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Groups > comp.lang.python > #55239
| From | Terry Reedy <tjreedy@udel.edu> |
|---|---|
| Subject | Tail recursion to while iteration in 2 easy steps |
| Date | 2013-10-01 17:30 -0400 |
| Newsgroups | comp.lang.python |
| Message-ID | <mailman.571.1380663065.18130.python-list@python.org> (permalink) |
Part of the reason that Python does not do tail call optimization is
that turning tail recursion into while iteration is almost trivial, once
you know the secret of the two easy steps. Here it is.
Assume that you have already done the work of turning a body recursive
('not tail recursive') form like
def fact(n): return 1 if n <= 1 else n * fact(n-1)
into a tail recursion like
def fact(n, _fac=1):
'''Return factorial for any count n.
Users are not expected to override private parameter _fac.
'''
if n <= 1:
return _fac
else: # optional
return fact(n-1, n * _fac)
(This conversion nearly requires adding an accumulator parameter, as
done here.
Turn this into while iteration with two easy steps.
1. If not already done, make if-else a statement, rather than an
expression, with the recursive call in the if branch. If nothing else,
just use 'not condition' to invert the condition.
def fact(n, _fac=1):
if n > 1: # not n <= 1
return fact(n-1, n * _fac)
else: # optional
return _fac
While contrary to what is often published, this order makes logical
sense. The recursive call means 'go to the top of this function with new
bindings for the parameters'. So put it closest to the top. The base
case means 'we are done, time to leave'. So put it at the bottom.
2. This order also makes the follow substeps work:
2a. Replace 'if' with 'while'.
2b. Replace the recursive call with multiple assignment, using the
parameters as targets and the arguments as source.
For our example:
def fact(n, _fac=1):
while n > 1:
n, _fac = n-1, n * _fac
else:
return _fac
The proof of correctness for this conversion might argue that the
recursive form is equivalent to the following pseudo-Python:
def fact(n, _fac=1):
label top
if n > 1:
n, _fac = n-1, n * _fac
goto top
else:
return _fac
and that this is equivalent to the real Python with while.
At this point, you call pull the initialization of the private parameter
into the body, remove the else, and even add a value check.
def fact(n):
if n < 0 or n != int(n):
raise ValueError('fact input {} is not a count'.format(n))
fac = 1
while n > 1:
n, fac = n-1, n * fac
return fac
With care, the multiple-assignment statement can usually be turned into
multiple assignment statements for greater efficiency.
fac *= n
n -= 1
But note that the reverse order would be a bug. So I would not do this,
especially in more complicated situations, without having tests first.
--
Terry Jan Reedy
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Tail recursion to while iteration in 2 easy steps Terry Reedy <tjreedy@udel.edu> - 2013-10-01 17:30 -0400
Re: Tail recursion to while iteration in 2 easy steps rusi <rustompmody@gmail.com> - 2013-10-01 22:16 -0700
Re: Tail recursion to while iteration in 2 easy steps Alain Ketterlin <alain@dpt-info.u-strasbg.fr> - 2013-10-02 10:23 +0200
Re: Tail recursion to while iteration in 2 easy steps rusi <rustompmody@gmail.com> - 2013-10-02 06:29 -0700
Re: Tail recursion to while iteration in 2 easy steps Ravi Sahni <ganeshsahni07@gmail.com> - 2013-10-03 22:57 +0530
Re: Tail recursion to while iteration in 2 easy steps rusi <rustompmody@gmail.com> - 2013-10-04 03:52 -0700
Re: Tail recursion to while iteration in 2 easy steps Alain Ketterlin <alain@dpt-info.u-strasbg.fr> - 2013-10-02 10:17 +0200
Re: Tail recursion to while iteration in 2 easy steps Mark Janssen <dreamingforward@gmail.com> - 2013-10-02 11:59 -0700
Re: Tail recursion to while iteration in 2 easy steps Mark Janssen <dreamingforward@gmail.com> - 2013-10-02 14:05 -0700
Re: Tail recursion to while iteration in 2 easy steps Alain Ketterlin <alain@dpt-info.u-strasbg.fr> - 2013-10-04 11:49 +0200
Re: Tail recursion to while iteration in 2 easy steps Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-10-04 10:51 +0000
Re: Tail recursion to while iteration in 2 easy steps Terry Reedy <tjreedy@udel.edu> - 2013-10-04 18:32 -0400
Re: Tail recursion to while iteration in 2 easy steps Alain Ketterlin <alain@dpt-info.u-strasbg.fr> - 2013-10-07 19:15 +0200
Re: Tail recursion to while iteration in 2 easy steps Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2013-10-07 19:57 +0200
Re: Tail recursion to while iteration in 2 easy steps Alain Ketterlin <alain@dpt-info.u-strasbg.fr> - 2013-10-08 10:56 +0200
Re: Tail recursion to while iteration in 2 easy steps Jussi Piitulainen <jpiitula@ling.helsinki.fi> - 2013-10-08 12:49 +0300
Re: Tail recursion to while iteration in 2 easy steps Terry Reedy <tjreedy@udel.edu> - 2013-10-07 16:42 -0400
Re: Tail recursion to while iteration in 2 easy steps random832@fastmail.us - 2013-10-07 17:19 -0400
Re: Tail recursion to while iteration in 2 easy steps Alain Ketterlin <alain@dpt-info.u-strasbg.fr> - 2013-10-08 10:41 +0200
Re: Tail recursion to while iteration in 2 easy steps MRAB <python@mrabarnett.plus.com> - 2013-10-07 22:39 +0100
Re: Tail recursion to while iteration in 2 easy steps Piet van Oostrum <piet@vanoostrum.org> - 2013-10-07 18:03 -0400
Re: Tail recursion to while iteration in 2 easy steps Mark Janssen <dreamingforward@gmail.com> - 2013-10-07 15:47 -0700
Re: Tail recursion to while iteration in 2 easy steps Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-10-07 23:50 +0000
Re: Tail recursion to while iteration in 2 easy steps Mark Janssen <dreamingforward@gmail.com> - 2013-10-07 17:24 -0700
Formal-ity and the Church-Turing thesis rusi <rustompmody@gmail.com> - 2013-10-07 20:17 -0700
Re: Formal-ity and the Church-Turing thesis Ravi Sahni <ganeshsahni07@gmail.com> - 2013-10-08 10:46 +0530
Re: Formal-ity and the Church-Turing thesis rusi <rustompmody@gmail.com> - 2013-10-07 22:44 -0700
Re: Formal-ity and the Church-Turing thesis Mark Lawrence <breamoreboy@yahoo.co.uk> - 2013-10-08 07:43 +0100
Re: Formal-ity and the Church-Turing thesis Ravi Sahni <ganeshsahni07@gmail.com> - 2013-10-08 18:31 +0530
Re: Formal-ity and the Church-Turing thesis rusi <rustompmody@gmail.com> - 2013-10-08 06:33 -0700
Re: Formal-ity and the Church-Turing thesis Steven D'Aprano <steve@pearwood.info> - 2013-10-08 07:50 +0000
Re: Formal-ity and the Church-Turing thesis Ravi Sahni <ganeshsahni07@gmail.com> - 2013-10-08 18:16 +0530
Re: Formal-ity and the Church-Turing thesis Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-10-08 13:11 +0000
Re: Formal-ity and the Church-Turing thesis Robert Day <robertkday@gmail.com> - 2013-10-08 14:25 +0100
Re: Formal-ity and the Church-Turing thesis Chris Angelico <rosuav@gmail.com> - 2013-10-09 08:36 +1100
Re: Formal-ity and the Church-Turing thesis Mark Janssen <dreamingforward@gmail.com> - 2013-10-07 22:19 -0700
Re: Formal-ity and the Church-Turing thesis rusi <rustompmody@gmail.com> - 2013-10-07 23:01 -0700
Re: Formal-ity and the Church-Turing thesis Mark Janssen <dreamingforward@gmail.com> - 2013-10-08 10:39 -0700
Re: Tail recursion to while iteration in 2 easy steps Mark Janssen <dreamingforward@gmail.com> - 2013-10-07 17:16 -0700
Re: Tail recursion to while iteration in 2 easy steps Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-10-08 02:36 +0000
Re: Tail recursion to while iteration in 2 easy steps Mark Janssen <dreamingforward@gmail.com> - 2013-10-07 20:27 -0700
Re: Tail recursion to while iteration in 2 easy steps Steven D'Aprano <steve@pearwood.info> - 2013-10-08 09:22 +0000
Re: Tail recursion to while iteration in 2 easy steps Charles Hixson <charleshixsn@earthlink.net> - 2013-10-09 15:45 -0700
Re: Tail recursion to while iteration in 2 easy steps Piet van Oostrum <piet@vanoostrum.org> - 2013-10-07 22:46 -0400
Re: Tail recursion to while iteration in 2 easy steps Jussi Piitulainen <jpiitula@ling.helsinki.fi> - 2013-10-08 10:25 +0300
Re: Tail recursion to while iteration in 2 easy steps Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2013-10-08 11:18 +0200
Re: Tail recursion to while iteration in 2 easy steps Piet van Oostrum <piet@vanoostrum.org> - 2013-10-07 22:45 -0400
Re: Tail recursion to while iteration in 2 easy steps Mark Janssen <dreamingforward@gmail.com> - 2013-10-07 20:34 -0700
Re: Tail recursion to while iteration in 2 easy steps Terry Reedy <tjreedy@udel.edu> - 2013-10-02 18:17 -0400
Re: Tail recursion to while iteration in 2 easy steps Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-10-03 01:24 +0000
Re: Tail recursion to while iteration in 2 easy steps Dave Angel <davea@davea.name> - 2013-10-03 01:39 +0000
Re: Tail recursion to while iteration in 2 easy steps MRAB <python@mrabarnett.plus.com> - 2013-10-03 02:46 +0100
Re: Tail recursion to while iteration in 2 easy steps Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-10-03 02:34 +0000
Re: Tail recursion to while iteration in 2 easy steps Chris Angelico <rosuav@gmail.com> - 2013-10-03 14:14 +1000
Re: Tail recursion to while iteration in 2 easy steps random832@fastmail.us - 2013-10-03 10:16 -0400
Re: Tail recursion to while iteration in 2 easy steps Terry Reedy <tjreedy@udel.edu> - 2013-10-03 15:04 -0400
Re: Tail recursion to while iteration in 2 easy steps Terry Reedy <tjreedy@udel.edu> - 2013-10-02 22:41 -0400
Re: Tail recursion to while iteration in 2 easy steps Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-10-04 01:30 +0000
Re: Tail recursion to while iteration in 2 easy steps Terry Reedy <tjreedy@udel.edu> - 2013-10-02 23:06 -0400
Re: Tail recursion to while iteration in 2 easy steps random832@fastmail.us - 2013-10-03 10:14 -0400
Literal syntax for frozenset, frozendict (was: Tail recursion to while iteration in 2 easy steps) Ben Finney <ben+python@benfinney.id.au> - 2013-10-04 10:18 +1000
Re: Literal syntax for frozenset, frozendict Ethan Furman <ethan@stoneleaf.us> - 2013-10-03 18:31 -0700
Re: Tail recursion to while iteration in 2 easy steps Duncan Booth <duncan.booth@invalid.invalid> - 2013-10-03 14:52 +0000
Re: Tail recursion to while iteration in 2 easy steps Neil Cerutti <neilc@norwich.edu> - 2013-10-03 16:03 +0000
Re: Tail recursion to while iteration in 2 easy steps Duncan Booth <duncan.booth@invalid.invalid> - 2013-10-04 10:16 +0000
Re: Tail recursion to while iteration in 2 easy steps Ian Kelly <ian.g.kelly@gmail.com> - 2013-10-04 04:41 -0600
Re: Tail recursion to while iteration in 2 easy steps Ian Kelly <ian.g.kelly@gmail.com> - 2013-10-04 04:46 -0600
Re: Tail recursion to while iteration in 2 easy steps Duncan Booth <duncan.booth@invalid.invalid> - 2013-10-04 11:16 +0000
Re: Tail recursion to while iteration in 2 easy steps Jussi Piitulainen <jpiitula@ling.helsinki.fi> - 2013-10-04 14:11 +0300
Re: Tail recursion to while iteration in 2 easy steps Terry Reedy <tjreedy@udel.edu> - 2013-10-04 17:14 -0400
Re: Tail recursion to while iteration in 2 easy steps Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2013-10-05 09:39 +0200
Re: Tail recursion to while iteration in 2 easy steps random832@fastmail.us - 2013-10-07 17:27 -0400
Re: Tail recursion to while iteration in 2 easy steps Jussi Piitulainen <jpiitula@ling.helsinki.fi> - 2013-10-08 10:11 +0300
Re: Tail recursion to while iteration in 2 easy steps Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2013-10-08 11:43 +0200
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