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Re: Throw the cat among the pigeons

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On Wed, May 6, 2015 at 9:12 AM, Paul Rubin <no.email@nospam.invalid> wrote:
> 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.

That was my initial thought as well, but the problem is that this
actually predicts the *opposite* of what is being reported: upward
should be less expensive, not more.

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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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