# Performance Comparison

Measuring performance is a difficult task. All the benchmarks on this page are synthetic in the sense that they test one function repeatedly. Measurements in live systems are much harder to produce reliably. So take the following data with a grain of salt. That being said, a stated feature of Sorted Containers is performance so we would be remiss not to produce this page with comparisons.

The source for all benchmarks can be found under the “tests” directory in the files prefixed “benchmark.” Measurements are made from the min, max, and median of 5 repetitions. In the graphs below, the line follows the median at each point. Note that the axes are log-log so properly reading two different lines would describe one metric as “X times” faster rather than “X seconds” faster. In all graphs, lower is better. Measurements are made by powers of ten: 100 through 10,000,000.

Measurements up to ten billion elements have been successfully tested and benchmarked. Read Performance at Scale for details. Only a couple implementations (including Sorted Containers) are capable of handling so many elements. The major limiting factor at that size is memory. Consider the simple case of storing CPython’s integers in a Sorted List. Each integer object requires ~24 bytes so one hundred million elements will require about three gigabytes of memory. If the implementation adds significant overhead then most systems will run out of memory. For all datasets which may be kept in memory, Sorted Containers is an excellent choice.

A good effort has been made to find competing implementations. Seven in total were found with various list, set, and dict implementations.

1. blist – Provides list, dict, and set containers based on the blist data-type. Uses a B-Tree data structure. Implemented in Python and C. BSD License. Last updated March, 2014. blist on PyPI
2. bintrees – Provides several tree-based implementations for dict and set containers. Fastest were AVL-Tree and Red-Black-Tree data structures.. Extends the conventional API to provide set operations for the dict type. Now deprecated in favor of Sorted Containers Implemented in C. MIT License. Last updated April, 2017. bintrees on PyPI
3. sortedmap – Provides a fast, C++ implemenation for dict data types. Uses the C++ standard library std::map data structure which is usually a red-black tree. Last updated February, 2016. sortedmap on PyPI
4. banyan – Provides a fast, C++ implementation for dict and set data types. Offers some features also found in sortedcontainers like accessing the n-th item in a set or dict. Uses sources from the tree implementation in GNU libstdc++. GPLv3 License. Last updated April, 2013. banyan on PyPI
5. treap – Uses Cython for improved performance and provides a dict container. Apache V2 License. Last updated June, 2017. treap on PyPI
6. skiplistcollections – Pure-Python implementation based on skip-lists providing a limited API for dict and set types. MIT License. Last updated January, 2014. skiplistcollections on PyPI
7. sortedcollection – Pure-Python implementation of sorted list based solely on a list. Feature-poor and inefficient for writes but included because it is written by Raymond Hettinger and linked from the official Python docs. MIT License. Last updated April, 2011. sortedcollection recipe

Several alternative implementations were omitted for reasons documented below:

1. rbtree – C-implementation that only supports Python 2. Provides a fast, C-implementation for dict and set data types. GPLv3 License. Last updated March, 2012. rbtree on PyPI
2. ruamel.ordereddict.sorteddict – C-implementation that only supports Python 2. Performance was measured in correspondence with the module author. Performance was generally very good except for `__delitem__`. At scale, deleting entries became exceedingly slow. MIT License. Last updated July, 2017. ruamel.ordereddict on PyPI
3. pyskiplist – Pure-Python skip-list based implementation supporting a sorted-list-like interface. Now deprecated in favor of Sorted Containers. MIT License. Last updated July, 2015. pyskiplist on PyPI
4. sorteddict – Pure-Python lazily-computed sorted dict implementation. Now deprecated in favor of Sorted Containers. GPLv3 License. Last updated September, 2007. sorteddict on PyPI
5. rbtree from NewCenturyComputers – Pure-Python tree-based implementation. Not sure when this was last updated. Unlikely to be fast. Unknown license. Unknown last update. rbtree from NewCenturyComputers
6. python-avl-tree from GitHub user pgrafov – Pure-Python tree-based implementation. Unlikely to be fast. MIT License. Last updated October, 2010. python-avl-tree from GitHub user pgrafov
7. pyavl – C-implementation for AVL tree-based dict and set containers. Claims to be fast. Lacking documentation and failed to build. Public Domain License. Last updated December, 2008. pyavl on PyPI
8. skiplist – C-implementation of sorted list based on skip-list data structure. Only supports Python 2. Zlib/libpng License. Last updated Septemeber, 2013. skiplist from Bitbucket user mojaves

The most similar module to Sorted Containers is skiplistcollections given that each is implemented in Python. But as is displayed below, Sorted Containers is several times faster and provides a richer API. Often the pure-Python implementation in Sorted Containers is faster even than the C-implementation counterparts. Where it lacks, performance is generally on the same magnitude.

Because Sorted Containers is implemented in pure-Python, its performance depends directly on the Python runtime. A runtime performance comparison is also included with data from popular runtimes.

Sorted Containers uses a segmented-list data structure similar to a B-tree limited to two levels of nodes. As part of the implementation, a load factor is used to determine how many values should be stored in each node. This can have a significant impact on performance and a load factor performance comparison is also provided.

Though these benchmarks exercise only one API repeatedly, an effort has also been made to simulate real-world workloads. The simulated workload performance comparison contains examples with comparisons to other implementations, load factors, and runtimes.

Some final notes about the graphs below. Missing data indicates the benchmark either took too long or failed. The set operations with tiny, small, medium, and large variations indicate the size of the container involved in the right-hand-side of the operation: tiny is exactly 10 elements; small is 10% of the size of the left-hand-side; medium is 50%; and large is 100%. Sorted Containers uses a different algorithm based on the size of the right-hand-side of the operation for a dramatic improvement in performance.

The legends of the graphs below correlate the underlying data structure used the Python project. The correlation is as follows:

Data Structure | Project
--- | ---
`SortedList` | Sorted Containers
`SortedKeyList` | Sorted Containers
B-Tree | blist on PyPI
List | sortedcollection recipe
AVL-Tree | bintrees on PyPI
RB-Tree | banyan on PyPI
Skip-List | skiplistcollections on PyPI
std::map | sortedmap on PyPI
Treap | treap on PyPI

## Sorted List

Graphs comparing Sorted List performance.

### __init__

Initializing with a list of random numbers using `SortedList.__init__()`.

### add

Randomly adding values using `SortedList.add()`.

### contains

Randomly testing membership using `SortedList.__contains__()`.

### count

Counting objects at random using `SortedList.count()`.

### __delitem__

Deleting objects at random using `SortedList.__delitem__()`.

### __getitem__

Retrieving objects by index using `SortedList.__getitem__()`.

### index

Finding the index of an object using `SortedList.index()`.

### iter

Iterating a SortedList using `SortedList.__iter__()`.

### pop

Removing the last object using `SortedList.pop()`.

### remove

Remove an object at random using `SortedList.remove()`.

### update_large

Updating a SortedList with a large iterable using `SortedList.update()`.

### update_small

Updating a SortedList with a small iterable using `SortedList.update()`.

## Sorted Dict

Graphs comparing Sorted Dict performance.

### __init__

Initializing with a list of pairs of random numbers using `SortedDict.__init__()`.

### __contains__

Given a key at random, test whether the key is in the dictionary using `SortedDict.__contains__()`.

### __getitem__

Given a key at random, retrieve the value using `SortedDict.__getitem__()`.

### __setitem__

Given a key at random, set the value using `SortedDict.__setitem__()`.

### __delitem__

Given a key at random, delete the value using `SortedDict.__delitem__()`.

### iter

Iterate the keys of a SortedDict using `SortedDict.__iter__()`.

### setitem_existing

Given an existing key at random, set the value using `SortedDict.__setitem__()`.

## Sorted Set

Graphs comparing Sorted Set performance.

### __init__

Initializing with a list of random numbers using `SortedSet.__init__()`.

### add

Randomly add values using `SortedSet.add()`.

### contains

Randomly test membership using `SortedSet.__contains__()`.

### difference_large

Set difference using `SortedSet.difference()`.

### difference_medium

Set difference using `SortedSet.difference()`.

### difference_small

Set difference using `SortedSet.difference()`.

### difference_tiny

Set difference using `SortedSet.difference()`.

### difference_update_large

Set difference using `SortedSet.difference_update()`.

### difference_update_medium

Set difference using `SortedSet.difference_update()`.

### difference_update_small

Set difference using `SortedSet.difference_update()`.

### difference_update_tiny

Set difference using `SortedSet.difference_update()`.

### intersection_large

Set intersection using `SortedSet.intersection()`.

### intersection_medium

Set intersection using `SortedSet.intersection()`.

### intersection_small

Set intersection using `SortedSet.intersection()`.

### intersection_tiny

Set intersection using `SortedSet.intersection()`.

### intersection_update_large

Set intersection using `SortedSet.intersection_update()`.

### intersection_update_medium

Set intersection using `SortedSet.intersection_update()`.

### intersection_update_small

Set intersection using `SortedSet.intersection_update()`.

### intersection_update_tiny

Set intersection using `SortedSet.intersection_update()`.

### iter

Iterating a set using `SortedSet.__iter__()`.

### pop

Remove the last item in a set using `SortedSet.pop()`.

### remove

Remove an item at random using `SortedSet.remove()`.

### union_large

Set union using `SortedSet.union()`.

### union_medium

Set union using `SortedSet.union()`.

### union_small

Set union using `SortedSet.union()`.

### union_tiny

Set union using `SortedSet.union()`.

### update_large

Set update using `SortedSet.update()`.

### update_medium

Set update using `SortedSet.update()`.

### update_small

Set update using `SortedSet.update()`.

### update_tiny

Set update using `SortedSet.update()`.

### symmetric_difference_large

Set symmetric-difference using `SortedSet.symmetric_difference()`.

### symmetric_difference_medium

Set symmetric-difference using `SortedSet.symmetric_difference()`.

### symmetric_difference_small

Set symmetric-difference using `SortedSet.symmetric_difference()`.

### symmetric_difference_tiny

Set symmetric-difference using `SortedSet.symmetric_difference()`.

### symm_diff_update_large

Set symmetric-difference using `SortedSet.symmetric_difference_update()`.

### symm_diff_update_medium

Set symmetric-difference using `SortedSet.symmetric_difference_update()`.

### symm_diff_update_small

Set symmetric-difference using `SortedSet.symmetric_difference_update()`.

### symm_diff_update_tiny

Set symmetric-difference using `SortedSet.symmetric_difference_update()`.