ----------------            |
   yes\|/     no\|/   ----------------
   --------- ------   |  org = T_3   |
   |org=T_3| |auth|   | rec = T_4    |
   |rec=T_4| |err |   ----------------
   --------- ------         \ | /
     \|/              ----------------
   ---------          | return       |
   |packet |          ----------------
   ---------

                      Figure 16: Timestamp Processing



















Burbank, et al.          Expires April 26, 2007                [Page 35]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   ----------------
   | packet       |
   ----------------
        \ | /
   ----------------
   | copy header  |
   ----------------
        \ | /
   ----------------bad----------------
   | header?      |-->|header error  |
   ----------------   ----------------
        \ | /
   ----------------
   | reach |= 1   |
   ----------------
        \ | /
   ----------------
   | poll update  |
   ----------------
        \ | /
   ----------------------------------------
   | theta = 1/2*(T_2-T_1)+(T_3-T_4)      |
   | del = (T_4-T_1)-(T_3-T_2)            |
   | epsilon = rho_r+rho+capphi*((T_4-T_1)|
   ----------------------------------------
        \ | /
   ----------------
   | clock filter |
   ----------------

   Peer Variables <-- Packet Variables
   p.leap <-- r.leap
   p.mode <-- r.mode
   p.stratum <-- r.stratum
   p.ppoll <-- r.ppoll
   p.rootdelay <-- r.rootdelay
   p.rootdisp <-- r.rootdisp
   p.refid <-- r.refid
   p.reftime <-- r.reftime

                       Figure 17: Packet Processing










Burbank, et al.          Expires April 26, 2007                [Page 36]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   +----------------+--------------------------------------------------+
   | Packet Type    | Description                                      |
   +----------------+--------------------------------------------------+
   | 1 duplicate    | The packet is at best an old duplicate or at     |
   | packet         | worst a replay by a hacker.  This can happen in  |
   |                | symmetric modes if the poll intervals are        |
   |                | uneven.                                          |
   | 2 bogus packet |                                                  |
   | 3 invalid      | One or more timestamp fields are invalid.  This  |
   |                | normally happens in symmetric modes when one     |
   |                | peer sends the first packet to the other and     |
   |                | before the other has received its first reply.   |
   | 4 access       | The access controls have black                   |
   | denied         |                                                  |
   | 5              | The cryptographic message digest does not match  |
   | authentication | the MAC.                                         |
   | failure        |                                                  |
   | 6              | The server is not synchronized to a valid        |
   | unsynchronized | source.                                          |
   | 7 bad header   | One or more header fields are invalid.           |
   | data           |                                                  |
   | 8 autokey      | Public key cryptography has failed to            |
   | error          | authenticate the packet.                         |
   | 9 crypto error | Mismatched or missing cryptographic keys or      |
   |                | certificates.                                    |
   +----------------+--------------------------------------------------+

                       Table 3: Packet Error Checks

   The 8-bit p.reach shift register in the poll process described later
   is used to determine whether the server is reachable or not and
   provide information useful to insure the server is reachable and the
   data are fresh.  The register is shifted left by one bit when a
   packet is sent and the rightmost bit is set to zero.  As valid
   packets arrive, the rightmost bit is set to one.  If the register
   contains any nonzero bits, the server is considered reachable;
   otherwise, it is unreachable.  Since the peer poll interval might
   have changed since the last packet, the poll_update() routine in
   Section A.8 is called to re-determine the host poll interval.

   The on-wire protocol calculates the clock offset theta and roundtrip
   delay del from the four most recent timestamps as shown in Figure 12.
   While it is in principle possible to do all calculations except the
   first-order timestamp differences in fixed-point arithmetic, it is
   much easier to convert the first-order differences to floating
   doubles and do the remaining calculations in that arithmetic, and
   this will be assumed in the following description.  The dispersion
   statistic epsilon(t) represents the maximum error due to the



Burbank, et al.          Expires April 26, 2007                [Page 37]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   frequency tolerance and time since the last measurement.  It is
   initialized

   epsilon(t_o) = rho_r + rho +cappsi(T_4-T_1)

   when the measurement is made at t _0.  Here rho_r is the peer
   precision in the packet header r.precision and rho the system
   precision s.precision, both expressed in seconds.  These terms are
   necessary to account for the uncertainty in reading the system clock
   in both the server and the client.  The dispersion then grows at
   constant rate TOLERANCE (cappsi); in other words, at time t,
   epsilon(t) = epsilon(t_0) + cappsi(t-t_0).  With the default value
   cappsi = 15 PPM, this amounts to about 1.3 s per day.  With this
   understanding, the argument t will be dropped and the dispersion
   represented simply as epsilon.  The remaining statistics are computed
   by the clock filter algorithm described in the next section.



































Burbank, et al.          Expires April 26, 2007                [Page 38]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


9.  Clock Filter Algorithm
   -----------------------
   | clock filter        |
   -----------------------
            \ | /
   -----------------------
   | shift sample theta, |
   | del, epsilon, and t |
   | filter shift registr|
   -----------------------
            \ | /
   -----------------------
   | copy filter to a    |
   | temporary list. sort|
   | list by increasing  |
   | del.  Let theta_i   |
   | del_i, epsilon_i,   |
   | t_i be the ith entry|
   | on the sorted list. |
   -----------------------
            \ | /
   -----------------------   no
   |     t_0 > t?        |----\
   -----------------------    |
            \ | / yes         |
   -----------------------    |
   | theta = theta_0     |    |
   | del = del_0         |    |
   | epsilon             |    |
   | = sum(epsilon_i)    |    |
   |       ----------    |    |
   |        2^(i+1)      |    |
   | varphi              |    |
   | = sqrt(1/7* ...     |    |
   |    ... sum( ...     |    |
   | (theta_0-theta_i)^2 |    |
   | t = t_0             |    |
   -----------------------    |
            \ | /             |
   -----------------------    |
   | clock_select()      |    |
   -----------------------    |
            \ | /<------------/
   -----------------------
   | return              |
   -----------------------

                    Figure 18: Clock Filter Processing



Burbank, et al.          Expires April 26, 2007                [Page 39]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   The clock filter algorithm grooms the stream of on-wire data to
   select the samples most likely to represent the correct time.  The
   algorithm produces the p.offset theta, p.delay del, p.dispersion
   epsilon, p.jitter varphi, and time of arrival p.t t used by the
   mitigation algorithms to determine the best and final offset used to
   discipline the system clock.  They are also used to determine the
   server health and whether it is suitable for synchronization.  The
   core processing steps of this algorithm are shown in Figure 18 with
   more detail in the clock_filter() routine in Section A.5.

   The clock filter algorithm saves the most recent sample tuples
   (theta, del, epsilon, t) in an 8-stage shift register in the order
   that packets arrive.  Here t is the system timer, not the peer
   variable of the same name.  The following scheme is used to insure
   sufficient samples are in the register and that old stale data are
   discarded.  Initially, the tuples of all stages are set to the dummy
   tuple (0,MAXDISP, MAXDISP, t).  As valid packets arrive, the (theta,
   del, epsilon, t) tuples are shifted into the register causing old
   samples to be discarded, so eventually only valid samples remain.  If
   the three low order bits of the reach register are zero, indicating
   three poll intervals have expired with no valid packets received, the
   poll process calls the clock filter algorithm with the dummy tuple
   just as if the tuple had arrived from the network.  If this persists
   for eight poll intervals, the register returns to the initial
   condition.

   In the next step the shift register stages are copied to a temporary
   list and the list sorted by increasing del.  Let j index the stages
   starting with the lowest del.  If the sample epoch t_0 is not later
   than the last valid sample epoch p.t, the routine exits without
   affecting the current peer variables.  Otherwise, let epsilon_j be
   the dispersion of the jth entry, then
         i=n-1
         ---     e_i
   e=    \     --------
         /        (i+1)
         ---     2
         i=0

   is the peer dispersion p.disp.  Note the overload of epsilon, whether
   input to the clock filter or output, the meaning should be clear from
   context.

   The observer should note (a) if all stages contain the dummy tuple
   with dispersion MAXDISP, the computed dispersion is a little less
   than 16 s, (b) each time a valid tuple is shifted into the register,
   the dispersion drops by a little less than half, depending on the
   valid tuples dispersion, (c) after the fourth valid packet the



Burbank, et al.          Expires April 26, 2007                [Page 40]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   dispersion is usually a little less than 1 s, which is the assumed
   value of the MAXDIST parameter used by the selection algorithm to
   determine whether the peer variables are acceptable or not.

   Let the first stage offset in the sorted list be theta_0; then, for
   the other stages in any order, the jitter is the RMS average
              +-----                                    -----+
              |                                        1/2   |
              |            +-----                 -----+     |
              |            |  n-1                      |     |
              |            |  ---                      |     |
              |    1       |  \                     2  |     |
   varphi   = | -------- * |  /    (theta_0-theta_j)   |     |
              |  (n-1)     |  ---                      |     |
              |            |  j=1                      |     |
              |            +-----                 -----+     |
              |                                              |
              +-----                                    -----+

   where n is the number of valid tuples in the register.  In order to
   insure consistency and avoid divide exceptions in other computations,
   the varphi is bounded from below by the system precision rho
   expressed in seconds.  While not in general considered a major factor
   in ranking server quality, jitter is a valuable indicator of
   fundamental timekeeping performance and network congestion state.

   Of particular importance to the mitigation algorithms is the peer
   synchronization distance, which is computed from the root delay and
   root dispersion.  The root delay is

   del ' = delta_r + del

   and the root dispersion is

   epsilon ' = E_r + epsilon + varphi

   Note that epsilon and therefore increase at rate capphi.  The peer
   synchronization distance is defined

   lambda = (del ' / 2) + epsilon

   and recalculated as necessary.  The lambda is a component of the root
   synchronization distance caplambda used by the mitigation algorithms
   as a metric to evaluate the quality of time available from each
   server.  Note that there is no state variable for lambda, as it
   depends on the time since the last update.





Burbank, et al.          Expires April 26, 2007                [Page 41]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


10.  System Process

   As each new sample (theta, delta, epsilon, t) is produced by the
   clock filter algorithm, the sample is processed by the mitigation
   algorithms consisting of the selection, clustering, combining and
   clock discipline algorithms in the system process.  The selection
   algorithm scans all associations and casts off the falsetickers,
   which have demonstrably incorrect time, leaving the truechimers as
   result.  In a series of rounds the clustering algorithm discards the
   association statistically furthest from the centroid until a minimum
   number of survivors remain.  The combining algorithm produces the
   best and final offset on a weighted average basis and selects one of
   the associations as the system peer providing the best statistics for
   performance evaluation.  The final offset is passed to the clock
   discipline algorithm to steer the system clock to the correct time.
   The statistics (theta, delta, epsilon, t) associated with the system
   peer are used to construct the system variables inherited by
   dependent servers and clients and made available to other
   applications running on the same machine.

   The discussion in following sections covers only the basic variables
   and routines necessary for a conforming NTPv4 implementation.
   Additional implementation details are in Section B.6.  An interface
   that might be considered in a formal specification is represented by
   the function prototypes in Section B.1.

10.1.  System Process Variables

   The variables and parameters associated with the system process are
   summarized in Figure 21, which gives the variable name, formula name
   and short description.  Unless noted otherwise, all variables have
   assumed prefix s.
   Name/Formula/Description
   t/t/epoch
   leap/leap/leap indicator
   stratum/stratum/stratum
   precision/rho/precision
   p/p/system peer pointer
   offset/captheta/combined offset
   jitter/varsigma/combined jitter
   rootdelay/capdelta/root delay
   rootdisp/E/root dispersion
   refid/refid/reference ID
   reftime/reftime/reference time
   NMIN/3/minimum survivors
   CMIN/1/minimum candidates

            Figure 21: System Process Variables and Parameters



Burbank, et al.          Expires April 26, 2007                [Page 42]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   All the variables except s.t and s.p have the same format and
   interpretation as the peer variables of the same name.  The remaining
   variables are defined below.

   s.t: Integer representing the value of the system timer at the last
   update.

   s.p: System peer association pointer.

   s.precision: 8-bit signed integer representing the precision of the
   system clock, in log2 seconds.

   s.offset: Offset computed by the combining algorithm.

   s.jitter: Jitter computed by the cluster and combining algorithms.

   The variables defined below are updated from the system peer process
   as described later.  They are interpreted in the same way as the as
   the peer variables of the same names.

   s.leap, s.stratum, s.rootdelay, s.rootdisp, s.refid, s.reftime

   Initially, all variables are cleared to zero, then the s.leap is set
   to 3 (unsynchronized) and s.stratum is set to MAXSTRAT (16).  The
   remaining statistics are determined as described below.

10.2.  System Process Operations

   The system process implements the selection, clustering, combining
   and clock discipline algorithms.  The clock_select() routine in
   Figure 22 includes the selection algorithm of Section 9.2.1 that
   produces a majority clique of truechimers based on agreement
   principles.  The clustering algorithm of Section 9.2.2 discards the
   outliers of the clique to produce the survivors used by the combining
   algorithm in Section 9.2.3, which in turn provides the final offset
   for the clock discipline algorithm in Section 9.2.4.  If the
   selection algorithm cannot produce a majority clique, or if the
   clustering algorithm cannot produce at least CMIN survivors, the
   system process terminates with no further processing.  If successful,
   the clustering algorithm selects the statistically best candidate as
   the system peer and its variables are inherited as the system
   variables.  The selection and clustering algorithms are described
   below separately, but combined in the code skeleton.








Burbank, et al.          Expires April 26, 2007                [Page 43]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


                            -------------------------
                            | clock_select()        |
                            -------------------------
                                     \|/
   -----------------------------------|---------------
   |              ----------- ---------------------- |
   |          /---| accept? | |  scan candidates   | |
   |          |   ----------- |                    | |
   |          | yes       no| |                    | |
   |     -----------      |   |                    | |
   |     | add peer|      |   |                    | |
   |     -----------      |   |                    | |
   |          |          \|/  |                    | |
   |          \-------->----->|                    | |
   |                          |                    | |
   |  selection algorithm     ---------------------- |
   |                                  \|/            |
   ------------------------------------|--------------
                  no          -----------------------
               /--------------| survivors?          |
               |              -----------------------
               |                      \|/ yes
               |              -----------------------
               |              | clustering algorithm|
               |              -----------------------
               |                      \|/
               |              -----------------------
               |<---------yes-| n < CMIN?           |
              \|/             -----------------------
   -------------------------          \|/ no
   | s.p = NULL            |  -----------------------
   -------------------------  | s.p = vo.p          |
              \|/             -----------------------
   -------------------------          \|/
   | return (UNSYNC)       |  -----------------------
   -------------------------  | return (SYNC)       |
                              -----------------------


                     Figure 22: clock_select() routine

10.2.1.  Selection Algorithm

   The selection algorithm operates to find the truechimers using
   Byzantine agreement principles originally proposed by Marzullo [7],
   but modified to improve accuracy.  An overview of the algorithm is
   listed below and the first half of the clock_select() routine in
   Section A.6.1.  First, those servers which are unusable according to



Burbank, et al.          Expires April 26, 2007                [Page 44]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   the rules of the protocol are detected and discarded by the accept()
   routine in Figure 23 and Section B.6.3.  Next, a set of tuples {p,
   type, edge} is generated for the remaining servers, where p is an
   association pointer, type and edge identifies the upper (+1), middle
   (0) and lower (-1) endpoint of a correctness interval [theta -
   lambda, theta + lambda], where lambda is the root distance.

   1.  1.  For each of m associations, construct a correctness interval
       [(theta - rootdist()), (theta + rootdist())].

   2.  2.  Select the lowpoint, midpoint and highpoint of these
       intervals.  Sort these values in a list from lowest to highest.
       Set the number of falsetickers f = 0.

   3.  3.  Set the number of midpoints d = 0.  Set c = 0.  Scan from
       lowest endpoint to highest.  Add one to c for every lowpoint,
       subtract one for every highpoint, add one to d for every
       midpoint.  If c >= m - f, stop; set l = current lowpoint

   4.  4.  Set c = 0.  Scan from highest endpoint to lowest.  Add one to
       c for every highpoint, subtract one for every lowpoint, add one
       to d for every midpoint.  If c >= m - f, stop; set u = current
       highpoint.

   5.  5.  Is d = f and l < u?

   6.  if yes, then follow step 5y, else, follow step 5n.

   7.  5y.  Success: the intersection interval is [l, u].

   8.  5n.  Add one to f.  Is f < (m / 2)?  If yes, then go to step 3
       again.  If no, then go to step 6.

   9.  6.  Failure; a majority clique could not be found.  Stop
       algorithm.

   The tuples are placed on a list and sorted by edge.  The list is
   processed from the lowest to the highest, then from highest to lowest
   as described in detail in [8].  The algorithm starts with the
   assumption that there are no falsetickers (f = 0) and attempts to
   find a nonempty intersection interval containing the midpoints of all
   correct servers, i.e., truechimers.  If a nonempty interval cannot be
   found, it increases the number of assumed falsetickers by one and
   tries again.  If a nonempty interval is found and the number of
   falsetickers is less than the number of truechimers, a majority
   clique has been found and the midpoints (offsets) represent the
   survivors available for the clustering algorithm.  Otherwise, there
   are no suitable candidates to synchronize the system clock.



Burbank, et al.          Expires April 26, 2007                [Page 45]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   --------------------
   | accept()         |
   --------------------
           \|/
   --------------------
   | leap = 11?       |
   | stratum >=       |--any yes---\ server not
   | MAXSTRAT?        |            | synchronized
   --------------------            |
           \|/ all no              |
   --------------------            |
   | reach = 0?       |---yes----->| server not
   --------------------            | reachable
           \|/ no                  |
   --------------------            |
   | root_dist() >=   |            |
   | MAXDIST?         |---yes----->| root distance
   --------------------            | exceeded
           \|/ no                  |
   --------------------            |
   | refid = addr?    |---yes----->| server/client
   --------------------            | sync loop
           \|/ no                  |
   --------------------            |
   | return (YES)     | -----------------------
   -------------------- | return (NO)         |
                        -----------------------

                        Figure 23: accept() routine

10.2.2.  Clustering Algorithm

   The members of the majority clique are placed on the survivor list,
   and sorted first by stratum, then by root distance lambda.  The
   sorted list is processed by the clustering algorithm below and the
   second half of the clock_select() algorithm in Section B.6.1.

      1.  Let (theta, phi, Lambda) represent a candidate peer with
      offset theta, jitter j and a weight factor Lambda = stratum *
      MAXDIST + rootdist().

      2.  Sort the candidates by increasing Lambda.  Let n be the number
      of candidates and NMIN the minimum number of survivors.

      3.  For each candidate compute the selection jitter jsubS (RMS
      peer offset differences between this and all other candidates).





Burbank, et al.          Expires April 26, 2007                [Page 46]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


      4.  Select j_max as the candidate with maximum j_S.

      5.  Select j_min as the candidate with minimum j_S.

      If yes, go to step 6y.  If no, go to step 6n.

      6y.  Done.  The remaining cluster survivors are correct.  The
      survivors are in the v. structure sorted by Lambda.

      6n.  Delete the outlyer candidate with j_max; reduce n by one, and
      go back to step 3.

   It operates in a series of rounds where each round discards the
   furthest statistical outlier until a specified minimum number of
   survivors NMIN (3) are left or until no further improvement is
   possible.  In each round let n be the number of survivors and s index
   the survivor list.  Assume jp is the peer jitter of the s survivor.
   Compute
              +-----                                    -----+
              |                                        1/2   |
              |            +-----                 -----+     |
              |            |  n-1                      |     |
              |            |  ---                      |     |
              |    1       |  \                     2  |     |
   varphi_s = | -------- * |  /    (theta_s-theta_j)   |     |
              |  (n-1)     |  ---                      |     |
              |            |  j=1                      |     |
              |            +-----                 -----+     |
              |                                              |
              +-----                                    -----+

   as the selection jitter.  Then choose varphi_max = max  (varphi) and
   varphi_min = min (varphi).  If varphi_max < varphi_min or n < NMIN,
   no further reduction in selection jitter is possible, so the
   algorithm terminates and the remaining survivors are processed by the
   combining algorithm.  Otherwise, the algorithm case off the
   varphi_max survivor, reduces n by one and makes another round.














Burbank, et al.          Expires April 26, 2007                [Page 47]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


10.2.3.  Combining Algorithm
   ---------------------
   | clock_combine()   |
   ---------------------
           \|/
   ---------------------
   | y = z = w = 0     |
   ---------------------
           \|/
   ---------------------
   | scan cluster      |   ------------------
   | survivors         |-->| x = rootdist() |
   |                   |   ------------------
   |                   |          \|/
   |                   |   ------------------
   |                   |<--| y+= 1/x        |
   |                   |   | z+=theta_i/x   |
   |                   |   | w+=(theta_i -  |
   |                   |   | theta_o)^2     |
   ---------------------   ------------------
           \|/ done
   -----------------------
   | captheta = z/y      |
   | vartheta = sqrt(w/y)|
   -----------------------
           \|/
   -----------------------
   | return              |
   -----------------------

   Variable/Process/Description
   captheta/system/combined clock offset
   vartheta_p/system/combined jitter
   theta_0/survivor list/first survivor offset
   theta_i/survivor list/ith survivor offset
   x,y,z,w/ /temporaries


                    Figure 25: clock_combine() routine












Burbank, et al.          Expires April 26, 2007                [Page 48]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


                         --------------------
                         | clock_update()   |
                         --------------------
                                 \|/
                         --------------------
            /----no----->| p.t > s.t        |
            |            --------------------
            |                    \|/ yes
            |            --------------------
            |            | s.t = p.t        |
            |            --------------------
            |                    \|/
            |            --------------------
            |            | local_clock()    |
            |            --------------------
            |                    \|/
            |<--------------------+-----------------\
            | panic\|/            | adj        step\|/
            | -------------       |       -------------------
            | | panic exit|       |       | clear all assoc.|
            | -------------       |       -------------------
            |             -----------------        \|/
            |             |*update system | -----------------
            |             | variables     | | leap = 3      |
            |             ----------------- | quamtum =     |
            |                    \|/        | MAXSTRAT      |
            |                     |         -----------------
            \---------------------+----------------/
                                  |
                          ---------------
                          | return      |
                          ---------------

   System Variables <-- System Peer Variables
   leap <-- leap
   stratum <-- stratum + 1
   refid <-- refid
   reftime <-- reftime
   capdelta <-- capdelta_r + del
   E <-- E_r+epsilon+cappsi*mu+varphi+|captheta|
   * update system variables

                     Figure 26: clock_update() routine

   The remaining survivors are processed by the clock_combine() routine
   in Figure 25 and Section A.6.4 to produce the best and final data for
   the clock discipline algorithm.  The routine processes the peer
   offset theta and jitter varphi to produce the system offset captheta



Burbank, et al.          Expires April 26, 2007                [Page 49]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   and system peer jitter vartheta_p, where each server statistic is
   weighted by the reciprocal of the root distance and the result
   normalized.  The system peer jitter vartheta_p is a component of the
   system jitter described later.

   The system statistics are passed to the clock_update() routine in
   Figure 26 and Section A.6.4.  If there is only one survivor, the
   offset passed to the clock discipline algorithm is captheta = theta
   and the system peer jitter is vartheta=varphi.  Otherwise, the
   selection jitter vartheta_s is computed as in (8), where theta_0
   represents the offset of the system peer and j ranges over the
   survivors.
   Peer Variables         Client        System Variables
   ----------------                     -----------------
   | theta = 1/2* |-------------------->| captheta =    |
   | [(T_2 - T_1)+|                     | (combine      |
   | (T_3 - T_4)] |                     | (theta_j))    |
   ----------------                     -----------------
   | del = [(T_4 -|--sum--------------->| capdelta=     |
   | T_1) - (T_3 -|  /|\                | capdelta_r +  |
   | T_2)]        |   |                 | del           |
   ----------------   |                 -----------------
   | epsilon =    |   |                 | E = E_r +     |
   | rho_r + rho +|   |                 | epsilon +     |
   | captheta*(   |   |                 | vartheta +    |
   | T_4 - T_1)   |------------sum----->| absolutevalue(|
   ----------------   |        /|\      | theta)        |
   | varphi =     |   |         |       -----------------
   | sqrt((1/n)-1)*|  |         |       | varphi_s =    |
   | (sum(theta_0)|   |         |       | sqrt(1/(m-1)* |
   | -theta_i)^2))|---|---\     |       | sum(theta_0-  |
   ----------------   |   |     |       | theta_j)^2)   |
         /|\          |   |     |       -----------------
          |           |   |     |             \|/
          |           |   \------------------>sum
    server|           |         |              |
   ----------------   |         |             \|/
   |    rho_r     |   |         |              |
   ----------------   |         |       -----------------
   |  capdelta_r  |>--/         |       | vartheta =    |
   ----------------             |       | sqrt(         |
   |     E_r      |>------------/       | (vartheta_p)^2|
   ----------------                     | +             |
                                        | (vartheta_s)^2|
                                        -----------------

                  Figure 27: System Variables Processing




Burbank, et al.          Expires April 26, 2007                [Page 50]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   The first survivor on the survivor list is selected as the system
   peer, here represented by the statistics (theta, del, epsilon,
   varphi).  By rule, an update is discarded if its time of arrival p.t
   is not strictly later than the last update used s.t.  Let mu = p.t -
   s.t be the time since the last update or update interval.  If the
   update interval is less than or equal to zero, the update is
   discarded.  Otherwise, the system variables are updated from the
   system peer variables as shown in Figure 26.  Note that s.stratum is
   set to p.stratum plus one.

   The arrows labeled IGNOR, PANIC, ADJ and STEP refer to return codes
   from the local_clock() routine described in the next section.  IGNORE
   means the update has been ignored as an outlier.  PANIC means the
   offset is greater than the panic threshold PANICT (1000 s) and
   normally causes the program to exit with a diagnostic message to the
   system log.  STEP means the offset is less than the panic threshold,
   but greater than the step threshold STEPT (125 ms).  Since this means
   all peer data have been invalidated, all associations are reset and
   the client begins as at initial start.  ADJ means the offset is less
   than the step threshold and thus a valid update for the local_clock()
   routine described later.  In this case the system variables are
   updated as shown in Figure 26.

   There is one exception not shown.  The dispersion increment is
   bounded from below by MINDISP.  In subnets with very fast processors
   and networks and very small dispersion and delay this forces a
   monotone-definite increase in , which avoids loops between peers
   operating at the same stratum.

   Figure 27 shows how the error budget grows from the packet variables,
   on-wire protocol and system peer process to produce the system
   variables that are passed to dependent applications and clients.  The
   system jitter is defined

   vartheta = sqrt((vartheta_p)^2+(vartheta_s)^2)

   where vartheta_s is the selection jitter relative to the system peer.
   The system jitter is passed to dependent applications programs as the
   nominal error statistic.  The root delay capdelta and root dispersion
   E statistics are relative to the primary server reference clock and
   thus inherited by each server along the path.  The system
   synchronization distance is defined

   caplambda = capdelta/2 + E

   which is passed to dependent application programs as the maximum
   error statistic.




Burbank, et al.          Expires April 26, 2007                [Page 51]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


10.2.4.  Clock Discipline Algorithm
                        ---------
             thetar +  |         \        +----------------+
         NTP --------->|  Phase   \  V_d  |                |  V_s
             thetac -  | Detector  ------>|  Clock Filter  |-----+
             +-------->|          /       |                |     |
             |         |         /        +----------------+     |
             |          ---------                                |
             |                                                   |
           -----                                                 |
          /     \                                                |
          | VFO |                                                |
          \     /                                                |
           -----    +-------------------------------------+      |
             ^      |            Loop Filter              |      |
             |      |                                     |      |
             |      | +---------+   x  +-------------+    |      |
             |      | |         |<-----|             |    |      |
             +------|-|  Clock  |   y  | Phase/Freq  |<---|------+
                    | | Adjust  |<-----| Prediction  |    |
                    | |         |      |             |    |
                    | +---------+      +-------------+    |
                    |                                     |
                    +-------------------------------------+

                 Figure 28: Clock Discipline Feedback Loop

   The NTPv4 clock discipline algorithm, shortened to discipline in the
   following, functions as a combination of two philosophically quite
   different feedback control systems.  In a phase-locked loop (PLL)
   design, periodic phase updates at update intervals m are used
   directly to minimize the time error and indirectly the frequency
   error.  In a frequency-locked loop (FLL) design, periodic frequency
   updates at intervals mu are used directly to minimize the frequency
   error and indirectly the time error.  As shown in [8], a PLL usually
   works better when network jitter dominates, while a FLL works better
   when oscillator wander dominates.  This section contains an outline
   of how the NTPv4 design works.  An in-depth discussion of the design
   principles is provided in [8], which also includes a performance
   analysis.

   The clock discipline and clock adjust processes interact with the
   other algorithms in NTPv4.  The output of the combining algorithm
   represents the best estimate of the system clock offset relative to
   the server ensemble.  The discipline adjusts the frequency of the VFO
   to minimize this offset.  Finally, the timestamps of each server are
   compared to the timestamps derived from the VFO in order to calculate
   the server offsets and close the feedback loop.



Burbank, et al.          Expires April 26, 2007                [Page 52]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   The discipline is implemented as the feedback control system shown in
   Figure 28.  The variable theta_r represents the combining algorithm
   offset (reference phase) and theta_c the VFO offset (control phase).
   Each update produces a signal Vd representing the instantaneous phase
   difference theta_r - theta_c.  The clock filter for each server
   functions as a tapped delay line, with the output taken at the tap
   selected by the clock filter algorithm.  The selection, clustering
   and combining algorithms combine the data from multiple filters to
   produce the signal Vs.  The loop filter, with impulse response F(t),
   produces the signal Vc which controls the VFO frequency omega_c and
   thus its phase theta_c = integral (omega_c, dt) which closes the
   loop.  The Vc signal is generated by the clock adjust process in
   Section 9.3.  The characteristic behavior of this model, which is
   determined by F(t) and the various gain factors given in Section
   A.6.6.

   The transient behavior of the PLL/FLL feedback loop is determined by
   the impulse response of the loop filter F(t).  The loop filter shown
   in Figure 29 predicts a phase adjustment x as a function of Vs.  The
   PLL predicts a frequency adjustment yFLL as an integral of Vs*mu with
   repsect to t, while the FLL predicts an adjustment yPLL as a function
   of Vs /mu.  The two adjustments are combined to correct the frequency
   y as shown in Figure 29.  The x and y are then used by the
   clock_adjust()routine to control the VFO frequency.  The detailed
   equations that implement these functions are best presented in the
   routines of Sections A.6.6 and A.7.1.
                     x <------(Phase Correction)<--.
                                                   |
                           y_FLL                   |
                            .-(FLL Predict)<-------+<--V_s
                            |                      |
                           \|/                     |
                     y <--(Sum)                    |
                            ^                      |
                            |                      |
                            '-(PLL Predict)<-------'
                           y_PLL

                  Figure 29: Clock Discipline Loop Filter

   Ordinarily, the pseudo-linear feedback loop described above operates
   to discipline the system clock.  However, there are cases where a
   nonlinear algorithm offers considerable improvement.  One case is
   when the discipline starts without knowledge of the intrinsic clock
   frequency.  The pseudo-linear loop takes several hours to develop an
   accurate measurement and during most of that time the poll interval
   cannot be increased.  The nonlinear loop described below does this in
   15 minutes.  Another case is when occasional bursts of large jitter



Burbank, et al.          Expires April 26, 2007                [Page 53]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   are present due to congested network links.  The state machine
   described below resists error bursts lasting less than 15 minutes.

   The remainder of this section describes how the discipline works.
   Figure 30 contains a summary of the variables and parameters
   including the program name, formula name and short description.
   Unless noted otherwisse, all variables have assumed prefix c.  The
   variables c.t, c.tc, c.state, and c.count are integers; the memainder
   are floating doubles.  The function of each will be explained in the
   algorithm descriptions below.

   Name     Formula     Description
   ----     -------     -----------
   t        timer       seconds counter
   offset   captheta    combined offset
   resid    captheta_r  residual offset
   freq     phi         clock frequency
   jitter   varphi      clock jitter
   wander   cappsi      frequency wander
   tc       tau         time constant(log2)
   state    state       state
   adj      adj         frequency adjustment
   count    count       hysteresis counter
   STEPT    125         step threshold (.125 s)
   WATCH    900         stepout thresh(s)
   PANICT   1000        panic threshold(1000 s)
   LIMIT    30          hysteresis limit
   PGATE    4           hysteresis gate
   TC       16          time constant scale
   AVG      8           averaging constant

                                 Figure 30



















Burbank, et al.          Expires April 26, 2007                [Page 54]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   =====================================================================
   | State |  captheta < STEP  | captheta > STEP   |    Comments       |
   ---------------------------------------------------------------------
   | NSET  | > FREQ; adjust    | > FREQ; step      | no frequency      |
   |       | time              | time              | file              |
   ---------------------------------------------------------------------
   | FSET  | > SYNC; adjust    | > SYNC; step      | frequency file    |
   |       | time              | time              |                   |
   ---------------------------------------------------------------------
   | SPIK  | > SYNC; adjust    | if (<900 s)>SPIK  | outlier detected  |
   |       | freq, adjust time | else SYNC; step   |                   |
   |       |                   | freq; step time   |                   |
   ---------------------------------------------------------------------
   | FREQ  | if (<900 s)> FREQ | if (<900 s)>FREQ  | initial frequency |
   |       | else >SYNC; step  | else >SYNC; step  |                   |
   |       | freq, adjust time | freq, adjust time |                   |
   ---------------------------------------------------------------------
   | SYNC  | >SYNC; adjust freq| if (<900 s)>SPIK  | normal operation  |
   |       | adjust time       | else >SYNC; step  |                   |
   |       |                   | freq; step time   |                   |
   ---------------------------------------------------------------------

                                 Figure 31

   The discipline is implemented by the local_clock() routine, which is
   called from the clock_update() routine.  The local_clock() routine
   pseudo code in Section B.6.6 has two parts; first the state machine
   shown in Figure 32 and second the algorithm that determines the time
   constant and thus the poll interval in Figure 33.  The state
   transition function in Figure 32 is implemented by the rst() function
   shown at the lower left of the figure.  The local_clock() routine
   exits immediately if the offset is greater than the panic threshold.
                               ---
                              | A |
                               ---
                                ||
                                \/
                               --- yes ---
                              | B |-->| C |
                               ---     ---
                             no ||
                                \/
                               ---
                              | D |
                               ---
                                ||
                                \/
                       --- no  ---  yes    SYNC         SPIK FREQ



Burbank, et al.          Expires April 26, 2007                [Page 55]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


                      | E |<--| F |----------------------------------
                       ---     ---         ||             ||
           SYNC         ||                 \/             \/
           SPIKE  FSET  \/ FREQ    NSET   ---            ---
            -------------------------    | G |          | H |
           ||     ||        ||      ||    ---            ---
           ||     ||        \/      \/     ||      yes  ||  ||  no
           ||     ||       ---     ---     ||           ||  \/
           ||    ---      | H |   | I |    ||           ||  ---
           \/   | I |      ---     ---     ||           || | J |
          ---    ---   no || ||yes  ||     ||           ||  ---
         | K |    ||      || ||     \/     ||           || ||  || yes
          ---     ||      \/ ||    ---     ||           || ||  \/
           ||     ||     --- ||   | L |    ||           || ||  ---
           ||     ||    | M |||    ---     ||           || || | M |
           ||     ||     --- ||     ||     ||           || ||  ---
           ||     ||      || \/     \/     \/           \/ ||   ||
           ||     ||      ||  ------------>\/<-----------  \/   \/
           ||     ||      ||              ---               --->\/<-----
           ||     ||      ||             | N |                 ---
           ||     ||      ||              ---                 | O |
           ||     ||      ||                                   ---
           ||     ||      ||                                    ||
           ||     ||      ||                                    \/
           ||     ||      ||    ---                ---         ---
            ----->-------->----| P |----><--------| Q |<------| R |
                                ---     ||         ---         ---
         ---                            \/                      ||
        | S |                          ---                      \/
         ---                          | T |                    ---
          ||                           ---                    | U |
          \/                                                   ---
         ---                                                    ||
        | V |                                                   \/
         ---                                                   ---
          ||                                                  | W |
          \/                                                   ---
         ---
        | X |
         ---

   A: local_clock()
   B: |captheta|>PANICT?
   C: return(PANIC)
   D: freq=0
      rval=IGNOR
   E:
   F: |captheta|>STEPT?



Burbank, et al.          Expires April 26, 2007                [Page 56]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   G: state=SPIK
   H: mu<WATCH
   I: captheta_g=captheta
   J: FREQ?
   K: Calculate new freq adjustment from captheta, tau, and mu using
   hybrid PLL and FLL
   L: rst(FREQ,0)
   M: freq=((captheta-captheta_B-captheta_R)/mu)
   N: return(rval)
   O: step_time(captheta)
      rval=STEP
   P: rval=ADJ
   Q: rst(SYNC,0)
   R: state=NSET?
   S: rst(new,off)
   T: tc
   U: rst(FREQ,0)
   V: state=new
      captheta_B=off-captheta_R
      captheta_R=off
   W: return(rval)
   X: return

                 Figure 32: local_clock() routine (1 of 2)

   -----
   | A |
   -----
    \|/
   -----
   | B |
   -----
    \|/
   -----
   | C |-no-----\
   -----        |
    \|/yes      |
   -----      -----
   | D |      | E |
   -----      -----
    \|/        \|/
   -----      -----
   | F |no\   | G |no\
   -----  |   -----  |
    \|/yes|    \|/yes|
     |    |     |    |
   -----  |   -----  |
   | H |  |   | I |  |



Burbank, et al.          Expires April 26, 2007                [Page 57]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   -----  |   -----  |
   | J |  |   | K |  |
   -----  |   -----  |
   |y  no-><-no  y|  |
   ----   |    ----  |
   | L|   |    | M|  |
   -------><---------/
         \|/
        -----
        | N |
        -----
         \|/
        -----
        | O |
        -----
         \|/
        -----
        | P |
        -----

   A: tc
   B: state=SYNC
   C: |captheta_g| > PGATE?
   D: count -= 2*tau
   E: count += tau
   F: count <= -LIMIT?
   G: count >= LIMIT?
   H: count = 0
   I: count = 0
   J: tau>MINPOLL
   K: tau<MAXPOLL
   L: tau--
   M: tau++
   N: phi += freq
   O: cappsi = sqrt(expectationvalue(phi^2))
   P: return(rval)

                 Figure 33: local_clock() routine (2 of 2)

   The remaining portion of the local_clock() routine is shown in
   Figure 33.  The time constant tau is determined by comparing the
   clock jitter varphi with the magnitude of the current residual offset
   captheata_R. produced by the clock adjust routine in the next
   section.  If the residual offset is greater than PGATE (4) times the
   clock jitter, be hysteresis counter is reduced by two; otherwise, it
   is increased by one.  If the hysteresis counter increases to the
   upper limit LIMIT (30), the time constant is increased by one; if it
   decreases to the lower limit -LIMIT (-30), the time constant is



Burbank, et al.          Expires April 26, 2007                [Page 58]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   decreased by one.  Normally, the time constant hovers near MAXPOLL,
   but quickly decreases it frequency surges due to a temperature spike,
   for example.

   The clock jitter statistic vartheta and the clock wander statistic
   cappsi are implemented as exponential averages of RMS offset
   differences and RMS frequency differences, respectively.  Let x_i be
   a measurement at time i of either vartheta or cappsi,y_i = x_i -
   x_(i-1) the first-order sample difference and y_i_HAT the exponential
   average.  Then,

   y_(i+1)_HAT = sqrt((y_i_HAT)^2+[(y_i)^2-(y_i_HAT)^2)/AVG])

   where AVG (4) is the averaging parameter in Figure 30, is the
   exponential average at time i + 1.  The clock jitter statistic is
   used by the poll-adjust algorithm above; the clock wander statistic
   issued only for performance monitoring.


































Burbank, et al.          Expires April 26, 2007                [Page 59]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


10.3.  Clock Adjust Process
   -----
   | A |
   -----
    \|/
   -----
   | B |
   -----
    \|/
   -----
   | C |
   -----
    \|/
   -----
   | D |
   -----
    \|/
   -----
   | E |
   -----
    \|/
   -----
   | F |-----no----\
   -----           |
    \|/yes        \|/
   -----         -----
   | H |<--------| G |
   -----         -----

   A: clock_adjust()
   B: E += captheta
   C: tmp = captheta_r/TC(tau)
   D: captheta_R -= tmp
   E: adjust_time(phi + tmp)
   F: next < timer?
   G: poll()
   H: return

                     Figure 34: clock_adjust() Routine

   The actual clock adjustment is performed by the clock_adjust()
   routine shown in Figure 34 and Section B.7.1.  It runs at one-second
   intervals to add the frequency offset in Figure 33 and a fixed
   percentage of the residual offset captheta_R. The captheta_R is in
   effect the exponential decay of the captheta value produced by the
   loop filter at each update.  The TC parameter scales the time
   constant to match the poll interval for convenience.  Note that the
   dispersion E increases by capphi at each second.



Burbank, et al.          Expires April 26, 2007                [Page 60]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   The clock adjust process includes a timer interrupt facility driving
   the system timer c.t.  It begins at zero when the service starts and
   increments once each second.  At each interrupt the clock_adjust()
   routine is called to incorporate the clock discipline time and
   frequency adjustments, then the associations are scanned to determine
   if the system timer equals or exceeds the p.next state variable
   defined in the next section.  If so, the poll process is called to
   send a packet and compute the next p.next value.


11.  Poll Process

   Each association supports a poll process that runs at regular
   intervals to construct and send packets in symmetric, client and
   broadcast server associations.  It runs continuously, whether or not
   servers are reachable.  The discussion in this section covers only
   the variables and routines necessary for a conforming NTPv4
   implementation.  Additional implementation details are in Section
   B.8.  Further details and rationale for the engineering design are
   discussed in [8].

   Name     Formula    Description
   ----     -------    -----------
   hpoll    hpoll      host poll exponent
   last     last       last poll time
   next     next       next poll time
   reach    reach      reach register
   unreach  unreach    unreach counter
   UNREACH  24         unreach limit
   BCOUNT   8          burst count
   BURST    flag       burst enable
   IBURST   flag       iburst enable

                                 Figure 35

11.1.  Poll Process Variables and Parameters

   The poll process variables are allocated in the association data
   structure along with the peer process variables.  Figure 35 shows the
   names, formula names and short definition for each one.  Following is
   a detailed description of the variables, all of which carry the p
   prefix.

   p.hpoll: Signed integer representing the poll exponent, in log2
   seconds.

   p.last: Integer representing the system timer value when the most
   recent packet was sent.



Burbank, et al.          Expires April 26, 2007                [Page 61]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   p.next: Integer representing the system timer value when the next
   packet is to be sent.

   p.reach: 8-bit integer shift register.  When a packet is sent, the
   register is shifted left one bit, with zero entering from the right
   and overflow bits discarded.

   p.unreach: Integer representing the number of seconds the server has
   been unreachable.

11.2.  Poll Process Operations

   As described previously, once each second the clock_adjust() routine
   is called.  This routine calls the poll() routine in Section B.8.1
   for each association in turn.  If the time for the next poll message
   is greater than the system timer, the routine returns immediately.  A
   mode-5 (broadcast server) association always sends a packet, but a
   mode-6 (broadcast client) association never sends a packet, but runs
   the routine to update the p.reach and p.unreach variables.  The
   poll() routine calls the peer_xmit() routine in Section B.8.3 to send
   a packet.  If in a burst (p.burst > 0), nothing further is done
   except call the poll_update() routine to set the next poll interval.

   If not in a burst, the p.reach variable is shifted left by one bit,
   with zero replacing the rightmost bit.  If the server has not been
   heard for the last three poll intervals, the clock_filter() routine
   is called to increase the dispersion as described in Section 8.3.  If
   the BURST flag is lit and the server is reachable and a valid source
   of synchronization is available, the client sends a burst of BCOUNT
   (8) packets at each poll interval.  This is useful to accurately
   measure jitter with long poll intervals.  If the IBURST flag is lit
   and this is the first packet sent when the server becomes
   unreachable, the client sends a burst.  This is useful to quickly
   reduce the synchronization distance below the distance threshold and
   synchronize the clock.  The figure also shows the mechanism which
   backs off the poll interval if the server becomes unreachable.  If
   p.reach is nonzero, the server is reachable and p.unreach is set to
   zero; otherwise, p.unreach is incremented by one for each poll to the
   maximum UNREACH (24).  Thereafter for each poll p.hpoll is increased
   by one, which doubles the poll interval up to the maximum MAXPOLL
   determined by the poll_update() routine.  When the server again
   becomes reachable, p.unreach is set to zero, p.hpoll is reset to tau
   and operation resumes normally.

   When a packet is sent from an association, some header values are
   copied from the peer variables left by a previous packet and others
   from the system variables. includes a flow diagram and a table
   showing which values are copied to each header field.  In those



Burbank, et al.          Expires April 26, 2007                [Page 62]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   implementations using floating double data types for root delay and
   root dispersion, these must be converted to NTP short format.  All
   other fields are either copied intact from peer and system variables
   or struck as a timestamp from the system clock.

   The poll_update() routine shown in Section B.8.2 is called when a
   valid packet is received and immediately after a poll message is
   sent.  If in a burst, the poll interval is fixed at 2 s; otherwise,
   the host poll exponent is set to the minimum of p.poll from the last
   packet received and p.hpoll from the poll() routine, but not less
   than MINPOLL nor greater than MAXPOLL.  Thus the clock discipline can
   be oversampled, but not undersampled.  This is necessary to preserve
   subnet dynamic behavior and protect against protocol errors.
   Finally, the poll exponent is converted to an interval which
   establishes the time at the next poll p.next.


12.  Security Considerations

   NTPv4 provides an optional authentication field that utilizes the MD5
   algorithm.  MD5, as the case for SHA-1, is derived from MD4, which
   has long been known to be weak.  In 2004, techniques for efficiently
   finding collisions in MD5 were announced.  A summary of the weakness
   of MD5 can be found in [9].

   In the case of NTP as specified herein, NTP broadcast clients are
   vulnerable to disruption by misbehaving or hostile SNTP or NTP
   broadcast servers elsewhere in the Internet.  Access controls and/or
   cryptographic authentication means should be provided for additional
   security in such cases.


13.  IANA Considerations

   UDP/TCP Port 123 was previously assigned by IANA for this protocol.
   The IANA has assigned the IPv4 multicast group address 224.0.1.1 and
   the IPv6 multicast address ending :101 for NTP.  This document
   introduces NTP extension fields allowing for the development of
   future extensions to the protocol, where a particular extension is to
   be identified by the Field Type sub-field within the extension field.
   IANA is requested to establish and maintain a registry for Extension
   Field Types associated with this protocol, populating this registry
   with no initial entries.  As future needs arise, new Extension Field
   Types may be defined.  Following the policies outlined in [10], new
   values are to be defined by IETF Consensus.






Burbank, et al.          Expires April 26, 2007                [Page 63]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


14.  Acknowledgements

   This authors would like to thank Brian Haberman, Greg Dowd, Mark
   Elliot, and Harlan Stenn for technical reviews of this document.


15.  References

15.1.  Normative References

   [1]  Mills, D., "Network Time Protocol (Version 3) Specification,
        Implementation", RFC 1305, March 1992.

15.2.  Informative References

   [2]   Mills, D., "Simple Network Time Protocol (SNTP) Version 4 for
         IPv4, IPv6 and OSI", RFC 4330, January 2006.

   [3]   University of Delaware, "The Autokey security architecture,
         protocol and algorithms. Electrical and Com puter Engineering
         Technical Report 06-1-1", NDSS , January 2006.

   [4]   Bradner, S., "Key words for use in RFCs to Indicate Requirement
         Levels", BCP 14, RFC 2119, March 1997.

   [5]   Postel, J., "Internet Protocol", STD 5, RFC 791,
         September 1981.

   [6]   Rivest, R., "The MD5 Message-Digest Algorithm", RFC 1321,
         April 1992.

   [7]   Marzullo and S. Owicki, "Maintaining the time in a distributed
         system.", ACM Operating Systems Review 19 , July 1985.

   [8]   Mills, D. L., "Computer Network Time Synchronization - the
         Network Time Protocol. CRC Press, 304pp.", 2006.

   [9]   Bellovin, S. and E. Rescorla, Proceedings of the 13th annual
         ISOC Network and Distributed System Security Symposium,
         "Deploying a new Hash Algorithm", February 2006.

   [10]  Narten, T. and H. Alvestrand, "Guidelines for Writing an IANA
         Considerations Section in RFCs", BCP 26, RFC 2434,
         October 1998.







Burbank, et al.          Expires April 26, 2007                [Page 64]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


Appendix A.  Code Skeleton

   This appendix is intended to describe the protocol and algorithms of
   an implementation in a general way using what is called a code
   skeleton program.  This consists of a set of definitions, structures
   and code segments which illustrate the protocol operations without
   the complexities of an actual implementation of the protocol.  This
   program is not an executable and is not designed to run in the
   ordinary sense.  It is designed to be compiled only in order to
   verify consistent variable and type usage.  The program is not
   intended to be fast or compact, just to demonstrate the algorithms
   with sufficient fidelity to understand how they work.  Reword or
   remove The code skeleton consists of five segments, a header segment
   included by each of the other segments, plus a code segment for the
   main program and peer, system, clock_adjust and poll processes.
   These are presented in order below along with definitions and
   variables specific to each process.

A.1.  Global Definitions

   Following are definitions and other data shared by all programs.
   These values are defined in a header file ntp4.h which is included in
   all files.

A.2.  Definitions, Constants, Parameters
   #include <math.h> s/* avoids complaints about sqrt() */
   #include <sys/time.h> /* for gettimeofday() and friends */
   #include <stdlib.h> /* for malloc() and friends */

   /*
   * Data types
   *
   * This program assumes the int data type is 32 bitsand
    the long data
   * type is 64 bits. The native data
    type used in most calculations is
   * floating double. The data types used
   in some packet header fields
   * require conversion to and from this
    representation. Some header
   * fields involve partitioning an octet, here
    represented by individual
   * octets.
   *
   * The 64-bit NTP timestamp format used in
    timestamp calculations is
   * unsigned seconds and fraction with the
    decimal point to the left of



Burbank, et al.          Expires April 26, 2007                [Page 65]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   * bit 32. The only operation permitted
    with these values is
   * subtraction, yielding a signed 31-bit
    difference. The 32-bit NTP
   * short format used in delay and dispersion
   calculations is seconds and
   * fraction with the decimal point to the
    left of bit 16. The only
   * operations permitted with these values
    are addition and
   * multiplication by a constant.
   *
   * The IPv4 address is 32 bits, while the
    IPv6 address is 128 bits. The
   * message digest field is 128 bits as
    constructed by the MD5 algorithm.
   * The precision and poll interval fields
    are signed log2 seconds.
   */

   typedef unsigned long tstamp;
   typedef unsigned int tdist;
   typedef unsigned long ipaddr;
   typedef unsinged int ipport;
   typedef unsigned long digest;
   typedef signed char s_char;

   /*
   * Arithmetic conversion macroni
   */

   /* NTP timestamp format */
   /* NTP short format */
   /* IPv4 or IPv6 address */
   /* IP port number */
   /* md5 digest */
   /* precision and poll interval (log2) */

   #define LOG2D(a) ((a) < 0 ? 1. / (1L << -(a)) : \

   1L << (a)) /* poll, etc. */

   #define LFP2D(a) ((double)(a) / 0x100000000L) /* NTP timestamp */

   #define D2LFP(a) ((tstamp)((a) * 0x100000000L))

   #define FP2D(a) (double)(a) / 0x10000L)  /* NTP short */
   #define D2FP(a) ((tdist)((a) * 0x10000L))



Burbank, et al.          Expires April 26, 2007                [Page 66]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   #define SQUARE(x) (x * x)
   #define SQRT(x) (sqrt(x))

   /*
   * Global constants. Some of these might be
    converted to variables
   * which can be tinkered by configuration
    or computed on-fly. For
   * instance, PRECISION could be calculated
    on-fly and
   * provide performance tuning for the defines
    marked with % below.
   */
   #define VERSION 4 /* version number */
   #define PORT 123 /* NTP poert number */
   #define MINDISP .01 /* % minimum dispersion (s) */
   #define MAXDISP 16 /* % maximum dispersion (s) */
   #define MAXDIST 1 /* % distance threshold (s) */
   #define NOSYNC 3 /* leap unsync */
   #define MAXSTRAT 16 /* maximum stratum (infinity metric) */
   #define MINPOLL 4 /* % minimum poll interval (16 s)*/
   #define MAXPOLL 17 /* % maximum poll interval (36.4 h) */
   #define PHI 15e-6 /* % frequency tolerance (15 PPM) */
   #define NSTAGE 8 /* clock register stages */
   #define NMAX 50 /* % maximum number of peers */
   #define NSANE 1 /* % minimum intersection survivors */
   #define NMIN 3 /* % minimum cluster survivors */

   /*
   * Global return values
   */
   #define TRUE 1 /* boolean true */
   #define FALSE 0 /* boolean false */
   #define NULL 0 /* empty pointer */

   /*
   * Local clock process return codes
   */
   #define IGNORE 0 /* ignore */
   #define SLEW 1 /* slew adjustment */
   #define STEP 2 /* step adjustment */
   #define PANIC 3 /* panic - no adjustment */

   /*
   * System flags
   */
   #define S_FLAGS 0 /* any system flags */
   #define S_BCSTENAB 0x1 /* enable broadcast client */



Burbank, et al.          Expires April 26, 2007                [Page 67]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   /*
   * Peer flags
   */
   #define P_FLAGS 0 /* any peer flags */
   #define P_EPHEM 0x01 /* association is ephemeral */
   #define P_BURST 0x02 /* burst enable */
   #define P_IBURST 0x04 /* intial burst enable */
   #define P_NOTRUST 0x08 /* authenticated access */
   #define P_NOPEER 0x10 /* authenticated mobilization */

   /*
   * Authentication codes
   */
   #define A_NONE 0 /* no authentication */
   #define A_OK 1 /* authentication OK */
   #define A_ERROR 2 /* authentication error */
   #define A_CRYPTO 3 /* crypto-NAK */

   /*
   * Association state codes
   */
   #define X_INIT 0 /* initialization */
   #define X_STALE 1 /* timeout */
   #define X_STEP 2 /* time step */
   #define X_ERROR 3 /* authentication error */
   #define X_CRYPTO 4 /* crypto-NAK received */
   #define X_NKEY 5 /* untrusted key */

   /*
   * Protocol mode definitionss
   */
   #define M_RSVD 0 /* reserved */
   #define M_SACT 1 /* symmetric active */
   #define M_PASV 2 /* symmetric passive */
   #define M_CLNT 3 /* client */
   #define M_SERV 4 /* server */
   #define M_BCST 5 /* broadcast server */
   #define M_BCLN 6 /* broadcast client */
   /*
   * Clock state definitions
   */
   #define NSET 0 /* clock never set */
   #define FSET 1 /* frequency set from file */
   #define SPIK 2 /* spike detected */
   #define FREQ 3 /* frequency mode */
   #define SYNC 4 /* clock synchronized */

A.3.  Packet Data Structures



Burbank, et al.          Expires April 26, 2007                [Page 68]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   /*
   * The receive and transmit packets may
   contain an optional message
   * authentication code (MAC) consisting of a
   key identifier (keyid) and * message digest (mac).
   NTPv4 supports optional extension fields which * are
    inserted after the the header and before the MAC,
    but these are * not described here.
   *

   * Receive packet
   *
   * Note the dst timestamp is not part of the packet
    itself. It is
   * captured upon arrival and returned in the
    receive buffer along with
   * the buffer length and data. Note that some
    of the char fields are
   * packed in the actual header, but the
    details are omited here.
   */
   struct r {
   ipaddr  srcaddr;  /* source (remote) address */
   ipaddr  dstaddr;  /* destination (local) address */
   char  version;  /* version number */
   char  leap;  /* leap indicator */
   char  mode;  /* mode */
   char  stratum;  /* stratum */
   char  poll;  /* poll interval */
   s_char  precision;  /* precision */
   tdist  rootdelay;  /* root delay */
   tdist  rootdisp;  /* root dispersion */
   char  refid;  /* reference ID */
   tstamp  reftime;  /* reference time */
   tstamp  org;  /* origin timestamp */
   tstamp  rec;  /* receive timestamp */
   tstamp  xmt;  /* transmit timestamp */
   int  keyid;  /* key ID */
   digest  digest;  /* message digest */
   tstamp  dst;  /* destination timestamp */
   } r;

   /*
   * Transmit packet
   */
   struct x {
   ipaddr  dstaddr;  /* source (local) address */
   ipaddr  srcaddr;  /* destination (remote) address */



Burbank, et al.          Expires April 26, 2007                [Page 69]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   char  version;  /* version number */
   char  leap;  /* leap indicator */
   char  mode;  /* mode */
   char  stratum;  /* stratum */
   char  poll;  /* poll interval */
   s_char  precision;  /* precision */
   tdist  rootdelay;  /* root delay */
   tdist  rootdisp;  /* root dispersion */
   char  refid;  /* reference ID */
   tstamp  reftime;  /* reference time */
   tstamp  org;  /* origin timestamp */
   tstamp  rec;  /* receive timestamp */
   tstamp  xmt;  /* transmit timestamp */
   int keyid; /* key ID */
   digest digest; /* message digest */
   } x;

   A.1.3 Association Data Structures

   /*
   * Filter stage structure. Note the t member in this and other
   * structures refers to process time, not real time. Process time
   * increments by one second for every elapsed second of real time.
   */
   struct f {
   tstamp   t;   /* update time */
   double   offset;   /* clock ofset */
   double   delay;   /* roundtrip delay */
   double   disp;   /* dispersion */
   } f;

   /*
   * Association structure. This is shared between the
    peer process and * poll process.
   */
   struct p {

   /*
   * Variables set by configuration
   */
   ipaddr   srcaddr;   /* source (remote) address */
   ipport   srcport;   /* source port number *.
   ipaddr   dstaddr;   /* destination (local) address */
   ipport   dstport;   /* destination port number */
   char   version;   /* version number */
   char   mode;   /* mode */
   int   keyid;   /* key identifier */
   int   flags;   /* option flags */



Burbank, et al.          Expires April 26, 2007                [Page 70]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   /*
   * Variables set by received packet
   */
   char   leap;   /* leap indicator */
   char   mode;   /* mode */
   char   stratum;   /* stratum */
   char   ppoll;   /* peer poll interval */
   double   rootdelay;   /* root delay */
   double   rootdisp;   /* root dispersion */
   char   refid;   /* reference ID */
   tstamp   reftime;   /* reference time */
   #define   begin_clear org   /* beginning of clear area */
   tstamp   org;   /* originate timestamp */
   tstamp   rec;   /* receive timestamp */
   tstamp   xmt;   /* transmit timestamp */

   /*
   * Computed data
   */
   double   t;   /* update time */
   struct f f[NSTAGE];   /* clock filter */
   double   offset;   /* peer offset */
   double   delay;   /* peer delay */
   double   disp;   /* peer dispersion */
   double   jitter;   /* RMS jitter */

   /*
   * Poll process variables
   */
   char   hpoll;   /* host poll interval */
   int   burst;   /* burst counter */
   int   reach;   /* reach register */
   #define   end_clear unreach   /* end of clear area */
   int   unreach;   /* unreach counter */
   int   last;   /* last poll time */
   int   next;   /* next poll time */
   } p;
   A.1.4 System Data Structures

   /*
   * Chime list. This is used by the intersection algorithm.
   */
   struct m {   /* m is for Marzullo */
   struct p *p;   /* peer structure pointer */
   int   type;   /* high +1, mid 0, low -1 */
   double   edge;   /* correctness interval edge */
   } m;




Burbank, et al.          Expires April 26, 2007                [Page 71]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   /*
   * Survivor list. This is used by the clustering algorithm.
   */
   struct v {
   struct p *p;   /* peer structure pointer */
   double   metric;   /* sort metric */
   } v;
   /*
   * System structure
   */
   struct s {
   tstamp   t;   /* update time */
   char   leap;   /* leap indicator */
   char   stratum;   /* stratum */
   char   poll;   /* poll interval */
   char   precision;   /* precision */
   double   rootdelay;   /* root delay */
   double   rootdisp;   /* root dispersion */
   char   refid;   /* reference ID */
   tstamp   reftime;   /* reference time */
   struct m m[NMAX];   /* chime list */
   struct v v[NMAX];   /* survivor list */
   struct p *p;   /* association ID */
   double   offset;   /* combined offset */
   double   jitter;   /* combined jitter */
   int   flags;   /* option flags */
   } s;
   A.1.5 Local Clock Data Structure

   /*
   * Local clock structure
   */
   struct c {
   tstamp   t;   /* update time */
   int   state;   /* current state */
   double   offset;   /* current offset */
   double   base;   /* base offset */
   double   last;   /* previous offset */
   int   count;   /* jiggle counter */
   double   freq;   /* frequency */
   double   jitter;   /* RMS jitter */
   double   wander;   /* RMS wander */
   } c;
   A.1.6 Function Prototypes

   /*
   * Peer process
   */



Burbank, et al.          Expires April 26, 2007                [Page 72]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   void   receive(struct r *);   /* receive packet */
   void   fast_xmit(struct r *, int, int);
   /* transmit a reply packet */
   struct p *find_assoc(struct r *);
   /* search the association table */
   void   packet(struct p *, struct r *);
   /* process packet */
   void   clock_filter(struct p *, double, double, double);
   /* filter */
   int   accept(struct p *);
   /* determine fitness of server */
   int   access(struct r *);
   /* determine access restrictions */


   /*
   * System process
   */
   void   clock_select();   /* find the best clocks */
   void   clock_update(struct p *);   /* update the system clock */
   void   clock_combine();   /* combine the offsets */
   double   root_dist(struct p *);   /* calculate root distance */

   /*
   * Clock discipline process
   */
   int   local_clock(struct p *, double); /* clock discipline */
   void   rstclock(int, double, double); /* clock state transition */

   /*
   * Clock adjust process
   */
   void   clock_adjust();   /* one-second timer process */

   /*
   * Poll process
   */
   void   poll(struct p *);   /* poll process */
   void   poll_update(struct p *, int); /* update the poll interval */
   void   peer_xmit(struct p *);   /* transmit a packet */

   /*
   * Main program and utility routines
   */
   int   main();   /* main program */
   struct p *mobilize(ipaddr, ipaddr, int, int, int, int);
    /* mobilize */
   void   clear(struct p *, int);   /* clear association */



Burbank, et al.          Expires April 26, 2007                [Page 73]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   digest   md5(int);   /* generate a message digest */

   /*
   * Kernel I/O Interface
   */
   struct r *recv_packet();   /* wait for packet */
   void   xmit_packet(struct x *);   /* send packet */

   .*
   * Kernel system clock interface
   */
   void   step_time(double);   /* step time */
   void   adjust_time(double);   /* adjust (slew) time */
   tstamp   get_time();   /* read time */
   A.2 Main Program and Utility Routines

   #include "ntp4.h"

   /*
   * Definitions
   */
   #define PRECISION -18   /* precision (log2 s)    */
   #define IPADDR   0   /* any IP address */
   #define MODE   0   /* any NTP mode */
   #define KEYID   0   /* any key identifier */

   /*
   * main() - main program
   */
   int
   main()
   {
   struct p *p;   /* peer structure pointer */
   struct r *r;   /* receive packet pointer */

   /*
   * Read command line options and initialize system
    variables. * Implementations MAY measure the precision
    specific * to each machine by measuring the clock
    increments to read the * system clock.
   */
   memset(&s, sizeof(s), 0);
   s.leap = NOSYNC;
   s.stratum = MAXSTRAT;
   s.poll = MINPOLL;
   s.precision = PRECISION;
   s.p = NULL;




Burbank, et al.          Expires April 26, 2007                [Page 74]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   /*
   * Initialize local clock variables
   */
   memset(&c, sizeof(c), 0);
   if (/* frequency file */ 0) {
      c.freq = /* freq */ 0;
      rstclock(FSET, 0, 0);
    } else {
   rstclock(NSET, 0, 0);
   }
   c.jitter = LOG2D(s.precision);

   /*
   * Read the configuration file and mobilize persistent
   * associations with spcified addresses, version, mode,
    key ID * and flags.
   */
   while (/* mobilize configurated associations */ 0) {
      p = mobilize(IPADDR, IPADDR, VERSION, MODE, KEYID,
      P_FLAGS);
   }

   /*
   * Start the system timer, which ticks once per second. Then
   * read packets as they arrive, strike receive timestamp and
   * call the receive() routine.
   */
   while (0) {
   r = recv_packet(); r->dst = get_time(); receive(r);
   }
   }

   /*
   * mobilize() - mobilize and initialize an association
   */
   struct p
   *mobilize(
   ipaddr   srcaddr,   /* IP source address */
   ipaddr   dstaddr,   /* IP destination address */
   int   version,   /* version */
   int   mode,   /* host mode */
   int   keyid,   /* key identifier */
   int   flags   /* peer flags */
   )
   {
   struct p *p;   /* peer process pointer */

   /*



Burbank, et al.          Expires April 26, 2007                [Page 75]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   * Allocate and initialize association memory
   */
   p = malloc(sizeof(struct p));
   p->srcaddr = srcaddr;
   p->srcport = PORT;
   p->dstaddr = dstaddr;
   p->dstport = PORT;
   p->version = version;
   p->mode = mode;
   p->keyid = keyid;
   p->hpoll = MINPOLL;
   clear(p, X_INIT);
   p->flags == flags;
   return (p);
   }

   /*
   * clear() - reinitialize for persistent association,
    demobilize * for ephemeral association.
   */
   void
   clear(
   struct p *p,   /* peer structure pointer */
   int   kiss   /* kiss code */
   )
   {
   int i;

   /*
   * The first thing to do is return all resources to
    the bank. * Typical resources are not detailed here
   , but they include * dynamically allocated structures
    for keys, certificates, etc. * If an ephemeral
    association and not initialization, return * the association
    memory as well.
   */
   /* return resources */
   if (s.p == p)
   s.p = NULL;
   if (kiss != X_INIT && (p->flags & P_EPHEM)) {
      free(p);
   return;
   }

   /*
   * Initialize the association fields for general reset.
   */
   memset(BEGIN_CLEAR(p), LEN_CLEAR, 0); p->leap = NOSYNC;



Burbank, et al.          Expires April 26, 2007                [Page 76]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   p->stratum = MAXSTRAT;
   p->ppoll = MAXPOLL;
   p->hpoll = MINPOLL;
   p->disp = MAXDISP;
   p->jitter = LOG2D(s.precision); p->refid = kiss;
   for (i = 0; i < NSTAGE; i++)
      p->f[i].disp = MAXDISP;

   /*
   * Randomize the first poll just in case thousands
   of broadcast * clients have just been stirred up after
    a long absence of the * broadcast server.
   */
   p->last = p->t = c.t;
   p->next = p->last + (random() & ((1 << MINPOLL) - 1));
   }

   /*
   * md5() - compute message digest
   */
   digest
   md5(
   int   keyid   /* key identifier */
   )
   {
   /*
   * Compute a keyed cryptographic message digest.
   The key
   * identifier is associated with a key in the local
    key cache.
    * The key is prepended to the packet header and
   extension fieds * and the result hashed by the MD5
    algorithm as described in * RFC-1321. Return a MAC
    consisting of the 32-bit key ID
   * concatenated with the 128-bit digest.
   */
   return (/* MD5 digest */ 0);
   }
   A.3 Kernel Input/Output Interface

   /*
   * Kernel interface to transmit and receive packets. Details are
   * deliberately vague and depend on the operating system.
   *
   * recv_packet - receive packet from network
   */
   struct r   /* receive packet pointer*/
   *recv_packet() {



Burbank, et al.          Expires April 26, 2007                [Page 77]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   return (/* receive packet r */ 0);
   }

   /*
   * xmit_packet - transmit packet to network
   */
   void
   xmit_packet(
   struct x *x   /* transmit packet pointer */
   )
   {
   /* send packet x */
   }
   A.4 Kernel System Clock Interface

   *
   * There are three time formats: native (Unix),
   NTP and floating double.
   * The get_time() routine returns the time in NTP long
    format. The Unix
   * routines expect arguments as a structure of two
    signed 32-bit words
   * in seconds and microseconds (timeval) or
    nanoseconds (timespec). The
   * step_time() and adjust_time() routines ex
   pect signed arguments in
   * floating double. The simplified code shown
   here is for illustration
   * only and has not been verified.
   */
   #define JAN_1970   2208988800UL   /* 1970 - 1900 in seconds */

   /*
   * get_time - read system time and convert to NTP format
   */
   tstamp
   get_time()
   {
   struct timeval unix_time;

   /*
   * There are only two calls on this routine in the program. One
   * when a packet arrives from the network and the other when a
   * packet is placed on the send queue. Call the kernel time of
   * day routine (such as gettimeofday()) and convert to NTP
   * format.
   */
   gettimeofday(&unix_time, NULL);



Burbank, et al.          Expires April 26, 2007                [Page 78]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   return ((unix_time.tv_sec + JAN_1970) * 0x100000000L +
      (unix_time.tv_usec * 0x100000000L) / 1000000);
    }

   /*
   * step_time() - step system time to given offset valuet
   */
   void
   step_time(
   double   offset   /* clock offset */
   )
   {
   struct timeval unix_time;
   tstamp   ntp_time;

   /*
   * Convert from double to native format (signed) and add to the
   * current time. Note the addition is done in native format to
   * avoid overflow or loss of precision.
   */
   ntp_time = D2LFP(offset); gettimeofday(&unix_time, NULL);
   unix_time.tv_sec += ntp_time / 0x100000000L;
   unix_time.tv_usec += ntp_time % 0x100000000L;
   unix_time.tv_sec += unix_time.tv_usec / 1000000;
   unix_time.tv_usec %= 1000000;
   settimeofday(&unix_time, NULL);
   }

   /*
   * adjust_time() - slew system clock to given offset value
   */
   void
   adjust_time(
   double   offset   /* clock offset */
   )
   {
   struct timeval unix_time;
   tstamp   ntp_time;

   /*
   * Convert from double to native format (signed) and add to the
   * current time.
   */
   ntp_time = D2LFP(offset);
   unix_time.tv_sec = ntp_time / 0x100000000L;
   unix_time.tv_usec = ntp_time % 0x100000000L;
   unix_time.tv_sec += unix_time.tv_usec / 1000000;
   unix_time.tv_usec %= 1000000;



Burbank, et al.          Expires April 26, 2007                [Page 79]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   adjtime(&unix_time, NULL);
   }
   A.5 Peer Process

   #include "ntp4.h"

   /*
   * A crypto-NAK packet includes the NTP header followed
    by a MAC
   * consisting only of the key identifier with value zero.
    It tells the
   * receiver that a prior request could not be properly
    authenticated,
   * but the NTP header fields are correct.
   *
   * A kiss-o'-death packet has an NTP header with leap 3
    (NOSYNC) and
   * stratum 0. It tells the receiver that something drastic
   * has happened, as revealled by the kiss code in the
    refid field. The
   * NTP header fields may or may not be correct.
   */
   /*
   * Definitions
   */
   #define SGATE   3   /* spike gate (clock filter */
   #define BDELAY   .004   /* broadcast delay (s) */

   /*
   * Dispatch codes
   */
   #define ERR   -1   /* error */
   #define DSCRD   0   /* discard packet */
   #define PROC   1   /* process packet */
   #define BCST   2   /* broadcast packet */
   #define FXMIT   3   /* client packet */
   #define NEWPS   4   /* new symmetric passive client */
   #define NEWBC   5   /* new broadcast client */

   /*
   * Dispatch matrix
   *   active passv client server bcast */
   int table[7][5] = {
   /* nopeer    */{ NEWPS, DSCRD, FXMIT, DSCRD, NEWBC },
   /* active    */{ PROC, PROC, DSCRD, DSCRD, DSCRD },
   /* passv    */{ PROC, ERR, DSCRD, DSCRD, DSCRD },
   /* client    */{ DSCRD, DSCRD, DSCRD, PROC, DSCRD },
   /* server    */{ DSCRD, DSCRD, DSCRD, DSCRD, DSCRD },



Burbank, et al.          Expires April 26, 2007                [Page 80]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   /* bcast    */{ DSCRD, DSCRD, DSCRD, DSCRD, DSCRD },
   /* bclient */{ DSCRD, DSCRD, DSCRD, DSCRD, PROC}
   };

   /*
   * Miscellaneous macroni
   *
   * This macro defines the authentication state. If x is 0,
   * authentication is optional, othewise it is required.
   */
   #define AUTH(x, y)((x) ? (y) == A_OK : (y) == A_OK || \
      (y) == A_NONE)

   /*
   * These are used by the clear() routine
   */
   #define BEGIN_CLEAR(p)   ((char *)&((p)->begin_clear))
   #define END_CLEAR(p)   ((char *)&((p)->end_clear))
   #define LEN_CLEAR (END_CLEAR ((struct p *)0) - \
      BEGIN_CLEAR((struct p *)0))
   A.5.1 receive()

   /*
   * receive() - receive packet and decode modes
   */
   void
   receive(
   struct r *r   /* receive packet pointer */
   )
   {
   struct p *p;   /* peer structure pointer
   int   auth;   /* authentication code */
   int   has_mac;   /* size of MAC */
   int   synch;   /* synchronized switch */
   int   auth;   /* authentication code */

   /*
   * Check access control lists. The intent here is to implement a
   * whitelist of those IP addresses specifically accepted and/or
   * a blacklist of those IP addresses specifically rejected.
   * There could be different lists for authenticated clients and
   * unauthenticated clients.
   */
   if (!access(r))
   return;   /* access denied */

   /*
   * The version must not be in the future. Format checks include



Burbank, et al.          Expires April 26, 2007                [Page 81]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   * packet length, MAC length and extension field lengths, if
   * present.
   */
   if (r->version > VERSION /* or format error */)
   return;   /* format error */

   /*
   * Authentication is conditioned by two switches which can be
   * specified on a per-client basis.
   *
   * P_NOPEER   do not mobilize an association unless
   *   authenticated
   * P_NOTRUST   do not allow access unless authenticated
   *   (implies P_NOPEER)*
   * There are four outcomes:
   *
   * A_NONE the packet has no MAC
   * A_OK   the packet has a MAC and authentication
   *   succeeds
   * A_ERROR   the packet has a MAC and authentication fails
   * A_CRYPTO   crypto-NAK. the MAC has four octets only.
   *
   * Note: The AUTH(x, y) macro is used to filter outcomes. If x
   * is zero, acceptable outcomes of y are NONE and OK. If x is
   * one, the only acceptable outcome of y is OK.
   */
   has_mac = /* length of MAC field */ 0; if (has_mac == 0) {
   auth = A_NONE;   /* not required */
   } else if (has_mac == 4) {
   auth == A_CRYPTO;   /* crypto-NAK */
   } else {
   if (r->mac != md5(r->keyid))
   auth = A_ERROR;   /* auth error */
   else
   auth = A_OK;   /* auth OK */
   }

   /*
   * Find association and dispatch code. If there is no
   * association to match, the value of p->mode is assumed NULL.
   */
   p = find_assoc(r);
   switch(table[p->mode][r->mode]) {

   /*
   * Client packet. Send server reply (no association). If
   * authentication fails, send a crypto-NAK packet.
   */



Burbank, et al.          Expires April 26, 2007                [Page 82]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   case FXMIT:
   if (AUTH(p->flags & P_NOTRUST, auth))
      fast_xmit(r, M_SERV, auth);
   else if (auth == A_ERROR)
      fast_xmit(r, M_SERV, A_CRYPTO);
   return;   /* M_SERV packet sent */

   /*
   * New symmetric passive client (ephemeral association). It is
   * mobilized in the same version as in the packet. If
   * authentication fails, send a crypto-NAK packet. If restrict
   * no-moblize, send a symmetric active packet instead.
   */
   case NEWPS:
   if (!AUTH(p->flags & P_NOTRUST, auth)) {
      if (auth == A_ERROR)
   fast_xmit(r, M_SACT, A_CRYPTO);
   return;   /* crypto-NAK packet sent */
   }
   if (!AUTH(p->flags & P_NOPEER, auth)) {
      fast_xmit(r, M_SACT, auth);
   return;   /* M_SACT packet sent */
   }
   p = mobilize(r->srcaddr, r->dstaddr, r->version, M_PASV,
      r->keyid, P_EPHEM);
   break;

   /*
   * New broadcast client (ephemeral association). It is mobilized
   * in the same version as in the packet. If authentication
   * error, ignore the packet.
   */
   case NEWBC:
   if (!AUTH(p->flags & (P_NOTRUST | P_NOPEER), auth))
   return;   /* authentication error */

   if (!(s.flags & S_BCSTENAB))
   return;   /* broadcast not enabled */

   p = mobilize(r->srcaddr, r->dstaddr, r->version, M_BCLN,
      r->keyid, P_EPHEM);
   break;   /* processing continues */

   /*
   * Process packet. Placeholdler only.
   */
   case PROC:
   break;   /* processing continues */



Burbank, et al.          Expires April 26, 2007                [Page 83]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   /*
   * Invalid mode combination. We get here only in case of
   * ephemeral associations, so the correct action is simply to
   * toss it.
   */
   case ERR:
   clear(p, X_ERROR);
   return;   /* invalid mode combination */

   /*
   * No match; just discard the packet.
   */
   case DSCRD:
   return;   /* orphan abandoned */
   }

   /*
   * Next comes a rigorous schedule of timestamp checking. If the
   * transmit timestamp is zero, the server is horribly broken.
   */
   if (r->xmt == 0)
   return;   /* invalid timestamp */

   /*
   * If the transmit timestamp duplicates a previous one, the
   * packet is a replay.
   */
   if (r->xmt == p->xmt)
   return;   /* duplicate packet */

   /*
   * If this is a broadcast mode packet, skip further checking.
   * If the origin timestamp is zero, the sender has not yet heard
   * from us. Otherwise, if the origin timestamp does not match
   * the transmit timestamp, the packet is bogus.
   */
   synch = TRUE;
   if (r->mode != M_BCST) {
      if (r->org == 0)
   synch = FALSE;/* unsynchronized */

   else if (r->org != p->xmt)
   synch = FALSE;/* bogus packet */
   }

   /*
   * Update the origin and destination timestamps. If
   * unsynchronized or bogus, abandon ship.



Burbank, et al.          Expires April 26, 2007                [Page 84]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   */
   p->org = r->xmt;
   p->rec = r->dst;
   if (!synch)
   return;   /* unsynch */

   /*
   * The timestamps are valid and the receive packet matches the
   * last one sent. If the packet is a crypto-NAK, the server
   * might have just changed keys. We demobilize the association
   * and wait for better times.
   */
   if (auth == A_CRYPTO) {
      clear(p, X_CRYPTO);
   return;   /* crypto-NAK */
   }

   /*
   * If the association is authenticated, the key ID is nonzero
   * and received packets must be authenticated. This is designed *
    to avoid a bait-and-switch attack, which was possible in past
   * versions.
   */
   if (!AUTH(p->keyid || (p->flags & P_NOTRUST), auth))
   return;   /* bad auth */

   /*
   * Everything possible has been done to validate the timestamps
   * and prevent bad guys from disrupting the protocol or
   * injecting bogus data. Earn some revenue.
   */
   packet(p, r);
   }

   /*
   * find_assoc() - find a matching association
   */
   struct p   /* peer structure pointer or NULL */
   *find_assoc(
   struct r *r   /* receive packet pointer */
   )
   {
   struct p *p;   /* dummy peer structure pointer */

   /*
   * Search association table for matching source * address and
    source port.
   */



Burbank, et al.          Expires April 26, 2007                [Page 85]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   while (/* all associations */ 0) {
   if (r->srcaddr == p->srcaddr && r->port == p->port)
      return(p);
   }
   return (NULL);
   }
   A.5.2 packet()

   /*
   * packet() - process packet and compute offset, delay and
   * dispersion.
   */
   void
   packet(
   struct p *p,   /* peer structure pointer */
   struct r *r   /* receive packet pointer */
   )
   {
   double   offset;   /* sample offsset */
   double   delay;   /* sample delay */
   double   disp;   /* sample dispersion */

   /*
   * By golly the packet is valid. Light up the remaining header
   * fields. Note that we map stratum 0 (unspecified) to MAXSTRAT
   * to make stratum comparisons simpler and to provide a natural
   * interface for radio clock drivers that operate for
   * convenience at stratum 0.
   */
   p->leap = r->leap;
   if (r->stratum == 0)
      p->stratum = MAXSTRAT; else
   p->stratum = r->stratum; p->mode = r->mode;
   p->ppoll = r->poll;
   p->rootdelay = FP2D(r->rootdelay); p->rootdisp = FP2D(r->rootdisp);
   p->refid = r->refid;
   p->reftime = r->reftime;

   /*
   * Verify the server is synchronized with valid stratum and
   * reference time not later than the transmit time.
   */
   if (p->leap == NOSYNC || p->stratum >= MAXSTRAT)
   return;   /* unsynchronized */

   /*
   * Verify valid root distance.
   */



Burbank, et al.          Expires April 26, 2007                [Page 86]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   if (r->rootdelay / 2 + r->rootdisp >= MAXDISP || p->reftime >
      r->xmt)
   return;   /* invalid header values */

   poll_update(p, p->hpoll);
   p->reach |= 1;

   /*
   * Calculate offset, delay and dispersion, then pass to the
   * clock filter. Note carefully the implied processing. The
   * first-order difference is done directly in 64-bit arithmetic,
   * then the result is converted to floating double. All further
   * processing is in floating double arithmetic with rounding
   * done by the hardware. This is necessary in order to avoid
   * overflow and preseve precision.
   *
   * The delay calculation is a special case. In cases where the
   * server and client clocks are running at different rates and
   * with very fast networks, the delay can appear negative. In
   * order to avoid violating the Principle of Least Astonishment,
   * the delay is clamped not less than the system precision.
   */
   if (p->mode == M_BCST) {
   offset = LFP2D(r->xmt - r->dst); delay = BDELAY;
   disp = LOG2D(r->precision) + LOG2D(s.precision) + PHI *
      2 * BDELAY;
   } else {
   offset = (LFP2D(r->rec - r->org) + LFP2D(r->dst
      r->xmt)) / 2;
   delay = max(LFP2D(r->dst - r->org) - LFP2D(r->rec
      r->xmt), LOG2D(s.precision));
   disp = LOG2D(r->precision) + LOG2D(s.precision) + PHI *
      LFP2D(r->dst - r->org);
   }
   clock_filter(p, offset, delay, disp);
   }
   A.5.3 clock_filter()

   /*
   * clock_filter(p, offset, delay, dispersion) - select the best
    from the * latest eight delay/offset samples.
   */
   void
   clock_filter(
   struct p *p,   /* peer structure pointer */
   double   offset,   /* clock offset */
   double   delay,   /* roundtrip delay */
   double   disp   /* dispersion */



Burbank, et al.          Expires April 26, 2007                [Page 87]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   )
   {
   struct f f[NSTAGE];/* sorted list */
   double   dtemp;
   int   i;

   /*
   * The clock filter contents consist of eight tuples (offset,
   * delay, dispersion, time). Shift each tuple to the left,
   * discarding the leftmost one. As each tuple is shifted,
   * increase the dispersion since the last filter update. At the
   * same time, copy each tuple to a temporary list. After this,
   * place the (offset, delay, disp, time) in the vacated
   * rightmost tuple.
   */
   for (i = 1; i < NSTAGE; i++) {
      p->f[i] = p->f[i - 1];
   p->f[i].disp += PHI * (c.t - p->t); f[i] = p->f[i];
   }
   p->f[0].t = c.t;
   p->f[0].offset = offset;
   p->f[0].delay = delay;
   p->f[0].disp = disp;
   f[0] = p->f[0];

   /*
   * Sort the temporary list of tuples by increasing f[].delay. *
    The first entry on the sorted list represents the best * sample,
    but it might be old.
   */
   dtemp = p->offset;
   p->offset = f[0].offset;
   p->delay = f[0].delay;
   for (i = 0; i < NSTAGE; i++) {
      p->disp += f[i].disp / (2 ^ (i + 1));
      p->jitter += SQUARE(f[i].offset - f[0].offset);
    }
   p->jitter = max(SQRT(p->jitter), LOG2D(s.precision));

   /*
   * Prime directive: use a sample only once and never a sample
    * older than the latest one, but anything goes before first
    * synchronized.
   */
   if (f[0].t - p->t <= 0 && s.leap != NOSYNC)
      return;

   /*



Burbank, et al.          Expires April 26, 2007                [Page 88]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   * Popcorn spike suppressor. Compare the difference between the
   * last and current offsets to the current jitter. If greater
   * than SGATE (3) and if the interval since the last offset is
   * less than twice the system poll interval, dump the spike.
   * Otherwise, and if not in a burst, shake out the truechimers.
   */
   if (fabs(p->offset - dtemp) > SGATE * p->jitter && (f[0].t
      p->t) < 2 * s.poll)
   return;

   p->t = f[0].t;
   if (p->burst == 0)
      clock_select();
   return;
   }
   A.5.4 fast_xmit()

   /*
   * fast_xmit() - transmit a reply packet for receive packet r
   */
   void
   fast_xmit(
   struct r *r,   /* receive packet pointer */
   int   mode,   /* association mode */
   int   auth   /* authentication code */
   )
   {
   struct x x;

   /*
   * Initialize header and transmit timestamp. Note that
   the * transmit version is copied from the receive version.
    This is * for backward compatibility.
   */
   x.version = r->version;
   x.srcaddr = r->dstaddr;
   x.dstaddr = r->srcaddr;
   x.leap = s.leap;
   x.mode = mode;
   if (s.stratum == MAXSTRAT)
      x.stratum = 0;
   else
   x.stratum = s.stratum; x.poll = r->poll;
   x.precision = s.precision;
   x.rootdelay = D2FP(s.rootdelay); x.rootdisp = D2FP(s.rootdisp);
    x.refid = s.refid;
   x.reftime = s.reftime;
   x.org = r->xmt;



Burbank, et al.          Expires April 26, 2007                [Page 89]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   x.rec = r->dst;
   x.xmt = get_time();

   /*
   * If the authentication code is A.NONE, include only the
   * header; if A.CRYPTO, send a crypto-NAK; if A.OK, send a valid
   * MAC. Use the key ID in the received packet and the key in the
   * local key cache.
   */
   if (auth != A_NONE) {
      if (auth == A_CRYPTO) {
      x.keyid = 0;
   } else {
   x.keyid = r->keyid;
   x.digest = md5(x.keyid);
   }
   }
   xmit_packet(&x);
   }
   A.5.5 access()

   /*
   * access() - determine access restrictions
   */
   int
   access(
   struct r *r   /* receive packet pointer */
   )
   {
   /*
   * The access control list is an ordered set of tuples
   * consisting of an address, mask and restrict word containing
   * defined bits. The list is searched for the first match on the
   * source address (r->srcaddr) and the associated restrict word
   * is returned.
   */
   return (/* access bits */ 0);
   }
   A.6 System Process

   #include "ntp4.h"

   A.6.1 clock_select()

   /*
   * clock_select() - find the best clocks
   */
   void



Burbank, et al.          Expires April 26, 2007                [Page 90]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   clock_select() {
   struct p *p, *osys;   /* peer structure pointers */
   double   low, high;   /* correctness interval extents */
   int   allow, found, chime; /* used by intersecion algorithm */
   int   n, i, j;

   /*
   * We first cull the falsetickers from the server population,
   * leaving only the truechimers. The correctness interval for
   * association p is the interval from offset - root_dist() to
   * offset + root_dist(). The object of the game is to find a
   * majority clique; that is, an intersection of correctness
   * intervals numbering more than half the server population.
   *
   * First construct the chime list of tuples (p, type, edge) as
   * shown below, then sort the list by edge from lowest to
   * highest.
   */
   osys = s.p;
   s.p = NULL;
   n = 0;
   while (accept(p)) {
      s.m[n].p = p;
   s.m[n].type = +1;
   s.m[n].edge = p->offset + root_dist(p);
   n++;
   s.m[n].p = p;
   s.m[n].type = 0;
   s.m[n].edge = p->offset;
   n++;
   s.m[n].p = p;
   s.m[n].type = -1;
   s.m[n].edge = p->offset - root_dist(p);
   n++;
   }

   /*
   * Find the largest contiguous intersection of correctness
   * intervals. Allow is the number of allowed falsetickers; found
   * is the number of midpoints. Note that the edge values are
   * limited to the range +-(2 ^ 30) < +-2e9 by the timestamp
   * calculations.
   */
   low = 2e9; high = -2e9;
   for (allow = 0; 2 * allow < n; allow++) {
   /*
   * Scan the chime list from lowest to highest to find
   * the lower endpoint.



Burbank, et al.          Expires April 26, 2007                [Page 91]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   */
   found = 0;
   chime = 0;
   for (i = 0; i < n; i++) {
      chime -= s.m[i].type;
      if (chime >= n - found) {
      low = s.m[i].edge;
   break;
   }
   if (s.m[i].type == 0)
      found++;
   }

   /*
   * Scan the chime list from highest to lowest to find
   * the upper endpoint.
   */
   chime = 0;
   for (i = n - 1; i >= 0; i--) {
      chime += s.m[i].type;
   if (chime >= n - found) {
      high = s.m[i].edge;
      break;
   }
   if (s.m[i].type == 0)
      found++;
   }

   /*
   * If the number of midpoints is greater than the number
   * of allowed falsetickers, the intersection contains at
   * least one truechimer with no midpoint. If so,
   * increment the number of allowed falsetickers and go
   * around again. If not and the intersection is
   * nonempty, declare success.
   */
   if (found > allow)
      continue;

   if (high > low)
      break;
   }

   /*
   * Clustering algorithm. Construct a list of survivors
   (p, * metric) from the chime list, where metric is dominated
    first * by stratum and then by root distance. All other
    things being * equal, this is the order of preference.



Burbank, et al.          Expires April 26, 2007                [Page 92]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   */
   n = 0;
   for (i = 0; i < n; i++) {
   if (s.m[i].edge < low || s.m[i].edge > high)
      continue;

   p = s.m[i].p;
   s.v[n].p = p;
   s.v[n].metric = MAXDIST * p->stratum + root_dist(p);
   n++;
   }

   /*
   * There must be at least NSANE survivors to satisfy the
   * correctness assertions. Ordinarily, the Byzantine criteria
   * require four, susrvivors, but for the demonstration here, one
   * is acceptable.
   */
   if (n == NSANE)
      return;

   /*
   * For each association p in turn, calculate the selection
   * jitter p->sjitter as the square root of the sum of squares
   * (p->offset - q->offset) over all q associations. The idea is
   * to repeatedly discard the survivor with maximum selection
   * jitter until a termination condition is met.
   */
   while (1) {
   struct p *p, *q, *qmax;/* peer structure pointers */
   double   max, min, dtemp;

   max = -2e9; min = 2e9; for (i = 0; i < n; i++) {
      p = s.v[i].p;
   if (p->jitter < min)
      min = p->jitter;
   dtemp = 0;
   for (j = 0; j < n; j++) {
      q = s.v[j].p;
   dtemp += SQUARE(p->offset - q->offset);
   }
   dtemp = SQRT(dtemp); if (dtemp > max) {
      max = dtemp;
   qmax = q;
   }
   }

   /*



Burbank, et al.          Expires April 26, 2007                [Page 93]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   * If the maximum selection jitter is less than the
   * minimum peer jitter, then tossing out more survivors
   * will not lower the minimum peer jitter, so we might
   * as well stop. To make sure a few survivors are left
   * for the clustering algorithm to chew on, we also stop
   * if the number of survivors is less than or equal to
   * NMIN (3).
   */
   if (max < min || n <= NMIN)
      break;

   /*
   * Delete survivor qmax from the list and go around * again.
   */
   n--;
   }

   /*
   * Pick the best clock. If the old system peer is on the list
   * and at the same stratum as the first survivor on the list,
   * then don't do a clock hop. Otherwise, select the first
   * survivor on the list as the new system peer.
   */
   if (osys->stratum == s.v[0].p->stratum)
      s.p = osys;
   else
   s.p = s.v[0].p;
   clock_update(s.p);
   }
   A.6.2 root_dist()

   /*
   * root_dist() - calculate root distance
   */
   double
   root_dist(
   struct p *p   /* peer structure pointer */
   )
   {
   /*
   * The root synchronization distance is the maximum error due to
   * all causes of the local clock relative to the primary server.
   * It is defined as half the total delay plus total dispersion
   * plus peer jitter.
   */
   return (max(MINDISP, p->rootdelay + p->delay) / 2 +
      p->rootdisp + p->disp + PHI * (c.t - p->t) + p->jitter);
    }



Burbank, et al.          Expires April 26, 2007                [Page 94]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   A.6.3 accept()

   /*
   * accept() - test if association p is acceptable for
    synchronization
   */
   int
   accept(
   struct p *p   /* peer structure pointer */
   )
   {
   /*
   * A stratum error occurs if (1) the server has never been
   * synchronized, (2) the server stratum is invalid.
   */
   if (p->leap == NOSYNC || p->stratum >= MAXSTRAT)
      return (FALSE);

   /*
   * A distance error occurs if the root distance exceeds the
   * distance threshold plus an increment equal to one poll
   * interval.
   */
   if (root_dist(p) > MAXDIST + PHI * LOG2D(s.poll))
      return (FALSE);

   /*
   * A loop error occurs if the remote peer is synchronized to the
   * local peer or the remote peer is synchronized to the current
   * system peer. Note this is the behavior for IPv4; for IPv6 the
   * MD5 hash is used instead.
   */
   if (p->refid == p->dstaddr || p->refid == s.refid)
      return (FALSE);

   /*
   * An unreachable error occurs if the server is unreachable.
   */
   if (p->reach == 0)
      return (FALSE);

   return (TRUE);
   }
   A.6.4 clock_update()

   /*
   * clock_update() - update the system clock
   */



Burbank, et al.          Expires April 26, 2007                [Page 95]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   void
   clock_update(
   struct p *p   /* peer structure pointer */
   )
   {
   double dtemp;

   /*
   * If this is an old update, for instance as the result of a
   * system peer change, avoid it. We never use an old sample or
   * the same sample twice.
   *
   if (s.t >= p->t)
   return;

   /*
   * Combine the survivor offsets and update the system clock; the
   * local_clock() routine will tell us the good or bad news.
   */
   s.t = p->t;
   clock_combine();
   switch (local_clock(p, s.offset)) {

   /*
   * The offset is too large and probably bogus. Complain to the
   * system log and order the operator to set the clock manually
   * within PANIC range. An implementation MAY include a
   * command line option to disable this check and to change the
   * panic threshold from the default 1000 s as required.
   */
   case PANIC:
   exit (0);

   /*
   * The offset is more than the step threshold (0.125 s by
   * default). After a step, all associations now have
   * inconsistent time valurs, so they are reset and started
   * fresh. The step threshold MAY be changed in an
   * implementation in order to lessen the chance the clock might
   * be stepped backwards. However, there may be serious
   * consequences.
   */
   case STEP:
   while (/* all associations */ 0)
   clear(p, X_STEP);
   s.stratum = MAXSTRAT;
   s.poll = MINPOLL;
   break;



Burbank, et al.          Expires April 26, 2007                [Page 96]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   /*
   * The offset was less than the step threshold, which is the
   * normal case. Update the system variables from the peer
   * variables. The lower clamp on the dispersion increase is to
   * avoid timing loops and clockhopping when highly precise
   * sources are in play. The clamp MAY be changed from the
   * suggested default of .01 s.
   */
   case SLEW:
   s.leap = p->leap;
   s.stratum = p->stratum + 1; s.refid = p->refid;
   s.reftime = p->reftime;
   s.rootdelay = p->rootdelay + p->delay;
   dtemp = SQRT(SQUARE(p->jitter) + SQUARE(s.jitter));
   dtemp += max(p->disp + PHI * (c.t - p->t) +
   fabs(p->offset), MINDISP);
   s.rootdisp = p->rootdisp + dtemp; break;

   /*
   * Some samples are discarded while, for instance, a direct
   * frequency measurement is being made.
   */
   case IGNORE:
   break;
   }
   }
   A.6.5 clock_combine()

   /*
   * clock_combine() - combine offsets
   */
   void
   clock_combine()
   {
   struct p *p;/* peer structure pointer */
   double x, y, z, w;
   int i;

   /*
   * Combine the offsets of the clustering algorithm survivors
   * using a weighted average with weight determined by the root
   * distance. Compute the selection jitter as the weighted RMS
   * difference between the first survivor and the remaining
   * survivors. In some cases the inherent clock jitter can be
   * reduced by not using this algorithm, especially when frequent
   * clockhopping is involved.
   */
   y = z = w = 0;



Burbank, et al.          Expires April 26, 2007                [Page 97]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   for (i = 0; s.v[i].p != NULL; i++) {
   p = s.v[i].p;
   x = root_dist(p);
   y += 1 / x;
   z += p->offset / x;
   w += SQUARE(p->offset - s.v[0].p->offset) / x;
   }
   s.offset = z / y;
   s.jitter = SQRT(w / y);
   }
   A.6.6 local_clock()

   #include "ntp4.h"

   /*
   * Constants
   */
   #define STEPT.128/* step threshold (s) */
   #define WATCH900/* stepout threshold (s) */
   #define PANICT1000/* panic threshold (s) */
   #define PLL65536/* PLL loop gain */
   #define FLLMAXPOLL + 1/* FLL loop gain */
   #define AVG 4/* parameter averaging constant */
   #define ALLAN1500/* compromise Allan intercept (s) */
   #define LIMIT  30  /* poll-adjust threshold */
   #define MAXFREQ  500e-6
    /* maximum frequency tolerance (s/s) */
   #define PGATE  4  /* poll-adjust gate */

   /*
   * local_clock() - discipline the local clock
   */
   int  /* return code */
   local_clock(
   struct p *p,  /* peer structure pointer */
   double  offset  /* clock offset from combine() */
   )
   {
   int  state;  /* clock discipline state */
   double  freq;  /* frequency */
   double  mu;  /* interval since last update */
   int  rval;
   double  etemp, dtemp;

   /*
   * If the offset is too large, give up and go home.
   */
   if (fabs(offset) > PANICT)



Burbank, et al.          Expires April 26, 2007                [Page 98]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


     return (PANIC);

   /*
   * Clock state machine transition function. This is where the
   * action is and defines how the system reacts to large time
   * and frequency errors. There are two main regimes: when the
   * offset exceeds the step threshold and when it does not.
   */
   rval = SLEW;
   mu = p->t - s.t;
   freq = 0;
   if (fabs(offset) > STEPT) {
     switch (c.state) {

   /*
   * In S_SYNC state we ignore the first outlyer amd
   * switch to S_SPIK state.
   */
   case SYNC:
     state = SPIK;
     return (rval);
   /*
   * In S_FREQ state we ignore outlyers and inlyers. At
   * the first outlyer after the stepout threshold,
   * compute the apparent frequency correction and step
   * the time.
   */
   case FREQ:
   if (mu < WATCH)
     return (IGNORE);

   freq = (offset - c.base - c.offset) / mu;
   /* fall through to S_SPIK */

   /*
   * In S_SPIK state we ignore succeeding outlyers until
   * either an inlyer is found or the stepout threshold is
   * exceeded.
   */
   case SPIK:
   if (mu < WATCH)
     return (IGNORE);

   /* fall through to default */

   /*
   * We get here by default in S_NSET and S_FSET states
   * and from above in S_FREQ state. Step the time and



Burbank, et al.          Expires April 26, 2007                [Page 99]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   * clamp down the poll interval.
   *
   * In S_NSET state an initial frequency correction is
   * not available, usually because the frequency file has
   * not yet been written. Since the time is outside the
   * capture range, the clock is stepped. The frequency
   * will be set directly following the stepout interval.
   *
   * In S_FSET state the initial frequency has been set
   * from the frequency file. Since the time is outside
   * the capture range, the clock is stepped immediately,
   * rather than after the stepout interval. Guys get
   * nervous if it takes 17 minutes to set the clock for
   * the first time.
   *
   * In S_SPIK state the stepout threshold has expired and
   * the phase is still above the step threshold. Note
   * that a single spike greater than the step threshold
   * is always suppressed, even at the longer poll
   * intervals.
   */
   default:

   /*
   * This is the kernel set time function, usually
   * implemented by the Unix settimeofday() system
   * call.
   */
   step_time(offset); c.count = 0;
   rval = STEP;
   if (state == NSET) {
     rstclock(FREQ, p->t, 0);
     return (rval);
   }
   break;
   }
   rstclock(SYNC, p->t, 0);
   } else {

   /*
   * Compute the clock jitter as the RMS of exponentially
   * weighted offset differences. This is used by the
   * poll-adjust code.
   */
   etemp = SQUARE(c.jitter);
   dtemp = SQUARE(max(fabs(offset - c.last),
     LOG2D(s.precision)));
   c.jitter = SQRT(etemp + (dtemp - etemp) / AVG);



Burbank, et al.          Expires April 26, 2007               [Page 100]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   switch (c.state) {

   /*
   * In S_NSET state this is the first update received and
   * the frequency has not been initialized. The first
   * thing to do is directly measure the oscillator
   * frequency.
   */
   case NSET:
   c.offset = offset;
   rstclock(FREQ, p->t, offset); return (IGNORE);

   /*
   * In S_FSET state this is the first update and the
   * frequency has been initialized. Adjust the phase, but
   * don't adjust the frequency until the next update.
   */
   case FSET:
   c.offset = offset; break;

   /*
   * In S_FREQ state ignore updates until the stepout
   * threshold. After that, correct the phase and
   * frequency and switch to S_SYNC state.
   */
   case FREQ:
   if (c.t - s.t < WATCH)
     return (IGNORE);

   freq = (offset - c.base - c.offset) / mu;
   break;

   /*
   * We get here by default in S_SYNC and S_SPIK states.
   * Here we compute the frequency update due to PLL and
   * FLL contributions.
   */
   default:

   /*
   * The FLL and PLL frequency gain constants
   * depend on the poll interval and Allan
   * intercept. The FLL is not used below one-half
   * the Allan intercept. Above that the loop gain
   * increases in steps to 1 / AVG.
   */
   if (LOG2D(s.poll) > ALLAN / 2) {
     etemp = FLL - s.poll;



Burbank, et al.          Expires April 26, 2007               [Page 101]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   if (etemp < AVG)
     etemp = AVG;
   freq += (offset - c.offset) / (max(mu,
     ALLAN) * etemp);
   }

   /*
   * For the PLL the integration interval
   * (numerator) is the minimum of the update
   * interval and poll interval. This allows
   * oversampling, but not undersampling.
   */
   etemp = min(mu, LOG2D(s.poll));
   dtemp = 4 * PLL * LOG2D(s.poll);
   freq += offset * etemp / (dtemp * dtemp);
   break;
   }
   rstclock(SYNC, p->t, offset);
   }

   /*
   * Calculate the new frequency and frequency stability (wander).
   * Compute the clock wander as the RMS of exponentially weighted
   * frequency differences. This is not used directly, but can,
   * along withthe jitter, be a highly useful monitoring and
   * debugging tool
   */
   freq += c.freq;
   c.freq = max(min(MAXFREQ, freq), -MAXFREQ);
   etemp = SQUARE(c.wander);
   dtemp = SQUARE(freq);
   c.wander = SQRT(etemp + (dtemp - etemp) / AVG);

   /*
   * Here we adjust the poll interval by comparing the current
   * offset with the clock jitter. If the offset is less than the
   * clock jitter times a constant, then the averaging interval is
   * increased, otherwise it is decreased. A bit of hysteresis
   * helps calm the dance. Works best using burst mode.
   */
   if (fabs(c.offset) < PGATE * c.jitter) {
     c.count += s.poll;
   if (c.count > LIMIT) {
     c.count = LIMIT;
   if (s.poll < MAXPOLL) {
     c.count = 0;
   s.poll++;
   }



Burbank, et al.          Expires April 26, 2007               [Page 102]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   }
   } else {
   c.count -= s.poll << 1; if (c.count < -LIMIT) {
     c.count = -LIMIT;
   if (s.poll > MINPOLL) {
     c.count = 0;
   s.poll--;
   }
   }
   }
   return (rval);
   }
   A.6.7 rstclock()

   /*
   * rstclock() - clock state machine
   */
   void
   rstclock(
   int  state,  /* new state */
   double  offset,  /* new offset */
   double  t  /* new update time */
   )
   {
   /*
   * Enter new state and set state variables. Note we use the
   time
   * of the last clock filter sample, which must be
   earlier than
   * the current time.
   */
   c.state = state;
   c.base = offset - c.offset;
   c.last = c.offset = offset;
   s.t = t;
   }

   A.7 Clock Adjust Process

   A.7.1 clock_adjust()

   /*
   * clock_adjust() - runs at one-second intervals
   */
   void
   clock_adjust() {
   double  dtemp;




Burbank, et al.          Expires April 26, 2007               [Page 103]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   /*
   * Update the process time c.t. Also increase the dispersion
   * since the last update. In contrast to NTPv3, NTPv4 does not
   * declare unsynchronized after one day, since the dispersion
   * threshold serves this function. When the dispersion exceeds
   * MAXDIST (1 s), the server is considered unaccept for
   * synchroniztion.
   */
   c.t++;
   s.rootdisp += PHI;

   /*
   * Implement the phase and frequency adjustments. The gain
   * factor (denominator) is not allowed to increase beyond the
   * Allan intercept. It doesn't make sense to average phase noise
   * beyond this point and it helps to damp residual offset at the
   * longer poll intervals.
   */
   dtemp = c.offset / (PLL * min(LOG2D(s.poll), ALLAN));
   c.offset -= dtemp;

   /*
   * This is the kernel adjust time function, usually implemented
   * by the Unix adjtime() system call.
   */
   adjust_time(c.freq + dtemp);

   /*
   * Peer timer. Call the poll() routine when the poll timer
   * expires.
   */
   while (/* all associations */ 0) {
   struct p *p;/* dummy peer structure pointer */

   if (c.t >= p->next)
   poll(p);
   }

   /*
   * Once per hour write the clock frequency to a file
   */
   if (c.t % 3600 == 3599)
   /* write c.freq to file */ 0;
   }
   A.8 Poll Process

   #include "ntp4.h"




Burbank, et al.          Expires April 26, 2007               [Page 104]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   /*
   * Constants
   */
   #define UNREACH  12  /* unreach counter threshold */
   #define BCOUNT  8  /* packets in a burst */
   #define BTIME  2  /* burst interval (s) */
   A.8.1 poll()

   /*
   * poll() - determine when to send a packet for association p->
   */
   void
   poll(
   struct p *p  /* peer structure pointer */
   )
   {
   int  hpoll;
   int  oreach;

   /*
   * This routine is called when the current time c.t catches up
   * to the next poll time p->next. The value p->last is
   * the last time this routine was executed. The poll_update()
   * routine determines the next execution time p->next.
   *
   * If broadcasting, just do it, but only if we are synchronized.
   */
   hpoll = p->hpoll;
   if (p->mode == M_BCST) {
     p->last = c.t;
   if (s.p != NULL)
     peer_xmit(p);
   poll_update(p, hpoll); return;
   }
   if (p->burst == 0) {

   /*
   * We are not in a burst. Shift the reachability
   * register to the left. Hopefully, some time before the
   * next poll a packet will arrive and set the rightmost
   * bit.
   */
   p->last = c.t;
   oreach = p->reach;
   p->reach << 1;
   if (!p->reach) {

   /*



Burbank, et al.          Expires April 26, 2007               [Page 105]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   * The server is unreachable, so bump the
   * unreach counter. If the unreach threshold has
   * been reached, double the poll interval to
   * minimize wasted network traffic.
   */
   if (p->flags & P_IBURST && p->unreach == 0) {
     p->burst = BCOUNT;
   } else if (p->unreach < UNREACH)
     p->unreach++;
   else
   hpoll++;
   p->unreach++;
   } else {

   /*
   * The server is reachable. However, if has not
   * been heard for three consecutive poll
   * intervals, stuff the clock register to
   * increase the peer dispersion. This makes old
   * servers less desirable and eventually boots
   * them off the island.
   */
   p->unreach = 0;
   if (!(p->reach & 0x7))
   clock_filter(p, 0, 0, MAXDISP); hpoll = s.poll;
   if (p->flags & P_BURST && accept(p))
     p->burst = BCOUNT;
   }
   } else {

   /*
   * If in a burst, count it down. When the reply comes
   * back the clock_filter() routine will call
   * clock_select() to process the results of the burst.
   */
   p->burst--;
   }

   /*
   * Do not transmit if in broadcast client mode.
   */
   if (p->mode != M_BCLN)
     peer_xmit(p);
   poll_update(p, hpoll);
   }
   A.8.2 poll_update()

   /*



Burbank, et al.          Expires April 26, 2007               [Page 106]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   * poll_update() - update the poll interval for association p
   *
   * Note: This routine is called by both the packet() and
    poll() routine.
   * Since the packet() routine is executed when a network
    packet arrives
   * and the poll() routine is executed as the result of
    timeout, a
   * potential race can occur, possibly causing an incorrect
    interval for
   * the next poll. This is considered so unlikely as to
    be negligible.
   */
   void
   poll_update(
   struct p *p,  /* peer structure pointer */
   int  hpoll  /* poll interval (log2 s) */
   )
   {
   int  poll;

   /*
   * This routine is called by both the poll() and packet()
   * routines to determine the next poll time. If within a burst
   * the poll interval is two seconds. Otherwise, it is the
   * minimum of the host poll interval and peer poll interval, but
   * not greater than MAXPOLL and not less than MINPOLL. The
   * design insures that a longer interval can be preempted by a
   * shorter one if required for rapid response.
   */
   p->hpoll = min(MAXPOLL, max(MINPOLL, hpoll)); if (p->burst != 0) {
   if(c.t != p->next)
     return;

   p->next += BTIME;
   } else {
   poll = min(p->hpoll, max(MINPOLL, ppoll));
   }
   /*
   * While not shown here, an implementation
   * SHOULD randomize the poll interval by a small factor.
   */
   p->next = p->last + (1 << poll);
   }

   /*
   * It might happen that the due time has already passed. If so,
   * make it one second in the future.



Burbank, et al.          Expires April 26, 2007               [Page 107]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   */
   if (p->next <= c.t)
   p->next = c.t + 1;
   }
   A.8.3 transmit()

   /*
   * transmit() - transmit a packet for association p
   */
   void
   peer_xmit(
   struct p *p/* peer structure pointer */
   )
   {
   struct x x;/* transmit packet */

   /*
   * Initialize header and transmit timestamp
   */
   x.srcaddr = p->dstaddr;
   x.dstaddr = p->srcaddr;
   x.leap = s.leap;
   x.version = VERSION;
   x.mode = p->mode;
   if (s.stratum == MAXSTRAT)
     x.stratum = 0;
   else
   x.stratum = s.stratum; x.poll = p->hpoll;
   x.precision = s.precision;
   x.rootdelay = D2FP(s.rootdelay); x.rootdisp = D2FP(s.rootdisp);
    x.refid = s.refid;
   x.reftime = s.reftime;
   x.org = p->org;
   x.rec = p->rec;
   x.xmt = get_time();
   p->xmt = x.xmt;

   /*
   * If the key ID is nonzero, send a valid MAC using the key ID
   * of the association and the key in the local key cache. If
   * something breaks, like a missing trusted key, don't send the
   * packet; just reset the association and stop until the problem
   * is fixed.
   */
   if (p->keyid)
   if (/* p->keyid invalid */ 0) {
     clear(p, X_NKEY);
   return;



Burbank, et al.          Expires April 26, 2007               [Page 108]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


   }
   x.digest = md5(p->keyid); xmit_packet(&x);
   }


Authors' Addresses

   Jack Burbank (editor)
   The Johns Hopkins University Applied Physics Laboratory
   11100 Johns Hopkins Road
   Laurel, MD  20723-6099
   US

   Phone: +1 443 778 7127
   Email: jack.burbank@jhuapl.edu


   Jim Martin (editor)
   Netzwert AG
   An den Treptowers 1
   Berlin  12435
   Germany

   Phone: +49.30/5 900 80-1180
   Email: jim@netzwert.ag


   Dr. David L. Mills
   University of Delaware
   Newark, DE  19716
   US

   Phone: +1 302 831 8247
   Email: mills@udel.edu

















Burbank, et al.          Expires April 26, 2007               [Page 109]

Internet-Draft  NTPv4 Reference and Implementation Guide    October 2006


Full Copyright Statement

   Copyright (C) The Internet Society (2006).

   This document is subject to the rights, licenses and restrictions
   contained in BCP 78, and except as set forth therein, the authors
   retain all their rights.

   This document and the information contained herein are provided on an
   "AS IS" basis and THE CONTRIBUTOR, THE ORGANIZATION HE/SHE REPRESENTS
   OR IS SPONSORED BY (IF ANY), THE INTERNET SOCIETY AND THE INTERNET
   ENGINEERING TASK FORCE DISCLAIM 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.


Intellectual Property

   The IETF takes no position regarding the validity or scope of any
   Intellectual Property Rights or other rights that might be claimed to
   pertain to the implementation or use of the technology described in
   this document or the extent to which any license under such rights
   might or might not be available; nor does it represent that it has
   made any independent effort to identify any such rights.  Information
   on the procedures with respect to rights in RFC documents can be
   found in BCP 78 and BCP 79.

   Copies of IPR disclosures made to the IETF Secretariat and any
   assurances of licenses to be made available, or the result of an
   attempt made to obtain a general license or permission for the use of
   such proprietary rights by implementers or users of this
   specification can be obtained from the IETF on-line IPR repository at
   http://www.ietf.org/ipr.

   The IETF invites any interested party to bring to its attention any
   copyrights, patents or patent applications, or other proprietary
   rights that may cover technology that may be required to implement
   this standard.  Please address the information to the IETF at
   ietf-ipr@ietf.org.


Acknowledgment

   Funding for the RFC Editor function is provided by the IETF
   Administrative Support Activity (IASA).





Burbank, et al.          Expires April 26, 2007               [Page 110]


Html markup produced by rfcmarkup 1.108, available from http://tools.ietf.org/tools/rfcmarkup/