### Table Of Contents

- A proposal for implementing some date/time types in NumPy
  - Executive summary
  - Types proposed
  - Time units
  - `datetime64`
    - Building a `datetime64` dtype
    - Setting and getting values
    - Comparisons
    - Compatibility issues
  - `timedelta64`
    - Building a `timedelta64` dtype
    - Setting and getting values
    - Comparisons
    - Compatibility issues
  - Examples of use
  - Operating with date/time arrays
    - `datetime64` vs `datetime64`
      - Casting rules
    - `datetime64` vs `timedelta64`
      - Casting rules
    - `timedelta64` vs `timedelta64`
      - Casting rules
  - dtype vs time units conversions
  - Necessary changes to NumPy
    - Addition of metadata to dtypes
    - Ufunc interface extension
    - Array Interface Extensions
  - Final considerations
    - Why the fractional time and events: [3Y/12]//50
    - Why the `origin` metadata disappeared
    - Operations with mixed time units

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A (third) proposal for implementing some date/time types in NumPy

# A proposal for implementing some date/time types in NumPy

Author: | Travis Oliphant
Contact: | oliphant@enthought.com
Date: | 2009-06-09

Revised only slightly from the third proposal by

Author: | Francesc Alted i Abad
Contact: | faltet@pytables.com
Author: | Ivan Vilata i Balaguer
Contact: | ivan@selidor.net
Date: | 2008-07-30

## Executive summary

A date/time mark is something very handy to have in many fields where one has to deal with data sets. While Python has several modules that define a date/time type (like the integrated `datetime` [1] or `mx.DateTime` [2]), NumPy has a lack of them.

We are proposing the addition of date/time types to fill this gap. The requirements for the proposed types are two-fold: 1) they have to be fast to operate with and 2) they have to be as compatible as possible with the existing `datetime` module that comes with Python.

## Types proposed

It is virtually impossible to come up with a single date/time type that fills the needs of every use case. As a result, we propose two general date-time types: 1) `timedelta64` – a relative time and 2) `datetime64` – an absolute time.

Each of these times are represented internally as 64-bit signed integers that refer to a particular unit (hour, minute, microsecond, etc.). There are several pre-defined units as well as the ability to create rational multiples of these units. A representation is also supported such that the stored date-time integer can encode both the number of a particular unit as well as a number of sequential events tracked for each unit.

The `datetime64` represents an absolute time. Internally it is represented as the number of time units between the intended time and the epoch (12:00am on January 1, 1970 — POSIX time including its lack of leap seconds).

## Time units

The 64-bit integer time can represent several different basic units as well as derived units. The basic units are listed in the following table:

Time unit | Time span | Time span (years)
--- | --- | ---
Code | Meaning | Relative Time | Absolute Time
Y | year | +- 9.2e18 years | [9.2e18 BC, 9.2e18 AD]
M | month | +- 7.6e17 years | [7.6e17 BC, 7.6e17 AD]
W | week | +- 1.7e17 years | [1.7e17 BC, 1.7e17 AD]
B | business day | +- 3.5e16 years | [3.5e16 BC, 3.5e16 AD]
D | day | +- 2.5e16 years | [2.5e16 BC, 2.5e16 AD]
h | hour | +- 1.0e15 years | [1.0e15 BC, 1.0e15 AD]
m | minute | +- 1.7e13 years | [1.7e13 BC, 1.7e13 AD]
s | second | +- 2.9e12 years | [ 2.9e9 BC, 2.9e9 AD]
ms | millisecond | +- 2.9e9 years | [ 2.9e6 BC, 2.9e6 AD]
us | microsecond | +- 2.9e6 years | [290301 BC, 294241 AD]
ns | nanosecond | +- 292 years | [ 1678 AD, 2262 AD]
ps | picosecond | +- 106 days | [ 1969 AD, 1970 AD]
fs | femtosecond | +- 2.6 hours | [ 1969 AD, 1970 AD]
as | attosecond | +- 9.2 seconds | [ 1969 AD, 1970 AD]

A time unit is specified by a string consisting of a base-type given in the above table

Besides these basic code units, the user can create derived units consisting of multiples of any basic unit: 100ns, 3M, 15m, etc.

A limited number of divisions of any basic unit can be used to create multiples of a higher-resolution unit provided the divisor can be divided evenly into the number of higher-resolution units available. For example: Y/4 is just short-hand for -> (12M)/4 -> 3M and Y/4 will be represented after creation as 3M. The first lower unit found to have an even divisor will be chosen (up to 3 lower units). The following standardized definitions are used in this specific case to find acceptable divisors

Code | Interpreted as
--- | ---
Y | 12M, 52W, 365D
M | 4W, 30D, 720h
W | 5B, 7D, 168h, 10080m
B | 24h, 1440m, 86400s
D | 24h, 1440m, 86400s
h | 60m, 3600s
m | 60s, 60000ms

s, ms, us, ns, ps, fs (use 1000 and 1000000 of the next two available lower units respectively).

Finally, a date-time data-type can be created with support for tracking sequential events within a basic unit: [D]//100, [Y]//4 (notice the required brackets). These `modulo` event units provide the following interpretation to the date-time integer:

> - the divisor is the number of events in each period
> - the (integer) quotient is the integer number representing the base units
> - the remainder is the particular event in the period.

Modulo event-units can be combined with any derived units, but brackets are required. Thus [100ns]//50 which allows recording 50 events for every 100ns so that 0 represents the first event in the first 100ns tick, 1 represents the second event in the first 100ns tick, while 50 represents the first event in the second 100ns tick, and 51 represents the second event in the second 100ns tick.

To fully specify a date-time type, the time unit string must be combined with either the string for a datetime64 (‘M8’) or a timedelta64 (‘m8’) using brackets ‘[]’. Therefore, a fully-specified string representing a date-time dtype is ‘M8[Y]’ or (for a more complicated example) ‘M8[7s/9]//5’.

If a time unit is not specified, then it defaults to [us]. Thus ‘M8’ is equivalent to ‘M8[us]’ (except when modulo event-units are desired – i.e. you cannot specify ‘M8[us]//5’ as ‘M8//5’ or as ‘//5’

## `datetime64`

This dtype represents a time that is absolute (i.e. not relative). It is implemented internally as an `int64` type. The integer represents units from the internal POSIX epoch (see [3]). Like POSIX, the representation of a date doesn’t take leap seconds into account.

In time unit conversions and time representations (but not in other time computations), the value -2**63 (0x8000000000000000) is interpreted as an invalid or unknown date, Not a Time or NaT. See the section on time unit conversions for more information.

The value of an absolute date is thus an integer number of units of the chosen time unit passed since the epoch. If the integer is a negative number, then the magnitude of the integer represents the number of units prior to the epoch. When working with business days, Saturdays and Sundays are simply ignored from the count (i.e. day 3 in business days is not Saturday 1970-01-03, but Monday 1970-01-05).

### Building a `datetime64` dtype

The proposed ways to specify the time unit in the dtype constructor are:

Using the long string notation:

    dtype('datetime64[us]')

Using the short string notation:

    dtype('M8[us]')

If a time unit is not specified, then it defaults to [us]. Thus ‘M8’ is equivalent to ‘M8[us]’.

### Setting and getting values

The objects with this dtype can be set in a series of ways:

    t = numpy.ones(3, dtype='M8[s]')
    t[0] = 1199164176    # assign to July 30th, 2008 at 17:31:00
    t[1] = datetime.datetime(2008, 7, 30, 17, 31, 01) # with datetime module
    t[2] = '2008-07-30T17:31:02'    # with ISO 8601

And can be get in different ways too:

    str(t[0])  -->  2008-07-30T17:31:00
    repr(t[1]) -->  datetime64(1199164177, 's')
    str(t[0].item()) --> 2008-07-30 17:31:00  # datetime module object
    repr(t[0].item()) --> datetime.datetime(2008, 7, 30, 17, 31)  # idem
    str(t)  -->  [2008-07-30T17:31:00  2008-07-30T17:31:01  2008-07-30T17:31:02]
    repr(t)  -->  array([1199164176, 1199164177, 1199164178],
                        dtype='datetime64[s]')

### Comparisons

The comparisons will be supported too:

    numpy.array(['1980'], 'M8[Y]') == numpy.array(['1979'], 'M8[Y]')
    --> [False]

including applying broadcasting:

    numpy.array(['1979', '1980'], 'M8[Y]') == numpy.datetime64('1980', 'Y')
    --> [False, True]

The following should also work:

    numpy.array(['1979', '1980'], 'M8[Y]') == '1980-01-01'
    --> [False, True]

because the right hand expression can be broadcasted into an array of 2 elements of dtype ‘M8[Y]’.

### Compatibility issues

This will be fully compatible with the `datetime` class of the `datetime` module of Python only when using a time unit of microseconds. For other time units, the conversion process will lose precision or will overflow as needed. The conversion from/to a `datetime` object doesn’t take leap seconds into account.

## `timedelta64`

It represents a time that is relative (i.e. not absolute). It is implemented internally as an `int64` type.

In time unit conversions and time representations (but not in other time computations), the value -2**63 (0x8000000000000000) is interpreted as an invalid or unknown time, Not a Time or NaT. See the section on time unit conversions for more information.

The value of a time delta is an integer number of units of the chosen time unit.

### Building a `timedelta64` dtype

The proposed ways to specify the time unit in the dtype constructor are:

Using the long string notation:

    dtype('timedelta64[us]')

Using the short string notation:

    dtype('m8[us]')

If a time unit is not specified, then a default of [us] is assumed. Thus ‘m8’ and ‘m8[us]’ are equivalent.

### Setting and getting values

The objects with this dtype can be set in a series of ways:

    t = numpy.ones(3, dtype='m8[ms]')
    t[0] = 12    # assign to 12 ms
    t[1] = datetime.timedelta(0, 0, 13000)   # 13 ms
    t[2] = '0:00:00.014'    # 14 ms

And can be get in different ways too:

    str(t[0])  -->  0:00:00.012
    repr(t[1]) -->  timedelta64(13, 'ms')
    str(t[0].item()) --> 0:00:00.012000   # datetime module object
    repr(t[0].item()) --> datetime.timedelta(0, 0, 12000)  # idem
    str(t)     -->  [0:00:00.012  0:00:00.014  0:00:00.014]
    repr(t)    -->  array([12, 13, 14], dtype="timedelta64[ms]")

### Comparisons

The comparisons will be supported too:

    numpy.array([12, 13, 14], 'm8[ms]') == numpy.array([12, 13, 13], 'm8[ms]')
    --> [True, True, False]

or by applying broadcasting:

    numpy.array([12, 13, 14], 'm8[ms]') == numpy.timedelta64(13, 'ms')
    --> [False, True, False]

The following should work too:

    numpy.array([12, 13, 14], 'm8[ms]') == '0:00:00.012'
    --> [True, False, False]

because the right hand expression can be broadcasted into an array of 3 elements of dtype ‘m8[ms]’.

### Compatibility issues

This will be fully compatible with the `timedelta` class of the `datetime` module of Python only when using a time unit of microseconds. For other units, the conversion process will lose precision or will overflow as needed.

## Examples of use

Here is an example of use for the `datetime64`:

    In [5]: numpy.datetime64(42, 'us')
    Out[5]: datetime64(42, 'us')

    In [6]: print numpy.datetime64(42, 'us')
    1970-01-01T00:00:00.000042  # representation in ISO 8601 format

    In [7]: print numpy.datetime64(367.7, 'D')  # decimal part is lost
    1971-01-02  # still ISO 8601 format

    In [8]: numpy.datetime('2008-07-18T12:23:18', 'm')  # from ISO 8601
    Out[8]: datetime64(20273063, 'm')

    In [9]: print numpy.datetime('2008-07-18T12:23:18', 'm')
    Out[9]: 2008-07-18T12:23

    In [10]: t = numpy.zeros(5, dtype="datetime64[ms]")

    In [11]: t[0] = datetime.datetime.now()  # setter in action

    In [12]: print t
    [2008-07-16T13:39:25.315  1970-01-01T00:00:00.000
     1970-01-01T00:00:00.000  1970-01-01T00:00:00.000
     1970-01-01T00:00:00.000]

    In [13]: repr(t)
    Out[13]: array([267859210457, 0, 0, 0, 0], dtype="datetime64[ms]")

    In [14]: t[0].item()     # getter in action
    Out[14]: datetime.datetime(2008, 7, 16, 13, 39, 25, 315000)

    In [15]: print t.dtype
    dtype('datetime64[ms]')

And here it goes an example of use for the `timedelta64`:

    In [5]: numpy.timedelta64(10, 'us')
    Out[5]: timedelta64(10, 'us')

    In [6]: print numpy.timedelta64(10, 'us')
    0:00:00.000010

    In [7]: print numpy.timedelta64(3600.2, 'm')  # decimal part is lost
    2 days, 12:00

    In [8]: t1 = numpy.zeros(5, dtype="datetime64[ms]")

    In [9]: t2 = numpy.ones(5, dtype="datetime64[ms]")

    In [10]: t = t2 - t1

    In [11]: t[0] = datetime.timedelta(0, 24)  # setter in action

    In [12]: print t
    [0:00:24.000  0:00:01.000  0:00:01.000  0:00:01.000  0:00:01.000]

    In [13]: print repr(t)
    Out[13]: array([24000, 1, 1, 1, 1], dtype="timedelta64[ms]")

    In [14]: t[0].item()     # getter in action
    Out[14]: datetime.timedelta(0, 24)

    In [15]: print t.dtype
    dtype('timedelta64[s]')

## Operating with date/time arrays

### `datetime64` vs `datetime64`

The only arithmetic operation allowed between absolute dates is subtraction:

    In [10]: numpy.ones(3, "M8[s]") - numpy.zeros(3, "M8[s]")
    Out[10]: array([1, 1, 1], dtype=timedelta64[s])

But not other operations:

    In [11]: numpy.ones(3, "M8[s]") + numpy.zeros(3, "M8[s]")
    TypeError: unsupported operand type(s) for +: 'numpy.ndarray' and 'numpy.ndarray'

Comparisons between absolute dates are allowed.

#### Casting rules

When operating (basically, only the subtraction will be allowed) two absolute times with different unit times, the outcome would be to raise an exception. This is because the ranges and time-spans of the different time units can be very different, and it is not clear at all what time unit will be preferred for the user. For example, this should be allowed:

    >>> numpy.ones(3, dtype="M8[Y]") - numpy.zeros(3, dtype="M8[Y]")
    array([1, 1, 1], dtype="timedelta64[Y]")

But the next should not:

    >>> numpy.ones(3, dtype="M8[Y]") - numpy.zeros(3, dtype="M8[ns]")
    raise numpy.IncompatibleUnitError  # what unit to choose?

### `datetime64` vs `timedelta64`

It will be possible to add and subtract relative times from absolute dates:

    In [10]: numpy.zeros(5, "M8[Y]") + numpy.ones(5, "m8[Y]")
    Out[10]: array([1971, 1971, 1971, 1971, 1971], dtype=datetime64[Y])

    In [11]: numpy.ones(5, "M8[Y]") - 2 * numpy.ones(5, "m8[Y]")
    Out[11]: array([1969, 1969, 1969, 1969, 1969], dtype=datetime64[Y])

But not other operations:

    In [12]: numpy.ones(5, "M8[Y]") * numpy.ones(5, "m8[Y]")
    TypeError: unsupported operand type(s) for *: 'numpy.ndarray' and 'numpy.ndarray'

#### Casting rules

In this case the absolute time should have priority for determining the time unit of the outcome. That would represent what the people wants to do most of the times. For example, this would allow to do:

    >>> series = numpy.array(['1970-01-01', '1970-02-01', '1970-09-01'],
    dtype='datetime64[D]')
    >>> series2 = series + numpy.timedelta(1, 'Y')  # Add 2 relative years
    >>> series2
    array(['1972-01-01', '1972-02-01', '1972-09-01'],
    dtype='datetime64[D]')  # the 'D'ay time unit has been chosen

### `timedelta64` vs `timedelta64`

Finally, it will be possible to operate with relative times as if they were regular int64 dtypes as long as the result can be converted back into a `timedelta64`:

    In [10]: numpy.ones(3, 'm8[us]')
    Out[10]: array([1, 1, 1], dtype="timedelta64[us]")

    In [11]: (numpy.ones(3, 'm8[M]') + 2) ** 3
    Out[11]: array([27, 27, 27], dtype="timedelta64[M]")

But:

    In [12]: numpy.ones(5, 'm8') + 1j
    TypeError: the result cannot be converted into a ``timedelta64``

#### Casting rules

When combining two `timedelta64` dtypes with different time units the outcome will be the shorter of both (“keep the precision” rule). For example:

    In [10]: numpy.ones(3, 'm8[s]') + numpy.ones(3, 'm8[m]')
    Out[10]: array([61, 61, 61],  dtype="timedelta64[s]")

However, due to the impossibility to know the exact duration of a relative year or a relative month, when these time units appear in one of the operands, the operation will not be allowed:

    In [11]: numpy.ones(3, 'm8[Y]') + numpy.ones(3, 'm8[D]')
    raise numpy.IncompatibleUnitError  # how to convert relative years to days?

In order to being able to perform the above operation a new NumPy function, called `change_timeunit` is proposed. Its signature will be:

    change_timeunit(time_object, new_unit, reference)

where ‘time_object’ is the time object whose unit is to be changed, ‘new_unit’ is the desired new time unit, and ‘reference’ is an absolute date (NumPy datetime64 scalar) that will be used to allow the conversion of relative times in case of using time units with an uncertain number of smaller time units (relative years or months cannot be expressed in days).

With this, the above operation can be done as follows:

    In [10]: t_years = numpy.ones(3, 'm8[Y]')

    In [11]: t_days = numpy.change_timeunit(t_years, 'D', '2001-01-01')

    In [12]: t_days + numpy.ones(3, 'm8[D]')
    Out[12]: array([366, 366, 366],  dtype="timedelta64[D]")

## dtype vs time units conversions

For changing the date/time dtype of an existing array, we propose to use the `.astype()` method. This will be mainly useful for changing time units.

For example, for absolute dates:

    In[10]: t1 = numpy.zeros(5, dtype="datetime64[s]")

    In[11]: print t1
    [1970-01-01T00:00:00  1970-01-01T00:00:00  1970-01-01T00:00:00
     1970-01-01T00:00:00  1970-01-01T00:00:00]

    In[12]: print t1.astype('datetime64[D]')
    [1970-01-01  1970-01-01  1970-01-01  1970-01-01  1970-01-01]

For relative times:

    In[10]: t1 = numpy.ones(5, dtype="timedelta64[s]")

    In[11]: print t1
    [1 1 1 1 1]

    In[12]: print t1.astype('timedelta64[ms]')
    [1000 1000 1000 1000 1000]

Changing directly from/to relative to/from absolute dtypes will not be supported:

    In[13]: numpy.zeros(5, dtype="datetime64[s]").astype('timedelta64')
    TypeError: data type cannot be converted to the desired type

Business days have the peculiarity that they do not cover a continuous line of time (they have gaps at weekends). Thus, when converting from any ordinary time to business days, it can happen that the original time is not representable. In that case, the result of the conversion is Not a Time (NaT):

    In[10]: t1 = numpy.arange(5, dtype="datetime64[D]")

    In[11]: print t1
    [1970-01-01  1970-01-02  1970-01-03  1970-01-04  1970-01-05]

    In[12]: t2 = t1.astype("datetime64[B]")

    In[13]: print t2  # 1970 begins in a Thursday
    [1970-01-01  1970-01-02  NaT  NaT  1970-01-05]

When converting back to ordinary days, NaT values are left untouched (this happens in all time unit conversions):

    In[14]: t3 = t2.astype("datetime64[D]")

    In[13]: print t3
    [1970-01-01  1970-01-02  NaT  NaT  1970-01-05]

## Necessary changes to NumPy

In order to facilitate the addition of the date-time data-types a few changes to NumPy were made:

### Addition of metadata to dtypes

All data-types now have a metadata dictionary. It can be set using the metadata keyword during construction of the object.

Date-time data-types will place the word “__frequency__” in the meta-data dictionary containing a 4-tuple with the following parameters.

(basic unit string (str),
  number of multiples (int), number of sub-divisions (int), number of events (int)).

Simple time units like ‘D’ for days will thus be specified by (‘D’, 1, 1, 1) in the “__frequency__” key of the metadata. More complicated time units (like ‘[2W/5]//50’) will be indicated by (‘D’, 2, 5, 50).

The “__frequency__” key is reserved for metadata and cannot be set with a dtype constructor.

### Ufunc interface extension

ufuncs that have datetime and timedelta arguments can use the Python API during ufunc calls (to raise errors).

There is a new ufunc C-API call to set the data for a particular function pointer (for a particular set of data-types) to be the list of arrays passed in to the ufunc.

### Array Interface Extensions

The array interface is extended to both handle datetime and timedelta typestr (including extended notation).

In addition, the typestr element of the __array_interface__ can be a tuple as long as the version string is 4. The tuple is (‘typestr’, metadata dictionary).

This extension to the typestr concept extends to the descr portion of the __array_interface__. Thus, the second element in the tuple of a list of tuples describing a data-format can itself be a tuple of (‘typestr’, metadata dictionary).

## Final considerations

### Why the fractional time and events: [3Y/12]//50

It is difficult to come up with enough units to satisfy every need. For example, in C# on Windows the fundamental tick of time is 100ns. Multiple of basic units are simple to handle. Divisors of basic units are harder to handle arbitrarily, but it is common to mentally think of a month as 1/12 of a year, or a day as 1/7 of a week. Therefore, the ability to specify a unit in terms of a fraction of a “larger” unit was implemented.

The event notion (//50) was added to solve a use-case of a commercial sponsor of this NEP. The idea is to allow timestamp to carry both event number and timestamp information. The remainder carries the event number information, while the quotient carries the timestamp information.

### Why the `origin` metadata disappeared

During the discussion of the date/time dtypes in the NumPy list, the idea of having an `origin` metadata that complemented the definition of the absolute `datetime64` was initially found to be useful.

However, after thinking more about this, we found that the combination of an absolute `datetime64` with a relative `timedelta64` does offer the same functionality while removing the need for the additional `origin` metadata. This is why we have removed it from this proposal.

### Operations with mixed time units

Whenever an operation between two time values of the same dtype with the same unit is accepted, the same operation with time values of different units should be possible (e.g. adding a time delta in seconds and one in microseconds), resulting in an adequate time unit. The exact semantics of this kind of operations is defined int the “Casting rules” subsections of the “Operating with date/time arrays” section.

Due to the peculiarities of business days, it is most probable that operations mixing business days with other time units will not be allowed.

[1] | http://docs.python.org/lib/module-datetime.html

[2] | http://www.egenix.com/products/python/mxBase/mxDateTime

[3] | http://en.wikipedia.org/wiki/Unix_time