— George Carlin, Again! (1978)
So let's say you want to ask the time to your friend who is fortunate enough to own a radio clock. Now imagine voice takes a long, undeterminate (and variable) amount of time to travel between you and them (alternatively, imagine you want to know what time is it with an extreme precision). When your interlocutor hears your question, it is already too late. They can give you the time it was when the heard the question, but they have no idea when you asked. Now, when you receive their answer you have the same problem. You neither know when they heard your question, nor when they answered. You only know that the time you get corresponds to some point between the moment you asked and the moment you heard the answer. Now let's say you pick a random point in this interval, and adjust your own watch to that time. Maybe you make an error, but at least your synchronized _within some tolerance_ right? No luck! Since it is extremely unlikely both of your watches have exactly the same consistent speed, your watch will drift and wander away from your friend's clock. You could ask again and again. But each time you will get a different error, so your watch will be very noisy (and still drift in between exchanges). Fortunately for us humans, we don't typically require a high precision compared to the time it takes for sound to travel between two persons speaking to each other. For computers though, it can be crucial to be synchronized within a few microseconds, and network communications can take full seconds. Their clock are also drifting and jittery, sometimes at an astonishingly high rate. Clearly there has to be ways to mitigate the errors generated by such adverse conditions. ## The Network Time Protocol The ubiquitous solution to time synchronization on computer networks is the Network Time Protocol. It allows to synchronize clocks to a common reference (usually Coordinated Universal Time) with an accuracy of a few milliseconds over the Internet, and can typically provide sub-millisecond accuracy on Local Area Networks. NTP was pioneered by Pr. David Mills, [whose webpage](https://www.eecis.udel.edu/~mills/) is a treasure trove of informations about time synchronization. The protocol was described in various RFCs, from its first version [(RFC1059)](https://datatracker.ietf.org/doc/html/rfc1059) to the current fourth [RFC5905](https://datatracker.ietf.org/doc/html/rfc5905). Other clock synchronization protocols exist, e.g. PTP (IEEE 1588-2019), and some implementations of NTP such as [Chrony](https://chrony.tuxfamily.org) include different error mitigation techniques than those described by the specification. I will focus here on NTP since it's the most documented and widely used, and it doesn't require specialized hardware like PTP. ## The NTP Network To maintain a consistent notion of time accross the internet, you first need some reference time signal, which is typically provided by atomic clocks. Since it is neiter practical nor desirable to connect every computer in the world to these atomic clocks, the time signal is distributed accross a network of peers organized in serveral strata. Primary servers sit at stratum 1 and are directly connected (through wire or radio) to a reference clock. Peers at strata 2 can synchronize on servers at strata 1 or 2, and act as a synchronization sources for peers at strata 3. The layering continues up to stratum 15. Strata 16 represents unsynchronized devices.  The protocol selects sources in order to avoid loops and minimize the round-trip delay to a primary server. As such peers collaborate to automatically reorganize the network to produce the most accurate time, even in the presence of failures in the network. ## NTP Architecture Now let's see the implementation of one node of the network. The following diagram shows the various stages of the pipeline used to collect time information and mitigate errors caused by network delays and clock inaccuracies. I'll explain each one in a short paragraph and give links to the relevant parts of the RFC, and to other references if you want to dig deeper.  ### On-Wire Protocol The first stage consists of getting time estimates from each peer. In the simplest mode of operations, the node polls a peer by sending a request packet timestamped with the transmission time, $t_1$. Upon reception of the request, the peer stores a timestamp $t_2$, processes the message, and sends a response packet containing $t_1$, $t_2$ and the response transmission time $t_3$. The node receives the response at time $t_4$.  The node then compute the tuple $(\delta, \theta, \epsilon)$, where: - $\delta$ is the round-trip delay. - $\theta$ is the estimated offset of the server clock with respect to the local clock. - $\varepsilon$ is the dispersion of the sample, i.e. the maximum error due to the frequency tolerances $\varphi_p$ and $\varphi_c$ of the peer's clock and of the client's clock, and the time elapsed since the request was sent. $\begin{align*} \delta = (t_4 - t_1) - (t_3 - t_2) \, ,\qquad \theta = ((t_2 - t_1) + (t_3 - t_4))/2 \, ,\qquad \varepsilon = \varphi_p \times \varphi_c \times \delta\,. \end{align*}$ Note that peers also transmit the delay and dispersion statistics accumulated at each stratum from the root down to the peer, yielding the root delay and dispersion, $\theta_r$ and $\varepsilon_r$. These statistics are used to assess the "quality" of the samples computed from each peer. Simple NTP clients that are only synchronized to one server, that don't act as a source for other peers, and that don't need a high precision, can implement only the on-wire protocol and directly use $\theta$ to correct their local clock. However this estimate is vulnerable to network jitter, delay asymetry, clock drift and wander. To get better precision, the samples produced by the on-wire protocol must be processed by a number of mitigation algorithms. Links: [Mills, Analysis and Simulation of the NTP On-Wire Protocols](https://www.eecis.udel.edu/~mills/onwire.html), [RFC5905 - section 8](https://datatracker.ietf.org/doc/html/rfc5905#section-8), [SNTP (RFC4330)](https://datatracker.ietf.org/doc/html/rfc4330) ### Clock Filter The clock filter is a shift register containing the last 8 samples produced by the on-wire protocol. The filter algorithm select the sample with maximum expected accuracy. It is based on the observations that: * The samples with the low network delay were likely to exhibit a low error at the time they were produced. * Older samples carry more accuracy than newer ones due to clock drift. As a new sample is pushed to the register, it evicts the oldest sample. The dispersion values of the other samples are the incremented by $\varphi_c\times\Delta_t$, where $\Delta_t$ is the time elapsed since the last update from the server. A distance metric $\lambda_i$ is affected to each sample: $\lambda_i = \frac{\delta_i}{2}+\varepsilon_i \,.$ The samples are then sorted in a temporary list by increasing value of $\lambda_i$. The list is pruned to leave only samples whose dispersion is less than a given maximum. The first sample in the list is chosen as the new best candidate, likely to give the most accurate estimate of the time offset $\theta$. However it is only used if it is not older than the last selected sample. The peer's dispersion $\varepsilon_p$ is computed as an exponentially weighted average of the sorted samples' dispersions: $\varepsilon_p = \sum_{i=0}^{N-1}\frac{\varepsilon_i}{2^{(i+1)}} \,.$ The server's jitter $\psi_p$ is computed as the root mean square (RMS) of the offsets differences with respect to the offset of the first sample's in the list: $\psi_p = \frac{1}{n-1}\sqrt{\sum_{i=0}^{N-1}(\theta_0-\theta_i)^2} \,.$ Links: [Mills, Clock Filter Algorithm](https://www.eecis.udel.edu/~mills/ntp/html/filter.html), [RFC5905 - section 10](https://datatracker.ietf.org/doc/html/rfc5905#section-10) ### Clock Selection The estimates we get from the clock filters of each peer can be in contradiction, either because of network perturbation or because some peers are faulty (or malicious!). The clock selection algorithm tries find a majority group of peers with consistent time estimates (the "truechimers"), and eliminates the other peers (the "falsetickers"). The algorithm is based on the observation that for a non-faulty peer, the time offset error at the time of measurement is bounded by half the round-trip delay to the reference clock. This bound then increases with the age of the sample, due to the accumulated dispersion. The true offset thus lies in the correctness interval $[\theta - \lambda_r, \theta + \lambda_r]$ ($\lambda_r$ being the accumulated distance to the root). Two peers whose correctness intervals do not intersect can not possibly agree on the time, and one of them must be wrong. The algorithm tries to find the biggest majority of candidates whose correctness intervals share a common intersection, and discards the other candidates. Links: [Mills, Clock Select Algorithm](https://www.eecis.udel.edu/~mills/ntp/html/select.html), [RFC5905 - section 11.2.1](https://datatracker.ietf.org/doc/html/rfc5905#section-11.2.1), [Marzullo and Owicki, 1983](https://dl.acm.org/doi/pdf/10.1145/800221.806730) ### Cluster Algorithm Once falsetickers have been eliminated, truechimers are placed in a survivor list, that is pruned by the cluster algorithm in a series of rounds. For each candidate, it compute the selection jitter, which is the root mean square of offset differences between this candidate and all other peers. Candidates are ranked by their selection jitter and the candidate with the greatest one is pruned from the survivor list. The cluster algorithm continues until a specified minimum of survivors remain, or until the maximum selection jitter is less than the minimum peer jitter (in which case removing the outlier wouldn't improve the accuracy of the selection). To get some grasp of _why_ it is designed that way, imagine all samples are coming from the same "idealized" peer, and that we select one "most likely accurate" sample. Then as we already saw in the clock filter algorithm, we can compute the jitter of that idealized peer. The selection jitter is essentially a measure of the jitter implied by the decision to consider that sample the most accurate. Now to understand the termination condition, remember that each sample is produced by a peer that itself exhibits some jitter. There is no point in trying to get a better jitter from the combination of all samples, than the minimum peer jitter. Links: [Mills, Cluster Algorithm](https://www.eecis.udel.edu/~mills/ntp/html/cluster.html), [RFC5905 - section 11.2.2](https://datatracker.ietf.org/doc/html/rfc5905#section-11.2.2) ### Combine The combined offset and jitter are computed as an average of the survivor's offsets and jitters, weighted by the inverse of the root server's distance. ### Clock Discipline The combined estimates are passed to the clock discipline algorithm which implements a feedback control loop, whose role is to direct the local system clock towards the reference clock. At its core the clock discipline consists of the non linear combination of a phase locked loop (PLL) and a frequency locked loop (FLL). It results in a frequency correction and a phase correction. The discipline is further enhanced by a state machine that is designed to adapt the polling interval, and the relative contribution of the PLL and FLL, in order to allow fast initial convergence and high stability in steady state. It also handles special situations such as bursts of high latency and jitter caused by temporarily degraded network conditions. Links: [Mills, Clock Discipline Algorithm](https://www.eecis.udel.edu/~mills/ntp/html/discipline.html), [Mills, Clock State Machine](https://www.eecis.udel.edu/~mills/ntp/html/clock.html), [Mills, Clock Displine Principles](https://www.eecis.udel.edu/~mills/database/brief/clock/clock.pdf), [RFC5905 - section 11.3](https://datatracker.ietf.org/doc/html/rfc5905#section-11.3) ### Clock Adjust The clock adjust process is called every second to adjust the system clock. It sums the frequency correction and a percentage of the offset correction to produce an adjustment value. The residual offset correction then replaces the offset correction. Thus, the offset correction decays exponentially over time. When the time since the last poll exceeds the poll interval, the clock adjust process triggers a new poll. It is worth noting that because it is crucially important to preserve a monotony property, the system clock is never actually stepped back or forth: instead, the system usually throttles the clock up or down until the desired correction has been achieved. Links: [RFC5905 - section 12](https://datatracker.ietf.org/doc/html/rfc5905#section-12) And this concludes our tour of NTP! # How long things take: durations Computer clocks --- TODO: - Style check: - em dashes - "Earth" and "Sun" are always capitalized - "time zone" is two words - "daylight saving time", not "daylight savings time" --- EVERYTHING BELOW HERE IS OUR INITIAL BRAINSTORM This will be our article three. Ben will get to this when he has time, unless someone else wants to jump in and lead the content of this. - Timezones - They are not always on the hour - Difference time offset and timezone - (locale stuff, formatting, DST transition dates, etc.) - Daylight savings - Days can be 23 or 25 hours long - Countries change their DST rules all the time - Dates, times, datetimes - Maybe you don't actually want to store full timestamps for literally everything - Time math is tricky - Adding 24 hours != adding one day (leap days / seconds) - Calendars - Historical calendars are very weird (kings just removing or adding days when they felt like it) - The calendar we use, and its extensions: Gregorian calendar, proleptic Gregorian calendar - Other calendars: Jewish calendar, Chinese lunar calendar (?), Hijiri, Japanese calendar (?) - Primarily used for establishing holidays, but not really for common use any more (with the exception of China...?) - Computer clocks - CPU time vs. wall time - Monotonic clocks - Two kinds on Linux: one that smears forward, one that does not - Jiffies - Atomic clocks - NTP / chrony - Useful specs: - RFC3339: https://datatracker.ietf.org/doc/html/rfc3339 - iCal: https://icalendar.org/RFC-Specifications/iCalendar-RFC-5545/ - Recurrence rules (RRULE): https://icalendar.org/iCalendar-RFC-5545/3-8-5-3-recurrence-rule.html - NOBODY USES ISO8601 STOP SAYING THAT THEY DO - NO ONE KNOWS WHAT IT IS - RFC3339 IS THE ONLY ONE ANYONE SHOULD USE - Accuracy of onboard clocks - Quartz oscillators - subject to drift - How to correct inaccurate clocks - Time smearing - Presentation and formatting? - The UNIX epoch, and the year 2038 problem - ISO "week date" (does this matter to anyone) - Falsehoods I think are actually important - "Always store time in UTC" - "Always store fully-qualified timestamps" i.e. datetimes with timezone, not just dates - "The smallest unit of time is X" (i.e. store the start and end of your time ranges precisely, never store 11:59:59) - Other advice - If anyone ever tells you to "store things for a month", clarify whether you need an actual calendar month or simply a 30-day period. You get a time you trust - then you work with it in some way (???) - https://infiniteundo.com/post/25326999628/falsehoods-programmers-believe-about-time - https://engineering.fb.com/2021/08/11/open-source/time-appliance/ - https://github.com/opencomputeproject/Time-Appliance-Project/tree/master/Open-Time-Server/ - https://lettier.github.io/posts/2016-04-26-lets-make-a-ntp-client-in-c.html - https://docs.ntpsec.org/latest/leapsmear.html - https://aws.amazon.com/blogs/aws/look-before-you-leap-the-coming-leap-second-and-aws/ - https://sudonull.com/post/29903-Writing-a-Simple-NTP-Client - https://www.oreilly.com/library/view/linux-device-drivers/9781785280009/4041820a-bbe4-4502-8ef9-d1913e133332.xhtml - https://www.youtube.com/watch?v=-5wpm-gesOY - Official timezone database: https://www.iana.org/time-zones - Lots of excellent information and links here: https://data.iana.org/time-zones/tz-link.html - https://data.iana.org/time-zones/tz-how-to.html - "When Alaska was purchased from Russia in 1867, the Date Line moved from the Alaska/Canada border to the Bering Strait; and the time in Alaska was then 24 hours earlier than it had been. " ## How to use dates and times ## Time accuracy / how to get accurate times ## Fun tangents East Asian countries treat birthdays differently: https://en.wikipedia.org/wiki/East_Asian_age_reckoning. In particular, Koreans (and others??) all celebrate their birthday on January 1, and start counting at 1 instead of 0.