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Re: find all multiplicands and multipliers for a number

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Date Sun, 12 Apr 2015 22:35:56 -0400
From Dave Angel <davea@davea.name>
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Subject Re: find all multiplicands and multipliers for a number
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On 04/12/2015 09:56 PM, Paul Rubin wrote:
> Marko Rauhamaa <marko@pacujo.net> writes:
>> And in fact, the sqrt optimization now makes the original version 20%
>> faster: ...
>>      bound = int(math.sqrt(n))
>
> That could conceivably fail because of floating point roundoff or
> overflow, e.g. fac(3**1000).  A fancier approach to finding the integer
> square root might be worthwhile though.
>

If I were trying to get a bound for stopping the divide operation, on a 
value too large to do exact real representation, I'd try doing just a 
few iterations of Newton's method.  Even if you don't converge it to get 
an exact value, you can arrange that you have a number that's for sure 
no less than the square root.  And you can get pretty close in just a 
few times around.

-- 
DaveA

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find all multiplicands and multipliers for a number ravas <ravas@outlook.com> - 2015-04-10 16:37 -0700
  Re: find all multiplicands and multipliers for a number Dave Angel <d@davea.name> - 2015-04-10 21:16 -0400
  Re: find all multiplicands and multipliers for a number Dave Angel <davea@davea.name> - 2015-04-10 21:06 -0400
    Re: find all multiplicands and multipliers for a number Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-04-11 12:04 +1000
      Re: find all multiplicands and multipliers for a number Stephen Tucker <stephen_tucker@sil.org> - 2015-04-11 06:11 +0100
      Re: find all multiplicands and multipliers for a number Paul Rubin <no.email@nospam.invalid> - 2015-04-10 23:08 -0700
        Re: find all multiplicands and multipliers for a number Marko Rauhamaa <marko@pacujo.net> - 2015-04-11 10:14 +0300
          Re: find all multiplicands and multipliers for a number Paul Rubin <no.email@nospam.invalid> - 2015-04-11 09:59 -0700
            Re: find all multiplicands and multipliers for a number Marko Rauhamaa <marko@pacujo.net> - 2015-04-11 20:31 +0300
              Re: find all multiplicands and multipliers for a number Paul Rubin <no.email@nospam.invalid> - 2015-04-11 10:52 -0700
                Re: find all multiplicands and multipliers for a number Chris Angelico <rosuav@gmail.com> - 2015-04-12 07:10 +1000
                Re: find all multiplicands and multipliers for a number Terry Reedy <tjreedy@udel.edu> - 2015-04-11 19:58 -0400
                Re: find all multiplicands and multipliers for a number Chris Angelico <rosuav@gmail.com> - 2015-04-12 10:16 +1000
          Re: find all multiplicands and multipliers for a number wolfram.hinderer@googlemail.com - 2015-04-11 16:17 -0700
            Re: find all multiplicands and multipliers for a number Marko Rauhamaa <marko@pacujo.net> - 2015-04-12 10:17 +0300
              Primes [was Re: find all multiplicands and multipliers for a number] Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-04-12 20:48 +1000
              Re: find all multiplicands and multipliers for a number Paul Rubin <no.email@nospam.invalid> - 2015-04-12 18:56 -0700
                Re: find all multiplicands and multipliers for a number Dave Angel <davea@davea.name> - 2015-04-12 22:35 -0400
                Re: find all multiplicands and multipliers for a number Paul Rubin <no.email@nospam.invalid> - 2015-04-12 20:30 -0700
                Re: find all multiplicands and multipliers for a number Dave Angel <davea@davea.name> - 2015-04-13 00:35 -0400
                Re: find all multiplicands and multipliers for a number Paul Rubin <no.email@nospam.invalid> - 2015-04-12 22:25 -0700
                Re: find all multiplicands and multipliers for a number Dave Angel <davea@davea.name> - 2015-04-13 01:43 -0400
                Re: find all multiplicands and multipliers for a number Paul Rubin <no.email@nospam.invalid> - 2015-04-12 22:57 -0700
                Re: find all multiplicands and multipliers for a number Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-04-13 17:21 +1000
                Re: find all multiplicands and multipliers for a number Paul Rubin <no.email@nospam.invalid> - 2015-04-13 19:42 -0700
                Re: find all multiplicands and multipliers for a number Chris Angelico <rosuav@gmail.com> - 2015-04-14 12:47 +1000
                Re: find all multiplicands and multipliers for a number Paul Rubin <no.email@nospam.invalid> - 2015-04-13 19:54 -0700
                Re: find all multiplicands and multipliers for a number Rustom Mody <rustompmody@gmail.com> - 2015-04-14 03:35 -0700
                Re: find all multiplicands and multipliers for a number Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-04-14 23:30 +1000
                Re: find all multiplicands and multipliers for a number Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-04-14 23:40 +1000
                Re: find all multiplicands and multipliers for a number Paul Rubin <no.email@nospam.invalid> - 2015-04-14 19:37 -0700
                Re: find all multiplicands and multipliers for a number Ian Kelly <ian.g.kelly@gmail.com> - 2015-04-15 09:59 -0600
                Re: find all multiplicands and multipliers for a number Paul Rubin <no.email@nospam.invalid> - 2015-04-15 09:21 -0700
                Re: find all multiplicands and multipliers for a number Chris Kaynor <ckaynor@zindagigames.com> - 2015-04-15 09:46 -0700
                Re: find all multiplicands and multipliers for a number Paul Rubin <no.email@nospam.invalid> - 2015-04-15 10:37 -0700
                Searching the archives Gil Dawson <Gil@GilDawson.com> - 2015-04-15 11:47 -0700
                Installing Python Gil Dawson <Gil@GilDawson.com> - 2015-04-15 12:09 -0700
                Re: Searching the archives Tim Golden <mail@timgolden.me.uk> - 2015-04-15 20:16 +0100
                Re: Installing Python Ned Deily <nad@acm.org> - 2015-04-15 13:32 -0700
                Re: find all multiplicands and multipliers for a number Rustom Mody <rustompmody@gmail.com> - 2015-04-15 21:17 -0700
        Re: find all multiplicands and multipliers for a number Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-04-11 17:35 +1000
          Re: find all multiplicands and multipliers for a number jonas.thornvall@gmail.com - 2015-04-11 01:47 -0700
          Re: find all multiplicands and multipliers for a number Paul Rubin <no.email@nospam.invalid> - 2015-04-11 09:31 -0700
            Re: find all multiplicands and multipliers for a number Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-04-12 12:22 +1000
              Re: find all multiplicands and multipliers for a number Paul Rubin <no.email@nospam.invalid> - 2015-04-11 21:24 -0700
                Re: find all multiplicands and multipliers for a number Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-04-12 14:29 +1000
          Re: find all multiplicands and multipliers for a number Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2015-04-11 12:41 -0400
            Re: find all multiplicands and multipliers for a number Paul Rubin <no.email@nospam.invalid> - 2015-04-11 10:02 -0700
        Re: find all multiplicands and multipliers for a number Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2015-04-11 12:37 -0400
      Re: find all multiplicands and multipliers for a number Brian Gladman <blindanagram@nowhere.net> - 2015-04-12 10:34 +0100
        Re: find all multiplicands and multipliers for a number Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-04-13 00:29 +1000
          Re: find all multiplicands and multipliers for a number Paul Rubin <no.email@nospam.invalid> - 2015-04-12 10:20 -0700
            Re: find all multiplicands and multipliers for a number Paul Rubin <no.email@nospam.invalid> - 2015-04-12 10:23 -0700
            Re: find all multiplicands and multipliers for a number Brian Gladman <blindanagram@nowhere.net> - 2015-04-12 20:15 +0100
              Re: find all multiplicands and multipliers for a number Paul Rubin <no.email@nospam.invalid> - 2015-04-12 12:45 -0700
          Re: find all multiplicands and multipliers for a number Brian Gladman <blindanagram@nowhere.net> - 2015-04-12 20:07 +0100
  Re: find all multiplicands and multipliers for a number Paul Rubin <no.email@nospam.invalid> - 2015-04-10 18:28 -0700
  Re: find all multiplicands and multipliers for a number Dave Farrance <DaveFarrance@OMiTTHiSyahooANDTHiS.co.uk> - 2015-04-11 10:03 +0100
  Re: find all multiplicands and multipliers for a number ravas <ravas@outlook.com> - 2015-04-11 10:11 -0700

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