Tail Call Optimization in Python
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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.
The following example is in Python:
def factorial(n):
if n == 0:
return 1
return n * factorial(n-1)
>>> factorial(1000)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "<stdin>", line 4, in factorial
File "<stdin>", line 4, in factorial
File "<stdin>", line 4, in factorial
[Previous line repeated 995 more times]
File "<stdin>", line 2, in factorial
RecursionError: maximum recursion depth exceeded in comparison
Implementation
To get around this in Python, we need some sort of trampoline, 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 from 2006.
"""
Python Decorator that enables tail call
optimization through Exception Trampolines.
"""
from dataclasses import dataclass, field
from typing import Any, Dict, List
import functools
import inspect
@dataclass
class TailRecurseException(Exception):
"""Exception to enable tail call recursion."""
args: List[Any] = field(default_factory=list)
kwargs: Dict[Any, Any] = field(default_factory=dict)
def tail_call(func):
"""
Decorator that performs tail call optimization.
Notes
=====
Works by throwing an exception to exit the stack
when the function sees itself as its grandparent in
the stack trace. It then calls itself with its new
arguments.
"""
@functools.wraps(func)
def recurse(*args, **kwargs):
frame = inspect.currentframe()
if frame.f_back is not None \
and frame.f_back.f_back is not None \
and frame.f_back.f_back.f_code == frame.f_code:
raise TailRecurseException(args, kwargs)
while True:
try:
return func(*args, **kwargs)
except TailRecurseException as exception:
args = exception.args
kwargs = exception.kwargs
return recurse
Example: Factorial
Now let’s redefine factorial in a tail-call way:
@tail_call
def factorial(n, acc=1):
if n == 0:
return acc
return factorial(n - 1, n * acc)
For the moment of truth…
>>> factorial(1000)
402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Example: Fibonacci Numbers
@tail_call
def fib(n, a=0, b=1):
if n == 0:
return a
if n == 1:
return b
return fib(n - 1, b, a + b)
>>> fib(1000)
43466557686937456435688527675040625802564660517371780402481729089536555417949051890403879840079255169295922593080322634775209689623239873322471161642996440906533187938298969649928516003704476137795166849228875
Conclusion
You can install the package via pypi:
pip install tail-recurse
It is also available on Github.