Crate hifitime

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Introduction to Hifitime

Hifitime is a powerful Rust and Python library designed for time management. It provides extensive functionalities with precise operations for time calculation in different time scales, making it suitable for engineering and scientific applications where general relativity and time dilation matter. Hifitime guarantees nanosecond precision for 65,536 years around 01 January 1900 TAI. Hifitime is also formally verified using the Kani model checker, read more about it this verification here.

Most users of Hifitime will only need to rely on the Epoch and Duration structures, and optionally the Weekday enum for week based computations. Scientific applications may make use of the TimeScale enum as well.


First, install hifitime either with cargo add hifitime in your Rust project or pip install hifitime in Python.

If building from source, note that the Python package is only built if the python feature is enabled.

Epoch (“datetime” equivalent)

Create an epoch in different time scales.

use hifitime::prelude::*;
use core::str::FromStr;
// Create an epoch in UTC
let epoch = Epoch::from_gregorian_utc(2000, 2, 29, 14, 57, 29, 37);
// Or from a string
let epoch_from_str = Epoch::from_str("2000-02-29T14:57:29.000000037 UTC").unwrap();
assert_eq!(epoch, epoch_from_str);
// Creating it from TAI will effectively show the number of leap seconds in between UTC an TAI at that epoch
let epoch_tai = Epoch::from_gregorian_tai(2000, 2, 29, 14, 57, 29, 37);
// The difference between two epochs is a Duration
let num_leap_s = epoch - epoch_tai;
assert_eq!(format!("{num_leap_s}"), "32 s");

// Trivially convert to another time scale
// Either by grabbing a subdivision of time in that time scale
assert_eq!(epoch.to_gpst_days(), 7359.623402777777); // Compare to the GPS time scale

// Or by fetching the exact duration
let mjd_offset = Duration::from_str("51603 days 14 h 58 min 33 s 184 ms 37 ns").unwrap();
assert_eq!(epoch.to_mjd_tt_duration(), mjd_offset); // Compare to the modified Julian days in the Terrestrial Time time scale.

In Python:

>>> from hifitime import *
>>> epoch = Epoch("2000-02-29T14:57:29.000000037 UTC")
>>> epoch
2000-02-29T14:57:29.000000037 UTC
>>> epoch_tai = Epoch.init_from_gregorian_tai(2000, 2, 29, 14, 57, 29, 37)
>>> epoch_tai
2000-02-29T14:57:29.000000037 TAI
>>> epoch.timedelta(epoch_tai)
32 s
>>> epoch.to_gpst_days()
>>> epoch.to_mjd_tt_duration()
51603 days 14 h 58 min 33 s 184 ms 37 ns

Hifitime provides several date time formats like RFC2822, ISO8601, or RFC3339.

use hifitime::efmt::consts::{ISO8601, RFC2822, RFC3339};
use hifitime::prelude::*;

let epoch = Epoch::from_gregorian_utc(2000, 2, 29, 14, 57, 29, 37);
// The default Display shows the UTC time scale
assert_eq!(format!("{epoch}"), "2000-02-29T14:57:29.000000037 UTC");
// Format it in RFC 2822
let fmt = Formatter::new(epoch, RFC2822);
assert_eq!(format!("{fmt}"), format!("Tue, 29 Feb 2000 14:57:29"));

// Or in ISO8601
let fmt = Formatter::new(epoch, ISO8601);
    format!("2000-02-29T14:57:29.000000037 UTC")

// Which is somewhat similar to RFC3339
let fmt = Formatter::new(epoch, RFC3339);

Need some custom format? Hifitime also supports the C89 token, cf. the documentation.

use core::str::FromStr;
use hifitime::prelude::*;

let epoch = Epoch::from_gregorian_utc_hms(2015, 2, 7, 11, 22, 33);

// Parsing with a custom format
    Epoch::from_format_str("Sat, 07 Feb 2015 11:22:33", "%a, %d %b %Y %H:%M:%S").unwrap(),

// And printing with a custom format
let fmt = Format::from_str("%a, %d %b %Y %H:%M:%S").unwrap();
    format!("{}", Formatter::new(epoch, fmt)),
    "Sat, 07 Feb 2015 11:22:33"

You can also grab the current system time in UTC, if the std feature is enabled (default), and find the next or previous day of the week.

use hifitime::prelude::*;

#[cfg(feature = "std")]
    let now = Epoch::now().unwrap();
    println!("{}", now.previous(Weekday::Sunday));

Oftentimes, we’ll want to query something at a fixed step between two epochs. Hifitime makes this trivial with TimeSeries.

use hifitime::prelude::*;

let start = Epoch::from_gregorian_utc_at_midnight(2017, 1, 14);
let end = start + 12.hours();
let step = 2.hours();

let time_series = TimeSeries::inclusive(start, end, step);
let mut cnt = 0;
for epoch in time_series {
    #[cfg(feature = "std")]
    println!("{}", epoch);
    cnt += 1
// Check that there are indeed seven two-hour periods in a half a day,
// including start and end times.
assert_eq!(cnt, 7)

In Python:

>>> from hifitime import *
>>> start = Epoch.init_from_gregorian_utc_at_midnight(2017, 1, 14)
>>> end = start + Unit.Hour*12
>>> iterator = TimeSeries(start, end, step=Unit.Hour*2, inclusive=True)
>>> for epoch in iterator:
...     print(epoch)
2017-01-14T00:00:00 UTC
2017-01-14T02:00:00 UTC
2017-01-14T04:00:00 UTC
2017-01-14T06:00:00 UTC
2017-01-14T08:00:00 UTC
2017-01-14T10:00:00 UTC
2017-01-14T12:00:00 UTC


use hifitime::prelude::*;
use core::str::FromStr;

// Create a duration using the `TimeUnits` helping trait.
let d = 5.minutes() + 7.minutes() + 35.nanoseconds();
assert_eq!(format!("{d}"), "12 min 35 ns");

// Or using the built-in enums
let d_enum = 12 * Unit::Minute + 35.0 * Unit::Nanosecond;

// But it can also be created from a string
let d_from_str = Duration::from_str("12 min 35 ns").unwrap();
assert_eq!(d, d_from_str);

Hifitime guarantees nanosecond precision, but most human applications don’t care too much about that. Durations can be rounded to provide a useful approximation for humans.

use hifitime::prelude::*;

// Create a duration using the `TimeUnits` helping trait.
let d = 5.minutes() + 7.minutes() + 35.nanoseconds();
// Round to the nearest minute
let rounded = d.round(1.minutes());
assert_eq!(format!("{rounded}"), "12 min");

// And this works on Epochs as well.
let previous_post = Epoch::from_gregorian_utc_hms(2015, 2, 7, 11, 22, 33);
let example_now = Epoch::from_gregorian_utc_hms(2015, 8, 17, 22, 55, 01);

// We'll round to the nearest fifteen days
let this_much_ago = example_now - previous_post;
assert_eq!(format!("{this_much_ago}"), "191 days 11 h 32 min 29 s");
let about_this_much_ago_floor = this_much_ago.floor(15.days());
assert_eq!(format!("{about_this_much_ago_floor}"), "180 days");
let about_this_much_ago_ceil = this_much_ago.ceil(15.days());
assert_eq!(format!("{about_this_much_ago_ceil}"), "195 days");

In Python:

>>> from hifitime import *
>>> d = Duration("12 min 32 ns")
>>> d.round(Unit.Minute*1)
12 min
>>> d
12 min 32 ns

hifitime on hifitime on minimum rustc: 1.70 Build Status Build Status codecov

Comparison with time and chrono

First off, both time and chrono are fantastic libraries in their own right. There’s a reason why they have millions and millions of downloads. Secondly, hifitime was started in October 2017, so quite a while before the revival of time (~ 2019).

One of the key differences is that both chrono and time separate the concepts of “time” and “date.” Hifitime asserts that this is physically invalid: both a time and a date are an offset from a reference in a given time scale. That’s why, Hifitime does not separate the components that make up a date, but instead, only stores a fixed duration with respect to TAI. Moreover, Hifitime is formally verified with a model checker, which is much more thorough than property testing.

More importantly, neither time nor chrono are suitable for astronomy, astrodynamics, or any physics that must account for time dilation due to relativistic speeds or lack of the Earth as a gravity source (which sets the “tick” of a second).

Hifitime also natively supports the UT1 time scale (the only “true” time) if built with the ut1 feature.


  • Initialize a high precision Epoch from the system time in UTC
  • Leap seconds (as announced by the IETF on a yearly basis)
  • UTC representation with ISO8601 and RFC3339 formatting and blazing fast parsing (45 nanoseconds)
  • Trivial support of time arithmetic: addition (e.g. 2.hours() + 3.seconds()), subtraction (e.g. 2.hours() - 3.seconds()), round/floor/ceil operations (e.g. 2.hours().round(3.seconds()))
  • Supports ranges of Epochs and TimeSeries (linspace of Epochs and Durations)
  • Trivial conversion between many time scales
  • High fidelity Ephemeris Time / Dynamic Barycentric Time (TDB) computations from ESA’s Navipedia
  • Julian dates and Modified Julian dates
  • Embedded device friendly: no-std and const fn where possible

This library is validated against NASA/NAIF SPICE for the Ephemeris Time to Universal Coordinated Time computations: there are exactly zero nanoseconds of difference between SPICE and hifitime for the computation of ET and UTC after 01 January 1972. Refer to the leap second section for details. Other examples are validated with external references, as detailed on a test-by-test basis.

Supported time scales

  • Temps Atomique International (TAI)
  • Universal Coordinated Time (UTC)
  • Terrestrial Time (TT)
  • Ephemeris Time (ET) without the small perturbations as per NASA/NAIF SPICE leap seconds kernel
  • Dynamic Barycentric Time (TDB), a higher fidelity ephemeris time
  • Global Positioning System (GPST)
  • Galileo System Time (GST)
  • BeiDou Time (BDT)
  • UNIX


  • Time-agnostic / date-only epochs. Hifitime only supports the combination of date and time, but the Epoch::{at_midnight, at_noon} is provided as helper functions.


No software is perfect, so please report any issue or bug on Github.


Under the hood, a Duration is represented as a 16 bit signed integer of centuries (i16) and a 64 bit unsigned integer (u64) of the nanoseconds past that century. The overflowing and underflowing of nanoseconds is handled by changing the number of centuries such that the nanoseconds number never represents more than one century (just over four centuries can be stored in 64 bits).


  1. Exact precision of a duration: using a floating point value would cause large durations (e.g. Julian Dates) to have less precision than smaller durations. Durations in hifitime have exactly one nanosecond of precision for 65,536 years.
  2. Skipping floating point operations allows this library to be used in embedded devices without a floating point unit.
  3. Duration arithmetics are exact, e.g. one third of an hour is exactly twenty minutes and not “0.33333 hours.”


  1. Most astrodynamics applications require the computation of a duration in floating point values such as when querying an ephemeris. This design leads to an overhead of about 5.2 nanoseconds according to the benchmarks (Duration to f64 seconds benchmark). You may run the benchmarks with cargo bench.


The Epoch is simply a wrapper around a Duration. All epochs are stored in TAI duration with respect to 01 January 1900 at noon (the official TAI epoch). The choice of TAI meets the Standard of Fundamental Astronomy (SOFA) recommendation of opting for a glitch-free time scale (i.e. without discontinuities like leap seconds or non-uniform seconds like TDB).

Printing and parsing

Epochs can be formatted and parsed in the following time scales:

  • UTC: {epoch}
  • TAI: {epoch:x}
  • TT: {epoch:X}
  • TDB: {epoch:e}
  • ET: {epoch:E}
  • UNIX: {epoch:p}
  • GPS: {epoch:o}

Leap second support

Leap seconds allow TAI (the absolute time reference) and UTC (the civil time reference) to not drift too much. In short, UTC allows humans to see the sun at zenith at noon, whereas TAI does not worry about that. Leap seconds are introduced to allow for UTC to catch up with the absolute time reference of TAI. Specifically, UTC clocks are “stopped” for one second to make up for the accumulated difference between TAI and UTC. These leap seconds are announced several months in advance by IERS, cf. in the IETF leap second reference.

The “placement” of these leap seconds in the formatting of a UTC date is left up to the software: there is no common way to handle this. Some software prevents a second tick, i.e. at 23:59:59 the UTC clock will tick for two seconds (instead of one) before hoping to 00:00:00. Some software, like hifitime, allow UTC dates to be formatted as 23:59:60 on strictly the days when a leap second is inserted. For example, the date 2016-12-31 23:59:60 UTC is a valid date in hifitime because a leap second was inserted on 01 Jan 2017.


Prior to the first leap second, NAIF SPICE claims that there were nine seconds of difference between TAI and UTC: this is different from the Standard of Fundamental Astronomy (SOFA). SOFA’s iauDat function will return non-integer leap seconds from 1960 to 1972. It will return an error for dates prior to 1960. Hifitime only accounts for leap seconds announced by IERS in its computations: there is a ten (10) second jump between TAI and UTC on 01 January 1972. This allows the computation of UNIX time to be a specific offset of TAI in hifitime. However, the prehistoric (pre-1972) leap seconds as returned by SOFA are available in the leap_seconds() method of an epoch if the iers_only parameter is set to false.

Ephemeris Time vs Dynamic Barycentric Time (TDB)

In theory, as of January 2000, ET and TDB should now be identical. However, the NASA NAIF leap seconds files (e.g. naif00012.tls) use a simplified algorithm to compute the TDB:

Equation [4], which ignores small-period fluctuations, is accurate to about 0.000030 seconds.

In order to provide full interoperability with NAIF, hifitime uses the NAIF algorithm for “ephemeris time” and the ESA algorithm for “dynamical barycentric time.” Hence, if exact NAIF behavior is needed, use all of the functions marked as et instead of the tdb functions, such as epoch.to_et_seconds() instead of epoch.to_tdb_seconds().


3.9.0 (WIP)

  • Update to der version 0.7.x.
  • Introduce %y formatter by @gwbres in
  • Possible breaking change: Fix day of year computation by @ChristopherRabotin in


Changes from 3.8.2 are only dependency upgrades until this release.

Minimum Supported Rust version bumped from 1.64 to 1.70.


  • Clarify README and add a section comparing Hifitime to time and chrono, cf. #221
  • Fix incorrect printing of Gregorian dates prior to to 1900, cf. #204

3.8.1 (unreleased)

  • Fix documentation for the formatter, cf. #202
  • Update MSRV to 1.59 for rayon v 1.10


Thanks again to @gwbres for his work in this release!

  • Fix CI of the formal verification and upload artifacts, cf. #179
  • Introduce time of week construction and conversion by @gwbres, cf.#180 and #188
  • Fix minor typo in src/ by @gwbres, cf. #189
  • Significantly extend formal verification of Duration and Epoch, and introduce kani::Arbitrary to Duration and Epoch for users to formally verify their use of time, cf. #192
  • It is now possible to specify a Leap Seconds file (in IERS format) using the LeapSecondsFile::from_path (requires the std feature to read the file), cf. #43.
  • UT1 time scale is now supported! You must build a Ut1Provider structure with data from the JPL Earth Orientation Parameters, or just use Ut1Provider::download_short_from_jpl() to automatically download the data from NASA JPL.
  • strptime and strftime equivalents from C89 are now supported, cf. #181. Please refer to the documentation for important limitations and how to build a custom formatter.
  • ISO Day of Year and Day In Year are now supported for initialization of an Epoch (provided a time scale and a year), and formatting, cf. #182.
  • Python: the representation of an epoch is now in the time scale it was initialized in


Huge thanks to @gwbres who put in all of the work for this release. These usability changes allow Rinex to use hifitime, check out this work.

  • derive serdes traits when feasible by @gwbres in
  • introduce format/display by @gwbres in
  • readme: fix BeiDou typo by @gwbres in
  • epoch: derive Hash by @gwbres in
  • timescale: identify GNSS timescales from standard 3 letter codes by @gwbres in
  • timescale: standard formatting is now available by @gwbres in
  • epoch, duration: improve and fix serdes feature by @gwbres in
  • epoch, timescale: implement default trait by @gwbres in


  • Galileo System Time and BeiDou Time are now supported, huge thanks to @gwbres for all that work!
  • Significant speed improvement in the initialization of Epochs from their Gregorian representation, thanks @conradludgate for #160.
  • Epoch and Duration now have a min and max function which respectively returns a copy of the epoch/duration that is the smallest or the largest between self and other, cf. #164.
  • [Python] Duration and Epochs now support the operators >, >=, <, <=, ==, and !=. Epoch now supports init_from_gregorian with a time scape, like in Rust. Epochs can also be subtracted from one another using the timedelta function, cf. #162.
  • TimeSeries can now be formatted in different time scales, cf. #163


  • Epoch now store the time scale that they were defined in: this allows durations to be added in their respective time scales. For example, adding 36 hours to 1971-12-31 at noon when the Epoch is initialized in UTC will lead to a different epoch than adding that same duration to an epoch initialized at the same time in TAI (because the first leap second announced by IERS was on 1972-01-01), cf. the test_add_durations_over_leap_seconds test.
  • RFC3339 and ISO8601 fully supported for initialization of an Epoch, including the offset, e.g. Epoch::from_str("1994-11-05T08:15:30-05:00"), cf. #73.
  • Python package available on PyPI! To build the Python package, you must first install maturin and then build with the python feature flag. For example, maturin develop -F python && python will build the Python package in debug mode and start a new shell where the package can be imported.
  • Fix bug when printing Duration::MIN (or any duration whose centuries are minimizing the number of centuries).
  • TimeSeries can now be formatted
  • Epoch can now be ceil-ed, floor-ed, and round-ed according to the time scale they were initialized in, cf. #145.
  • Epoch can now be initialized from Gregorian when specifying the time system: from_gregorian, from_gregorian_hms, from_gregorian_at_noon, from_gregorian_at_midnight.
  • Fix bug in Duration when performing operations on durations very close to Duration::MIN (i.e. minus thirty-two centuries).
  • Duration parsing now supports multiple units in a string and does not use regular expressions. THis allows it to work with no-std.
  • Epoch parsing no longer requires regex.
  • Functions are not more idiomatic: all of the as_* functions become to_* and in_* also becomes to_*, cf. #155.


  • Ephemeris Time and Dynamical Barycentric Time fixed to use the J2000 reference epoch instead of the J1900 reference epoch. This is a potentially breaking change if you relied on the previous one century error when converting from/to ET/TDB into/from UTC and storing the data as a string. There is no difference if the original representation was used.
  • Ephemeris Time now strictly matches NAIF SPICE: the error between SPICE and hifitime is now zero nanoseconds. after the introduction of the first leap second. Prior to the first leap second, NAIF SPICE claims that there were nine seconds of difference between TAI and UTC: this is different from SOFA. Hifitime instead does not account for leap seconds in prehistoric (pre-1972) computations at all.
  • The Standard of Fundamentals of Astronomy (SOFA) leap seconds from 1960 to 1972 are now available with the leap_seconds() -> Option<f64> function on an instance of Epoch. Importantly, no difference in the behavior of hifitime should be noticed here: the prehistoric leap seconds are ignored in all calculations in hifitime and only provided to meet the SOFA calculations.
  • Epoch and Duration now have the C memory representation to allow for hifitime to be embedded in C more easily.
  • Epoch and Duration can now be encoded or decoded as ASN1 DER with the asn1der crate feature (disabled by default).


  • Formal verification of the normalization operation on Duration, which in turn guarantees that Epoch operations cannot panic, cf. #127
  • Fix len and size_hint for TimeSeries, cf. #131, reported by @d3v-null, thanks for the find!
  • Epoch now implements Eq and Ord, cf. #133, thanks @mkolopanis for the PR!
  • Epoch can now be printed in different time systems with format modifiers, cf. #130
  • (minor) as_utc_duration in Epoch is now public, cf. #129
  • (minor) The whole crate now uses num-traits thereby skipping the explicit use of libm. Basically, operations on f64 look like normal Rust again, cf. #128
  • (minor) Move the tests to their own folder to make it obvious that this is thoroughly tested


  • Fix no-std implementation by using libm for non-core f64 operations
  • Add UNIX timestamp, thanks @mkolopanis
  • Enums now derive Eq and some derive Ord (where relevant) #118
  • Use const fn where possible and switch to references where possible #119
  • Allow extracting the centuries and nanoseconds of a Duration and Epoch, respectively with to_parts and to_tai_parts #122
  • Add ceil, floor, round operations to Epoch and Duration


  • Add #![no_std] support
  • Add to_parts to Duration to extract the centuries and nanoseconds of a duration
  • Allow building an Epoch from its duration and parts in TAI system
  • Add pure nanosecond (u64) constructor and getter for GPST since GPS based clocks will count in nanoseconds

Possibly breaking change

  • Errors::ParseError no longer contains a String but an enum ParsingErrors instead. This is considered possibly breaking because it would only break code in the cases where a datetime parsing or unit parsing was caught and handled (uncommon). Moreover, the output is still Display-able.


  • Backend rewritten from TwoFloat to a struct of the centuries in i16 and nanoseconds in u64. Thanks to @pwnorbitals for proposing the idea in #107 and writing the proof of concept. This leads to at least a 2x speed up in most calculations, cf. this comment.
  • Fix GPS epoch, and addition of a helper functions in Epoch by @cjordan

Important Update on Versioning Strategy

We want to inform our users of an important change in Hifitime’s versioning approach. Starting with version 3.9.0, minor version updates may include changes that could potentially break backward compatibility. While we strive to maintain stability and minimize disruptions, this change allows us to incorporate significant improvements and adapt more swiftly to evolving user needs. We recommend users to carefully review the release notes for each update, even minor ones, to understand any potential impacts on their existing implementations. Our commitment to providing a robust and dynamic time management library remains steadfast, and we believe this change in versioning will better serve the evolving demands of our community.




  • Defines generally usable durations for nanosecond precision valid for 32,768 centuries in either direction, and only on 80 bits / 10 octets.
  • Defines a nanosecond-precision Epoch.
  • An iterator of a sequence of evenly spaced Epochs.


  • An Enum to convert frequencies to their approximate duration, rounded to the closest nanosecond.
  • Enum of the different time systems available
  • An Enum to perform time unit conversions.



  • A trait to automatically convert some primitives to an approximate frequency as a duration, rounded to the closest nanosecond Does not support more than 1 GHz (because max precision of a duration is 1 nanosecond)
  • A trait to automatically convert some primitives to a duration


  • Returns true if the provided Gregorian date is valid. Leap second days may have 60 seconds.