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125 lines
5.9 KiB
Markdown
125 lines
5.9 KiB
Markdown
---
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title: "Tail Call Optimization in Python"
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date: 2020-10-11T20:46:54-04:00
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draft: false
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tags: ["Python"]
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medium_enabled: true
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---
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In a standard recursive function, a new stack frame is created every time a recursive call is made. This can lead to bad memory performance and as a protective measure, some programming languages have a maximum stack frame limit.
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The following example is in Python:
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```python
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def factorial(n):
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if n == 0:
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return 1
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return n * factorial(n-1)
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```
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```python
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>>> factorial(1000)
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Traceback (most recent call last):
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File "<stdin>", line 1, in <module>
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File "<stdin>", line 4, in factorial
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File "<stdin>", line 4, in factorial
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File "<stdin>", line 4, in factorial
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[Previous line repeated 995 more times]
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File "<stdin>", line 2, in factorial
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RecursionError: maximum recursion depth exceeded in comparison
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```
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## Implementation
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To get around this in Python, we need some sort of [trampoline](https://en.wikipedia.org/wiki/Tail_call#Through_trampolining), or way to exit part the stack and call the recursive function again. This technique is often used in Tail Call Optimization, and we can do this in Python using exceptions. This code is heavily inspired by Crutcher Dunnavant's [code snippet](https://code.activestate.com/recipes/474088-tail-call-optimization-decorator/) from 2006.
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```python
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"""
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Python Decorator that enables tail call
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optimization through Exception Trampolines.
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"""
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from dataclasses import dataclass, field
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from typing import Any, Dict, List
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import functools
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import inspect
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@dataclass
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class TailRecurseException(Exception):
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"""Exception to enable tail call recursion."""
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args: List[Any] = field(default_factory=list)
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kwargs: Dict[Any, Any] = field(default_factory=dict)
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def tail_call(func):
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"""
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Decorator that performs tail call optimization.
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Notes
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=====
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Works by throwing an exception to exit the stack
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when the function sees itself as its grandparent in
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the stack trace. It then calls itself with its new
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arguments.
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"""
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@functools.wraps(func)
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def recurse(*args, **kwargs):
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frame = inspect.currentframe()
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if frame.f_back is not None \
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and frame.f_back.f_back is not None \
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and frame.f_back.f_back.f_code == frame.f_code:
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raise TailRecurseException(args, kwargs)
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while True:
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try:
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return func(*args, **kwargs)
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except TailRecurseException as exception:
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args = exception.args
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kwargs = exception.kwargs
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return recurse
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```
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## Example: Factorial
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Now let's redefine `factorial` in a tail-call way:
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```python
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@tail_call
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def factorial(n, acc=1):
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if n == 0:
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return acc
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return factorial(n - 1, n * acc)
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```
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For the moment of truth...
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```python
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>>> factorial(1000)
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402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
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```
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## Example: Fibonacci Numbers
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```python
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@tail_call
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def fib(n, a=0, b=1):
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if n == 0:
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return a
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if n == 1:
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return b
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return fib(n - 1, b, a + b)
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```
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```python
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>>> fib(1000)
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43466557686937456435688527675040625802564660517371780402481729089536555417949051890403879840079255169295922593080322634775209689623239873322471161642996440906533187938298969649928516003704476137795166849228875
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```
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## Conclusion
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You can install the package via pypi:
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```bash
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pip install tail-recurse
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```
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It is also available on [Github](https://github.com/Brandon-Rozek/tail-recurse/).
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