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Predict the likely worst-case order-of-growth function for an arbitrary Python function.

Project description

Tada!: auTomAtic orDer-of-growth Analysis

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This repository contains the source code and usage instructions for a tool called "Tada: auTomAtic orDer-of-growth Analysis" that is implemented in the Python 3 language. The tool systematically runs a doubling experiment to ascertain the likely worst-case order-of-growth function for an arbitrary Python function. This documentation provides a brief overview about how to run the tool, its provided test suite, and more.

Install Tada

  • Operating system: Unix/Linux · macOS/OS X · Windows
  • Dependency Management: Pipenv · Poetry

Pipenv

If you haven't done so already, you can run the following command to install pipenv on your local machine:

pip install pipenv

Once you have installed pipenv, you can then run the test suite for Tada's functions by typing the following in your terminal window:

  • pipenv install

You can also activate the pipenv shell by running this command: pipenv shell

Poetry

Similarly, you can run the following command to install poetry on your local machine:

pip install poetry

To install dependencies with poetry, you can just run:

poetry install --no-dev

You can activate the poetry shell with this command:

poetry shell

Run Command

There are multiple ways to use either pipenv or poetry to run and test Tada. You can have pipenv run or poetry run followed by the command like this:

pipenv run python
poetry run python

You can also just spawn a shell with the virtualenv activated by either pipenv or poetry. For ease of reading, the commands provided in the documentation will just be the ones that you would run in the shell.

Use Tada

Checks

Tada is currently under continuous development, it is not yet feature complete. However, the documentation here and in Speed-Surprises have featured some examples on how to run the tool to automatically suggest the likely worst-case order-of-growth function for various types of provided Python function.

If you want to run the tool, then you can run:

python tada_a_bigoh.py [-h] --directory DIRECTORY --module MODULE --function FUNCTION --types TYPES [TYPES ...]

You can learn about Tada's checks and defaults by typing python tada_a_bigoh.py -h in your terminal window and then reviewing the following output.

usage: tada_a_bigoh.py [-h] --directory DIRECTORY [DIRECTORY ...] --module
                       MODULE [MODULE ...] --function FUNCTION [FUNCTION ...]
                       --types TYPES [TYPES ...]
                       [--data_directory DATA_DIRECTORY]
                       [--data_module DATA_MODULE]
                       [--data_function DATA_FUNCTION] [--schema SCHEMA]
                       [--startsize STARTSIZE] [--steps STEPS]
                       [--runningtime RUNNINGTIME] [--expect EXPECT]
                       [--backfill] [--indicator INDICATOR]
                       [--maxsize MAXSIZE] [--sorted] [--log] [--md]
                       [--contrast] [--level LEVEL]
                       [--position POSITION [POSITION ...]]

optional arguments:
  -h, --help            show this help message and exit
  --directory DIRECTORY [DIRECTORY ...]
                        Path to the package directory with functions to
                        analyze (default: None)
  --module MODULE [MODULE ...]
                        Module name with functions to analyze (default: None)
  --function FUNCTION [FUNCTION ...]
                        Name of the function to analyze (default: None)
  --types TYPES [TYPES ...]
                        Data generation type: hypothesis or parameter types of
                        the function (default: None)
  --data_directory DATA_DIRECTORY
                        Path to the package directory with function to
                        generate data (default: None)
  --data_module DATA_MODULE
                        Module name with functions to generate data (default:
                        None)
  --data_function DATA_FUNCTION
                        Name of the data generation function (default: None)
  --schema SCHEMA       The path to the JSON schema that describes the data
                        format (default: None)
  --startsize STARTSIZE
                        Starting size of the doubling experiment (default: 1)
  --steps STEPS         Maximum rounds of the doubling experiment (default:
                        10)
  --runningtime RUNNINGTIME
                        Maximum running time of the doubling experiment
                        (default: 200)
  --expect EXPECT       Expected Growth Ratio: O(1) | O(logn) | O(n) |
                        O(nlogn) | O(n^2) | O(n^3) | O(c^n). By using this
                        argument, the experiment result will be stored in a
                        csv file (default: None)
  --backfill            Enable backfill to shrink experiments size according
                        to the Predicted True Value (default: False)
  --indicator INDICATOR
                        Indicator value (default: 0.1)
  --maxsize MAXSIZE     Maximum size of the doubling experiment (default:
                        1500)
  --sorted              Enable input data to be sorted (default: False)
  --log                 Show log/debug/diagnostic output (default: False)
  --md                  Show results table in markdown format (default: False)
  --contrast            Show contrast result table. Only works with multiple
                        experiments (default: False)
  --viz                 Visualize a simple graph for the result (default:
                        False)
  --level LEVEL         The level of nested data structure to apply doubling
                        experiment (default: 1)
  --position POSITION [POSITION ...]
                        The position of input data to double in the
                        multivariable doubling experiment. Must be the last
                        argument (default: [0])

Sample usage: python tada_a_bigoh.py --directory
/Users/myname/projectdirectory --module modulename.file --function
function_name --types hypothesis

It is worth noting that when the provided function is relied on an external Python library, it is likely that Tada might not have this dependency, and thus, it might cause an error when running the experiment. You can simply resolve this issue by installing the required dependencies.

Type in this command if you are using pipenv:

pipenv install <library-name>

or this command if you are using poetry:

poetry add <library-name>

Otherwise, type in the installation command that is appropriate for your own chosen installation method.

Data Generation

Tada adopts Hypothesis and Hypothesis-jsonschema to generate random data for the provided Python function. Therefore, we encourage you to create a file of a JSON array that contains JSON schemas of each parameter passed into the provided function. Tada also supports data generation through our built-in data generation functions including these following types: int, int_list, char, char_list, boolean, string, float, bitdepth

To specify the data generation strategy, we encourage you to set argument --types TYPES [TYPES ...] with hypothesis or one of the aforementioned generation types. When using hypothesis to generate experiment data, you can simply set the maxItems and minItems in the json schema to zero. The size doubling will be enabled through the command line check --startsize STARTSIZE, which will be the starting size of the doubling experiment.

For further usage of JSON schemas and how to write them for various data types: please refer to JSON schema and sample JSON schemas.

When completed, Tada will be used to estimate the worst-case time complexity for Python functions.

Speed-Surprises

We have provided an extensive library of functions and sample JSON schemas in Speed-Surprises repository. You can use or test Tada in conjunction with functions in this repository.

Sample Output

$ python tada_a_bigoh.py --directory ../speed-surprises/ --module speedsurprises.lists.sorting --function insertion_sort --types hypothesis --schema ../speed-surprises/speedsurprises/jsonschema/single_int_list.json --startsize 50

      Tada!: auTomAtic orDer-of-growth Analysis!
        https://github.com/Tada-Project/tada/
    For Help Information Type: python tada_a_bigoh.py -h

Start running experiment for size 50 →


→ Done running experiment for size 50
.
.
.
→ Done running experiment for size 800

+-----------------------------------------------------------------------------+
|             insertion_sort: O(n) linear or O(nlogn) linearithmic            |
+------+------------------------+------------------------+--------------------+
| Size |          Mean          |         Median         |       Ratio        |
+------+------------------------+------------------------+--------------------+
|  50  | 5.254574352518718e-06  | 5.080362350463869e-06  |         0          |
| 100  | 1.013776767171224e-05  | 1.0109862487792971e-05 | 1.929322337375019  |
| 200  | 2.041813344523112e-05  | 1.9827050170898433e-05 | 2.0140660258179457 |
| 400  | 4.1289982617187504e-05 | 4.0720488891601556e-05 | 2.0222212146836194 |
| 800  | 9.176736091308593e-05  | 9.089502807617187e-05  |  2.22250907111999  |
+------+------------------------+------------------------+--------------------+
O(n) linear or O(nlogn) linearithmic

Compare two algorithms' performance with Tada

If you would like to run Tada to compare the performance of two functions, you will just need to specify the additional function with it's directory and module (if it's different from the first function) like this:

$ python tada_a_bigoh.py --directory ../speed-surprises/ --module speedsurprises.lists.sorting --function insertion_sort bubble_sort --types hypothesis --schema ../speed-surprises/speedsurprises/jsonschema/single_int_list.json --startsize 25

      Tada!: auTomAtic orDer-of-growth Analysis!
        https://github.com/Tada-Project/tada/
    For Help Information Type: python tada_a_bigoh.py -h

Start running experiment insertion_sort for size 25 →
.
.
.
→ Done running experiment bubble_sort for size 800

+-----------------------------------------------------------------------------+
|             insertion_sort: O(n) linear or O(nlogn) linearithmic            |
+------+------------------------+------------------------+--------------------+
| Size |          Mean          |         Median         |       Ratio        |
+------+------------------------+------------------------+--------------------+
|  25  | 3.644364811706543e-06  | 3.498709533691405e-06  |         0          |
|  50  | 6.535123836263021e-06  | 6.483351989746092e-06  | 1.793213405878218  |
| 100  | 1.2902192108154296e-05 | 1.2540842590332028e-05 | 1.9742842571032526 |
| 200  | 2.5023900944010416e-05 | 2.4608139038085928e-05 | 1.9395077002608803 |
| 400  | 5.526396857910156e-05  | 5.3515207031250005e-05 | 2.2084473840729952 |
| 800  | 0.00011801120257161459 |  0.00011251379296875   | 2.1354094829925283 |
+------+------------------------+------------------------+--------------------+
+-----------------------------------------------------------------------------+
|                        bubble_sort: O(n^2) quadratic                        |
+------+------------------------+------------------------+--------------------+
| Size |          Mean          |         Median         |       Ratio        |
+------+------------------------+------------------------+--------------------+
|  25  | 2.8776128824869792e-05 | 2.846207250976562e-05  |         0          |
|  50  | 0.00010703222574869792 | 0.00010308191601562499 | 3.7194796562140504 |
| 100  | 0.0004109644687825521  | 0.00039437410449218743 | 3.8396330255474633 |
| 200  |   0.0015730586140625   | 0.0015326660937500002  | 3.8277241308051635 |
| 400  |    0.00632440301875    |  0.006229572156249999  | 4.020449690947576  |
| 800  |  0.029292134683333335  |  0.028519337000000006  | 4.631604690038055  |
+------+------------------------+------------------------+--------------------+

At the greatest common size 800:
Mean: insertion_sort is 99.60% faster than bubble_sort
Median: insertion_sort is 99.61% faster than bubble_sort
Contrast result tables of two algorithms' performance with Tada

If you would like to contrast run time of two different algorithms where the run time of one might be included in another, you can use the --contrast feature to get the result table generated based on the subtraction of the two algorithms with the growth ratio analysis of the run time difference:

$ python tada_a_bigoh.py --directory ../speed-surprises/ --module=speedsurprises.graph.graph_gen --function graph_gen graph_gen_BFS --types hypothesis --schema=../speed-surprises/speedsurprises/jsonschema/int_and_int.json --startsize=50  --max=1000 --position 0 --contrast

      Tada!: auTomAtic orDer-of-growth Analysis!
        https://github.com/Tada-Project/tada/
    For Help Information Type: python tada_a_bigoh.py -h

Start running experiment graph_gen for size 25 →
.
.
.
→ Done running experiment graph_gen_BFS for size 800

+-----------------------------------------------------------------------------+
|               graph_gen: O(n) linear or O(nlogn) linearithmic               |
+------+------------------------+------------------------+--------------------+
| Size |          Mean          |         Median         |       Ratio        |
+------+------------------------+------------------------+--------------------+
|  50  |  9.94538065592448e-06  | 9.501693725585938e-06  |         0          |
| 100  | 1.8558588460286458e-05 | 1.8363348388671875e-05 | 1.8660510947090876 |
| 200  | 3.7122855631510415e-05 | 3.560983886718751e-05  | 2.000305988300223  |
| 400  | 7.208413248697916e-05  | 7.197658691406252e-05  | 1.9417722925871337 |
| 800  | 0.00015173049479166666 | 0.00014575283203125002 | 2.104908383534675  |
+------+------------------------+------------------------+--------------------+
+-------------------------------------------------------------------------+
|                     graph_gen_BFS: O(n^2) quadratic                     |
+------+-----------------------+---------------------+--------------------+
| Size |          Mean         |        Median       |       Ratio        |
+------+-----------------------+---------------------+--------------------+
|  50  |   0.0010322848828125  |  0.000936182421875  |         0          |
| 100  | 0.0037961446354166668 |   0.0036485609375   | 3.6774195753733445 |
| 200  |  0.014912410624999999 |    0.01433645625    | 3.928304123576473  |
| 400  |  0.06095087833333333  | 0.05791582499999999 | 4.087258583877236  |
| 800  |      0.252504645      | 0.23859980000000003 | 4.1427564606875915 |
+------+-----------------------+---------------------+--------------------+

At the greatest common size 800:
Mean: graph_gen is 99.94% faster than graph_gen_BFS
Median: graph_gen is 99.94% faster than graph_gen_BFS

+----------------------------------------------------------------------------------------+
|               Contrast for graph_gen and graph_gen_BFS: O(n^2) quadratic               |
+-------+---------------------------+---------------------------+------------------------+
|  Size |            Mean           |           Median          |         Ratio          |
+-------+---------------------------+---------------------------+------------------------+
|   50  |   0.0010223395021565756   |   0.0009266807281494141   |           0            |
|  100  |   0.0037775860469563805   |    0.003630197589111328   |   3.6950406777667753   |
|  200  |    0.014875287769368488   |    0.014300846411132813   |   3.9377760253412575   |
|  400  |    0.06087879420084635    |    0.05784384841308593    |   4.092612872082332    |
|  800  |    0.25235291450520836    |    0.23845404716796878    |   4.145169394660909    |
+-------+---------------------------+---------------------------+------------------------+

Debug output with --log

$ python tada_a_bigoh.py --directory ../speed-surprises/ --module speedsurprises.lists.sorting --function insertion_sort --types hypothesis --schema ../speed-surprises/speedsurprises/jsonschema/single_int_list.json --startsize 50 --log

      Tada!: auTomAtic orDer-of-growth Analysis!
        https://github.com/Tada-Project/tada/
    For Help Information Type: python tada_a_bigoh.py -h

Start running experiment for size 50 →

.....................
tada_speedsurpriseslistssorting_insertionsort_50: Mean +- std dev: 6.76 us +- 0.38 us

Mean 6.756377457682293e-06
Median 6.655228393554689e-06
current indicator: 0.1
expected end time: 6.756377457682293e-06

→ Done running experiment for size 50

end time rate: 1
last end time rate: 1

Start running experiment for size 100 →
.
.
.
→ Done running experiment for size 800

end time rate: 1.0977868448462222
last end time rate: 1.0104045516442501

Quit due to reaching max size: 1500
+-----------------------------------------------------------------------------+
|             insertion_sort: O(n) linear or O(nlogn) linearithmic            |
+------+------------------------+------------------------+--------------------+
| Size |          Mean          |         Median         |       Ratio        |
+------+------------------------+------------------------+--------------------+
|  50  | 5.108458277893066e-06  | 4.995336715698241e-06  |         0          |
| 100  | 9.719848541259765e-06  | 9.592753784179686e-06  | 1.9026970589781584 |
| 200  | 1.9103883695475262e-05 | 1.881045025634766e-05  | 1.9654507592768782 |
| 400  | 4.1088669527180994e-05 | 4.0323755249023436e-05 | 2.1508019092951667 |
| 800  |    8.721809375e-05     | 8.493975268554687e-05  | 2.1226799201250226 |
+------+------------------------+------------------------+--------------------+

Tada-Generate-Functions

We have provided an extensive library of data generation functions in Tada-Generate-Functions repository. You can use or test Tada in conjunction with generation functions in this repository by using the --types custom argument followed by --data_directory, --data_module, and --data_function:

python tada_a_bigoh.py --directory ../speed-surprises/ --module speedsurprises.lists.python_basic --function list_copy --types custom --data_directory ../Tada-Generate-Functions/ --data_module generatefunctions.generate_lists  --data_function generate_single_int_list --startsize 25 --maxsize 1000

Record Tada Experiment Result(s)

If you would like to record the results of the doubling experiment, you can use the command line argument --expect by specifying with a string of the expected Big-Oh growth ratio of the provided function (e.g. "O(1)", "O(n^2)"). The following variables will be stored and exported to experiment_data.csv. :

  • EXPERIMENT_RELIABILITY: dummy variable := 1 if the result provided by tada tool is what user expected.
  • CPU_TYPE: string := type information of CPU.
  • CPU_TEMP: string := temperature information of CPU.
  • CPU_COUNT: int := the number of physical CPUs.
  • TOTAL_RUNNING_TIME: int := total time spent on running experiment.
  • QUIT_BY_MAX_RUNTIME: dummy variable := 1 if the tool exits by reaching the max_runtime.
  • QUIT_BY_INDICATOR: dummy variable := 1 if the tool exits by having indicator larger than the indicator bound.
  • QUIT_BY_BACKFILL: dummy variable := 1 if the tool exits by having multiple times of backfills
  • QUIT_BY_MAX_SIZE: dummy variable := 1 if the tool exits by reaching the max_size back-filling.
  • MEM_MAX_RSS: int := track of current machine memory usage.
  • MEM_PEAK_PAGEFILE_USAGE: int := track of current machine memory usage (windows).
  • OS: string := information of current operating system.
  • INDICATOR_VALUE: int := the value of the indicator boundary user set.
  • BACKFILL_TIMES: int := the value of the back-fill time boundary user set.
  • PYPERF_AVG_EXPERIMENT_ROUNDS: int := the average loops of all benchmarks in the experiment, the measurement of difficulty for PyPerf to analyze the target algorithm.
  • PYPERF_LAST_TWO_EXPERIMENT_ROUNDS_RATIO: int := the growth ratio of the total loops in the last two benchmarks, the total loops is usually decreasing when the input get larger, the measurement of reliability of the experiment analysis.
  • NAME_OF_EXPERIMENT: string := experiment information.
  • PYTHON_VERSION: string := current version of Python.
  • DATA_GEN_STRATEGY: string := the chosen data generation strategy
  • START_SIZE: int := initial size of the doubling experiment
  • ARGUMENTS: string := input argument to run the doubling experiment

To run with experiment data collected, add expect into the command like this:

python tada_a_bigoh.py --directory ../speed-surprises/ --module speedsurprises.lists.sorting --function insertion_sort --types hypothesis --schema ../speed-surprises/speedsurprises/jsonschema/single_int_list.json --startsize 50 --expect "O(n)"

Add New Features to Tada

You can follow these steps to add a new feature if you are already a collaborator on the project. First, you should type the following command, substituting the name of your feature for the word feature-name.

  • git checkout -b feature-name
  • git checkout master
  • git push -u origin feature-name

To install development dependencies, type the following commands in the terminal:

pipenv install --dev

or

poetry install

Finally, you should open a pull request on the GitHub repository for the new branch that you have created. This pull request should describe the new feature that you are adding and give examples of how to run it on the command line. Of course, if you are not a collaborator on this project, then you will need to fork the repository, add your new feature, document and test it as appropriate, and then create a pull request similarily.

We highly recommend you to provide tests along with the feature that you implemented and you should not break the existing test cases or features.

Test Tada

To run the test suite for Tada's functions by typing the following in your terminal window:

pytest

If you want to collect the coverage of the provided test suite, then you can run:

pytest --cov-config pytest.cov --cov

If you want to collect the coverage of the provided test suite and see what lines of code are not covered, then you can run:

pytest --cov-config pytest.cov --cov --cov-report term-missing

Future Works

  • Further verification of the accuracy and efficiency of the tool

Problems or Praise

If you have any problems with installing or using the Tada or its provided test suite, then please create an issue associated with this Git repository using the "Issues" link at the top of this site. The contributors to Tada will do all that they can to resolve your issue and ensure that all of its features and the test suite work well in your development environment.

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