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Re: Possibly Pythonic Tail Call Optimization (TCO/TRE)

From Paul Rubin <no.email@nospam.invalid>
Newsgroups comp.lang.python
Subject Re: Possibly Pythonic Tail Call Optimization (TCO/TRE)
Date 2015-07-13 22:41 -0700
Organization A noiseless patient Spider
Message-ID <87bnff1eks.fsf@jester.gateway.sonic.net> (permalink)
References (3 earlier) <CAPTjJmr92j+2DDPsZxynoHyZTTCpc-48cWCVrx_fT3dA0j_Osg@mail.gmail.com> <55A3C366.6060602@rece.vub.ac.be> <mailman.468.1436796350.3674.python-list@python.org> <87fv4r1fre.fsf@jester.gateway.sonic.net> <mailman.481.1436851550.3674.python-list@python.org>

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Chris Angelico <rosuav@gmail.com> writes:
> That's a prime example of recursion... but not of recursion that can
> be tail-call optimized into iteration. It's an example of forking
> recursion, where one call can result in multiple calls (same with tree
> traversal); it calls itself to sort the first part and the last part,
> and while you might be able to turn the second call into a goto, you
> still need stack space to maintain the first call. The claim that TCO
> means you don't need stack space for all those levels of recursion
> doesn't work if you still need stack space for all those levels of
> recursion *before* you get to the tail call.

You partition the array into two parts, one of which has at most N/2
elements.  You push that smaller one onto the stack and recurse, so at
the next recursive level you push at most an N/4 part, then N/8 and so
on.  In that way the total recursion depth is O(log N).  If N=1e6 you
enter 20 levels of recursion which is no big deal.

If you also push the larger part on the stack, it can have size as high
as N-1, so you can end up pushing N-1, N-2, N-3, etc.  If N=1e6 you
overflow the stack when you've barely gotten started.

So it's important in that example that both of the recursive calls
involving the larger partition are both tail calls.  It's fine that the
first call pushes stuff on the stack.  It's vital that the second call
be turned into a goto.

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Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Chris Angelico <rosuav@gmail.com> - 2015-07-14 00:05 +1000
  Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Steven D'Aprano <steve@pearwood.info> - 2015-07-14 13:20 +1000
    Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2015-07-14 09:26 +0200
    Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Ian Kelly <ian.g.kelly@gmail.com> - 2015-07-14 02:34 -0600
      Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Grant Edwards <invalid@invalid.invalid> - 2015-07-14 14:03 +0000
    Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2015-07-14 12:43 +0200
  Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Paul Rubin <no.email@nospam.invalid> - 2015-07-13 22:15 -0700
    Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Chris Angelico <rosuav@gmail.com> - 2015-07-14 15:25 +1000
      Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Paul Rubin <no.email@nospam.invalid> - 2015-07-13 22:41 -0700
        Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Chris Angelico <rosuav@gmail.com> - 2015-07-14 21:43 +1000
          Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Marko Rauhamaa <marko@pacujo.net> - 2015-07-14 15:28 +0300
            Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Chris Angelico <rosuav@gmail.com> - 2015-07-14 22:55 +1000
              Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Marko Rauhamaa <marko@pacujo.net> - 2015-07-14 16:38 +0300
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Chris Angelico <rosuav@gmail.com> - 2015-07-14 23:43 +1000
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Marko Rauhamaa <marko@pacujo.net> - 2015-07-14 20:29 +0300
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Steven D'Aprano <steve@pearwood.info> - 2015-07-15 03:48 +1000
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2015-07-15 10:28 +0200
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2015-07-14 16:02 +0200
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Chris Angelico <rosuav@gmail.com> - 2015-07-15 00:07 +1000
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Marko Rauhamaa <marko@pacujo.net> - 2015-07-14 20:31 +0300
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Terry Reedy <tjreedy@udel.edu> - 2015-07-14 20:41 -0400
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2015-07-15 11:10 +0200
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2015-07-16 10:43 +1200
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2015-07-16 09:31 +0200
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2015-07-17 10:41 +1200
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Chris Angelico <rosuav@gmail.com> - 2015-07-16 21:45 +1000
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2015-07-16 15:56 +0200
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Chris Angelico <rosuav@gmail.com> - 2015-07-17 00:00 +1000
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2015-07-16 16:32 +0200
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Chris Angelico <rosuav@gmail.com> - 2015-07-17 02:43 +1000
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Joonas Liik <liik.joonas@gmail.com> - 2015-07-16 19:50 +0300
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Chris Angelico <rosuav@gmail.com> - 2015-07-17 03:03 +1000
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Ethan Furman <ethan@stoneleaf.us> - 2015-07-16 10:04 -0700
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Joonas Liik <liik.joonas@gmail.com> - 2015-07-16 20:34 +0300
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Steven D'Aprano <steve@pearwood.info> - 2015-07-17 04:58 +1000
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Joonas Liik <liik.joonas@gmail.com> - 2015-07-16 22:14 +0300
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2015-07-17 11:41 +1200
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Ethan Furman <ethan@stoneleaf.us> - 2015-07-16 12:52 -0700
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Chris Angelico <rosuav@gmail.com> - 2015-07-17 03:49 +1000
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Joonas Liik <liik.joonas@gmail.com> - 2015-07-16 21:23 +0300
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Chris Angelico <rosuav@gmail.com> - 2015-07-17 04:29 +1000
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Terry Reedy <tjreedy@udel.edu> - 2015-07-16 16:19 -0400
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2015-07-17 12:48 +0200
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2015-07-19 10:57 +1200
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Chris Angelico <rosuav@gmail.com> - 2015-07-17 21:05 +1000
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2015-07-17 13:43 +0200
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Chris Angelico <rosuav@gmail.com> - 2015-07-17 21:49 +1000
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2015-07-17 14:54 +0200
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Chris Angelico <rosuav@gmail.com> - 2015-07-17 23:12 +1000
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Terry Reedy <tjreedy@udel.edu> - 2015-07-17 16:27 -0400
          Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2015-07-15 21:13 +1200
            Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Marko Rauhamaa <marko@pacujo.net> - 2015-07-15 12:55 +0300
            Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Mark Lawrence <breamoreboy@yahoo.co.uk> - 2015-07-15 12:22 +0100
              Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2015-07-16 10:34 +1200
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Mark Lawrence <breamoreboy@yahoo.co.uk> - 2015-07-16 00:34 +0100
            Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) MRAB <python@mrabarnett.plus.com> - 2015-07-15 13:00 +0100
            Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Chris Angelico <rosuav@gmail.com> - 2015-07-15 22:13 +1000
              Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2015-07-16 10:34 +1200
            Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Chris Angelico <rosuav@gmail.com> - 2015-07-15 22:22 +1000
      Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Marko Rauhamaa <marko@pacujo.net> - 2015-07-14 08:41 +0300
        Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Chris Angelico <rosuav@gmail.com> - 2015-07-14 21:33 +1000
          Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Marko Rauhamaa <marko@pacujo.net> - 2015-07-14 15:08 +0300
    Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Chris Angelico <rosuav@gmail.com> - 2015-07-14 15:31 +1000
    Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Ian Kelly <ian.g.kelly@gmail.com> - 2015-07-13 23:46 -0600
      Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Marko Rauhamaa <marko@pacujo.net> - 2015-07-14 08:57 +0300
        Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2015-07-14 18:29 +1200
          Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Marko Rauhamaa <marko@pacujo.net> - 2015-07-14 10:05 +0300
            Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2015-07-15 17:52 +1200
              Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Marko Rauhamaa <marko@pacujo.net> - 2015-07-15 09:44 +0300
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Ned Batchelder <ned@nedbatchelder.com> - 2015-07-15 03:45 -0700
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Marko Rauhamaa <marko@pacujo.net> - 2015-07-15 13:55 +0300
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2015-07-15 13:04 +0200
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Ned Batchelder <ned@nedbatchelder.com> - 2015-07-15 04:12 -0700
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Marko Rauhamaa <marko@pacujo.net> - 2015-07-15 14:24 +0300
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Rustom Mody <rustompmody@gmail.com> - 2015-07-16 21:28 -0700
          Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Mark Lawrence <breamoreboy@yahoo.co.uk> - 2015-07-14 08:47 +0100
        Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Ian Kelly <ian.g.kelly@gmail.com> - 2015-07-14 02:13 -0600
          Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Marko Rauhamaa <marko@pacujo.net> - 2015-07-14 11:33 +0300
            Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Ian Kelly <ian.g.kelly@gmail.com> - 2015-07-14 07:15 -0600
              Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Marko Rauhamaa <marko@pacujo.net> - 2015-07-14 20:27 +0300
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Ian Kelly <ian.g.kelly@gmail.com> - 2015-07-15 08:28 -0600
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Marko Rauhamaa <marko@pacujo.net> - 2015-07-15 17:55 +0300
            Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Steven D'Aprano <steve@pearwood.info> - 2015-07-15 03:34 +1000
              Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Marko Rauhamaa <marko@pacujo.net> - 2015-07-14 20:43 +0300
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Chris Angelico <rosuav@gmail.com> - 2015-07-15 03:52 +1000
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Steven D'Aprano <steve@pearwood.info> - 2015-07-15 04:06 +1000
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Marko Rauhamaa <marko@pacujo.net> - 2015-07-14 21:37 +0300
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Chris Angelico <rosuav@gmail.com> - 2015-07-15 04:55 +1000
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Marko Rauhamaa <marko@pacujo.net> - 2015-07-14 22:12 +0300
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Terry Reedy <tjreedy@udel.edu> - 2015-07-14 21:36 -0400
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Terry Reedy <tjreedy@udel.edu> - 2015-07-14 21:01 -0400
                Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Chris Angelico <rosuav@gmail.com> - 2015-07-15 13:05 +1000
              Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Paul Rubin <no.email@nospam.invalid> - 2015-07-14 10:54 -0700
    Re: Possibly Pythonic Tail Call Optimization (TCO/TRE) Terry Reedy <tjreedy@udel.edu> - 2015-07-14 20:23 -0400

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