====================================================================
 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).

.. Important:  The information that provides meaning to the integers stored in
   the date/time dtypes are stored as metadata which is a new feature to be
   added to the dtype object.

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 AC]
   M       month            +- 7.6e17 years         [7.6e17 BC, 7.6e17 AC]
   W       week             +- 1.7e17 years         [1.7e17 BC, 1.7e17 AC]
   B       business day     +- 3.5e16 years         [3.5e16 BC, 3.5e16 AC]
   D       day              +- 2.5e16 years         [2.5e16 BC, 2.5e16 AC]
   h       hour             +- 1.0e15 years         [1.0e15 BC, 1.0e15 AC]
   m       minute           +- 1.7e13 years         [1.7e13 BC, 1.7e13 AC]
   s       second           +- 2.9e12 years         [ 2.9e9 BC,  2.9e9 AC]
   ms      millisecond      +- 2.9e9 years          [ 2.9e6 BC,  2.9e6 AC]
   us      microsecond      +- 2.9e6 years          [290301 BC, 294241 AC]
   ns      nanosecond       +- 292 years            [  1678 AC,   2262 AC]
   ps      picosecond       +- 106 days             [  1969 AC,   1970 AC]
   fs      femtosecond      +- 2.6 hours            [  1969 AC,   1970 AC]
   as      attosecond       +- 9.2 seconds          [  1969 AC,   1970 AC]
======== ================ ======================= ==========================

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 loose
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 Intervace 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


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