Re: real to rational number

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From	Paul Rubin <no.email@nospam.invalid>
Newsgroups	comp.lang.forth
Subject	Re: real to rational number
Date	Wed, 19 Apr 2017 13:03:25 -0700
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rickman <gnuarm@gmail.com> writes:
> I don't understand all of the language you are using, but there are an
> infinite number of integers and the solution can be found arbitrarily
> close to any real value by finding larger value integers.  To my
> understanding there is *no* single solution unless you restrict the
> magnitude of the integers you use.

There's two questions being conflated:

1) given a floating point number x, find the smallest pair of integers
   a,b such that a/b == x to the same precision that x is given in.

2) given an irrational number x, find rational approximations that are
   as close as possible to x given their size.  E.g. for pi, the
   approximants are 3/1, 22/7, 333/106, 355/113, 103993/33102,
   104348/33215, 208341/66317, 312689/99532, 833719/265381,
   1146408/364913, etc.

Both of these are done with the continued fraction algorithm that I
posted.  It helps if you have bignum arithmetic for this sort of thing.

Thread

real to rational number krishna.myneni@ccreweb.org - 2017-04-18 04:49 -0700
  Re: real to rational number lehs <skydda.barnen@gmail.com> - 2017-04-18 06:48 -0700
    Re: real to rational number krishna.myneni@ccreweb.org - 2017-04-18 19:09 -0700
      Re: real to rational number lehs <skydda.barnen@gmail.com> - 2017-04-18 22:53 -0700
        Re: real to rational number krishna.myneni@ccreweb.org - 2017-04-19 04:43 -0700
          Re: real to rational number rickman <gnuarm@gmail.com> - 2017-04-19 15:41 -0400
            Re: real to rational number Paul Rubin <no.email@nospam.invalid> - 2017-04-19 13:03 -0700
              Re: real to rational number "Rudy Velthuis" <newsgroups@rvelthuis.de> - 2017-04-20 17:26 +0000
              Re: real to rational number hughaguilar96@gmail.com - 2017-04-20 14:29 -0700
      Re: real to rational number "Rudy Velthuis" <newsgroups@rvelthuis.de> - 2017-04-19 23:44 +0000
        Re: real to rational number Paul Rubin <no.email@nospam.invalid> - 2017-04-19 19:30 -0700
          Re: real to rational number "Rudy Velthuis" <newsgroups@rvelthuis.de> - 2017-04-20 17:08 +0000
            Re: real to rational number Paul Rubin <no.email@nospam.invalid> - 2017-04-20 11:46 -0700
              Re: real to rational number "Rudy Velthuis" <newsgroups@rvelthuis.de> - 2017-04-21 09:47 +0000
            Re: real to rational number lehs <skydda.barnen@gmail.com> - 2017-04-20 20:49 -0700
    Re: real to rational number rickman <gnuarm@gmail.com> - 2017-04-19 15:36 -0400
      Re: real to rational number krishna.myneni@ccreweb.org - 2017-04-20 18:44 -0700
  Re: real to rational number hughaguilar96@gmail.com - 2017-04-18 07:06 -0700
    Re: real to rational number krishna.myneni@ccreweb.org - 2017-04-18 19:17 -0700
      Re: real to rational number Paul Rubin <no.email@nospam.invalid> - 2017-04-18 19:45 -0700
        Re: real to rational number krishna.myneni@ccreweb.org - 2017-04-18 19:57 -0700
        Re: real to rational number anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2017-04-19 05:35 +0000
      Re: real to rational number hughaguilar96@gmail.com - 2017-04-18 23:42 -0700
        Re: real to rational number krishna.myneni@ccreweb.org - 2017-04-19 04:53 -0700
          Re: real to rational number hughaguilar96@gmail.com - 2017-04-19 11:32 -0700
  Re: real to rational number minforth@arcor.de - 2017-04-18 08:23 -0700
    Re: real to rational number krishna.myneni@ccreweb.org - 2017-04-18 19:24 -0700
      Re: real to rational number Paul Rubin <no.email@nospam.invalid> - 2017-04-18 19:48 -0700
        Re: real to rational number krishna.myneni@ccreweb.org - 2017-04-18 20:01 -0700
  Re: real to rational number Paul Rubin <no.email@nospam.invalid> - 2017-04-18 19:39 -0700
    Re: real to rational number krishna.myneni@ccreweb.org - 2017-04-18 19:56 -0700
      Re: real to rational number Paul Rubin <no.email@nospam.invalid> - 2017-04-19 00:41 -0700
        Re: real to rational number krishna.myneni@ccreweb.org - 2017-04-19 04:48 -0700
        Re: real to rational number hughaguilar96@gmail.com - 2017-04-19 11:30 -0700
      Re: real to rational number albert@cherry.spenarnc.xs4all.nl (Albert van der Horst) - 2017-04-20 20:15 +0200
        Re: real to rational number krishna.myneni@ccreweb.org - 2017-04-20 15:23 -0700
          Re: real to rational number Paul Rubin <no.email@nospam.invalid> - 2017-04-20 18:52 -0700
  Re: real to rational number Pablo Hugo Reda <pabloreda@gmail.com> - 2017-04-18 19:58 -0700
    Re: real to rational number krishna.myneni@ccreweb.org - 2017-04-18 20:05 -0700
      Re: real to rational number Pablo Hugo Reda <pabloreda@gmail.com> - 2017-04-19 05:30 -0700
        Re: real to rational number Pablo Hugo Reda <pabloreda@gmail.com> - 2017-04-19 05:35 -0700
          Re: real to rational number Pablo Hugo Reda <pabloreda@gmail.com> - 2017-04-19 05:41 -0700
            Re: real to rational number krishna.myneni@ccreweb.org - 2017-04-19 19:39 -0700
  Re: real to rational number "Rudy Velthuis" <newsgroups@rvelthuis.de> - 2017-04-19 23:16 +0000
    Re: real to rational number krishna.myneni@ccreweb.org - 2017-04-19 19:42 -0700
      Re: real to rational number "Rudy Velthuis" <newsgroups@rvelthuis.de> - 2017-04-20 17:15 +0000
        Re: real to rational number krishna.myneni@ccreweb.org - 2017-04-20 15:11 -0700
          Re: real to rational number hughaguilar96@gmail.com - 2017-04-20 15:49 -0700
            Re: real to rational number Alex <alex@rivadpm.com> - 2017-04-21 00:20 +0100
              Re: real to rational number krishna.myneni@ccreweb.org - 2017-04-20 18:49 -0700
                Re: real to rational number The Beez <the.beez.speaks@gmail.com> - 2017-04-21 03:18 -0700
                Re: real to rational number krishna.myneni@ccreweb.org - 2017-04-21 18:39 -0700
                Re: real to rational number krishna.myneni@ccreweb.org - 2017-04-21 18:46 -0700
                Re: real to rational number Paul Rubin <no.email@nospam.invalid> - 2017-04-21 21:55 -0700
                Re: real to rational number krishna.myneni@ccreweb.org - 2017-04-22 08:33 -0700
                Re: real to rational number Paul Rubin <no.email@nospam.invalid> - 2017-04-22 13:35 -0700
                Re: real to rational number The Beez <the.beez.speaks@gmail.com> - 2017-04-24 00:58 -0700
                Re: real to rational number minforth@arcor.de - 2017-04-24 01:08 -0700
                Re: real to rational number minforth@arcor.de - 2017-04-23 02:28 -0700
                Re: real to rational number hughaguilar96@gmail.com - 2017-04-21 18:43 -0700
                rationalising  reality,   was Re: real to rational number Jan Coombs <jenfhaomndgfwutc@murmic.plus.com> - 2017-04-22 10:28 +0100
                Re: rationalising  reality,   was Re: real to rational number Mark Wills <markwills1970@gmail.com> - 2017-04-22 02:33 -0700
            Re: real to rational number krishna.myneni@ccreweb.org - 2017-04-20 16:22 -0700
              Re: real to rational number hughaguilar96@gmail.com - 2017-04-20 22:02 -0700
                Re: real to rational number Julian Fondren <julian.fondren@gmail.com> - 2017-04-21 00:12 -0700
                Re: real to rational number "Rudy Velthuis" <newsgroups@rvelthuis.de> - 2017-04-21 09:55 +0000
                Re: real to rational number hughaguilar96@gmail.com - 2017-04-25 10:52 -0700
                Re: real to rational number "Rudy Velthuis" <newsgroups@rvelthuis.de> - 2017-04-29 03:16 +0000
              Re: real to rational number "Rudy Velthuis" <newsgroups@rvelthuis.de> - 2017-04-21 09:52 +0000
              Re: real to rational number lehs <skydda.barnen@gmail.com> - 2017-04-21 05:35 -0700
                Re: real to rational number hughaguilar96@gmail.com - 2017-04-21 19:05 -0700
                Re: real to rational number The Beez <the.beez.speaks@gmail.com> - 2017-04-24 01:14 -0700
                Re: real to rational number Cecil Bayona <cbayona@cbayona.com> - 2017-04-24 11:31 -0500
                Re: real to rational number The Beez <the.beez.speaks@gmail.com> - 2017-04-25 00:52 -0700
                Re: real to rational number hughaguilar96@gmail.com - 2017-04-24 11:43 -0700
                Re: real to rational number The Beez <the.beez.speaks@gmail.com> - 2017-04-25 00:35 -0700
                Re: real to rational number The Beez <the.beez.speaks@gmail.com> - 2017-04-25 01:09 -0700
                Re: real to rational number minforth@arcor.de - 2017-04-26 01:55 -0700

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