RFC 5905
Network Time Protocol Version 4: Protocol and Algorithms Specification
Pages: 110
Proposed Standard
→ Errata
Obsoletes: 1305 4330
Updated by: 7822 8573 9109
Proposed Standard
→ Errata
Obsoletes: 1305 4330
Updated by: 7822 8573 9109
Part 1 of 5 – Pages 1 to 16
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 SpecificationAbstract
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.
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
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
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-
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].
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.
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
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.
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
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
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
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.
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
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.
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.
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.
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