safe_cmp: safe comparisons (total ordering) for any object in Python 3

safe_cmp provides functions for safely sorting and ordering any value in Python 3. In fancy math terms, safe_cmp implements a total ordering of all values in Python 3.

Installation:

yarn add safe-cmp

- or -

pip install safe-cmp

Description

In Python 2, it was possible to compare any object:

>>> None > 2
False
>>> [] < object()
True

But this is no longer true in Python 3:

>>> None > 2
...
TypeError: '>' not supported between instances of 'NoneType' and 'int'
>>> [] < object()
...
TypeError: '<' not supported between instances of 'list' and 'object'

There are many cases when it can be convenient to safely compare arbitrary objects. For example:

• Sort heterogeneous lists (ie, lists that contain many types of object)
• Compare objects to None (for example, to find the max(...) of a list where some items may be None)
• Write generic functions which will have robust, deterministic behaviour on arbitrary input

safe_cmp implements Python 2 (mostly; see Python 2 Compatibility) compatible safe versions of the ordering functions:

• safe_cmp: a Python 2 compatible implementation of cmp for Python 3
• safe_sorted: a safe version of sorted(...)
• safe_min: a safe version of min(...)
• safe_max: a safe version of max(...)

And provides a wrapper - safe_order - which defines a total ordering for any object (for example, heterogeneous_list.sort(key=safe_order)).

Examples

Sorting a heterogeneous list:

>>> from safe_cmp import safe_sorted, safe_order
>>> items = [1, None, "foo", {}, object]
>>> list(safe_sorted(items)) # Using "safe_sorted"
[None, {}, 1, 'foo', object]
>>> items.sort(key=safe_order) # Using "safe_order" with key=
>>> items
[None, {}, 1, 'foo', object]

Finding the max of a list which includes nulls:

>>> from safe_cmp import safe_max
>>> safe_max([1, None, 3, None, 4])
4

The rare situation where Python 2 style cmp is useful:

>>> from safe_cmp import safe_cmp
>>> safe_cmp(None, 1)
-1
>>> safe_cmp(None, None)
0
>>> safe_cmp(1, None)
1

Note: safe_cmp will produce Python 2 compatible results when called with nan:

>>> from safe_cmp import safe_cmp
>>> nan = float("NaN")
>>> safe_cmp(nan, 1)
-1
>>> safe_cmp(1, nan)
1
>>> safe_cmp(nan, nan)
0

As will safe_sorted:

>>> from safe_cmp import safe_sorted
>>> list(safe_sorted([nan, 2, nan, 1]))
[nan, 2, nan, 1]

Values Without A Defined Ordering

Values without a naturally defined ordering - complex numbers, certain user-defined types, etc - will be ordered in terms of their type name and location in memory.

Specifically, the default ordering is defined as:

def default_ordering(obj):
    return (type(obj).__name__, id(type(obj)), id(obj))

Note: for Python 2 compatibility, None and NaN are handled as special cases. See the implementation of safe_cmp for details.

Another special case worth noting is sets, which implicitly have no defined ordering in Python 3:

>>> a = set([1])
>>> b = set([2])
>>> a < b
False
>>> b < a
False

safe_cmp does not attempt to detect or correct this behavior for sets (or any other type with an implicitly defined lack of ordering):

>>> from safe_cmp import safe_cmp
>>> a = set([1])
>>> b = set([2])
>>> safe_cmp(a, b)
1
>>> safe_cmp(a, b)
1

Python 2 Compatibility

safe_cmp and friends are compatible with their Python 2 counterparts in their dealings with NaN and None, but differ in their handling of types such as sets and complex numbers which are explicitly unorderable in Python 2:

>>> 1j > 2j
...
TypeError: no ordering relation is defined for complex numbers
>>> cmp(set(), set())
TypeError: cannot compare sets using cmp()

Contrast with safe_cmp:

>>> from safe_cmp import safe_cmp
>>> safe_cmp(1j, 2j)
-1
>>> safe_cmp(set(), set())
0

Performance

Currently safe_cmp methods are currently implemented in Python (in contrast to their unsafe builtin counterparts, which are implemented in C), so performance will be worse for large comparisons:

In [1]: %timeit safe_max(range(10000000))
2.8 s ± 42 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

In [2]: %timeit max(range(10000000))
345 ms ± 6.23 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

For smaller comparisons, hoever, the difference is negligible:

In [1]: %timeit safe_max(1, 2)
682 ns ± 7.12 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)

In [2]: %timeit max(1, 2)
218 ns ± 6.87 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)

If there is interest in performant implementations they will be straight forward to implement.

Additionally, where obvious, performance optimizations have been implemented (for example, caching the result of key= functions).