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rfc:rfc5905

Internet Engineering Task Force (IETF) D. Mills Request for Comments: 5905 U. Delaware Obsoletes: 1305, 4330 J. Martin, Ed. Category: Standards Track ISC ISSN: 2070-1721 J. Burbank

                                                              W. Kasch
                                                               JHU/APL
                                                             June 2010

Network Time Protocol Version 4: Protocol and Algorithms Specification

Abstract

 The Network Time Protocol (NTP) is widely used to synchronize
 computer clocks in the Internet.  This document describes NTP version
 4 (NTPv4), which is backwards compatible with NTP version 3 (NTPv3),
 described in RFC 1305, as well as previous versions of the protocol.
 NTPv4 includes a modified protocol header to accommodate the Internet
 Protocol version 6 address family.  NTPv4 includes fundamental
 improvements in the mitigation and discipline algorithms that extend
 the potential accuracy to the tens of microseconds with modern
 workstations and fast LANs.  It includes a dynamic server discovery
 scheme, so that in many cases, specific server configuration is not
 required.  It corrects certain errors in the NTPv3 design and
 implementation and includes an optional extension mechanism.

Status of This Memo

 This is an Internet Standards Track document.
 This document is a product of the Internet Engineering Task Force
 (IETF).  It represents the consensus of the IETF community.  It has
 received public review and has been approved for publication by the
 Internet Engineering Steering Group (IESG).  Further information on
 Internet Standards is available in Section 2 of RFC 5741.
 Information about the current status of this document, any errata,
 and how to provide feedback on it may be obtained at
 http://www.rfc-editor.org/info/rfc5905.

Mills, et al. Standards Track [Page 1] RFC 5905 NTPv4 Specification June 2010

Copyright Notice

 Copyright (c) 2010 IETF Trust and the persons identified as the
 document authors.  All rights reserved.
 This document is subject to BCP 78 and the IETF Trust's Legal
 Provisions Relating to IETF Documents
 (http://trustee.ietf.org/license-info) in effect on the date of
 publication of this document.  Please review these documents
 carefully, as they describe your rights and restrictions with respect
 to this document.  Code Components extracted from this document must
 include Simplified BSD License text as described in Section 4.e of
 the Trust Legal Provisions and are provided without warranty as
 described in the Simplified BSD License.
 This document may contain material from IETF Documents or IETF
 Contributions published or made publicly available before November
 10, 2008.  The person(s) controlling the copyright in some of this
 material may not have granted the IETF Trust the right to allow
 modifications of such material outside the IETF Standards Process.
 Without obtaining an adequate license from the person(s) controlling
 the copyright in such materials, this document may not be modified
 outside the IETF Standards Process, and derivative works of it may
 not be created outside the IETF Standards Process, except to format
 it for publication as an RFC or to translate it into languages other
 than English.

Table of Contents

 1. Introduction ....................................................4
    1.1. Requirements Notation ......................................5
 2. Modes of Operation ..............................................6
 3. Protocol Modes ..................................................6
    3.1. Dynamic Server Discovery ...................................7
 4. Definitions .....................................................8
 5. Implementation Model ...........................................10
 6. Data Types .....................................................12
 7. Data Structures ................................................16
    7.1. Structure Conventions .....................................16
    7.2. Global Parameters .........................................16
    7.3. Packet Header Variables ...................................17
    7.4. The Kiss-o'-Death Packet ..................................24
    7.5. NTP Extension Field Format ................................25
 8. On-Wire Protocol ...............................................26
 9. Peer Process ...................................................30
    9.1. Peer Process Variables ....................................31
    9.2. Peer Process Operations ...................................33
 10. Clock Filter Algorithm ........................................37

Mills, et al. Standards Track [Page 2] RFC 5905 NTPv4 Specification June 2010

 11. System Process ................................................39
    11.1. System Process Variables .................................40
    11.2. System Process Operations ................................41
         11.2.1. Selection Algorithm ...............................43
         11.2.2. Cluster Algorithm .................................44
         11.2.3. Combine Algorithm .................................45
    11.3. Clock Discipline Algorithm ...............................47
 12. Clock-Adjust Process ..........................................51
 13. Poll Process ..................................................51
    13.1. Poll Process Variables ...................................51
    13.2. Poll Process Operations ..................................52
 14. Simple Network Time Protocol (SNTP) ...........................54
 15. Security Considerations .......................................55
 16. IANA Considerations ...........................................58
 17. Acknowledgements ..............................................59
 18. References ....................................................59
    18.1. Normative References .....................................59
    18.2. Informative References ...................................59
 Appendix A.  Code Skeleton  .......................................61
   A.1.  Global Definitions  .......................................61
     A.1.1. Definitions, Constants, Parameters .....................61
     A.1.2. Packet Data Structures .................................65
     A.1.3. Association Data Structures ............................66
     A.1.4. System Data Structures .................................68
     A.1.5. Local Clock Data Structures ............................69
     A.1.6. Function Prototypes ....................................69
   A.2. Main Program and Utility Routines ..........................70
   A.3. Kernel Input/Output Interface ..............................73
   A.4. Kernel System Clock Interface ..............................74
   A.5. Peer Process ...............................................76
     A.5.1. receive() ..............................................77
     A.5.2. clock_filter() .........................................85
     A.5.3. fast_xmit() ............................................88
     A.5.4. access() ...............................................89
     A.5.5. System Process .........................................90
     A.5.6. Clock Adjust Process ..................................103
     A.5.7. Poll Process ..........................................104

Mills, et al. Standards Track [Page 3] RFC 5905 NTPv4 Specification June 2010

1. Introduction

 This document defines the Network Time Protocol version 4 (NTPv4),
 which is widely used to synchronize system clocks among a set of
 distributed time servers and clients.  It describes the core
 architecture, protocol, state machines, data structures, and
 algorithms.  NTPv4 introduces new functionality to NTPv3, as
 described in [RFC1305], and functionality expanded from Simple NTP
 version 4 (SNTPv4) as described in [RFC4330] (SNTPv4 is a subset of
 NTPv4).  This document obsoletes [RFC1305] and [RFC4330].  While
 certain minor changes have been made in some protocol header fields,
 these do not affect the interoperability between NTPv4 and previous
 versions of NTP and SNTP.
 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.  Precisely tuned
 algorithms mitigate errors that may result from network disruptions,
 server failures, and possible hostile actions.  Servers and clients
 are configured such that values flow towards clients from the primary
 servers at the root via branching secondary servers.
 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
 the floating double data type throughout the implementation.  As a
 result, the time resolution is better than one nanosecond, and
 frequency resolution is less than one nanosecond per second.
 Additional improvements include a new clock discipline algorithm that
 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 precise within a few tens of milliseconds
 with poll intervals up to 36 hours.
 The main body of this document describes the core protocol and data
 structures necessary to interoperate between conforming
 implementations.  Appendix A contains a full-featured example in the
 form of a skeleton program, including data structures and code
 segments for the core algorithms as well as the mitigation algorithms
 used to enhance reliability and accuracy.  While the skeleton program
 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.  The contents of Appendix A are non-

Mills, et al. Standards Track [Page 4] RFC 5905 NTPv4 Specification June 2010

 normative examples designed to illustrate the protocol's operation
 and are not a requirement for a conforming implementation.  While the
 NTPv3 symmetric key authentication scheme described in this document
 has been carried over from NTPv3, the Autokey public key
 authentication scheme new to NTPv4 is described in [RFC5906].
 The NTP protocol includes modes of operation described in Section 2
 using data types described in Section 6 and data structures described
 in Section 7.  The implementation model described in Section 5 is
 based on a threaded, multi-process architecture, although other
 architectures could be used as well.  The on-wire protocol described
 in Section 8 is based on a returnable-time design that depends only
 on measured clock offsets, but does not require reliable message
 delivery.  Reliable message delivery such as TCP [RFC0793] can
 actually make the delivered NTP packet less reliable since retries
 would increase the delay value and other errors.  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.
 This document includes material from [ref9], which contains flow
 charts and equations unsuited for RFC format.  There is much
 additional information in [ref7], including an extensive technical
 analysis and performance assessment of the protocol and algorithms in
 this document.  The reference implementation is available at
 www.ntp.org.
 The remainder of this document contains numerous variables and
 mathematical expressions.  Some variables take the form of Greek
 characters, which are spelled out by their full case-sensitive name.
 For example, DELTA refers to the uppercase Greek character, while
 delta refers to the lowercase character.  Furthermore, subscripts are
 denoted with '_'; for example, theta_i refers to the lowercase Greek
 character theta with subscript i, or phonetically theta sub i.  In
 this document, all time values are in seconds (s), and all
 frequencies will be specified as fractional frequency offsets (FFOs)
 (pure number).  It is often convenient to express these FFOs in parts
 per million (ppm).

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 [RFC2119].

Mills, et al. Standards Track [Page 5] RFC 5905 NTPv4 Specification June 2010

2. Modes of Operation

 An NTP implementation operates as a primary server, secondary server,
 or client.  A primary server is synchronized to a reference clock
 directly traceable to UTC (e.g., GPS, Galileo, etc.).  A client
 synchronizes to one or more upstream servers, but does not provide
 synchronization to dependent clients.  A secondary server has one or
 more upstream servers and one or more downstream servers or clients.
 All servers and clients who are fully NTPv4-compliant MUST implement
 the entire suite of algorithms described in this document.  In order
 to maintain stability in large NTP subnets, secondary servers SHOULD
 be fully NTPv4-compliant.  Alternative algorithms MAY be used, but
 their output MUST be identical to the algorithms described in this
 specification.

3. Protocol Modes

 There are three NTP protocol variants: symmetric, client/server, and
 broadcast.  Each is associated with an association mode (a
 description of the relationship between two NTP speakers) as shown in
 Figure 1.  In addition, persistent associations are mobilized upon
 startup and are never demobilized.  Ephemeral associations are
 mobilized upon the arrival of a packet and are demobilized upon error
 or timeout.
        +-------------------+-------------------+------------------+
        |  Association Mode | Assoc. Mode Value | Packet Mode Value|
        +-------------------+-------------------+------------------+
        | 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              |
        +-------------------+-------------------+------------------+
                Figure 1: Association and Packet Modes
 In the client/server variant, a persistent client sends packet mode 4
 packets to a server, which returns packet mode 3 packets.  Servers
 provide synchronization to one or more clients, but do not accept
 synchronization from them.  A server can also be a reference clock
 driver that obtains time directly from a standard source such as a
 GPS receiver or telephone modem service.  In this variant, clients
 pull synchronization from servers.

Mills, et al. Standards Track [Page 6] RFC 5905 NTPv4 Specification June 2010

 In the symmetric variant, a peer operates as both a server and client
 using either a symmetric active or symmetric passive association.  A
 persistent symmetric active association sends symmetric active (mode
 1) packets to a symmetric active peer association.  Alternatively, an
 ephemeral symmetric passive association can be mobilized upon the
 arrival of a symmetric active packet with no matching association.
 That association sends symmetric passive (mode 2) 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 references to client
 imply peer as well.
 In the broadcast variant, a persistent broadcast server association
 sends periodic broadcast server (mode 5) packets that can be received
 by multiple clients.  Upon reception of a broadcast server packet
 without a matching association, an ephemeral broadcast client (mode
 6) association is mobilized and persists until error or timeout.  It
 is useful to provide an initial volley where the client operating in
 client mode exchanges several packets with the server, so as to
 calibrate the propagation delay and to run the Autokey security
 protocol, after which the client reverts to broadcast client mode.  A
 broadcast server pushes synchronization to clients and other servers.
 Loosely following the conventions established by the telephone
 industry, the level of each server in the hierarchy is defined by a
 stratum number.  Primary servers are assigned stratum one; secondary
 servers at each lower level are assigned stratum numbers one greater
 than the preceding level.  As the stratum number increases, its
 accuracy degrades depending on the particular network path and system
 clock stability.  Mean errors, measured by synchronization distances,
 increase approximately in proportion to stratum numbers and measured
 round-trip delay.
 As a standard practice, timing network topology should be organized
 to avoid timing loops and minimize the synchronization distance.  In
 NTP, the subnet topology is determined using a variant of the
 Bellman-Ford distributed routing algorithm, which computes the
 shortest-path spanning tree rooted on the primary servers.  As a
 result of this design, the algorithm automatically reorganizes the
 subnet, so as to produce the most accurate and reliable time, even
 when there are failures in the timing network.

3.1. Dynamic Server Discovery

 There are two special associations, manycast client and manycast
 server, which provide a dynamic server discovery function.  There are
 two types of manycast client associations: persistent and ephemeral.
 The persistent manycast client sends client (mode 3) packets to a

Mills, et al. Standards Track [Page 7] RFC 5905 NTPv4 Specification June 2010

 designated IPv4 or IPv6 broadcast or multicast group address.
 Designated manycast servers within range of the time-to-live (TTL)
 field in the packet header listen for packets with that address.  If
 a server is suitable for synchronization, it returns an ordinary
 server (mode 4) packet using the client's unicast address.  Upon
 receiving this packet, the client mobilizes an ephemeral client (mode
 3) association.  The ephemeral client association persists until
 error or timeout.
 A manycast client continues sending packets to search for a minimum
 number of associations.  It starts with a TTL equal to one and
 continuously adding one to it until the minimum number of
 associations is made or when the TTL reaches a maximum value.  If the
 TTL reaches its maximum value and yet not enough associations are
 mobilized, the client stops transmission for a time-out period to
 clear all associations, and then repeats the search cycle.  If a
 minimum number of associations has been mobilized, then the client
 starts transmitting one packet per time-out period to maintain the
 associations.  Field constraints limit the minimum value to 1 and the
 maximum to 255.  These limits may be tuned for individual application
 needs.
 The ephemeral associations compete among themselves.  As new
 ephemeral associations are mobilized, the client runs the mitigation
 algorithms described in Sections 10 and 11.2 for the best candidates
 out of the population, the remaining ephemeral associations are timed
 out and demobilized.  In this way, the population includes only the
 best candidates that have most recently responded with an NTP packet
 to discipline the system clock.

4. Definitions

 A number of technical terms are defined in this section.  A timescale
 is a frame of reference where time is expressed as the value of a
 monotonically increasing binary counter with an indefinite number of
 bits.  It counts in seconds and fractions of a second, when a decimal
 point is employed.  The Coordinated Universal Time (UTC) timescale is
 defined by ITU-R TF.460 [ITU-R_TF.460].  Under the auspices of the
 Metre Convention of 1865, in 1975 the CGPM [CGPM] strongly endorsed
 the use of UTC as the basis for civil time.
 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 hardware
 and operating system.  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.

Mills, et al. Standards Track [Page 8] RFC 5905 NTPv4 Specification June 2010

 The date of an event is the UTC time at which the event takes place.
 Dates are ephemeral values designated with uppercase T.  Running time
 is another timescale that is coincident to the synchronization
 function of the NTP program.
 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, and D(t) the aging 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 at time t is
 T(t) = 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 10^(-6) s/s.
 It is important in computer timekeeping applications to assess the
 performance of the timekeeping function.  The NTP performance model
 includes four statistics that 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 (delta) represents the round-trip 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 (psi) is defined as
 the root-mean-square (RMS) average of the most recent offset
 differences, and it represents the nominal error in estimating the
 offset.
 While the theta, delta, epsilon, and psi statistics represent
 measurements of the system clock relative to each server clock
 separately, the NTP protocol includes mechanisms to combine the
 statistics of several servers to more accurately discipline and
 calibrate the system clock.  The system offset (THETA) represents the
 maximum-likelihood offset estimate for the server population.  The
 system jitter (PSI) represents the nominal error in estimating the
 system offset.  The delta and epsilon statistics are accumulated at
 each stratum level from the reference clock to produce the root delay
 (DELTA) and root dispersion (EPSILON) statistics.  The
 synchronization distance (LAMBDA) equal to EPSILON + DELTA / 2
 represents the maximum error due to all causes.  The detailed

Mills, et al. Standards Track [Page 9] RFC 5905 NTPv4 Specification June 2010

 formulations of these statistics are given in Section 11.2.  They are
 available to the dependent applications in order to assess the
 performance of the synchronization function.

5. Implementation Model

 Figure 2 shows the architecture of a typical, multi-threaded
 implementation.  It includes two processes dedicated to each server,
 a peer process to receive messages from the server or reference
 clock, and a poll process to transmit messages to the server or
 reference clock.
 .....................................................................
 . Remote   .   Peer/Poll  .              System          .  Clock   .
 . Servers  .   Processes  .              Process         .Discipline.
 .          .              .                              . Process  .
 .+--------+. +-----------+. +------------+               .          .
 .|        |->|           |. |            |               .          .
 .|Server 1|  |Peer/Poll 1|->|            |               .          .
 .|        |<-|           |. |            |               .          .
 .+--------+. +-----------+. |            |               .          .
 .          .       ^      . |            |               .          .
 .          .       |      . |            |               .          .
 .+--------+. +-----------+. |            |  +-----------+.          .
 .|        |->|           |. | Selection  |->|           |. +------+ .
 .|Server 2|  |Peer/Poll 2|->|    and     |  | Combine   |->| Loop | .
 .|        |<-|           |. | Cluster    |  | Algorithm |. |Filter| .
 .+--------+. +-----------+. | Algorithms |->|           |. +------+ .
 .          .       ^      . |            |  +-----------+.    |     .
 .          .       |      . |            |               .    |     .
 .+--------+. +-----------+. |            |               .    |     .
 .|        |->|           |. |            |               .    |     .
 .|Server 3|  |Peer/Poll 3|->|            |               .    |     .
 .|        |<-|           |. |            |               .    |     .
 .+--------+. +-----------+. +------------+               .    |     .
 ....................^.........................................|......
                     |                                    .    V     .
                     |                                    . +-----+  .
                     +--------------------------------------| VFO |  .
                                                          . +-----+  .
                                                          .  Clock   .
                                                          .  Adjust  .
                                                          .  Process .
                                                          ............
                    Figure 2: Implementation Model

Mills, et al. Standards Track [Page 10] RFC 5905 NTPv4 Specification June 2010

 These processes operate on a common data structure, called an
 association, which contains the statistics described above along with
 various other data described in Section 9.  A client sends packets to
 one or more servers and then processes returned packets when they are
 received.  The server interchanges source and destination addresses
 and ports, overwrites certain fields in the packet and returns it
 immediately (in the client/server mode) or at some time later (in the
 symmetric modes).  As each NTP message is received, the offset theta
 between the peer clock and the system clock is computed along with
 the associated statistics delta, epsilon, and psi.
 The system process includes the selection, cluster, and combine
 algorithms that 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
 fault detection principles to discard the presumably incorrect
 candidates called "falsetickers" from the incident population,
 leaving only good candidates called "truechimers".  A truechimer is a
 clock that maintains timekeeping accuracy to a previously published
 and trusted standard, while a falseticker is a clock that shows
 misleading or inconsistent time.  The cluster algorithm uses
 statistical principles to find the most accurate set of truechimers.
 The combine algorithm computes the final clock offset by
 statistically averaging the surviving truechimers.
 The clock discipline process is a system process that controls 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 that 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 clock jitter.  The
 RMS average of past frequency offset differences represents the
 oscillator frequency stability or frequency wander.  These terms are
 given precise interpretation in Section 11.3.
 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) to 17 (36 h).  The value of tau is determined by
 the clock discipline algorithm to match the loop-time constant T_c =
 2^tau.  In client/server mode, the server responds immediately;
 however, in symmetric modes, each of two peers manages tau as a
 function of current system offset and system jitter, so they may not
 agree with the same value.  It is important that the dynamic behavior
 of the clock discipline algorithm be carefully controlled in order to
 maintain stability in the NTP subnet at large.  This requires that

Mills, et al. Standards Track [Page 11] RFC 5905 NTPv4 Specification June 2010

 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.
 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 time in small
 increments advancing or retarding the time by a designated amount,
 for example, the Unix adjtime() function.  In this and following
 references, 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 as described in
 Section 10.

6. Data Types

 All NTP time values are represented in twos-complement format, with
 bits numbered in big-endian (as described in Appendix A of [RFC0791])
 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 Number field
 and a 32-bit Era Offset 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.

Mills, et al. Standards Track [Page 12] RFC 5905 NTPv4 Specification June 2010

     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 Formats
 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 and timestamp formats, 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

Mills, et al. Standards Track [Page 13] RFC 5905 NTPv4 Specification June 2010

 times after that date; values less than zero represent times before
 it.  Note that the Era Offset field of the date format and the
 Seconds field of the timestamp format have the same interpretation.
 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.
 +-------------+------------+-----+---------------+------------------+
 | Date        | MJD        | NTP | NTP Timestamp | Epoch            |
 |             |            | Era | Era Offset    |                  |
 +-------------+------------+-----+---------------+------------------+
 | 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 | First day        |
 |             |            |     |               | Gregorian        |
 | 31 Dec 1899 | 15019      | -1  | 4,294,880,896 | Last day NTP Era |
 |             |            |     |               | -1               |
 | 1 Jan 1900  | 15020      | 0   | 0             | First day NTP    |
 |             |            |     |               | Era 0            |
 | 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 day 20th    |
 |             |            |     |               | Century          |
 | 8 Feb 2036  | 64,731     | 1   | 63,104        | First day NTP    |
 |             |            |     |               | Era 1            |
 +-------------+------------+-----+---------------+------------------+
               Figure 4: Interesting Historic NTP Dates
 Let p be the number of significant bits in the second fraction.  The
 clock resolution is defined as 2^(-p), 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 the protocol, is the larger of the
 two.

Mills, et al. Standards Track [Page 14] RFC 5905 NTPv4 Specification June 2010

 The only arithmetic operation permitted on 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
 distinguish between signed and unsigned values (although comparisons
 can take sign into account); only the conditional branch instructions
 do.  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 is
 possible in 2036, might result in over-run.  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.  These are in 8-bit
 signed integer format in log2 (log base 2) seconds.  The only
 arithmetic 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 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.  To determine the integer era and
 timestamp given s,
 era = s / 2^(32) and timestamp = s - era * 2^(32),
 which works for positive and negative dates.  To determine s given
 the era and timestamp,
 s = era * 2^(32) + timestamp.
 Converting between NTP and system time can be a little messy, and is
 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.

Mills, et al. Standards Track [Page 15] RFC 5905 NTPv4 Specification June 2010

 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.

7. Data Structures

 The NTP state machines are defined in the following sections.  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
 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.  An example is described
 in Appendix A.

7.1. Structure Conventions

 In order to distinguish between different variables of the same name
 but used in different processes, the naming convention summarized in
 Figure 5 is adopted.  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.
                 +------+---------------------------------+
                 | Name | Description                     |
                 +------+---------------------------------+
                 | r.   | receive packet header variable  |
                 | x.   | transmit packet header variable |
                 | p.   | peer/poll variable              |
                 | s.   | system variable                 |
                 | c.   | clock discipline variable       |
                 +------+---------------------------------+
                     Figure 5: Prefix Conventions

7.2. 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 6.

Mills, et al. Standards Track [Page 16] RFC 5905 NTPv4 Specification June 2010

          +-----------+-------+----------------------------------+
          | Name      | Value | Description                      |
          +-----------+-------+----------------------------------+
          | PORT      | 123   | NTP port number                  |
          | VERSION   | 4     | NTP version number                   |
          | TOLERANCE | 15e-6 | frequency tolerance PHI (s/s)    |
          | MINPOLL   | 4     | minimum poll exponent (16 s)     |
          | MAXPOLL   | 17    | maximum poll exponent (36 h)     |
          | MAXDISP   | 16    | maximum dispersion (16 s)        |
          | MINDISP   | .005  | minimum dispersion increment (s) |
          | MAXDIST   | 1     | distance threshold (1 s)         |
          | MAXSTRAT  | 16    | maximum stratum number           |
          +-----------+-------+----------------------------------+
                      Figure 6: Global Parameters
 While these are the only global parameters needed for
 interoperability, a larger collection is necessary in any
 implementation.  Appendix A.1.1 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 (also called PHI), 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 of this document.
 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.

7.3. Packet Header Variables

 The most important state variables from an external point of view are
 the packet header variables described in Figure 7 and below.  The NTP
 packet header consists of an integral 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 [RFC5906].  The optional MAC is
 used by both Autokey and the symmetric key cryptographic algorithm
 described in this RFC.

Mills, et al. Standards Track [Page 17] RFC 5905 NTPv4 Specification June 2010

             +-----------+------------+-----------------------+
             | 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_r    | root delay            |
             | rootdisp  | epsilon_r  | 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                |
             | dgst      | dgst       | message digest        |
             +-----------+------------+-----------------------+
                   Figure 7: Packet Header Variables
 The NTP packet is a UDP datagram [RFC0768].  Some fields use multiple
 words and others are packed in smaller fields within a word.  The NTP
 packet header shown in Figure 8 has 12 words followed by optional
 extension fields and finally an optional message authentication code
 (MAC) consisting of the Key Identifier field and Message Digest
 field.

Mills, et al. Standards Track [Page 18] RFC 5905 NTPv4 Specification June 2010

     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 |    Stratum     |     Poll      |  Precision   |
    +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
    |                         Root Delay                            |
    +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
    |                         Root Dispersion                       |
    +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
    |                          Reference ID                         |
    +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
    |                                                               |
    +                     Reference Timestamp (64)                  +
    |                                                               |
    +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
    |                                                               |
    +                      Origin Timestamp (64)                    +
    |                                                               |
    +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
    |                                                               |
    +                      Receive Timestamp (64)                   +
    |                                                               |
    +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
    |                                                               |
    +                      Transmit Timestamp (64)                  +
    |                                                               |
    +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
    |                                                               |
    .                                                               .
    .                    Extension Field 1 (variable)               .
    .                                                               .
    |                                                               |
    +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
    |                                                               |
    .                                                               .
    .                    Extension Field 2 (variable)               .
    .                                                               .
    |                                                               |
    +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
    |                          Key Identifier                       |
    +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
    |                                                               |
    |                            dgst (128)                         |
    |                                                               |
    +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
                    Figure 8: Packet Header Format

Mills, et al. Standards Track [Page 19] RFC 5905 NTPv4 Specification June 2010

 The extension fields are used to add optional capabilities, for
 example, the Autokey security protocol [RFC5906].  The extension
 field format is presented in order for the packet to be parsed
 without the knowledge of the extension field functions.  The MAC is
 used by both Autokey and the symmetric key authentication scheme.
 A list of the packet header variables is shown in Figure 7 and
 described in detail below.  Except for a minor variation when using
 the IPv6 address family, these fields are backwards compatible with
 NTPv3.  The packet header fields apply to both transmitted packets (x
 prefix) and received packets (r prefix).  In Figure 8, the size of
 some multiple-word fields is shown in bits if not the default 32
 bits.  The basic header extends from the beginning of the packet to
 the end of the Transmit Timestamp field.
 The fields and associated packet variables (in parentheses) are
 interpreted as follows:
 LI Leap Indicator (leap): 2-bit integer warning of an impending leap
 second to be inserted or deleted in the last minute of the current
 month with values defined in Figure 9.
         +-------+----------------------------------------+
         | Value | Meaning                                |
         +-------+----------------------------------------+
         | 0     | no warning                             |
         | 1     | last minute of the day has 61 seconds  |
         | 2     | last minute of the day has 59 seconds  |
         | 3     | unknown (clock unsynchronized)         |
         +-------+----------------------------------------+
                       Figure 9: Leap Indicator
 VN Version Number (version): 3-bit integer representing the NTP
 version number, currently 4.
 Mode (mode): 3-bit integer representing the mode, with values defined
 in Figure 10.

Mills, et al. Standards Track [Page 20] RFC 5905 NTPv4 Specification June 2010

                    +-------+--------------------------+
                    | Value | Meaning                  |
                    +-------+--------------------------+
                    | 0     | reserved                 |
                    | 1     | symmetric active         |
                    | 2     | symmetric passive        |
                    | 3     | client                   |
                    | 4     | server                   |
                    | 5     | broadcast                |
                    | 6     | NTP control message      |
                    | 7     | reserved for private use |
                    +-------+--------------------------+
                     Figure 10: Association Modes
 Stratum (stratum): 8-bit integer representing the stratum, with
 values defined in Figure 11.
      +--------+-----------------------------------------------------+
      | Value  | Meaning                                             |
      +--------+-----------------------------------------------------+
      | 0      | unspecified or invalid                              |
      | 1      | primary server (e.g., equipped with a GPS receiver) |
      | 2-15   | secondary server (via NTP)                          |
      | 16     | unsynchronized                                      |
      | 17-255 | reserved                                            |
      +--------+-----------------------------------------------------+
                       Figure 11: Packet Stratum
 It is customary to map the stratum value 0 in received packets to
 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 clock selection algorithms used
 for external sources (see Appendix A.5.5.1 for an example).
 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.

Mills, et al. Standards Track [Page 21] RFC 5905 NTPv4 Specification June 2010

 Root Delay (rootdelay): Total round-trip delay to the reference
 clock, in NTP short format.
 Root Dispersion (rootdisp): Total dispersion to the reference clock,
 in NTP short format.
 Reference ID (refid): 32-bit code identifying the particular server
 or reference clock.  The interpretation depends on the value in the
 stratum field.  For packet stratum 0 (unspecified or invalid), this
 is a four-character ASCII [RFC1345] 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 reference clock.  The authoritative list of
 Reference Identifiers is maintained by IANA; however, any string
 beginning with the ASCII character "X" is reserved for unregistered
 experimentation and development.  The identifiers in Figure 12 have
 been used as ASCII identifiers:
   +------+----------------------------------------------------------+
   | ID   | Clock Source                                             |
   +------+----------------------------------------------------------+
   | GOES | Geosynchronous Orbit Environment Satellite               |
   | GPS  | Global Position System                                   |
   | GAL  | Galileo Positioning 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 Anthorn, UK 60 kHz                          |
   | JJY  | LF Radio JJY Fukushima, JP 40 kHz, Saga, JP 60 kHz       |
   | LORC | MF Radio LORAN C station, 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 Kauai, HI                                  |
   | NIST | NIST telephone modem                                     |
   | ACTS | NIST telephone modem                                     |
   | USNO | USNO telephone modem                                     |
   | PTB  | European telephone modem                                 |
   +------+----------------------------------------------------------+
                   Figure 12: Reference Identifiers
 Above stratum 1 (secondary servers and clients): this is the
 reference identifier of the server and can be used to detect timing
 loops.  If using the IPv4 address family, the identifier is the four-
 octet IPv4 address.  If using the IPv6 address family, it is the

Mills, et al. Standards Track [Page 22] RFC 5905 NTPv4 Specification June 2010

 first four octets of the MD5 hash of the IPv6 address.  Note that,
 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.
 Reference Timestamp: Time when the system clock was last set or
 corrected, in NTP timestamp format.
 Origin Timestamp (org): Time at the client when the request departed
 for the server, in NTP timestamp format.
 Receive Timestamp (rec): Time at the server when the request arrived
 from the client, in NTP timestamp format.
 Transmit Timestamp (xmt): Time at the server when the response left
 for the client, in NTP timestamp format.
 Destination Timestamp (dst): Time at the client when the reply
 arrived from the server, in NTP timestamp format.
 Note: The Destination Timestamp field is not included as a header
 field; it is determined upon arrival of the packet and made available
 in the packet buffer data structure.
 If the NTP has access to the physical layer, then the timestamps are
 associated with the beginning of the symbol after the start of frame.
 Otherwise, implementations should attempt to associate the timestamp
 to the earliest accessible point in the frame.
 The MAC consists of the Key Identifier followed by the Message
 Digest.  The message digest, or cryptosum, is calculated as in
 [RFC1321] over all NTP-header and optional extension fields, but not
 the MAC itself.
 Extension Field n: See Section 7.5 for a description of the format of
 this field.
 Key Identifier (keyid): 32-bit unsigned integer used by the client
 and server to designate a secret 128-bit MD5 key.
 Message Digest (digest): 128-bit MD5 hash computed over the key
 followed by the NTP packet header and extensions fields (but not the
 Key Identifier or Message Digest fields).
 It should be noted that the MAC computation used here differs from
 those defined in [RFC1305] and [RFC4330] but is consistent with how
 existing implementations generate a MAC.

Mills, et al. Standards Track [Page 23] RFC 5905 NTPv4 Specification June 2010

7.4. The Kiss-o'-Death Packet

 If the Stratum field is 0, which implies unspecified or invalid, the
 Reference Identifier field can be used to convey messages useful for
 status reporting and access control.  These 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, either NTPv4 or SNTPv4.  Kiss codes are encoded
 in four-character ASCII strings that are 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 in
 Figure 13.  Recipients of kiss codes MUST inspect them and, in the
 following cases, take these actions:
 a.  For kiss codes DENY and RSTR, the client MUST demobilize any
     associations to that server and stop sending packets to that
     server;
 b.  For kiss code RATE, the client MUST immediately reduce its
     polling interval to that server and continue to reduce it each
     time it receives a RATE kiss code.
 c.  Kiss codes beginning with the ASCII character "X" are for
     unregistered experimentation and development and MUST be ignored
     if not recognized.
 d.  Other than the above conditions, KoD packets have no protocol
     significance and are discarded after inspection.

Mills, et al. Standards Track [Page 24] RFC 5905 NTPv4 Specification June 2010

 +------+------------------------------------------------------------+
 | 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 13: Kiss Codes
 The Receive Timestamp and the Transmit Timestamp (set by the server)
 are undefined when in a KoD packet and MUST NOT be relied upon to
 have valid values and MUST be discarded.

7.5. 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 an extension
 field is present.  Other than defining the field format, this
 document makes no use of the field contents.  An extension field
 contains a request or response message in the format shown in
 Figure 14.

Mills, et al. Standards Track [Page 25] RFC 5905 NTPv4 Specification June 2010

     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             |
    +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
    .                                                               .
    .                            Value                              .
    .                                                               .
    +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
    |                       Padding (as needed)                     |
    +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
                   Figure 14: Extension Field Format
 All extension fields are zero-padded to a word (four octets)
 boundary.  The Field Type field is specific to the defined function
 and is not elaborated here.  While the minimum field length
 containing required fields is four words (16 octets), a maximum field
 length remains to be established.
 The Length field is a 16-bit unsigned integer that indicates the
 length of the entire extension field in octets, including the Padding
 field.

8. On-Wire Protocol

 The heart of the NTP on-wire protocol is the core mechanism that
 exchanges time values between servers, peers, and clients.  It is
 inherently resistant to lost or duplicate 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, which are 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 the
 case of link-level retransmission and corrected for the time to
 compute a MAC in 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
 as 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 the prefix determined by scoping rules.  Any other non-
 allocated multicast address may also be used in addition to these
 allocated multicast addresses.

Mills, et al. Standards Track [Page 26] RFC 5905 NTPv4 Specification June 2010

 The on-wire protocol uses four timestamps numbered t1 through t4 and
 three state variables org, rec, and xmt, as shown in Figure 15.  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 packet timestamps are shown in
 lowercase, while the state variables are shown in uppercase.  The
 state variables are copied from the packet timestamps upon arrival or
 departure of a packet.

Mills, et al. Standards Track [Page 27] RFC 5905 NTPv4 Specification June 2010

           t2            t3           t6            t7
      +---------+   +---------+   +---------+   +---------+
      |    0    |   |    t1   |   |   t3    |   |    t5   |
      +---------+   +---------+   +---------+   +---------+
      |    0    |   |    t2   |   |   t4    |   |    t6   |  Packet
      +---------+   +---------+   +---------+   +---------+ Timestamps
      |   t1    |   |t3=clock |   |   t5    |   |t7=clock |
      +---------+   +---------+   +---------+   +---------+
      |t2=clock |                 |t6=clock |
      +---------+                 +---------+
                                                             Peer B
      +---------+   +---------+   +---------+   +---------+
 org  |   T1    |   |    T1   |   | t5<>T1? |   |    T5   |
      +---------+   +---------+   +---------+   +---------+   State
 rec  |   T2    |   |    T2   |   |   T6    |   |    T6   | Variables
      +---------+   +---------+   +---------+   +---------+
 xmt  |    0    |   |    T3   |   |  t3=T3? |   |    T7   |
      +---------+   +---------+   +---------+   +---------+
                t2      t3                 t6          t7
      ---------------------------------------------------------
               /\         \                 /\            \
               /           \                /              \
              /             \              /                \
             /               \/           /                 \/
      ---------------------------------------------------------
           t1                t4         t5                  t8
          t1            t4            t5             t8
      +---------+   +---------+   +---------+   +---------+
      |    0    |   |    t1   |   |   t3    |   |    t5   |
      +---------+   +---------+   +---------+   +---------+
      |    0    |   |    t2   |   |   t4    |   |    t6   |  Packet
      +---------+   +---------+   +---------+   +---------+ Timestamps
      |t1=clock |   |    t3   |   |t5=clock |   |    t7   |
      +---------+   +---------+   +---------+   +---------+
                    |t4=clock |                 |t8=clock |
                    +---------+                 +---------+
                                                             Peer A
      +---------+   +---------+   +---------+   +---------+
 org  |    0    |   |  t3<>0? |   |   T3    |   | t7<>T3? |
      +---------+   +---------+   +---------+   +---------+   State
 rec  |    0    |   |    T4   |   |   T4    |   |    T8   | Variables
      +---------+   +---------+   +---------+   +---------+
 xmt  |   T1    |   |  t1=T1? |   |   T5    |   |  t5=T5? |
      +---------+   +---------+   +---------+   +---------+
                      Figure 15: On-Wire Protocol

Mills, et al. Standards Track [Page 28] RFC 5905 NTPv4 Specification June 2010

 In the figure, the first packet transmitted by A contains only the
 origin timestamp t1, which is then copied to T1.  B receives the
 packet at t2 and copies t1 to T1 and the receive timestamp t2 to T2.
 At this time or some time later at t3, B sends a packet to A
 containing t1 and t2 and the transmit timestamp t3.  All three
 timestamps are copied to the corresponding state variables.  A
 receives the packet at t4 containing the three timestamps t1, t2, and
 t3 and the destination timestamp t4.  These four timestamps are used
 to compute the offset and delay of B relative to A, as described
 below.
 Before the xmt and org state variables are updated, two sanity checks
 are performed in order to protect against duplicate, bogus, or
 replayed packets.  In the exchange above, a packet is duplicate or
 replay if the transmit timestamp t3 in the packet matches the org
 state variable T3.  A packet is bogus if the origin timestamp t1 in
 the packet does not match the xmt state variable T1.  In either of
 these cases, the state variables are updated, then the packet is
 discarded.  To protect against replay of the last transmitted packet,
 the xmt state variable is set to zero immediately after a successful
 bogus check.
 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 * [(T2-T1) + (T3-T4)]
 and the round-trip delay
 delta = T(ABA) = (T4-T1) - (T3-T2).
 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 sums and differences of these values, which contain
 62 significant bits and two sign bits, so they 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

Mills, et al. Standards Track [Page 29] RFC 5905 NTPv4 Specification June 2010

 the second-order terms are typically very small relative to the
 timestamp magnitudes, there is no loss in significance, yet the
 unambiguous range is restored from 34 years to 68 years.
 In some scenarios where the initial frequency offset of the client is
 relatively large and the actual propagation time small, it is
 possible for the delay computation to become negative.  For instance,
 if the frequency difference is 100 ppm and the interval T4-T1 is 64
 s, the apparent delay is -6.4 ms.  Since negative values are
 misleading in subsequent computations, the value of delta should be
 clamped not less than s.rho, where s.rho is the system precision
 described in Section 11.1, expressed in seconds.
 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 T3 and T4 from the client
 packet to T1 and T2 of the server packet and tacks on the transmit
 timestamp T3 before sending it to the client.  Additional details for
 filling in the remaining protocol fields are given in a Section 9 and
 following sections and in the appendix.
 Note that the on-wire protocol as described resists replay of a
 server response packet.  However, it does not resist replay of the
 client request packet, which would result in a server reply packet
 with new values of T2 and T3 and result in incorrect offset and
 delay.  This vulnerability can be avoided by setting the xmt state
 variable to zero after computing the offset and delay.

9. Peer Process

 The process descriptions to follow include a listing of the important
 state variables followed by an overview of the process operations
 implemented as routines.  Frequent reference is made to the skeleton
 in the appendix.  The skeleton includes C-language fragments that
 describe the functions in more detail.  It includes the parameters,
 variables, and declarations necessary for a conforming NTPv4
 implementation.  However, many additional variables and routines may
 be necessary in a working implementation.
 The peer process is called upon arrival of a server or peer packet.
 It runs the on-wire protocol to determine the clock offset and round-
 trip delay and 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
 process for each server.

Mills, et al. Standards Track [Page 30] RFC 5905 NTPv4 Specification June 2010

9.1. Peer Process Variables

 Figures 16, 17, 18, and 19 summarize the common names, formula names,
 and a short description of the peer variables.  The common names and
 formula names are interchangeable; formula names are intended to
 increase readability of equations in this specification.  Unless
 noted otherwise, all peer variables have assumed prefix p.
               +---------+----------+-----------------------+
               | Name    | Formula  | Description           |
               +---------+----------+-----------------------+
               | srcaddr | srcaddr  | source address        |
               | srcport | srcport  | source port           |
               | dstaddr | dstaddr  | destination address   |
               | dstport | destport | destination port      |
               | keyid   | keyid    | key identifier key ID |
               +---------+----------+-----------------------+
            Figure 16: Peer Process Configuration Variables
              +-----------+------------+---------------------+
              | Name      | Formula    | Description         |
              +-----------+------------+---------------------+
              | leap      | leap       | leap indicator      |
              | version   | version    | version number      |
              | mode      | mode       | mode                |
              | stratum   | stratum    | stratum             |
              | ppoll     | ppoll      | peer poll exponent  |
              | rootdelay | delta_r    | root delay          |
              | rootdisp  | epsilon_r  | root dispersion     |
              | refid     | refid      | reference ID        |
              | reftime   | reftime    | reference timestamp |
              +-----------+------------+---------------------+
               Figure 17: Peer Process Packet Variables
                   +------+---------+--------------------+
                   | Name | Formula | Description        |
                   +------+---------+--------------------+
                   | org  | T1      | origin timestamp   |
                   | rec  | T2      | receive timestamp  |
                   | xmt  | T3      | transmit timestamp |
                   | t    | t       | packet time        |
                   +------+---------+--------------------+
              Figure 18: Peer Process Timestamp Variables

Mills, et al. Standards Track [Page 31] RFC 5905 NTPv4 Specification June 2010

                   +--------+---------+-----------------+
                   | Name   | Formula | Description     |
                   +--------+---------+-----------------+
                   | offset | theta   | clock offset    |
                   | delay  | delta   | round-trip delay|
                   | disp   | epsilon | dispersion      |
                   | jitter | psi     | jitter          |
                   | filter | filter  | clock filter    |
                   | tp     | t_p     | filter time     |
                   +--------+---------+-----------------+
             Figure 19: Peer Process Statistics Variables
 The following configuration variables are normally initialized when
 the association is mobilized, either from a configuration file or
 upon the arrival of the first packet for an unknown association.
 srcaddr: IP address of the remote server or reference clock.  This
 becomes the destination IP address in packets sent from this
 association.
 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.
 dstaddr: IP address of the client.  This becomes the source IP
 address in packets sent from this association.
 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.
 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 in Figure 17 are updated from the packet header
 as each packet arrives.  They are interpreted in the same way as the
 packet variables of the same names.  It is convenient for later
 processing to convert the NTP short format packet values r.rootdelay
 and r.rootdisp to floating doubles as peer variables.
 The variables defined in Figure 18 include the timestamps exchanged
 by the on-wire protocol in Section 8.  The t variable is the seconds
 counter c.t associated with these values.  The c.t variable is
 maintained by the clock-adjust process described in Section 12.  It

Mills, et al. Standards Track [Page 32] RFC 5905 NTPv4 Specification June 2010

 counts the seconds since the service was started.  The variables
 defined in Figure 19 include the statistics computed by the
 clock_filter() routine described in Section 10.  The tp variable is
 the seconds counter associated with these values.

9.2. Peer Process Operations

 The receive routine defines the process flow upon the arrival of a
 packet.  An example is described by the receive() routine in
 Appendix A.5.1.  There is no specific method required for access
 control, although it is recommended that implementations include such
 a scheme, which is similar to many others now in widespread use.  The
 access() routine in Appendix A.5.4 describes a method of implementing
 access restrictions using an access control list (ACL).  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, then the MD5-keyed hash algorithm
 described in [RFC1321] must be supported.
 Next, the association table is searched for matching source address
 and source port, for example, using the find_assoc() routine in
 Appendix A.5.1.  Figure 20 is a dispatch table where the columns
 correspond to the packet mode and rows correspond to the association
 mode.  The intersection of the association and packet modes
 dispatches processing to one of the following steps.
         +------------------+---------------------------------------+
         |                  |              Packet Mode              |
         +------------------+-------+-------+-------+-------+-------+
         | Association Mode |   1   |   2   |   3   |   4   |   5   |
         +------------------+-------+-------+-------+-------+-------+
         | No Association 0 | NEWPS | DSCRD | FXMIT | MANY  | NEWBC |
         | Symm. Active   1 | PROC  | PROC  | DSCRD | DSCRD | DSCRD |
         | Symm. Passive  2 | PROC  | ERR   | DSCRD | DSCRD | DSCRD |
         | Client         3 | DSCRD | DSCRD | DSCRD | PROC  | DSCRD |
         | Server         4 | DSCRD | DSCRD | DSCRD | DSCRD | DSCRD |
         | Broadcast      5 | DSCRD | DSCRD | DSCRD | DSCRD | DSCRD |
         | Bcast Client   6 | DSCRD | DSCRD | DSCRD | DSCRD | PROC  |
         +------------------+-------+-------+-------+-------+-------+
                    Figure 20: Peer Dispatch Table
 DSCRD.  This indicates a non-fatal violation of protocol as the
 result of a programming error, long-delayed packet, or replayed
 packet.  The peer process discards the packet and exits.

Mills, et al. Standards Track [Page 33] RFC 5905 NTPv4 Specification June 2010

 ERR.  This indicates a fatal violation of protocol as the result of a
 programming error, long-delayed packet, or replayed packet.  The peer
 process discards the packet, demobilizes the symmetric passive
 association, and exits.
 FXMIT.  This indicates a client (mode 3) packet matching no
 association (mode 0).  If the destination address is not a broadcast
 address, the server constructs a server (mode 4) packet and returns
 it to the client without retaining state.  The server packet header
 is constructed.  An example is described by the fast_xmit() routine
 in Appendix A.5.3.  The packet header is assembled from the receive
 packet and system variables as shown in Figure 21.  If the
 s.rootdelay and s.rootdisp system variables are stored in floating
 double, they must be converted to NTP short format first.
                 +-----------------------------------+
                 | Packet Variable -->   Variable    |
                 +-----------------------------------+
                 | r.leap        -->     p.leap      |
                 | r.mode        -->     p.mode      |
                 | r.stratum     -->     p.stratum   |
                 | r.poll        -->     p.ppoll     |
                 | r.rootdelay   -->     p.rootdelay |
                 | r.rootdisp    -->     p.rootdisp  |
                 | r.refid       -->     p.refid     |
                 | r.reftime     -->     p.reftime   |
                 | r.keyid       -->     p.keyid     |
                 +-----------------------------------+
                   Figure 21: Receive Packet Header
 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 Figure 8, but with a MAC consisting of four
 octets of zeros.  The client MAY accept or reject the data in the
 message.  After these actions, the peer process exits.
 If the destination address is a multicast address, the sender is
 operating in manycast client mode.  If the packet is valid and the
 server stratum is less than the client stratum, the server sends an
 ordinary server (mode 4) packet, but one which uses its unicast
 destination address.  A crypto-NAK is not sent if authentication
 fails.  After these actions, the peer process exits.
 MANY: This indicates a server (mode 4) packet matching no
 association.  Ordinarily, this can happen only as the result of a
 manycast server reply to a previously sent multicast client packet.

Mills, et al. Standards Track [Page 34] RFC 5905 NTPv4 Specification June 2010

 If the packet is valid, an ordinary client (mode 3) association is
 mobilized and operation continues as if the association was mobilized
 by the configuration file.
 NEWBC.  This indicates a broadcast (mode 5) packet matching no
 association.  The client mobilizes either a client (mode 3) or
 broadcast client (mode 6) association.  Examples are shown in the
 mobilize() and clear() routines in Appendix A.2.  Then, the packet is
 validated and the peer variables initialized.  An example is provided
 by the packet() routine in Appendix A.5.1.1.
 If the implementation supports no additional security or calibration
 functions, the association mode is set to broadcast client (mode 6)
 and the peer process exits.  Implementations supporting public key
 authentication MAY run the Autokey or equivalent security protocol.
 Implementations SHOULD set the association mode to 3 and run a short
 client/server exchange to determine the propagation delay.  Following
 the exchange, the association mode is set to 6 and the peer process
 continues in listen-only mode.  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 indicates a symmetric active (mode 1) packet matching no
 association.  The client mobilizes a symmetric passive (mode 2)
 association.  An example is shown in the mobilize() and clear()
 routines in Appendix A.2.  Processing continues in the PROC section
 below.
 PROC.  This indicates a packet matching an existing association.  The
 packet timestamps are carefully checked to avoid invalid, duplicate,
 or bogus packets.  Additional checks are summarized in Figure 22.
 Note that all packets, including a crypto-NAK, are considered valid
 only if they survive these tests.

Mills, et al. Standards Track [Page 35] RFC 5905 NTPv4 Specification June 2010

 +--------------------------+----------------------------------------+
 | Packet Type              | Description                            |
 +--------------------------+----------------------------------------+
 | 1 duplicate packet       | The packet is at best an old duplicate |
 |                          | or at 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 denied          | The access controls have blacklisted   |
 |                          | the source.                            |
 | 5 authentication failure | The cryptographic message digest does  |
 |                          | not match the MAC.                     |
 | 6 unsynchronized         | The server is not synchronized to a    |
 |                          | valid source.                          |
 | 7 bad header data        | One or more header fields are invalid. |
 +--------------------------+----------------------------------------+
                    Figure 22: Packet Error Checks
 Processing continues by copying the packet variables to the peer
 variables as shown in Figure 21.  An example is described by the
 packet() routine in Appendix A.5.1.1.  The receive() routine
 implements tests 1-5 in Figure 22; the packet() routine implements
 tests 6-7.  If errors are found, the packet is discarded and the peer
 process exits.
 The on-wire protocol calculates the clock offset theta and round-trip
 delay delta from the four most recent timestamps as described in
 Section 8.  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.
 Next, the 8-bit p.reach shift register in the poll process described
 in Section 13 is used to determine whether 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

Mills, et al. Standards Track [Page 36] RFC 5905 NTPv4 Specification June 2010

 have changed since the last packet, the host poll interval is
 reviewed.  An example is provided by the poll_update() routine in
 Appendix A.5.7.2.
 The dispersion statistic epsilon(t) represents the maximum error due
 to the frequency tolerance and time since the last packet was sent.
 It is initialized
 epsilon(t_0) = r.rho + s.rho + PHI * (T4-T1)
 when the measurement is made at t_0 according to the seconds counter.
 Here, r.rho is the packet precision described in Section 7.3 and
 s.rho is the system precision described in Section 11.1, 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 PHI; in other words, at
 time t, epsilon(t) = epsilon(t_0) + PHI * (t-t_0).  With the default
 value PHI = 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.

10. Clock Filter Algorithm

 The clock filter algorithm is part of the peer process.  It grooms
 the stream of on-wire data to select the samples most likely to
 represent accurate time.  The algorithm produces the variables shown
 in Figure 19, including the offset (theta), delay (delta), dispersion
 (epsilon), jitter (psi), and time of arrival (t).  These data are
 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 clock filter algorithm saves the most recent sample tuples
 (theta, delta, epsilon, t) in the filter structure, which functions
 as an 8-stage shift register.  The tuples are saved in the order that
 packets arrive.  Here, t is the packet time of arrival according to
 the seconds counter and should not be confused with the peer variable
 tp.
 The following scheme is used to ensure sufficient samples are in the
 filter and that old stale data are discarded.  Initially, the tuples
 of all stages are set to the dummy tuple (0, MAXDISP, MAXDISP, 0).
 As valid packets arrive, tuples are shifted into the filter causing
 old tuples to be discarded, so eventually only valid tuples remain.

Mills, et al. Standards Track [Page 37] RFC 5905 NTPv4 Specification June 2010

 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 a
 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 delta.  Let i index the stages
 starting with the lowest delta.  If the first tuple epoch t_0 is not
 later than the last valid sample epoch tp, the routine exits without
 affecting the current peer variables.  Otherwise, let epsilon_i be
 the dispersion of the ith entry, then
                   i=n-1
                   ---     epsilon_i
    epsilon =       \     ----------
                    /        (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, and (c) after the fourth valid packet the
 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 or not the peer variables are acceptable.
 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  |
    psi   =  -------- * |  /    (theta_0-theta_j)   |
              (n-1)     |  ---                      |
                        |  j=1                      |
                        +-----                 -----+
 where n is the number of valid tuples in the filter (n > 1).  In
 order to ensure consistency and avoid divide exceptions in other

Mills, et al. Standards Track [Page 38] RFC 5905 NTPv4 Specification June 2010

 computations, the psi is bounded from below by the system precision
 s.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 delay and
 dispersion.
 lambda = (delta / 2) + epsilon.
 Note that epsilon and therefore lambda increase at rate PHI.  The
 lambda is not a state variable, since lambda is recalculated at each
 use.  It is a component of the root synchronization distance used by
 the mitigation algorithms as a metric to evaluate the quality of time
 available from each server.
 It is important to note that, unlike NTPv3, NTPv4 associations do not
 show a timeout condition by setting the stratum to 16 and leap
 indicator to 3.  The association variables retain the values
 determined upon arrival of the last packet.  In NTPv4, lambda
 increases with time, so eventually the synchronization distance
 exceeds the distance threshold MAXDIST, in which case the association
 is considered unfit for synchronization.
 An example implementation of the clock filter algorithm is shown in
 the clock_filter() routine of Appendix A.5.2.

11. System Process

 As each new sample (theta, delta, epsilon, jitter, t) is produced by
 the clock filter algorithm, all peer processes are scanned by the
 mitigation algorithms consisting of the selection, cluster, combine,
 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 cluster algorithm discards the
 association statistically furthest from the centroid until a
 specified minimum number of survivors remain.  The combine algorithm
 produces the best and final statistics on a weighted average basis.
 The final offset is passed to the clock discipline algorithm to steer
 the system clock to the correct time.
 The cluster algorithm selects one of the survivors as the system
 peer.  The associated statistics (theta, delta, epsilon, jitter, t)
 are used to construct the system variables inherited by dependent
 servers and clients and made available to other applications running
 on the same machine.

Mills, et al. Standards Track [Page 39] RFC 5905 NTPv4 Specification June 2010

11.1. System Process Variables

 Figure 23 summarizes the common names, formula names, and a short
 description of each system variable.  Unless noted otherwise, all
 variables have assumed prefix s.
              +-----------+------------+------------------------+
              | Name      | Formula    | Description            |
              +-----------+------------+------------------------+
              | t         | t          | update time            |
              | p         | p          | system peer identifier |
              | leap      | leap       | leap indicator         |
              | stratum   | stratum    | stratum                |
              | precision | rho        | precision              |
              | offset    | THETA      | combined offset        |
              | jitter    | PSI        | combined jitter        |
              | rootdelay | DELTA      | root delay             |
              | rootdisp  | EPSILON    | root dispersion        |
              | v         | v          | survivor list          |
              | refid     | refid      | reference ID           |
              | reftime   | reftime    | reference time         |
              | NMIN      | 3          | minimum survivors      |
              | CMIN      | 1          | minimum candidates     |
              +-----------+------------+------------------------+
                  Figure 23: System Process Variables
 Except for the t, p, offset, and jitter variables and the NMIN and
 CMIN constants, the variables have the same format and interpretation
 as the peer variables of the same name.  The NMIN and CMIN parameters
 are used by the selection and cluster algorithms described in the
 next section.
 The t variable is the seconds counter at the time of the last update.
 An example is shown by the clock_update() routine in
 Appendix A.5.5.4.  The p variable is the system peer identifier
 determined by the cluster() routine in Section 11.2.2.  The precision
 variable has the same format as the packet variable of the same name.
 The precision is defined as the larger of the resolution and time to
 read the clock, in log2 units.  For instance, the precision of a
 mains-frequency clock incrementing at 60 Hz is 16 ms, even when the
 system clock hardware representation is to the nanosecond.
 The offset and jitter variables are determined by the combine
 algorithm in Section 11.2.3.  These values represent the best and
 final offset and jitter used to discipline the system clock.

Mills, et al. Standards Track [Page 40] RFC 5905 NTPv4 Specification June 2010

 Initially, all variables are cleared to zero, then the leap is set to
 3 (unsynchronized) and stratum is set to MAXSTRAT (16).  Remember
 that MAXSTRAT is mapped to zero in the transmitted packet.

11.2. System Process Operations

 Figure 24 summarizes the system process operations performed by the
 clock select routine.  The selection algorithm described in
 Section 11.2.1 produces a majority clique of presumed correct
 candidates (truechimers) based on agreement principles.  The cluster
 algorithm described in Section 11.2.2 discards outliers to produce
 the most accurate survivors.  The combine algorithm described in
 Section 11.2.3 provides the best and final offset for the clock
 discipline algorithm.  An example is described in Appendix A.5.5.6.
 If the selection algorithm cannot produce a majority clique, or if it
 cannot produce at least CMIN survivors, the system process exits
 without disciplining the system clock.  If successful, the cluster
 algorithm selects the statistically best candidate as the system peer
 and its variables are inherited as the system variables.

Mills, et al. Standards Track [Page 41] RFC 5905 NTPv4 Specification June 2010

                        +-----------------+
                        | clock_select()  |
                        +-----------------+
 ................................|...........
 .                               V          .
 .      yes +---------+ +-----------------+ .
 .       +--| accept? | | scan candidates | .
 .       |  +---------+ |                 | .
 .       V        no |  |                 | .
 .  +---------+      |  |                 | .
 .  | add peer|      |  |                 | .
 .  +----------      |  |                 | .
 .       |           V  |                 | .
 .       +---------->-->|                 | .
 .                      |                 | .
 . Selection Algorithm  +-----------------+ .
 .................................|..........
                                  V
                     no +-------------------+
          +-------------|     survivors?    |
          |             +-------------------+
          |                       | yes
          |                       V
          |             +-------------------+
          |             | Cluster Algorithm |
          |             +-------------------+
          |                       |
          |                       V
          V         yes +-------------------+
          |<------------|     n < CMIN?     |
          |             +-------------------+
          V                       |
   +-----------------+            V no
   |   s.p = NULL    |  +-------------------+
   +-----------------+  |   s.p = v_0.p     |
          |             +-------------------+
          V                       |
   +-----------------+            V
   | return (UNSYNC) |  +-------------------+
   +-----------------+  |   return (SYNC)   |
                        +-------------------+
                    Figure 24: Clock Select Routine

Mills, et al. Standards Track [Page 42] RFC 5905 NTPv4 Specification June 2010

11.2.1. Selection Algorithm

 Note that the selection and cluster algorithms are described
 separately, but combined in the code skeleton.  The selection
 algorithm operates to find an intersection interval containing a
 majority clique of truechimers using Byzantine agreement principles
 originally proposed by Marzullo [ref6], but modified to improve
 accuracy.  An overview of the algorithm is given below and described
 in the first half of the clock_select() routine in Appendix A.5.5.1.
 First, those servers that are unusable according to the rules of the
 protocol are detected and discarded as shown by the accept() routine
 in Appendix A.5.5.3.  Next, a set of tuples (p, type, edge) is
 generated for the remaining candidates.  Here, p is the association
 identifier and type identifies the upper (+1), middle (0), and lower
 (-1) endpoints of a correctness interval centered on theta for that
 candidate.  This results in three tuples, lowpoint (p, -1, theta -
 lambda), midpoint (p, 0, theta), and highpoint (p, +1, theta +
 lambda), where lambda is the root synchronization distance.  An
 example of this calculation is shown by the rootdist() routine in
 Appendix A.5.1.1.  The steps of the algorithm are:
 1.  For each of m associations, place three tuples as defined above
 on the candidate list.
 2.  Sort the tuples on the list by the edge component.  Order the
 lowpoint, midpoint, and highpoint of these intervals from lowest to
 highest.  Set the number of falsetickers f = 0.
 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.  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.  Is d = f and l < u?  If yes, then follow step 5A; else, follow
 step 5B.
 5A. Success: the intersection interval is [l, u].
 5B. Add one to f.  Is f < (m / 2)?  If yes, then go to step 3 again.
 If no, then go to step 6.
 6.  Failure; a majority clique could not be found.  There are no
 suitable candidates to discipline the system clock.

Mills, et al. Standards Track [Page 43] RFC 5905 NTPv4 Specification June 2010

 The algorithm is described in detail in Appendix A.5.5.1.  Note that
 it starts with the assumption that there are no falsetickers (f = 0)
 and attempts to find a non-empty intersection interval containing the
 midpoints of all correct servers, i.e., truechimers.  If a non-empty
 interval cannot be found, it increases the number of assumed
 falsetickers by one and tries again.  If a non-empty interval is
 found and the number of falsetickers is less than the number of
 truechimers, a majority clique has been found and the midpoint of
 each truechimer (theta) represents the candidates available to the
 cluster algorithm.
 If a majority clique is not found, or if the number of truechimers is
 less than CMIN, there are insufficient candidates to discipline the
 system clock.  CMIN defines the minimum number of servers consistent
 with the correctness requirements.  Suspicious operators would set
 CMIN to ensure multiple redundant servers are available for the
 algorithms to mitigate properly.  However, for historic reasons the
 default value for CMIN is one.

11.2.2. Cluster Algorithm

 The candidates of the majority clique are placed on the survivor list
 v in the form of tuples (p, theta_p, psi_p, lambda_p), where p is an
 association identifier, theta_p, psi_p, and stratum_p the current
 offset, jitter and stratum of association p, respectively, and
 lambda_p is a merit factor equal to stratum_p * MAXDIST + lambda,
 where lambda is the root synchronization distance for association p.
 The list is processed by the cluster algorithm below.  An example is
 shown by the second half of the clock_select() algorithm in
 Appendix A.5.5.1.
 1.  Let (p, theta_p, psi_p, lambda_p) represent a survivor candidate.
 2.  Sort the candidates by increasing lambda_p.  Let n be the number
 of candidates and NMIN the minimum required number of survivors.
 3.  For each candidate, compute the selection jitter psi_s:
           +-----                       -----+^1/2
           |        n-1                      |
           |        ---                      |
           |   1    \                     2  |
   psi_s = | ---- * /  (theta_s - theta_j)   |
           |  n-1   ---                      |
           |        j=1                      |
           +-----                       -----+
 4.  Select psi_max as the candidate with maximum psi_s.

Mills, et al. Standards Track [Page 44] RFC 5905 NTPv4 Specification June 2010

 5.  Select psi_min as the candidate with minimum psi_p.
 6.  Is psi_max < psi_min or n <= NMIN?  If yes, follow step 6A;
 otherwise, follow step 6B.
 6A. Done.  The remaining candidates on the survivor list are ranked
 in the order of preference.  The first entry on the list represents
 the system peer; its variables are used later to update the system
 variables.
 6B. Delete the outlier candidate with psi_max; reduce n by one and go
 back to step 3.
 The algorithm operates in a series of rounds where each round
 discards the statistical outlier with maximum selection jitter psi_s.
 However, if psi_s is less than the minimum peer jitter psi_p, no
 improvement is possible by discarding outliers.  This and the minimum
 number of survivors represent the terminating conditions of the
 algorithm.  Upon termination, the final value of psi_max is saved as
 the system selection jitter PSI_s for use later.

11.2.3. Combine Algorithm

 The clock combine route processes the remaining survivors to produce
 the best and final data for the clock discipline algorithm.  The
 routine processes peer offset and jitter statistics to produce the
 combined system offset THETA and system peer jitter PSI_p, where each
 server statistic is weighted by the reciprocal of the root
 synchronization distance and the result normalized.  An example is
 shown by the clock_combine() routine in Appendix A.5.5.5
 The combined THETA is passed to the clock update routine.  The first
 candidate on the survivor list is nominated as the system peer with
 identifier p.  The system peer jitter PSI_p is a component of the
 system jitter PSI.  It is used along with the selection jitter PSI_s
 to produce the system jitter:
 PSI = [(PSI_s)^2 + (PSI_p)^2]^1/2
 Each time an update is received from the system peer, the clock
 update routine is called.  By rule, an update is discarded if its
 time of arrival p.t is not strictly later than the last update used
 s.t.  The labels 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
 SHOULD cause the program to exit with a diagnostic message to the

Mills, et al. Standards Track [Page 45] RFC 5905 NTPv4 Specification June 2010

 system log.  STEP means the offset is less than the panic threshold,
 but greater than the step threshold STEPT (125 ms).  In this case,
 the clock is stepped to the correct offset, but since this means all
 peer data have been invalidated, all associations MUST be reset and
 the client begins as at initial start.
 ADJ means the offset is less than the step threshold and thus a valid
 update.  In this case, the system variables are updated from the peer
 variables as shown in Figure 25.
                +-------------------------------------------+
                | System Variable <-- System Peer Variable  |        |
                +-------------------------------------------+
                | s.leap      <-- p.leap                    |
                | s.stratum   <-- p.stratum + 1             |
                | s.offset    <-- THETA                     |
                | s.jitter    <-- PSI                       |
                | s.rootdelay <-- p.delta_r + delta         |
                | s.rootdisp  <-- p.epsilon_r + p.epsilon + |
                |                 p.psi + PHI * (s.t - p.t) |
                |                 + |THETA|                 |
                | s.refid     <-- p.refid                   |
                | s.reftime   <-- p.reftime                 |
                | s.t         <-- p.t                       |
                +-------------------------------------------+
                  Figure 25: System Variables Update
 There is an important detail not shown.  The dispersion increment
 (p.epsilon + p.psi + PHI * (s.t - p.t) + |THETA|) is bounded from
 below by MINDISP.  In subnets with very fast processors and networks
 and very small delay and dispersion this forces a monotone-definite
 increase in s.rootdisp (EPSILON), which avoids loops between peers
 operating at the same stratum.
 The system variables are available to dependent application programs
 as nominal performance statistics.  The system offset THETA is the
 clock offset relative to the available synchronization sources.  The
 system jitter PSI is an estimate of the error in determining this
 value, elsewhere called the expected error.  The root delay DELTA is
 the total round-trip delay relative to the primary server.  The root
 dispersion EPSILON is the dispersion accumulated over the network
 from the primary server.  Finally, the root synchronization distance
 is defined as:

Mills, et al. Standards Track [Page 46] RFC 5905 NTPv4 Specification June 2010

 LAMBDA = EPSILON + DELTA / 2,
 which represents the maximum error due all causes and is designated
 the root synchronization distance.
 An example of the clock update routine is provided in
 Appendix A.5.5.4.

11.3. Clock Discipline Algorithm

 The NTPv4 clock discipline algorithm, shortened to discipline in the
 following, functions as a combination of two quite philosophically
 different feedback control systems.  In a phase-locked loop (PLL)
 design, periodic phase updates at update intervals mu seconds 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 [ref7], a PLL
 usually works better when network jitter dominates, while an 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 [ref7], which also includes a
 performance analysis.
 The discipline is implemented as the feedback control system shown in
 Figure 26.  The variable theta_r represents the combine algorithm
 offset (reference phase) and theta_c the VFO offset (control phase).
 Each update produces a signal V_d 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, cluster, and
 combine algorithms combine the data from multiple filters to produce
 the signal V_s.  The loop filter, with impulse response F(t),
 produces the signal V_c, which controls the VFO frequency omega_c and
 thus the integral of the phase theta_c which closes the loop.  The
 V_c signal is generated by the clock-adjust process in Section 12.
 The detailed equations that implement these functions are best
 presented in the routines of Appendices A.5.5.6 and A.5.6.1.

Mills, et al. Standards Track [Page 47] RFC 5905 NTPv4 Specification June 2010

              theta_r + +---------\        +----------------+
          NTP --------->|  Phase   \  V_d  |                | V_s
              theta_c - | Detector  ------>|  Clock Filter  |----+
              +-------->|          /       |                |    |
              |         +---------/        +----------------+    |
              |                                                  |
            -----                                                |
           /     \                                               |
           | VFO |                                               |
           \     /                                               |
            -----    .......................................     |
              ^      .            Loop Filter              .     |
              |      . +---------+   x  +-------------+    .     |
              | V_c  . |         |<-----|             |    .     |
              +------.-|  Clock  |   y  | Phase/Freq  |<---------+
                     . | Adjust  |<-----| Prediction  |    .
                     . |         |      |             |    .
                     . +---------+      +-------------+    .
                     .......................................
               Figure 26: Clock Discipline Feedback Loop
 Ordinarily, the pseudo-linear feedback loop described above operates
 to discipline the system clock.  However, there are cases where a
 non-linear 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 non-linear loop described below does this
 in 15 minutes.  Another case is when occasional bursts of large
 jitter are present due to congested network links.  The state machine
 described below resists error bursts lasting less than 15 minutes.
 Figure 27 contains a summary of the variables and parameters
 including the variable (lowercase) or parameter (uppercase) name,
 formula name, and short description.  Unless noted otherwise, all
 variables have assumed prefix c.  The variables t, tc, state, hyster,
 and count are integers; the remaining variables are floating doubles.
 The function of each will be explained in the algorithm descriptions
 below.

Mills, et al. Standards Track [Page 48] RFC 5905 NTPv4 Specification June 2010

              +--------+------------+--------------------------+
              | Name   | Formula    | Description              |
              +--------+------------+--------------------------+
              | t      | timer      | seconds counter          |
              | offset | theta      | combined offset          |
              | resid  | theta_r    | residual offset          |
              | freq   | phi        | clock frequency          |
              | jitter | psi        | clock offset jitter      |
              | wander | omega      | clock frequency wander   |
              | tc     | tau        | time constant (log2)     |
              | state  | state      | state                    |
              | adj    | adj        | frequency adjustment     |
              | hyster | hyster     | 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 27: Clock Discipline Variables and Parameters
 The process terminates immediately if the offset is greater than the
 panic threshold PANICT (1000 s).  The state transition function is
 described by the rstclock() function in Appendix A.5.5.7.  Figure 28
 shows the state transition function used by this routine.  It has
 four columns showing, respectively, the state name, predicate and
 action if the offset theta is less than the step threshold, the
 predicate and actions otherwise, and finally some comments.

Mills, et al. Standards Track [Page 49] RFC 5905 NTPv4 Specification June 2010

    +-------+---------------------+-------------------+--------------+
    | State | theta < STEP        | theta > STEP      | Comments     |
    +-------+---------------------+-------------------+--------------+
    | NSET  | ->FREQ              | ->FREQ            | no frequency |
    |       | adjust time         | step time         | file         |
    +-------+---------------------+-------------------+--------------+
    | FSET  | ->SYNC              | ->SYNC            | frequency    |
    |       | adjust time         | step time         | file         |
    +-------+---------------------+-------------------+--------------+
    | SPIK  | ->SYNC              | if < 900 s ->SPIK | outlier      |
    |       | adjust freq         | else ->SYNC       | detected     |
    |       | adjust time         | step freq         |              |
    |       |                     | step time         |              |
    +-------+---------------------+-------------------+--------------+
    | FREQ  | if < 900 s ->FREQ   | if < 900 s ->FREQ | initial      |
    |       | else ->SYNC         | else ->SYNC       | frequency    |
    |       | step freq           | step freq         |              |
    |       | adjust time         | adjust time       |              |
    +-------+---------------------+-------------------+--------------+
    | SYNC  | ->SYNC              | if < 900 s ->SPIK | normal       |
    |       | adjust freq         | else ->SYNC       | operation    |
    |       | adjust time         | step freq         |              |
    |       |                     | step time         |              |
    +-------+---------------------+-------------------+--------------+
                 Figure 28: State Transition Function
 In the table entries, the next state is identified by the arrow ->
 with the actions listed below.  Actions such as adjust time and
 adjust frequency are implemented by the PLL/FLL feedback loop in the
 local_clock() routine.  A step clock action is implemented by setting
 the clock directly, but this is done only after the stepout threshold
 WATCH (900 s) when the offset is more than the step threshold STEPT
 (.125 s).  This resists clock steps under conditions of extreme
 network congestion.
 The jitter (psi) and wander (omega) statistics are computed using an
 exponential average with weight factor AVG.  The time constant
 exponent (tau) is determined by comparing psi with the magnitude of
 the current offset theta.  If the offset is greater than PGATE (4)
 times the clock jitter, the hysteresis counter hyster is reduced by
 two; otherwise, it is increased by one.  If hyster increases to the
 upper limit LIMIT (30), tau is increased by one; if it decreases to
 the lower limit -LIMIT (-30), tau is decreased by one.  Normally, tau
 hovers near MAXPOLL, but quickly decreases if a temperature spike
 causes a frequency surge.

Mills, et al. Standards Track [Page 50] RFC 5905 NTPv4 Specification June 2010

12. Clock-Adjust Process

 The actual clock-adjust process runs at one-second intervals to add
 the frequency correction and a fixed percentage of the residual
 offset theta_r.  The theta_r is, in effect, the exponential decay of
 the theta 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 EPSILON increases by PHI at
 each second.
 The clock-adjust process includes a timer interrupt facility driving
 the seconds counter 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 seconds counter 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.
 An example of the clock-adjust process is shown by the clock_adjust()
 routine in Appendix A.5.6.1.

13. 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 in order to manage the clock filter and reach
 register.

13.1. Poll Process Variables

 Figure 29 summarizes the common names, formula names, and a short
 description of the poll process variables (lowercase) and parameters
 (uppercase).  Unless noted otherwise, all variables have assumed
 prefix p.

Mills, et al. Standards Track [Page 51] RFC 5905 NTPv4 Specification June 2010

                 +---------+---------+--------------------+
                 | 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 29: Poll Process Variables and Parameters
 The poll process variables are allocated in the association data
 structure along with the peer process variables.  The following is a
 detailed description of the variables.  The parameters will be called
 out in the following text.
 hpoll: signed integer representing the poll exponent, in log2 seconds
 last: integer representing the seconds counter when the most recent
 packet was sent
 next: integer representing the seconds counter when the next packet
 is to be sent
 reach: 8-bit integer shift register shared by the peer and poll
 processes
 unreach: integer representing the number of seconds the server has
 been unreachable

13.2. Poll Process Operations

 As described previously, once each second the clock-adjust process is
 called.  This routine calls the poll routine for each association in
 turn.  If the time for the next poll message is greater than the
 seconds counter, the routine returns immediately.  Symmetric (modes
 1, 2), client (mode 3), and broadcast server (mode 5) associations
 routinely send packets.  A broadcast client (mode 6) association runs
 the routine to update the reach and unreach variables, but does not
 send packets.  The poll process calls the transmit process to send a
 packet.  If in a burst (burst > 0), nothing further is done except
 call the poll update routine to set the next poll interval.

Mills, et al. Standards Track [Page 52] RFC 5905 NTPv4 Specification June 2010

 If not in a burst, the 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.  An example is shown in
 Appendix A.5.7.3.
 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.  The interval between
 packets in the burst is two seconds.  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 has been
 unreachable, the client sends a burst.  This is useful to quickly
 reduce the synchronization distance below the distance threshold and
 synchronize the clock.
 If the P_MANY flag is lit in the p.flags word of the association,
 this is a manycast client association.  Manycast client associations
 send client mode packets to designated multicast group addresses at
 MINPOLL intervals.  The association starts out with a TTL of 1.  If
 by the time of the next poll there are fewer than MINCLOCK servers
 have been mobilized, the ttl is increased by one.  If the ttl reaches
 the limit TTLMAX, without finding MINCLOCK servers, the poll interval
 increases until reaching BEACON, when it starts over from the
 beginning.
 The poll() routine includes a feature that backs off the poll
 interval if the server becomes unreachable.  If reach is nonzero, the
 server is reachable and unreach is set to zero; otherwise, unreach is
 incremented by one for each poll to the maximum UNREACH.  Thereafter
 for each poll 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, unreach is set to
 zero, hpoll is reset to the tc system variable, and operation resumes
 normally.
 A packet is sent by the transmit process.  Some header values are
 copied from the peer variables left by a previous packet and others
 from the system variables.  Figure 30 shows which values are copied
 to each header field.  In those 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.

Mills, et al. Standards Track [Page 53] RFC 5905 NTPv4 Specification June 2010

                 +-----------------------------------+
                 | Packet Variable <--   Variable    |
                 +-----------------------------------+
                 | x.leap        <--     s.leap      |
                 | x.version     <--     s.version   |
                 | x.mode        <--     s.mode      |
                 | x.stratum     <--     s.stratum   |
                 | x.poll        <--     s.poll      |
                 | x.precision   <--     s.precision |
                 | x.rootdelay   <--     s.rootdelay |
                 | x.rootdisp    <--     s.rootdisp  |
                 | x.refid       <--     s.refid     |
                 | x.reftime     <--     s.reftime   |
                 | x.org         <--     p.xmt       |
                 | x.rec         <--     p.dst       |
                 | x.xmt         <--     clock       |
                 | x.keyid       <--     p.keyid     |
                 | x.digest      <--     md5 digest  |
                 +-----------------------------------+
                 Figure 30: xmit_packet Packet Header
 The poll update routine is called when a valid packet is received and
 immediately after a poll message has been sent.  If in a burst, the
 poll interval is fixed at 2 s; otherwise, the host poll exponent
 hpoll is set to the minimum of ppoll from the last packet received
 and hpoll from the poll routine, but not less than MINPOLL or 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.
 The poll exponent is converted to an interval, which, when added to
 the last poll time variable, determines the value of the next poll
 time variable.  Finally, the last poll time variable is set to the
 current seconds counter.

14. Simple Network Time Protocol (SNTP)

 Primary servers and clients complying with a subset of NTP, called
 the Simple Network Time Protocol (SNTPv4) [RFC4330], do not need to
 implement the mitigation algorithms described in Section 9 and
 following sections.  SNTP is intended for primary servers equipped
 with a single reference clock, as well as for 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 intermixed in NTP subnets.

Mills, et al. Standards Track [Page 54] RFC 5905 NTPv4 Specification June 2010

 An SNTP primary server implementing the on-wire protocol described in
 Section 8 has no upstream servers except a single reference clock.
 In principle, it is indistinguishable from an NTP primary server that
 has the mitigation algorithms and therefore capable of mitigating
 between multiple reference clocks.
 Upon receiving a client request, an SNTP primary server constructs
 and sends the reply packet as described in Figure 31.  Note that the
 dispersion field in the packet header must be updated as described in
 Section 5.
                 +-----------------------------------+
                 | 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 31: fast_xmit Packet Header
 An SNTP client implementing the on-wire protocol has a single server
 and no dependent clients.  It can operate with any subset of the NTP
 on-wire protocol, the simplest approach 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 so that a full implementation is encouraged.

15. Security Considerations

 NTP security requirements are even more stringent than most other
 distributed services.  First, the operation of the authentication
 mechanism and the time synchronization mechanism are inextricably
 intertwined.  Reliable time synchronization requires cryptographic
 keys that are valid only over a designated time interval; but, time
 intervals can be enforced only when participating servers and clients

Mills, et al. Standards Track [Page 55] RFC 5905 NTPv4 Specification June 2010

 are reliably synchronized to UTC.  In addition, the NTP subnet is
 hierarchical by nature, so time and trust flow from the primary
 servers at the root through secondary servers to the clients at the
 leaves.
 An NTP client can claim to have authentic time to dependent
 applications only if all servers on the path to the primary servers
 are authenticated.  In NTP each server authenticates the next lower
 stratum servers and authenticates by induction the lowest stratum
 (primary) servers.  It is important to note that authentication in
 the context of NTP does not necessarily imply the time is correct.
 An NTP client mobilizes a number of concurrent associations with
 different servers and uses a crafted agreement algorithm to pluck
 truechimers from the population possibly including falsetickers.
 The NTP specification assumes that the goal of the intruder is to
 inject false time values, disrupt the protocol, or clog the network,
 servers, or clients with spurious packets that exhaust resources and
 deny service to legitimate applications.  There are a number of
 defense mechanisms already built in the NTP architecture, protocol,
 and algorithms.  The on-wire timestamp exchange scheme is inherently
 resistant to spoofing, packet-loss, and replay attacks.  The
 engineered clock filter, selection and clustering algorithms are
 designed to defend against evil cliques of Byzantine traitors.  While
 not necessarily designed to defeat determined intruders, these
 algorithms and accompanying sanity checks have functioned well over
 the years to deflect improperly operating but presumably friendly
 scenarios.  However, these mechanisms do not securely identify and
 authenticate servers to clients.  Without specific further
 protection, an intruder can inject any or all of the following
 attacks:
 1.  An intruder can intercept and archive packets forever, as well as
     all the public values ever generated and transmitted over the
     net.
 2.  An intruder can generate packets faster than the server, network
     or client can process them, especially if they require expensive
     cryptographic computations.
 3.  In a wiretap attack, the intruder can intercept, modify, and
     replay a packet.  However, it cannot permanently prevent onward
     transmission of the original packet; that is, it cannot break the
     wire, only tell lies and congest it.  Generally, the modified
     packet cannot arrive at the victim before the original packet,
     nor does it have the server private keys or identity parameters.

Mills, et al. Standards Track [Page 56] RFC 5905 NTPv4 Specification June 2010

 4.  In a middleman or masquerade attack, the intruder is positioned
     between the server and client, so it can intercept, modify and
     replay a packet and prevent onward transmission of the original
     packet.  However, the middleman does not have the server private
     keys.
 The NTP security model assumes the following possible limitations:
 1.  The running times for public key algorithms are relatively long
     and highly variable.  In general, the performance of the time
     synchronization function is badly degraded if these algorithms
     must be used for every NTP packet.
 2.  In some modes of operation, it is not feasible for a server to
     retain state variables for every client.  It is however feasible
     to regenerated them for a client upon arrival of a packet from
     that client.
 3.  The lifetime of cryptographic values must be enforced, which
     requires a reliable system clock.  However, the sources that
     synchronize the system clock must be trusted.  This circular
     interdependence of the timekeeping and authentication functions
     requires special handling.
 4.  Client security functions must involve only public values
     transmitted over the net.  Private values must never be disclosed
     beyond the machine on which they were created, except in the case
     of a special trusted agent (TA) assigned for this purpose.
 Unlike the Secure Shell (SSH) security model, where the client must
 be securely authenticated to the server, in NTP the server must be
 securely authenticated to the client.  In SSH, each different
 interface address can be bound to a different name, as returned by a
 reverse-DNS query.  In this design, separate public/private key pairs
 may be required for each interface address with a distinct name.  A
 perceived advantage of this design is that the security compartment
 can be different for each interface.  This allows a firewall, for
 instance, to require some interfaces to authenticate the client and
 others not.
 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.  Such disruption can be
 minimized by several approaches.  Filtering can be employed to limit
 the access of NTP clients to known or trusted NTP broadcast servers.
 Such filtering will prevent malicious traffic from reaching the NTP
 clients.  Cryptographic authentication at the client will only allow

Mills, et al. Standards Track [Page 57] RFC 5905 NTPv4 Specification June 2010

 timing information from properly signed NTP messages to be utilized
 in synchronizing its clock.  Higher levels of authentication may be
 gained by the use of the Autokey mechanism [RFC5906].
 Section 8 describes a potential security concern with the replay of
 client requests.  Following the recommendations in that section
 provides protection against such attacks.
 It should be noted that this specification is describing an existing
 implementation.  While the security shortfalls of the MD5 algorithm
 are well-known, its use in the NTP specification is consistent with
 widescale deployment in the Internet community.

16. 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 has established and will 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 [RFC5226], new
 values are to be defined by IETF Review.
 The IANA has created a new registry for NTP Reference Identifier
 codes.  This includes the current codes defined in Section 7.3, and
 may be extended on a First-Come-First-Serve (FCFS) basis.  The format
 of the registry is:
   +------+----------------------------------------------------------+
   | ID   | Clock Source                                             |
   +------+----------------------------------------------------------+
   | GOES | Geosynchronous Orbit Environment Satellite               |
   | GPS  | Global Position System                                   |
   | ...  | ...                                                      |
   +------+----------------------------------------------------------+
                 Figure 32: Reference Identifier Codes
 The IANA has created a new registry for NTP Kiss-o'-Death codes.
 This includes the current codes defined in Section 7.4, and may be
 extended on a FCFS basis.  The format of the registry is:

Mills, et al. Standards Track [Page 58] RFC 5905 NTPv4 Specification June 2010

 +------+------------------------------------------------------------+
 | Code |                           Meaning                          |
 +------+------------------------------------------------------------+
 | ACST | The association belongs to a unicast server.               |
 | AUTH | Server authentication failed.                              |
 | ...  | ...                                                        |
 +------+------------------------------------------------------------+
                         Figure 33: Kiss Codes
 For both Reference Identifiers and Kiss-o'-Death codes, IANA is
 requested to never assign a code beginning with the character "X", as
 this is reserved for experimentation and development.

17. Acknowledgements

 The editors would like to thank Karen O'Donoghue, Brian Haberman,
 Greg Dowd, Mark Elliot, Harlan Stenn, Yaakov Stein, Stewart Bryant,
 and Danny Mayer for technical reviews and specific text contributions
 to this document.

18. References

18.1. Normative References

 [RFC0768]       Postel, J., "User Datagram Protocol", STD 6, RFC 768,
                 August 1980.
 [RFC0791]       Postel, J., "Internet Protocol", STD 5, RFC 791,
                 September 1981.
 [RFC0793]       Postel, J., "Transmission Control Protocol", STD 7,
                 RFC 793, September 1981.
 [RFC1321]       Rivest, R., "The MD5 Message-Digest Algorithm",
                 RFC 1321, April 1992.
 [RFC2119]       Bradner, S., "Key words for use in RFCs to Indicate
                 Requirement Levels", BCP 14, RFC 2119, March 1997.

18.2. Informative References

 [CGPM]          Bureau International des Poids et Mesures, "Comptes
                 Rendus de la 15e CGPM", 1976.
 [ITU-R_TF.460]  International Telecommunications Union, "ITU-R TF.460
                 Standard-frequency and time-signal emissions",
                 February 2002.

Mills, et al. Standards Track [Page 59] RFC 5905 NTPv4 Specification June 2010

 [RFC1305]       Mills, D., "Network Time Protocol (Version 3)
                 Specification, Implementation and Analysis",
                 RFC 1305, March 1992.
 [RFC1345]       Simonsen, K., "Character Mnemonics and Character
                 Sets", RFC 1345, June 1992.
 [RFC4330]       Mills, D., "Simple Network Time Protocol (SNTP)
                 Version 4 for IPv4, IPv6 and OSI", RFC 4330,
                 January 2006.
 [RFC5226]       Narten, T. and H. Alvestrand, "Guidelines for Writing
                 an IANA Considerations Section in RFCs", BCP 26,
                 RFC 5226, May 2008.
 [RFC5906]       Haberman, B., Ed. and D. Mills, "Network Time
                 Protocol Version 4: Autokey Specification", RFC 5906,
                 June 2010.
 [ref6]          Marzullo and S. Owicki, "Maintaining the time in a
                 distributed system", ACM Operating Systems Review 19,
                 July 1985.
 [ref7]          Mills, D.L., "Computer Network Time Synchronization -
                 the Network Time Protocol", CRC Press, 304 pp, 2006.
 [ref9]          Mills, D.L., Electrical and Computer Engineering
                 Technical Report 06-6-1, NDSS, June 2006, "Network
                 Time Protocol Version 4 Reference and Implementation
                 Guide", 2006.

Mills, et al. Standards Track [Page 60] RFC 5905 NTPv4 Specification June 2010

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 fragments that 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.
 Most of the features of the reference implementation are included
 here, with the following exceptions: there are no provisions for
 reference clocks or public key (Autokey) cryptography.  There is no
 huff-n'-puff filter, anti-clockhop hysteresis, or monitoring
 provisions.  Many of the values that can be tinkered in the reference
 implementation are assumed constants here.  There are only minimal
 provisions for the kiss-o'-death packet and no responding code.
 The program is not intended to be fast or compact, just to
 demonstrate the algorithms with sufficient fidelity to understand how
 they work.  The code skeleton consists of eight segments, a header
 segment included by each of the other segments, plus a code segment
 for the main program, kernel I/O and system clock interfaces, 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

A.1.1. Definitions, Constants, Parameters

#include <math.h> /* avoids complaints about sqrt() */ #include <sys/time.h> /* for gettimeofday() and friends */ #include <stdlib.h> /* for malloc() and friends */ #include <string.h> /* for memset() */

/* * Data types * * This program assumes the int data type is 32 bits and 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

Mills, et al. Standards Track [Page 61] RFC 5905 NTPv4 Specification June 2010

* 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 long tstamp; /* NTP timestamp format */ typedef unsigned int tdist; /* NTP short format */ typedef unsigned long ipaddr; /* IPv4 or IPv6 address */ typedef unsigned long digest; /* md5 digest */ typedef signed char s_char; /* precision and poll interval (log2) */

/* * Timestamp conversion macroni */ #define FRIC 65536. /* 2^16 as a double */ #define D2FP® 1) /* NTP short */ #define FP2D® 2) /* NTP timestamp */ #define LFP2D(a) 3) : \

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

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

/* * Global constants. Some of these might be converted to variables * that can be tinkered by configuration or computed on-the-fly. For * instance, the reference implementation computes PRECISION on-the-fly * and provides performance tuning for the defines marked with % below. */ #define VERSION 4 /* version number */ #define MINDISP .01 /* % minimum dispersion (s) */

Mills, et al. Standards Track [Page 62] RFC 5905 NTPv4 Specification June 2010

#define MAXDISP 16 /* maximum dispersion (s) */ #define MAXDIST 1 /* % distance threshold (s) */ #define NOSYNC 0x3 /* leap unsync */ #define MAXSTRAT 16 /* maximum stratum (infinity metric) */ #define MINPOLL 6 /* % minimum poll interval (64 s)*/ #define MAXPOLL 17 /* % maximum poll interval (36.4 h) */ #define MINCLOCK 3 /* minimum manycast survivors */ #define MAXCLOCK 10 /* maximum manycast candidates */ #define TTLMAX 8 /* max ttl manycast */ #define BEACON 15 /* max interval between beacons */

#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 */

/* * 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 */

/* * 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 */ #define P_MANY 0x20 /* manycast client */

Mills, et al. Standards Track [Page 63] RFC 5905 NTPv4 Specification June 2010

/* * 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 definitions */ #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 */

#define min(a, b) 4) #define max(a, b) 5)

Mills, et al. Standards Track [Page 64] RFC 5905 NTPv4 Specification June 2010

A.1.2. Packet Data Structures

/* * The receive and transmit packets may contain an optional message * authentication code (MAC) consisting of a key identifier (keyid) and * message digest (mac in the receive structure and dgst in the transmit * structure). NTPv4 supports optional extension fields that * are inserted after 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 omitted 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  mac;            /* message digest */
      tstamp  dst;            /* destination timestamp */

} r;

/* * Transmit packet */ struct x {

      ipaddr  dstaddr;        /* source (local) address */
      ipaddr  srcaddr;        /* destination (remote) address */
      char    version;        /* version number */
      char    leap;           /* leap indicator */
      char    mode;           /* mode */
      char    stratum;        /* stratum */

Mills, et al. Standards Track [Page 65] RFC 5905 NTPv4 Specification June 2010

      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  dgst;           /* 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 */
         ipaddr  dstaddr;        /* destination (local) address */
         char    version;        /* version number */
         char    hmode;          /* host mode */
         int     keyid;          /* key identifier */
         int     flags;          /* option flags */
         /*
          * Variables set by received packet
          */
         char    leap;           /* leap indicator */
         char    pmode;          /* peer mode */

Mills, et al. Standards Track [Page 66] RFC 5905 NTPv4 Specification June 2010

         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 */
         int     ttl;            /* ttl (manycast) */
 #define end_clear unreach       /* end of clear area */
         int     unreach;        /* unreach counter */
         int     outdate;        /* last poll time */
         int     nextdate;       /* next poll time */
 } p;

Mills, et al. Standards Track [Page 67] RFC 5905 NTPv4 Specification June 2010

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;
 /*
  * 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 */
         int     n;              /* number of survivors */
 } s;

Mills, et al. Standards Track [Page 68] RFC 5905 NTPv4 Specification June 2010

A.1.5. Local Clock Data Structures

 /*
  * Local clock structure
  */
 struct c {
         tstamp  t;              /* update time */
         int     state;          /* current state */
         double  offset;         /* current 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
 */
void    receive(struct r *);    /* receive packet */
void    packet(struct p *, struct r *); /* process packet */
void    clock_filter(struct p *, double, double, double); /* filter */
double  root_dist(struct p *);  /* calculate root distance */
int     fit(struct p *);        /* determine fitness of server */
void    clear(struct p *, int); /* clear association */
int     access(struct r *);     /* determine access restrictions */
/*
 * System process
 */
int     main();                 /* main program */
void    clock_select();         /* find the best clocks */
void    clock_update(struct p *); /* update the system clock */
void    clock_combine();        /* combine the offsets */
/*
 * Local clock 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 */

Mills, et al. Standards Track [Page 69] RFC 5905 NTPv4 Specification June 2010

/*
 * 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 */
void    fast_xmit(struct r *, int, int); /* transmit a reply packet */
/*
 * Utility routines
 */
digest  md5(int);               /* generate a message digest */
struct p *mobilize(ipaddr, ipaddr, int, int, int, int); /* mobilize */
struct p *find_assoc(struct r *); /* search the association table */
/*
 * Kernel interface
 */
struct r *recv_packet();        /* wait for packet */
void    xmit_packet(struct x *); /* send packet */
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

/* * 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 */

Mills, et al. Standards Track [Page 70] RFC 5905 NTPv4 Specification June 2010

      /*
       * Read command line options and initialize system variables.
       * The reference implementation measures 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;
      /*
       * 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 specified 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);
      }
      return(0);

}

Mills, et al. Standards Track [Page 71] RFC 5905 NTPv4 Specification June 2010

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

}

/* * 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, source port and mode.
       */
      while (/* all associations */ 0) {
              if (r->srcaddr == p->srcaddr && r->mode == p->hmode)
                      return(p);
      }

Mills, et al. Standards Track [Page 72] RFC 5905 NTPv4 Specification June 2010

      return (NULL);

}

/* * 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 fields
      * 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() {
         return (/* receive packet r */ 0);
 }
 /*
  * xmit_packet - transmit packet to network
  */
 void
 xmit_packet(
         struct x *x             /* transmit packet pointer */
         )
 {
         /* send packet x */
 }

Mills, et al. Standards Track [Page 73] RFC 5905 NTPv4 Specification June 2010

A.4. Kernel System Clock Interface

/* * System clock utility functions * * 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 expect 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);
      return (U2LFP(unix_time));

}

Mills, et al. Standards Track [Page 74] RFC 5905 NTPv4 Specification June 2010

/* * step_time() - step system time to given offset value */ 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.
       */
      gettimeofday(&unix_time, NULL);
      ntp_time = D2LFP(offset) + U2LFP(unix_time);
      unix_time.tv_sec = ntp_time >> 32;
      unix_time.tv_usec = (long)(((ntp_time - unix_time.tv_sec) <<
          32) / FRAC * 1e6);
      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 >> 32;
      unix_time.tv_usec = (long)(((ntp_time - unix_time.tv_sec) <<
          32) / FRAC * 1e6);
      adjtime(&unix_time, NULL);

}

Mills, et al. Standards Track [Page 75] RFC 5905 NTPv4 Specification June 2010

A.5. Peer Process

 /*
  * 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 is an NTP header with leap 0x3 (NOSYNC) and
  * stratum 16 (MAXSTRAT).  It tells the receiver that something
  * drastic has happened, as revealed by the kiss code in the refid
  * field.  The NTP header fields may or may not be correct.
  */
 /*
  * Peer process parameters and constants
  */
 #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 MANY            4       /* manycast packet */
 #define NEWPS           5       /* new symmetric passive client */
 #define NEWBC           6       /* new broadcast client */
 /*
  * Dispatch matrix
  *              active  passv  client server bcast */
 int table[7][5] = {
 /* nopeer  */   { NEWPS, DSCRD, FXMIT, MANY, 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 },
 /* bcast   */   { DSCRD, DSCRD, DSCRD, DSCRD, DSCRD },
 /* bclient */   { DSCRD, DSCRD, DSCRD, DSCRD, PROC}
 };

Mills, et al. Standards Track [Page 76] RFC 5905 NTPv4 Specification June 2010

 /*
  * Miscellaneous macroni
  *
  * This macro defines the authentication state.  If x is 0,
  * authentication is optional; otherwise, 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 */
      /*
       * 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
       * packet length, MAC length and extension field lengths, if
       * present.
       */

Mills, et al. Standards Track [Page 77] RFC 5905 NTPv4 Specification June 2010

      if (r->version > VERSION /* or format error */)
              return;                 /* format error */
      /*
       * Authentication is conditioned by two switches that 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->hmode is assumed NULL.
       */
      p = find_assoc(r);
      switch(table[(unsigned int)(p->hmode)][(unsigned int)(r->mode)])
      {

Mills, et al. Standards Track [Page 78] RFC 5905 NTPv4 Specification June 2010

      /*
       * Client packet and no association.  Send server reply without
       * saving state.
       */
      case FXMIT:
              /*
               * If unicast destination address, send server packet.
               * If authentication fails, send a crypto-NAK packet.
               */
              /* not multicast dstaddr */
              if (0) {
                      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 */
              }
              /*
               * This must be manycast.  Do not respond if we are not
               * synchronized or if our stratum is above the
               * manycaster.
               */
              if (s.leap == NOSYNC || s.stratum > r->stratum)
                      return;
              /*
               * Respond only if authentication is OK.  Note that the
               * unicast address is used, not the multicast.
               */
              if (AUTH(p->flags & P_NOTRUST, auth))
                      fast_xmit(r, M_SERV, auth);
              return;
      /*
       * New manycast client ephemeral association.  It is mobilized
       * in the same version as in the packet.  If authentication
       * fails, ignore the packet.  Verify the server packet by
       * comparing the r->org timestamp in the packet with the p->xmt
       * timestamp in the multicast client association.  If they
       * match, the server packet is authentic.  Details omitted.
       */

Mills, et al. Standards Track [Page 79] RFC 5905 NTPv4 Specification June 2010

      case MANY:
              if (!AUTH(p->flags & (P_NOTRUST | P_NOPEER), auth))
                      return;         /* authentication error */
              p = mobilize(r->srcaddr, r->dstaddr, r->version, M_CLNT,
                  r->keyid, P_EPHEM);
              break;
     /*
      * New symmetric passive 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 association.  It is mobilized in the
       * same version as in the packet.  If authentication fails,
       * ignore the packet.  Note this code does not support the
       * initial volley feature in the reference implementation.
       */
      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 */

Mills, et al. Standards Track [Page 80] RFC 5905 NTPv4 Specification June 2010

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

Mills, et al. Standards Track [Page 81] RFC 5905 NTPv4 Specification June 2010

      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.
       */
      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 */

Mills, et al. Standards Track [Page 82] RFC 5905 NTPv4 Specification June 2010

      /*
       * 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);

}

A.5.1.1. 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->pmode = 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.
       */

Mills, et al. Standards Track [Page 83] RFC 5905 NTPv4 Specification June 2010

      if (p->leap == NOSYNC || p->stratum >= MAXSTRAT)
              return;                 /* unsynchronized */
      /*
       * Verify valid root distance.
       */
      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 preserve 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->pmode == 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);

}

Mills, et al. Standards Track [Page 84] RFC 5905 NTPv4 Specification June 2010

A.5.2. 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 */
      )

{

      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));

Mills, et al. Standards Track [Page 85] RFC 5905 NTPv4 Specification June 2010

              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;
      /*
       * 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;

}

/* * fit() - test if association p is acceptable for synchronization */ int fit(

      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);

Mills, et al. Standards Track [Page 86] RFC 5905 NTPv4 Specification June 2010

      /*
       * 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);

}

/* * 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;

Mills, et al. Standards Track [Page 87] RFC 5905 NTPv4 Specification June 2010

      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;
      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->outdate = p->t = c.t;
      p->nextdate = p->outdate + (random() & ((1 << MINPOLL) - 1));

}

A.5.3. 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.
       */

Mills, et al. Standards Track [Page 88] RFC 5905 NTPv4 Specification June 2010

      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;
      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.dgst = md5(x.keyid);
              }
      }
      xmit_packet(&x);

}

A.5.4. access()

/*

  • access() - determine access restrictions
  • /

int access(

       struct r *r             /* receive packet pointer */
       )

Mills, et al. Standards Track [Page 89] RFC 5905 NTPv4 Specification June 2010

{

       /*
        * 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.5.5. System Process

A.5.5.1. clock_select()

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

     struct p *p, *osys;     /* peer structure pointers */
     double  low, high;      /* correctness interval extents */
     int     allow, found, chime; /* used by intersection 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 (fit(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;

Mills, et al. Standards Track [Page 90] RFC 5905 NTPv4 Specification June 2010

              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.
               */
              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++;
              }

Mills, et al. Standards Track [Page 91] RFC 5905 NTPv4 Specification June 2010

              /*
               * 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
               * non-empty, 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.
       */
      s.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);
              s.n++;
      }
      /*
       * There must be at least NSANE survivors to satisfy the
       * correctness assertions.  Ordinarily, the Byzantine criteria
       * require four survivors, but for the demonstration here, one
       * is acceptable.
       */
      if (s.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.
       */

Mills, et al. Standards Track [Page 92] RFC 5905 NTPv4 Specification June 2010

      while (1) {
              struct p *p, *q, *qmax; /* peer structure pointers */
              double  max, min, dtemp;
              max = -2e9; min = 2e9;
              for (i = 0; i < s.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;
                      }
              }
              /*
               * 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.
               */
              s.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;

Mills, et al. Standards Track [Page 93] RFC 5905 NTPv4 Specification June 2010

      else
              s.p = s.v[0].p;
      clock_update(s.p);

}

A.5.5.2. 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);

}

A.5.5.3. 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.
       */

Mills, et al. Standards Track [Page 94] RFC 5905 NTPv4 Specification June 2010

      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.5.5.4. clock_update()

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

Mills, et al. Standards Track [Page 95] RFC 5905 NTPv4 Specification June 2010

      /*
       * 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.  The reference implementation includes 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 values, so they are reset and started
       * fresh.  The step threshold can be changed in the reference
       * implementation in order to lessen the chance the clock might
       * be stepped backwards.  However, there may be serious
       * consequences, as noted in the white papers at the NTP project
       * site.
       */
      case STEP:
              while (/* all associations */ 0)
                      clear(p, X_STEP);
              s.stratum = MAXSTRAT;
              s.poll = MINPOLL;
              break;
      /*
       * 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 can be changed from the
       * default .01 s in the reference implementation.
       */
      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;

Mills, et al. Standards Track [Page 96] RFC 5905 NTPv4 Specification June 2010

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

}

A.5.5.5. 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.  The reference implementation can
       * be configured to avoid this algorithm by designating a
       * preferred peer.
       */
      y = z = w = 0;
      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);

}

Mills, et al. Standards Track [Page 97] RFC 5905 NTPv4 Specification June 2010

A.5.5.6. local_clock()

/* * Clock discipline parameters and constants */ #define STEPT .128 /* step threshold (s) */ #define WATCH 900 /* stepout threshold (s) */ #define PANICT 1000 /* panic threshold (s) */ #define PLL 65536 /* PLL loop gain */ #define FLL MAXPOLL + 1 /* FLL loop gain */ #define AVG 4 /* parameter averaging constant */ #define ALLAN 1500 /* compromise Allan intercept (s) */ #define LIMIT 30 /* poll-adjust threshold */ #define MAXFREQ 500e-6 /* frequency tolerance (500 ppm) */ #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)
              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) {

Mills, et al. Standards Track [Page 98] RFC 5905 NTPv4 Specification June 2010

              /*
               * In S_SYNC state, we ignore the first outlier and
               * switch to S_SPIK state.
               */
              case SYNC:
                      state = SPIK;
                      return (rval);
              /*
               * In S_FREQ state, we ignore outliers and inliers.  At
               * the first outlier after the stepout threshold,
               * compute the apparent frequency correction and step
               * the time.
               */
              case FREQ:
                      if (mu < WATCH)
                              return (IGNORE);
                      freq = (offset - c.offset) / mu;
                      /* fall through to S_SPIK */
              /*
               * In S_SPIK state, we ignore succeeding outliers until
               * either an inlier 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
               * 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

Mills, et al. Standards Track [Page 99] RFC 5905 NTPv4 Specification June 2010

  • 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;
                      s.poll = MINPOLL;
                      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);
              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:
                      rstclock(FREQ, p->t, offset);
                      return (IGNORE);

Mills, et al. Standards Track [Page 100] RFC 5905 NTPv4 Specification June 2010

              /*
               * 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:
                      rstclock(SYNC, p->t, 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.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
                       * depending 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;
                              if (etemp < AVG)
                                      etemp = AVG;
                              freq += (offset - c.offset) / (max(mu,
                                  ALLAN) * etemp);
                      }

Mills, et al. Standards Track [Page 101] RFC 5905 NTPv4 Specification June 2010

                      /*
                       * 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);
                      rstclock(SYNC, p->t, offset);
                      break;
              }
      }
      /*
       * 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 with the 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++;
                      }
              }
      } else {
              c.count -= s.poll << 1;
              if (c.count < -LIMIT) {
                      c.count = -LIMIT;
                      if (s.poll > MINPOLL) {

Mills, et al. Standards Track [Page 102] RFC 5905 NTPv4 Specification June 2010

                              c.count = 0;
                              s.poll--;
                      }
              }
      }
      return (rval);

}

A.5.5.7. 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.last = c.offset = offset;
        s.t = t;
}

A.5.6. Clock Adjust Process

A.5.6.1. clock_adjust()

/*

  • clock_adjust() - runs at one-second intervals
  • /

void clock_adjust() {

       double  dtemp;
       /*
        * 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 unfit for
        * synchronization.

Mills, et al. Standards Track [Page 103] RFC 5905 NTPv4 Specification June 2010

  • /

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->nextdate)
                       poll(p);
       }
       /*
        * Once per hour, write the clock frequency to a file.
        */
       /*
        * if (c.t % 3600 == 3599)
        *   write c.freq to file
        */

}

A.5.7. Poll Process

 /*
  * Poll process parameters and constants
  */
 #define UNREACH         12      /* unreach counter threshold */
 #define BCOUNT          8       /* packets in a burst */
 #define BTIME           2       /* burst interval (s) */

Mills, et al. Standards Track [Page 104] RFC 5905 NTPv4 Specification June 2010

A.5.7.1. 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->nextdate.  The value p->outdate is
       * the last time this routine was executed.  The poll_update()
       * routine determines the next execution time p->nextdate.
       *
       * If broadcasting, just do it, but only if we are synchronized.
       */
      hpoll = p->hpoll;
      if (p->hmode == M_BCST) {
              p->outdate = c.t;
              if (s.p != NULL)
                      peer_xmit(p);
              poll_update(p, hpoll);
              return;
      }
      /*
       * If manycasting, start with ttl = 1.  The ttl is increased by
       * one for each poll until MAXCLOCK servers have been found or
       * ttl reaches TTLMAX.  If reaching MAXCLOCK, stop polling until
       * the number of servers falls below MINCLOCK, then start all
       * over.
       */
      if (p->hmode == M_CLNT && p->flags & P_MANY) {
              p->outdate = c.t;
              if (p->unreach > BEACON) {
                      p->unreach = 0;
                      p->ttl = 1;
                      peer_xmit(p);
              } else if (s.n < MINCLOCK) {
                      if (p->ttl < TTLMAX)
                              p->ttl++;
                      peer_xmit(p);
              }

Mills, et al. Standards Track [Page 105] RFC 5905 NTPv4 Specification June 2010

              p->unreach++;
              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.
               */
              oreach = p->reach;
              p->outdate = c.t;
              p->reach = p->reach << 1;
              if (!(p->reach & 0x7))
                      clock_filter(p, 0, 0, MAXDISP);
              if (!p->reach) {
                      /*
                       * 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.  Send a
                       * burst only if enabled and the unreach
                       * threshold has not been reached.
                       */
                      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.  Set the poll
                       * interval to the system poll interval.  Send a
                       * burst only if enabled and the peer is fit.
                       */
                      p->unreach = 0;
                      hpoll = s.poll;
                      if (p->flags & P_BURST && fit(p))
                              p->burst = BCOUNT;
              }
      } else {

Mills, et al. Standards Track [Page 106] RFC 5905 NTPv4 Specification June 2010

              /*
               * 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->hmode != M_BCLN)
              peer_xmit(p);
      poll_update(p, hpoll);

}

A.5.7.2. poll_update()

/* * 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     poll            /* poll interval (log2 s) */
      )

{

      /*
       * 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 ensures that a longer interval can be preempted by a
       * shorter one if required for rapid response.
       */
      p->hpoll = max(min(MAXPOLL, poll), MINPOLL);
      if (p->burst > 0) {
              if (p->nextdate != c.t)
                      return;
              else
                      p->nextdate += BTIME;
      } else {

Mills, et al. Standards Track [Page 107] RFC 5905 NTPv4 Specification June 2010

              /*
               * While not shown here, the reference implementation
               * randomizes the poll interval by a small factor.
               */
              p->nextdate = p->outdate + (1 << max(min(p->ppoll,
                  p->hpoll), MINPOLL));
      }
      /*
       * It might happen that the due time has already passed.  If so,
       * make it one second in the future.
       */
      if (p->nextdate <= c.t)
              p->nextdate = c.t + 1;

}

A.5.7.3. peer_xmit()

/* * 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 = p->version;
      x.mode = p->hmode;
      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;

Mills, et al. Standards Track [Page 108] RFC 5905 NTPv4 Specification June 2010

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

}

Mills, et al. Standards Track [Page 109] RFC 5905 NTPv4 Specification June 2010

Authors' Addresses

 Dr. David L. Mills
 University of Delaware
 Newark, DE  19716
 US
 Phone: +1 302 831 8247
 EMail: mills@udel.edu
 Jim Martin (editor)
 Internet Systems Consortium
 950 Charter Street
 Redwood City, CA  94063
 US
 Phone: +1 650 423 1378
 EMail: jrmii@isc.org
 Jack Burbank
 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
 William Kasch
 The Johns Hopkins University Applied Physics Laboratory
 11100 Johns Hopkins Road
 Laurel, MD  20723-6099
 US
 Phone: +1 443 778 7463
 EMail: william.kasch@jhuapl.edu

Mills, et al. Standards Track [Page 110]

1)
tdist)(® * FRIC
2)
double)® / FRIC) #define FRAC 4294967296. /* 2^32 as a double */ #define D2LFP(a) ((tstamp)((a) * FRAC
3)
double)(a) / FRAC) #define U2LFP(a) (((unsigned long long) \
                     ((a).tv_sec + JAN_1970) << 32) + \
                     (unsigned long long) \
                     ((a).tv_usec / 1e6 * FRAC))
/* * Arithmetic conversions */ #define LOG2D(a) ((a) < 0 ? 1. / (1L « -(a
4)
a) < (b) ? (a) : (b
5)
a) < (b) ? (b) : (a
/data/webs/external/dokuwiki/data/pages/rfc/rfc5905.txt · Last modified: 2010/06/21 18:20 (external edit)