2. How Does Natsort Work?¶
natsort
works by breaking strings into smaller sub-components (numbers
or everything else), and returning these components in a tuple. Sorting
tuples in Python is well-defined, and this fact is used to sort the input
strings properly. But how does one break a string into sub-components?
And what does one do to those components once they are split? Below I
will explain the algorithm that was chosen for the natsort
module,
and some of the thinking that went into those design decisions. I will
also mention some of the stumbling blocks I ran into because
getting sorting right is surprisingly hard.
If you are impatient, you can skip to TL;DR 1 - The Simple “No Special Cases” Algorithm for the algorithm in the simplest case, and TL;DR 2 - Handling Crappy, Real-World Input to see what extra code is needed to handle special cases.
2.1. First, How Does Natural Sorting Work At a High Level?¶
If I want to compare ‘2 ft 7 in’ to ‘2 ft 11 in’, I might do the following
>>> '2 ft 7 in' < '2 ft 11 in'
False
We as humans know that the above should be true, but why does Python think it is false? Here is how it is performing the comparison:
'2' <=> '2' ==> equal, so keep going
' ' <=> ' ' ==> equal, so keep going
'f' <=> 'f' ==> equal, so keep going
't' <=> 't' ==> equal, so keep going
' ' <=> ' ' ==> equal, so keep going
'7' <=> '1' ==> different, use result of '7' < '1'
‘7’ evaluates as greater than ‘1’ so the statement is false. When sorting, if a value is less than another it is placed first, so in our above example ‘2 ft 11 in’ would end up before ‘2 ft 7 in’, which is not correct. What to do?
The best way to handle this is to break the string into sub-components
of numbers and non-numbers, and then convert the numeric parts into
float()
or int()
types. This will force Python to
actually understand the context of what it is sorting and then “do the
right thing.” Luckily, it handles sorting lists of strings right out-of-the-box,
so the only hard part is actually making this string-to-list transformation
and then Python will handle the rest.
'2 ft 7 in' ==> (2, ' ft ', 7, ' in')
'2 ft 11 in' ==> (2, ' ft ', 11, ' in')
When Python compares the two, it roughly follows the below logic:
2 <=> 2 ==> equal, so keep going
' ft ' <=> ' ft ' ==> a string is a special type of sequence - evaluate each character individually
||
-->
' ' <=> ' ' ==> equal, so keep going
'f' <=> 'f' ==> equal, so keep going
't' <=> 't' ==> equal, so keep going
' ' <=> ' ' ==> equal, so keep going
<== Back to parent sequence
7 <=> 11 ==> different, use the result of 7 < 11
Clearly, seven is less than eleven, so our comparison is as we expect, and we would get the sorting order we wanted.
At its heart, natsort
is simply a tool to break strings into tuples,
turning numbers in strings (i.e. '79'
) into ints and floats as it does this.
2.2. Natsort’s Approach¶
2.2.1. Decomposing Strings Into Sub-Components¶
The first major hurtle to overcome is to decompose the string into sub-components. Remarkably, this turns out to be the easy part, owing mostly to Python’s easy access to regular expressions. Breaking an arbitrary string based on a pattern is pretty straightforward.
>>> import re
>>> re.split(r'(\d+)', '2 ft 11 in')
['', '2', ' ft ', '11', ' in']
Clear (assuming you can read regular expressions) and concise.
The reason I began developing natsort
in the first place was because I
needed to handle the natural sorting of strings containing real numbers, not just
unsigned integers as the above example contains. By real numbers, I mean those like
-45.4920E-23
. natsort
can handle just about any number definition;
to that end, here are all the regular expressions used in natsort
:
>>> unsigned_int = r'([0-9]+)'
>>> signed_int = r'([-+]?[0-9]+)'
>>> unsigned_float = r'((?:[0-9]+\.?[0-9]*|\.[0-9]+)(?:[eE][-+]?[0-9]+)?)'
>>> signed_float = r'([-+]?(?:[0-9]+\.?[0-9]*|\.[0-9]+)(?:[eE][-+]?[0-9]+)?)'
>>> unsigned_float_no_exponent = r'((?:[0-9]+\.?[0-9]*|\.[0-9]+))'
>>> signed_float_no_exponent = r'([-+]?(?:[0-9]+\.?[0-9]*|\.[0-9]+))'
Note that "inf"
and "nan"
are deliberately omitted from the float definition because you
wouldn’t want (for example) "banana"
to be converted into ['ba', 'nan', 'a']
,
Let’s see an example:
>>> re.split(signed_float, 'The mass of 3 electrons is 2.732815068E-30 kg')
['The mass of ', '3', ' electrons is ', '2.732815068E-30', ' kg']
Note
It is a bit of a lie to say the above are the complete regular expressions. In the
actual code there is also handling for non-ASCII unicode characters (such as ⑦),
but I will ignore that aspect of natsort
in this discussion.
Now, when the user wants to change the definition of a number, it is as easy as changing the pattern supplied to the regular expression engine.
Choosing the right default is hard, though (well, in this case it shouldn’t have been
but I was rather thick-headed).
In retrospect, it should have been obvious that since essentially all the code examples
I had/have seen for natural sorting were for unsigned integers, I should have made the default
definition of a number an unsigned integer. But, in the brash days of my youth I assumed
that since my use case was real numbers, everyone else would be happier sorting by real numbers;
so, I made the default definition of a number a signed float with exponent.
This astonished a lot of people
(and some people aren’t very nice when they are astonished).
Starting with natsort
version 4.0.0 the default number definition was
changed to an unsigned integer which satisfies the “least astonishment” principle, and
I have not heard a complaint since.
Wouldn’t itertools.groupby work as well as regex to split strings?
You could do it using something like itertools.groupby()
, but it is not clearer
nor more concise, I promise.
>>> import itertools
>>> import operator
>>> list(map(''.join, map(operator.itemgetter(1), itertools.groupby('2 ft 11 in', str.isdigit))))
['2', ' ft ', '11', ' in']
OK, but let’s assume for a moment that you really like itertools and think the above
is fine. We still have lost a lot of flexibility here because of the str.isdigit()
call which makes this method non-optimal; with a regular expression one can change
the pattern string and split on much more complicated patterns, but with
itertools.groupby()
it becomes much more complicated to change it up;
I implemented this strategy as part of my testing and it is anything but clear an concise.
Not to mention it’s way slower than regex. Just the simple example above (unsigned integers) is 50% slower than regex...
2.2.2. Coercing Strings Containing Numbers Into Numbers¶
There has been some debate on Stack Overflow as to what method is best to coerce a string to a number if it can be coerced, and leaving it alone otherwise (see this one for coercion and this one for checking for some high traffic questions), but it mostly boils down to two different solutions, shown here:
>>> def coerce_try_except(x):
... try:
... return int(x)
... except ValueError:
... return x
...
>>> def coerce_regex(x):
... # Note that precompiling the regex is more performant,
... # but I do not show that here for clarity's sake.
... return int(x) if re.match(r'[-+]?\d+$', x) else x
...
Here are some timing results run on my machine:
In [0]: numbers = list(map(str, range(100))) # A list of numbers as strings
In [1]: not_numbers = ['banana' + x for x in numbers]
In [2]: %timeit [coerce_try_except(x) for x in numbers]
10000 loops, best of 3: 51.1 µs per loop
In [3]: %timeit [coerce_try_except(x) for x in not_numbers]
1000 loops, best of 3: 289 µs per loop
In [4]: %timeit [coerce_regex(x) for x in not_numbers]
10000 loops, best of 3: 67.6 µs per loop
In [5]: %timeit [coerce_regex(x) for x in numbers]
10000 loops, best of 3: 123 µs per loop
What can we learn from this? The try: except
method (arguably the most “pythonic”
of the solutions) is best for numeric input, but performs over 5X slower for non-numeric
input. Conversely, the regular expression method, though slower than try: except
for
both input types, is more efficient for non-numeric input than for input that can be
converted to an int
. Further, even though the regular expression method is slower
for both input types, it is always at least twice as fast as the worst case for the
try: except
.
Why do I care? Shouldn’t I just pick a method and not worry about it? Probably. However,
I am very conscious about the performance of natsort
, and want it to be a true
drop-in replacement for sorted()
without having to incur a performance penalty.
For the purposes of natsort
, there is no clear winner between the two algorithms -
the data being passed to this function will likely be a mix of numeric and non-numeric
string content. Do I use the try: except
method and hope the speed gains on
numbers will offset the non-number performance, or do I use regular expressions and
take the more stable performance?
It turns out that within the context of natsort
, some assumptions can be
made that make a hybrid approach attractive. Because all strings are pre-split
into numeric and non-numeric content before being passed to this coercion function,
the assumption can be made that if a string begins with a digit or a sign, it
can be coerced into a number.
>>> def coerce_to_int(x):
... if x[0] in '0123456789+-':
... try:
... return int(x)
... except ValueError:
... return x
... else:
... return x
...
So how does this perform compared to the standard coercion methods?
In [6]: %timeit [coerce_to_int(x) for x in numbers]
10000 loops, best of 3: 71.6 µs per loop
In [7]: %timeit [coerce_to_int(x) for x in not_numbers]
10000 loops, best of 3: 26.4 µs per loop
The hybrid method eliminates most of the time wasted on numbers checking that it
is in fact a number before passing to int()
, and eliminates the time wasted
in the exception stack for input that is not a number.
That’s as fast as we can get, right? In pure Python, probably. At least, it’s
close. But because I am crazy and a glutton for punishment, I decided to see
if I could get any faster writing a C extension. It’s called
fastnumbers and contains a C implementation of the above coercion functions
called fast_int()
. How does it fair? Pretty well.
In [8]: %timeit [fast_int(x) for x in numbers]
10000 loops, best of 3: 30.9 µs per loop
In [9]: %timeit [fast_int(x) for x in not_numbers]
10000 loops, best of 3: 30 µs per loop
During development of natsort
, I wanted to ensure that using it did not
get in the way of a user’s program by introducing a performance penalty to their code.
To that end, I do not feel like my adventures down the rabbit hole of optimization
of coercion functions was a waste; I can confidently look users in the eye and
say I considered every option in ensuring natsort
is as efficient as possible.
This is why if fastnumbers is installed it will be used for this step,
and otherwise the hybrid method will be used.
Note
Modifying the hybrid coercion function for floats is straightforward.
>>> def coerce_to_float(x):
... if x[0] in '.0123456789+-' or x.lower().lstrip()[:3] in ('nan', 'inf'):
... try:
... return float(x)
... except ValueError:
... return x
... else:
... return x
...
2.2.3. TL;DR 1 - The Simple “No Special Cases” Algorithm¶
At this point, our natsort
algorithm is essentially the following:
>>> import re
>>> def natsort_key(x, as_float=False, signed=False):
... if as_float:
... regex = signed_float if signed else unsigned_float
... else:
... regex = signed_int if signed else unsigned_int
... split_input = re.split(regex, x)
... split_input = filter(None, split_input) # removes null strings
... coerce = coerce_to_float if as_float else coerce_to_int
... return tuple(coerce(s) for s in split_input)
...
I have written the above for clarity and not performance. This pretty much matches most natural sort solutions for python on Stack Overflow (except the above includes customization of the definition of a number).
2.3. Special Cases Everywhere!¶
If what I described in TL;DR 1 were
all that natsort
needed to
do then there probably wouldn’t be much need for a third-party module, right?
Probably. But it turns out that in real-world data there are a lot of
special cases that need to be handled, and in true 80%/20% fashion, the
majority of the code in natsort
is devoted to handling special cases
like those described below.
2.3.1. Sorting Filesystem Paths¶
The first major special case I encountered was sorting filesystem paths
(if you go to the link, you will see I didn’t handle it well for a year...
this was before I fully realized how much functionality I could really add
to natsort
). Let’s apply the natsort_key()
from above to some
filesystem paths that you might see being auto-generated from your operating
system:
>>> paths = ['/p/Folder (10)/file.tar.gz',
... '/p/Folder/file.tar.gz',
... '/p/Folder (1)/file (1).tar.gz',
... '/p/Folder (1)/file.tar.gz']
>>> sorted(paths, key=natsort_key)
['/p/Folder (1)/file (1).tar.gz', '/p/Folder (1)/file.tar.gz', '/p/Folder (10)/file.tar.gz', '/p/Folder/file.tar.gz']
Well that’s not right! What is '/p/Folder/file.tar.gz'
doing at the end?
It has to do with the numerical ASCII code assigned to the space and
/
characters in the ASCII table. According to the ASCII table, the
space character (number 32) comes before the /
character (number 47). If
we remove the common prefix in all of the above strings ('/p/Folder'
), we
can see why this happens:
>>> ' (1)/file.tar.gz' < '/file.tar.gz'
True
>>> ' ' < '/'
True
This isn’t very convenient... how do we solve it? We can split the path
across the path separators and then sort. A convenient way do to this is
with the Path.parts method from pathlib
:
>>> import pathlib
>>> sorted(paths, key=lambda x: tuple(natsort_key(s) for s in pathlib.Path(x).parts))
['/p/Folder/file.tar.gz', '/p/Folder (1)/file (1).tar.gz', '/p/Folder (1)/file.tar.gz', '/p/Folder (10)/file.tar.gz']
Almost! It seems like there is some funny business going on in the final filename component as well. We can solve that nicely and quickly with Path.suffixes and Path.stem.
>>> def decompose_path_into_components(x):
... path_split = list(pathlib.Path(x).parts)
... # Remove the final filename component from the path.
... final_component = pathlib.Path(path_split.pop())
... # Split off all the extensions.
... suffixes = final_component.suffixes
... stem = final_component.name.replace(''.join(suffixes), '')
... # Remove the '.' prefix of each extension, and make that
... # final component a list of the stem and each suffix.
... final_component = [stem] + [x[1:] for x in suffixes]
... # Replace the split final filename component.
... path_split.extend(final_component)
... return path_split
...
>>> def natsort_key_with_path_support(x):
... return tuple(natsort_key(s) for s in decompose_path_into_components(x))
...
>>> sorted(paths, key=natsort_key_with_path_support)
['/p/Folder/file.tar.gz', '/p/Folder (1)/file.tar.gz', '/p/Folder (1)/file (1).tar.gz', '/p/Folder (10)/file.tar.gz']
This works because in addition to breaking the input by path separators, the final
filename component is separated from its extensions as well [1]. Then, each of these
separated components is sent to the natsort
algorithm, so the result is
a tuple of tuples. Once that is done, we can see how comparisons can be done in
the expected manner.
>>> a = natsort_key_with_path_support('/p/Folder (1)/file (1).tar.gz')
>>> a
(('/',), ('p',), ('Folder (', 1, ')'), ('file (', 1, ')'), ('tar',), ('gz',))
>>>
>>> b = natsort_key_with_path_support('/p/Folder/file.tar.gz')
>>> b
(('/',), ('p',), ('Folder',), ('file',), ('tar',), ('gz',))
>>>
>>> a > b
True
2.3.2. Comparing Different Types on Python 3¶
The second major special case I encountered was sorting of different types.
If you are on Python 2 (i.e. legacy Python), this mostly doesn’t matter too
much since it uses an arbitrary heuristic to allow traditionally un-comparable
types to be compared (such as comparing 'a'
to 1
). However, on Python 3
(i.e. Python) it simply won’t let you perform such nonsense, raising a
TypeError
instead.
You can imagine that a module that breaks strings into tuples of numbers and strings is walking a dangerous line if it does not have special handling for comparing numbers and strings. My imagination was not so great at first. Let’s take a look at all the ways this can fail with real-world data.
>>> def natsort_key_with_poor_real_number_support(x):
... split_input = re.split(signed_float, x)
... split_input = filter(None, split_input) # removes null strings
... return tuple(coerce_to_float(s) for s in split_input)
>>>
>>> sorted([5, '4'], key=natsort_key_with_poor_real_number_support)
Traceback (most recent call last):
...
TypeError: ...
>>>
>>> sorted(['12 apples', 'apples'], key=natsort_key_with_poor_real_number_support)
Traceback (most recent call last):
...
TypeError: ...
>>>
>>> sorted(['version5.3.0', 'version5.3rc1'], key=natsort_key_with_poor_real_number_support)
Traceback (most recent call last):
...
TypeError: ...
Let’s break these down.
- The integer
5
is sent tore.split
which expects only strings or bytes, which is a no-no. natsort_key_with_poor_real_number_support('12 apples') < natsort_key_with_poor_real_number_support('apples')
is the same as(12.0, ' apples') < ('apples',)
, and thus a number gets compared to a string [2] which also is a no-no.- This one scores big on the astonishment scale, especially if one accidentally
uses signed integers or real numbers when they mean to use unsigned integers.
natsort_key_with_poor_real_number_support('version5.3.0') < natsort_key_with_poor_real_number_support('version5.3rc1')
is the same as('version', 5.3, 0.0) < ('version', 5.3, 'rc', 1.0)
, so in the third element a number gets compared to a string, once again the same old no-no. (The same would happen with'version5-3'
and'version5-a'
, which would be come('version', 5, -3)
and('version', 5, '-a')
).
As you might expect, the solution to the first issue is to wrap the re.split
call in a try: except:
block and handle the number specially if a
TypeError
is raised. The second and third cases could be handled
in a “special case” manner, meaning only respond and do something different
if these problems are detected. But a less error-prone method is to ensure
that the data is correct-by-construction, and this can be done by ensuring
that the returned tuples always start with a string, and then alternate
in a string-number-string-number-string patter;n this can be achieved by
adding an empty string wherever the pattern is not followed [3]. This ends
up working out pretty nicely because empty strings are always “less” than
any non-empty string, and we typically want numbers to come before strings.
Let’s take a look at how this works out.
>>> from natsort.utils import _sep_inserter
>>> list(_sep_inserter(iter(['apples']), ''))
['apples']
>>>
>>> list(_sep_inserter(iter([12, ' apples']), ''))
['', 12, ' apples']
>>>
>>> list(_sep_inserter(iter(['version', 5, -3]), ''))
['version', 5, '', -3]
>>>
>>> from natsort import natsort_keygen, ns
>>> natsort_key_with_good_real_number_support = natsort_keygen(alg=ns.REAL)
>>>
>>> sorted([5, '4'], key=natsort_key_with_good_real_number_support)
['4', 5]
>>>
>>> sorted(['12 apples', 'apples'], key=natsort_key_with_good_real_number_support)
['12 apples', 'apples']
>>>
>>> sorted(['version5.3.0', 'version5.3rc1'], key=natsort_key_with_good_real_number_support)
['version5.3.0', 'version5.3rc1']
How the “good” version works will be given in TL;DR 2 - Handling Crappy, Real-World Input.
2.3.3. Handling NaN¶
A rather unexpected special case I encountered was sorting collections containing NaN. Let’s see what happens when you try to sort a plain old list of numbers when there is a NaN floating around in there.
>>> danger = [7, float('nan'), 22.7, 19, -14, 59.123, 4]
>>> sorted(danger)
[7, nan, -14, 4, 19, 22.7, 59.123]
Clearly that isn’t correct, and for once it isn’t my fault! It’s hard to compare floating point numbers. By definition, NaN is unorderable to any other number, and is never equal to any other number, including itself.
>>> nan = float('nan')
>>> 5 > nan
False
>>> 5 < nan
False
>>> 5 == nan
False
>>> 5 != nan
True
>>> nan == nan
False
>>> nan != nan
True
The implication of all this for us is that if there is an NaN in the
data-set we are trying to sort, the data-set will end up being sorted in
two separate yet individually sorted sequences - the one before the NaN,
and the one after. This is because the <
operation that is used
to sort always returns False
with NaN.
Because natsort
aims to sort sequences in a way that does not surprise
the user, keeping this behavior is not acceptable (I don’t require my users
to know how NaN will behave in a sorting algorithm). The simplest way to
satisfy the “least astonishment” principle is to substitute NaN with
some other value. But what value is least astonishing? I chose to replace
NaN with \(-\infty\) so that these poorly behaved elements always
end up at the front where the users will most likely be alerted to their presence.
>>> def fix_nan(x):
... if x != x: # only true for NaN
... return float('-inf')
... else:
... return x
...
Let’s check out TL;DR 2 to see how this can be incorporated into the simple key function from TL;DR 1.
2.3.4. TL;DR 2 - Handling Crappy, Real-World Input¶
Let’s see how our elegant key function from TL;DR 1 has become bastardized in order to support handling mixed real-world data and user customizations.
>>> def natsort_key(x, as_float=False, signed=False, as_path=False):
... if as_float:
... regex = signed_float if signed else unsigned_float
... else:
... regex = signed_int if signed else unsigned_int
... try:
... if as_path:
... x = decompose_path_into_components(x) # Decomposes into list of strings
... # If this raises a TypeError, input is not a string.
... split_input = re.split(regex, x)
... except TypeError:
... try:
... # Does this need to be applied recursively (list-of-list)?
... return tuple(map(natsort_key, x))
... except TypeError:
... # Must be a number
... ret = ('', fix_nan(x)) # Maintain string-number-string pattern
... return (ret,) if as_path else ret # as_path returns tuple-of-tuples
... else:
... split_input = filter(None, split_input) # removes null strings
... # Note that the coerce_to_int/coerce_to_float functions
... # are also modified to use the fix_nan function.
... if as_float:
... coerced_input = (coerce_to_float(s) for s in split_input)
... else:
... coerced_input = (coerce_to_int(s) for s in split_input)
... return tuple(_sep_inserter(coerced_input, ''))
...
And this doesn’t even show handling bytes
type! Notice that we have
to do non-obvious things like modify the return form of numbers when as_path
is given, just to avoid comparing strings and numbers for the case in which a user provides
input like ['/home/me', 42]
.
Let’s take it out for a spin!
>>> danger = [7, float('nan'), 22.7, '19', '-14', '59.123', 4]
>>> sorted(danger, key=lambda x: natsort_key(x, as_float=True, signed=True))
[nan, '-14', 4, 7, '19', 22.7, '59.123']
>>>
>>> paths = ['/p/Folder (1)/file.tar.gz',
... '/p/Folder/file.tar.gz',
... 123456]
>>> sorted(paths, key=lambda x: natsort_key(x, as_path=True))
[123456, '/p/Folder/file.tar.gz', '/p/Folder (1)/file.tar.gz']
2.4. Here Be Dragons: Adding Locale Support¶
Probably the most challenging special case I had to handle was getting
natsort
to handle sorting the non-numerical parts of input
correctly, and also allowing it to sort the numerical bits in different
locales. This was in no way what I originally set out to do with this
library, so I was caught a bit off guard when the request was initially made.
I discovered the locale
library, and assumed that if it’s part of Python’s
StdLib there can’t be too many dragons, right?
INCOMPLETE LIST OF DRAGONS
- https://github.com/SethMMorton/natsort/issues/21
- https://github.com/SethMMorton/natsort/issues/22
- https://github.com/SethMMorton/natsort/issues/23
- https://github.com/SethMMorton/natsort/issues/36
- https://github.com/SethMMorton/natsort/issues/44
- https://bugs.python.org/issue2481
- https://bugs.python.org/issue23195
- https://stackoverflow.com/questions/3412933/python-not-sorting-unicode-properly-strcoll-doesnt-help
- https://stackoverflow.com/questions/22203550/sort-dictionary-by-key-using-locale-collation
- https://stackoverflow.com/questions/33459384/unicode-character-not-in-range-when-calling-locale-strxfrm
- https://stackoverflow.com/questions/36431810/sort-numeric-lines-with-thousand-separators
- https://stackoverflow.com/questions/45734562/how-can-i-get-a-reasonable-string-sorting-with-python
These can be summed up as follows:
locale
is a thin wrapper over your operating system’s locale library, so if that is broken (like it is on BSD and OSX) thenlocale
is broken in Python.- Because of a bug in legacy Python (i.e. Python 2), there is no uniform way to use
the
locale
sorting functionality between legacy Python and Python 3. - People have differing opinions of how capitalization should affect word order.
- There is no built-in way to handle locale-dependent thousands separators and decimal points robustly.
- Proper handling of Unicode is complicated.
- Proper handling of
locale
is complicated.
Easily over half of the the code in natsort
is in some way dealing with some
aspect of locale
or basic case handling. It would have been
impossible to get right without a really good testing strategy.
Don’t expect any more TL;DR’s... if you want to see how all this is fully
incorporated into the natsort
algorithm then please take a look
at the code. However, I will hint at how specific steps are taken in
each section.
Let’s see how we can handle some of the dragons, one-by-one.
2.4.1. Basic Case Control Support¶
Without even thinking about the mess that is adding locale
support,
natsort
can introduce support for controlling how case is interpreted.
First, let’s take a look at how it is sorted by default (due to where characters lie on the ASCII table).
>>> a = ['Apple', 'corn', 'Corn', 'Banana', 'apple', 'banana']
>>> sorted(a)
['Apple', 'Banana', 'Corn', 'apple', 'banana', 'corn']
All uppercase letters come before lowercase letters in the ASCII table,
so all capitalized words appear first. Not everyone agrees that this
is the correct order. Some believe that the capitalized words should
be last (['apple', 'banana', 'corn', 'Apple', 'Banana', 'Corn']
).
Some believe that both the lowercase and uppercase versions
should appear together (['Apple', 'apple', 'Banana', 'banana', 'Corn', 'corn']
).
Some believe that both should be true ☹. Some people don’t care at all [4].
Solving the first case (I call it LOWERCASEFIRST) is actually pretty
easy... just call the str.swapcase()
method on the input.
>>> sorted(a, key=lambda x: x.swapcase())
['apple', 'banana', 'corn', 'Apple', 'Banana', 'Corn']
The last (i call it IGNORECASE) should be super easy, right?
Simply call str.lowercase()
on the input. This will work but may
not always give the correct answer on non-latin character sets. It’s
a good thing that in Python 3.3
str.casefold()
was introduced, which does a better job of removing
all case information from unicode characters in
non-latin alphabets.
>>> def remove_case(x):
... try:
... return x.casefold()
... except AttributeError: # Legacy Python backwards compatibility
... return x.lowercase()
...
>>> sorted(a, key=remove_case)
['Apple', 'apple', 'Banana', 'banana', 'corn', 'Corn']
The middle case (I call it GROUPLETTERS) is less straightforward. The most efficient way to handle this is to duplicate each character with its lowercase version and then the original character.
>>> import itertools
>>> def groupletters(x):
... return ''.join(itertools.chain.from_iterable((remove_case(y), y) for y in x))
...
>>> groupletters('Apple')
'aAppppllee'
>>> groupletters('apple')
'aappppllee'
>>> sorted(a, key=groupletters)
['Apple', 'apple', 'Banana', 'banana', 'Corn', 'corn']
The effect of this is that both 'Apple'
and 'apple'
are
placed adjacent to each other because their transformations both begin
with 'a'
, and then the second character can be used to order them
appropriately with respect to each other.
There’s a problem with this, though. Within the context of natsort
we are trying to correctly sort numbers and those should be left alone.
>>> a = ['Apple5', 'apple', 'Apple4E10', 'Banana']
>>> sorted(a, key=lambda x: natsort_key(x, as_float=True))
['Apple5', 'Apple4E10', 'Banana', 'apple']
>>> sorted(a, key=lambda x: natsort_key(groupletters(x), as_float=True))
['Apple4E10', 'Apple5', 'apple', 'Banana']
>>> groupletters('Apple4E10')
'aAppppllee44eE1100'
We messed up the numbers! Looks like groupletters()
needs to be applied
after the strings are broken into their components. I’m not going to show
how this is done here, but basically it requires applying the function in
the else:
block of coerce_to_int()
/coerce_to_float()
.
>>> better_groupletters = natsort_keygen(alg=ns.GROUPLETTERS | ns.REAL)
>>> better_groupletters('Apple4E10')
('aAppppllee', 40000000000.0)
>>> sorted(a, key=better_groupletters)
['Apple5', 'Apple4E10', 'apple', 'Banana']
Of course, applying both LOWERCASEFIRST and GROUPLETTERS is just a matter of turning on both functions.
2.4.2. Basic Unicode Support¶
Unicode is hard and complicated. Here’s an example.
>>> b = [b'\x66', b'\x65', b'\xc3\xa9', b'\x65\xcc\x81', b'\x61', b'\x7a']
>>> a = [x.decode('utf8') for x in b]
>>> a
['f', 'e', 'é', 'é', 'a', 'z']
>>> sorted(a)
['a', 'e', 'é', 'f', 'z', 'é']
There are more than one way to represent the character ‘é’ in Unicode.
In fact, many characters have multiple representations. This is a challenge
because comparing the two representations would return False
even though
they look the same.
>>> a[2] == a[3]
False
Alas, since characters are compared based on the numerical value of their representation, sorting Unicode often gives unexpected results (like seeing ‘é’ come both before and after ‘z’).
The original approach that natsort
took with respect to non-ASCII
Unicode characters was to say “just use
the locale
or PyICU
library” and then cross it’s fingers
and hope those libraries take care of it. As you will find in the following
sections, that comes with its own baggage, and turned out to not always work anyway
(see https://stackoverflow.com/q/45734562/1399279). A more robust approach is to
handle the Unicode out-of-the-box without invoking a heavy-handed library
like locale
or PyICU
. To do this, we must use normalization.
To fully understand Unicode normalization, check out some official Unicode documentation. Just kidding... that’s too much text. The following StackOverflow answers do a good job at explaining Unicode normalization in simple terms: https://stackoverflow.com/a/7934397/1399279 and https://stackoverflow.com/a/7931547/1399279. Put simply, normalization ensures that Unicode characters with multiple representations are in some canonical and consistent representation so that (for example) comparisons of the characters can be performed in a sane way. The following discussion assumes you at least read the StackOverflow answers.
Looking back at our ‘é’ example, we can see that the two versions were
constructed with the byte strings b'\xc3\xa9'
and b'\x65\xcc\x81'
.
The former representation is actually
LATIN SMALL LETTER E WITH ACUTE
and is a single character in the Unicode standard. This is known as the
compressed form and corresponds to the ‘NFC’ normalization scheme.
The latter representation is actually the letter ‘e’ followed by
COMBINING ACUTE ACCENT
and so is two characters in the Unicode standard. This is known as the
decompressed form and corresponds to the ‘NFD’ normalization scheme.
Since the first character in the decompressed form is actually the letter ‘e’,
when compared to other ASCII characters it fits where you might expect.
Unfortunately, all Unicode compressed form characters come after the
ASCII characters and so they always will be placed after ‘z’ when sorting.
It seems that most Unicode data is stored and shared in the compressed form which makes it challenging to sort. This can be solved by normalizing all incoming Unicode data to the decompressed form (‘NFD’) and then sorting.
>>> import unicodedata
>>> c = [unicodedata.normalize('NFD', x) for x in a]
>>> c
['f', 'e', 'é', 'é', 'a', 'z']
>>> sorted(c)
['a', 'e', 'é', 'é', 'f', 'z']
Huzzah! Sane sorting without having to resort to locale
!
2.4.3. Using Locale to Compare Strings¶
The locale
module is actually pretty cool, and provides lowly
spare-time programmers like myself a way to handle the daunting task
of proper locale-dependent support of their libraries and utilities.
Having said that, it can be a bit of a bear to get right,
although they do point out in the documentation that it will be painful to use.
Aside from the caveats spelled out in that link, it turns out that just
comparing strings with locale
in a cross-platform and
cross-python-version manner is not as straightforward as one might hope.
First, how to use locale
to compare strings? It’s actually
pretty straightforward. Simply run the input through the locale
transformation function locale.strxfrm()
.
>>> import locale, sys
>>> locale.setlocale(locale.LC_ALL, 'en_US.UTF-8')
'en_US.UTF-8'
>>> a = ['a', 'b', 'ä']
>>> sorted(a)
['a', 'b', 'ä']
>>> # The below fails on OSX, so don't run doctest on darwin.
>>> is_osx = sys.platform == 'darwin'
>>> sorted(a, key=locale.strxfrm) if not is_osx else ['a', 'ä', 'b']
['a', 'ä', 'b']
>>>
>>> a = ['apple', 'Banana', 'banana', 'Apple']
>>> sorted(a, key=locale.strxfrm) if not is_osx else ['apple', 'Apple', 'banana', 'Banana']
['apple', 'Apple', 'banana', 'Banana']
It turns out that locale-aware sorting groups numbers in the same
way as turning on GROUPLETTERS and LOWERCASEFIRST.
The trick is that you have to apply locale.strxfrm()
only to non-numeric
characters; otherwise, numbers won’t be parsed properly. Therefore, it must
be applied as part of the coerce_to_int()
/coerce_to_float()
functions in a manner similar to groupletters()
.
As you might have guessed, there is a small problem.
It turns out the there is a bug in the legacy Python implementation of
locale.strxfrm()
that causes it to outright fail for unicode()
input (https://bugs.python.org/issue2481). locale.strcoll()
works,
but is intended for use with cmp
, which does not exist in current Python
implementations. Luckily, the functools.cmp_to_key()
function
makes locale.strcoll()
behave like locale.strxfrm()
(that is, of course,
unless you are on Python 2.6 where functools.cmp_to_key()
doesn’t exist,
in which case you simply copy-paste the implementation from Python 2.7
directly into your code ☹).
2.4.3.1. Handling Broken Locale On OSX¶
But what if the underlying locale implementation that locale
relies upon is simply broken? It turns out that the locale library on
OSX (and other BSD systems) is broken (and for some reason has never been
fixed?), and so locale
does not work as expected.
How do I define doesn’t work as expected?
>>> a = ['apple', 'Banana', 'banana', 'Apple']
>>> sorted(a)
['Apple', 'Banana', 'apple', 'banana']
>>>
>>> sorted(a, key=locale.strxfrm) if is_osx else sorted(a)
['Apple', 'Banana', 'apple', 'banana']
IT’S SORTING AS IF locale.stfxfrm()
WAS NEVER USED!! (and it’s worse
once non-ASCII characters get thrown into the mix.) I’m really not
sure why this is considered OK for the OSX/BSD maintainers to not fix,
but it’s more than frustrating for poor developers who have been dragged
into the locale game kicking and screaming. <deep breath>.
So, how to deal with this situation? There are two ways to do so.
Detect if
locale
is sorting incorrectly (i.e.dumb
) by seeing if'A'
is sorted before'a'
(incorrect) or not.>>> # This is genuinely the name of this function. >>> # See natsort.compat.locale.py >>> def dumb_sort(): ... return locale.strxfrm('A') < locale.strxfrm('a') ...
If a
dumb
locale implementation is found, then automatically turn on LOWERCASEFIRST and GROUPLETTERS.Use an alternate library if installed. ICU is a great and powerful library that has a pretty decent Python port called (you guessed it) PyICU. If a user has this library installed on their computer,
natsort
chooses to use that instead oflocale
. With a little bit of planning, one can write a set of wrapper functions that call the correct library under the hood such that the business logic never has to know what library is being used (see natsort.compat.locale.py).
Let me tell you, this little complication really makes a challenge of testing the code, since one must set up different environments on different operating systems in order to test all possible code paths. Not to mention that certain checks will fail for certain operating systems and environments so one must be diligent in either writing the tests not to fail, or ignoring those tests when on offending environments.
2.4.4. Handling Locale-Aware Numbers¶
Thousands separator support is a problem that I knew would someday be requested but had decided to push off until a rainy day. One day it finally rained, and I decided to tackle the problem.
So what is the problem? Consider the number 1,234,567
(assuming the
','
is the thousands separator). Try to run that through int()
and you will get a ValueError
. To handle this properly the thousands
separators must be removed.
>>> float('1,234,567'.replace(',', ''))
1234567.0
What if, in our current locale, the thousands separator is '.'
and
the ','
is the decimal separator (like for the German locale de_DE)?
>>> float('1.234.567'.replace('.', '').replace(',', '.'))
1234567.0
>>> float('1.234.567,89'.replace('.', '').replace(',', '.'))
1234567.89
This is pretty much what locale.atoi()
and locale.atof()
do
under the hood. So what’s the problem? Why doesn’t natsort
just
use this method under its hood?
Well, let’s take a look at what would happen if we send some possible
natsort
input through our the above function:
>>> natsort_key('1,234 apples, please.'.replace(',', ''))
('', 1234, ' apples please.')
>>> natsort_key('Sir, €1.234,50 please.'.replace('.', '').replace(',', '.'), as_float=True)
('Sir. €', 1234.5, ' please')
Any character matching the thousands separator was dropped, and anything
matching the decimal separator was changed to '.'
! If these characters
were critical to how your data was ordered, this would break natsort
.
The first solution one might consider would be to first decompose the input into sub-components (like we did for the GROUPLETTERS method above) and then only apply these transformations on the number components. This is a chicken-and-egg problem, though, because we cannot appropriately separate out the numbers because of the thousands separators and non-‘.’ decimal separators (well, at least not without making multiple passes over the data which I do not consider to be a valid option).
Regular expressions to the rescue! With regular expressions, we can remove the thousands separators and change the decimal separator only when they are actually within a number. Once the input has been pre-processed with this regular expression, all the infrastructure shown previously will work.
Beware, these regular expressions will make your eyes bleed.
>>> decimal = ',' # Assume German locale, so decimal separator is ','
>>> # Look-behind assertions cannot accept range modifiers, so instead of i.e.
>>> # (?<!\.[0-9]{1,3}) I have to repeat the look-behind for 1, 2, and 3.
>>> nodecimal = r'(?<!{dec}[0-9])(?<!{dec}[0-9]{{2}})(?<!{dec}[0-9]{{3}})'.format(dec=decimal)
>>> strip_thousands = r'''
... (?<=[0-9]{{1}}) # At least 1 number
... (?<![0-9]{{4}}) # No more than 3 numbers
... {nodecimal} # Cannot follow decimal
... {thou} # The thousands separator
... (?=[0-9]{{3}} # Three numbers must follow
... ([^0-9]|$) # But a non-number after that
... )
... '''.format(nodecimal=nodecimal, thou='.') # Thousands separator is '.' in German locale.
...
>>> re.sub(strip_thousands, '', 'Sir, €1.234,50 please.', flags=re.X)
'Sir, €1234,50 please.'
>>>
>>> # The decimal point must be preceded by a number or after
>>> # a number. This option only needs to be performed in the
>>> # case when the decimal separator for the locale is not '.'.
>>> switch_decimal = r'(?<=[0-9]){decimal}|{decimal}(?=[0-9])'
>>> switch_decimal = switch_decimal.format(decimal=decimal)
>>> re.sub(switch_decimal, '.', 'Sir, €1234,50 please.', flags=re.X)
'Sir, €1234.50 please.'
>>>
>>> natsort_key('Sir, €1234.50 please.', as_float=True)
('Sir, €', 1234.5, ' please.')
2.5. Final Thoughts¶
My hope is that users of natsort
never have to think about or worry
about all the bookkeeping or any of the details described above, and that using
natsort
seems to magically “just work”. For those of you who
took the time to read this engineering description, I hope it has enlightened
you to some of the issues that can be encountered when code is released
into the wild and has to accept “real-world data”, or to what happens
to developers who naïvely make bold assumptions that are counter to
what the rest of the world assumes.
Footnotes
[1] | To anyone looking through the actual code, you will note that I don’t
actually use pathlib to split the paths... I wrote my own version
to avoid adding an external dependency of pathlib on Python < 3.4. |
[2] | “But if you hadn’t removed the leading empty string from re.split this wouldn’t have happened!!” I can hear you saying. Well, that’s true. I don’t have a great reason for having done that except that in an earlier non-optimal incarnation of the algorithm I needed to it, and it kind of stuck, and it made other parts of the code easier if the assumption that there were no empty strings was valid. |
[3] | I’m not going to show how this is implemented in this document,
but if you are interested you can look at the code to
_sep_inserter() in util.py. |
[4] | Handling each of these is straightforward, but coupled with the rapidly
fracturing execution paths presented in TL;DR 2 one can imagine
this will get out of hand quickly. If you take a look at natsort.py and
util.py you can observe that to avoid this I take a more functional approach
to construting the natsort algorithm as opposed to the procedural approach
illustrated in TL;DR 1 and TL;DR 2. |