Notations

Statically estimate asymptotic notation for a given Python function by looking at the level of loop-nesting inside the function.

this is an early prototype

Example

from notations import notation

def my_example_function(arg1, arg2):
    f = 0
    for a in arg1:
        for i in a:
            f+=1
    for b in arg2:
        for j in b:
            f+=1

print(notation(my_example_function))

Will print Θ(n^2)

See test_notations.py for more examples.

TODO

This is a rough sketch of a concept at this stage.

• while operators
• Look at the relationship between input arguments in a function, just because a loop is nested, doesn't mean the O(n_n) is correct
• branches inside loops
• test comprehensions

FAQ

• Why not use the AST? The AST cannot be built at runtime (easily) from a code object, this library is intended to be used to evaluate the execution-order of a compiled function.
• How could you possibly calculate the order without running the code? This function equates the order by looking at the level of loop-nesting in a function, the use of comprehensions and the relationships between arguments. Dynamic runtime benchmarks are susceptible to environmental conditions (noisy neighbours) and there are already plenty of tools out there that do this

Research notes

• Paper on asymptotic heirarchy
• Notes on theta, O and omega functions

Changes

0.2.0

• Change to theta values for repr

0.1.0

• Initial prototype supporting basic for loops