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Re: Throw the cat among the pigeons

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Paul Rubin <no.email@nospam.invalid> writes:

> Steven D'Aprano <steve+comp.lang.python@pearwood.info> writes:
>> Multiplying upwards seems to be more expensive than multiplying
>> downwards... I can only guess that it has something to do with the way
>> multiplication is implemented, or perhaps the memory management
>> involved, or something. Who the hell knows?
>
> It seems pretty natural if multiplication uses the obvious
> quadratic-time pencil and paper algorithm.  The cost of multiplying m*n
> is basically w(m)*w(n) where w(x) is the width of x in machine words.
> So for factorial where m is the counter and n is the running product,
> w(m) is always 1 while w(n) is basically log2(n!).  From
>
>     from math import log
>     def xfac(seq):
>         cost = logfac = 0.0
>         for i in seq:
>             logfac += log(i,2)
>             cost += logfac
>         return cost
>
>     def upward(n): return xfac(xrange(1,n+1))
>     def downward(n): return xfac(xrange(n,1,-1))
>
>     print upward(40000),downward(40000)
>
> I get: 10499542692.6 11652843833.5
>
> A lower number for upward than downward.  The difference isn't as large
> as your timings, but I think it still gives some explanation of the
> effect.

Yes, plus the time for memory allocation. Since the code uses "r *=
...", space is reallocated when the result doesn't fit. The new size is
probably proportional to the current (insufficient) size. This means
that overall, you'll need fewer reallocations, because allocations are
made in bigger chunks.

-- Alain.

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Throw the cat among the pigeons Cecil Westerhof <Cecil@decebal.nl> - 2015-05-02 16:20 +0200
  Re: Throw the cat among the pigeons Cecil Westerhof <Cecil@decebal.nl> - 2015-05-03 17:12 +0200
    Re: Throw the cat among the pigeons Paul  Moore <p.f.moore@gmail.com> - 2015-05-05 08:47 -0700
      Re: Throw the cat among the pigeons Cecil Westerhof <Cecil@decebal.nl> - 2015-05-05 18:18 +0200
        Re: Throw the cat among the pigeons Dave Angel <davea@davea.name> - 2015-05-05 14:45 -0400
          Re: Throw the cat among the pigeons Cecil Westerhof <Cecil@decebal.nl> - 2015-05-05 21:42 +0200
            Re: Throw the cat among the pigeons Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-05-06 12:57 +1000
              Re: Throw the cat among the pigeons Chris Angelico <rosuav@gmail.com> - 2015-05-06 14:03 +1000
        Re: Throw the cat among the pigeons Ian Kelly <ian.g.kelly@gmail.com> - 2015-05-05 14:30 -0600
        Re: Throw the cat among the pigeons Terry Reedy <tjreedy@udel.edu> - 2015-05-05 16:46 -0400
          Re: Throw the cat among the pigeons Cecil Westerhof <Cecil@decebal.nl> - 2015-05-05 23:12 +0200
            Re: Throw the cat among the pigeons Terry Reedy <tjreedy@udel.edu> - 2015-05-05 19:22 -0400
        Re: Throw the cat among the pigeons Dave Angel <davea@davea.name> - 2015-05-05 17:00 -0400
        Re: Throw the cat among the pigeons Ian Kelly <ian.g.kelly@gmail.com> - 2015-05-05 15:23 -0600
          Re: Throw the cat among the pigeons Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-05-06 11:27 +1000
            Re: Throw the cat among the pigeons Ian Kelly <ian.g.kelly@gmail.com> - 2015-05-05 23:58 -0600
              Re: Throw the cat among the pigeons Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-05-06 17:08 +1000
                Re: Throw the cat among the pigeons Ian Kelly <ian.g.kelly@gmail.com> - 2015-05-06 10:17 -0600
                Re: Throw the cat among the pigeons Mark Lawrence <breamoreboy@yahoo.co.uk> - 2015-05-06 21:23 +0100
        Re: Throw the cat among the pigeons Ian Kelly <ian.g.kelly@gmail.com> - 2015-05-05 15:39 -0600
        Re: Throw the cat among the pigeons Dave Angel <davea@davea.name> - 2015-05-05 17:55 -0400
        Re: Throw the cat among the pigeons Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-05-06 12:19 +1000
  Re: Throw the cat among the pigeons Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-05-06 14:05 +1000
    Re: Throw the cat among the pigeons Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-05-06 16:26 +1000
      Re: Throw the cat among the pigeons Dave Angel <davea@davea.name> - 2015-05-06 09:12 -0400
        Re: Throw the cat among the pigeons Dan Sommers <dan@tombstonezero.net> - 2015-05-07 03:16 +0000
      Re: Throw the cat among the pigeons Chris Angelico <rosuav@gmail.com> - 2015-05-06 23:55 +1000
      Re: Throw the cat among the pigeons Dave Angel <davea@davea.name> - 2015-05-06 10:22 -0400
      Re: Throw the cat among the pigeons Paul Rubin <no.email@nospam.invalid> - 2015-05-06 08:12 -0700
        Re: Throw the cat among the pigeons Alain Ketterlin <alain@universite-de-strasbourg.fr.invalid> - 2015-05-06 17:36 +0200
          Re: Throw the cat among the pigeons Dave Angel <davea@davea.name> - 2015-05-06 16:23 -0400
            Re: Throw the cat among the pigeons Alain Ketterlin <alain@universite-de-strasbourg.fr.invalid> - 2015-05-07 11:14 +0200
              Re: Throw the cat among the pigeons Chris Angelico <rosuav@gmail.com> - 2015-05-07 19:38 +1000
        Re: Throw the cat among the pigeons Ian Kelly <ian.g.kelly@gmail.com> - 2015-05-06 09:47 -0600
          Re: Throw the cat among the pigeons Paul Rubin <no.email@nospam.invalid> - 2015-05-06 10:24 -0700

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