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Re: Converting Floats to Strings yields erratic results

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On 06/09/2011 06:03 AM, BartC wrote:
> "BartC" <bc@freeuk.com> wrote in message news:isoqbd$i94$1@dont-email.me...
> 
>> Code to convert binary floating point to decimal is very tricky to write. 
>> I've just had a go, and while the following sort of works, it's probably 
>> full of numerical problems too.
> 
> My code introduces errors in the lower bits of the number. I'm trying to 
> compare the results to printf(), but if I write:
> 
> printf("%f\n",1.0e40);
> 
> I get an impossibly clean result of 1 followed by loads of zeros, no matter 
> what numbers I stick inside %f. Clearly 1e40 can't be stored exactly (can 
> it? I thought it would need over 120 bits of precision), so how can I tell 
> printf to show it as it is?
> 
> (If I print 1e50, then I've noticed there is a '1' amongst the zeros; that 
> can't be right either..)

1e40 is 2^40*5^40. 2^40 is just absorbed into the exponent. 5^40
requires only 93 bits to be represented exactly, not 120. It's therefore
possible to store 1e40 exactly in a 128-bit type. I've heard of
implementations with 128-bit long double, but not 128-bit double.

With respect to %f, the standard says "The value is rounded to
the appropriate number of digits." (7.19.6.1p8). I think that this is a
little unclear, but it could be used to justify producing all zeros
after the last significant digit of the output string. That's what I've
usually seen real implementations do.
-- 
James Kuyper

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Converting Floats to Strings yields erratic results "Dirk T. Shelley" <nospam@nospam.com> - 2011-06-07 21:10 +0000
  Re: Converting Floats to Strings yields erratic results Keith Thompson <kst-u@mib.org> - 2011-06-07 14:25 -0700
    Re: Converting Floats to Strings yields erratic results Peter Nilsson <airia@acay.com.au> - 2011-06-07 20:13 -0700
      Re: Converting Floats to Strings yields erratic results Keith Thompson <kst-u@mib.org> - 2011-06-07 20:27 -0700
    Re: Converting Floats to Strings yields erratic results "Dirk T. Shelley" <nospam@nospam.com> - 2011-06-08 16:34 +0000
      Re: Converting Floats to Strings yields erratic results Ian Collins <ian-news@hotmail.com> - 2011-06-09 07:53 +1200
        Re: Converting Floats to Strings yields erratic results "Dirk T. Shelley" <nospam@nospam.com> - 2011-06-08 20:46 +0000
      Re: Converting Floats to Strings yields erratic results "BartC" <bc@freeuk.com> - 2011-06-08 22:40 +0100
        Re: Converting Floats to Strings yields erratic results "BartC" <bc@freeuk.com> - 2011-06-09 11:03 +0100
          Re: Converting Floats to Strings yields erratic results James Kuyper <jameskuyper@verizon.net> - 2011-06-09 08:06 -0400
            Re: Converting Floats to Strings yields erratic results "BartC" <bc@freeuk.com> - 2011-06-09 16:57 +0100
          Re: Converting Floats to Strings yields erratic results Noob <root@127.0.0.1> - 2011-06-09 14:13 +0200
          Re: Converting Floats to Strings yields erratic results Keith Thompson <kst-u@mib.org> - 2011-06-09 09:26 -0700
            Re: Converting Floats to Strings yields erratic results "BartC" <bc@freeuk.com> - 2011-06-09 19:07 +0100
              Re: Converting Floats to Strings yields erratic results Keith Thompson <kst-u@mib.org> - 2011-06-09 11:52 -0700
                Re: Converting Floats to Strings yields erratic results "BartC" <bc@freeuk.com> - 2011-06-09 20:30 +0100
            Re: Converting Floats to Strings yields erratic results "io_x" <a@b.c.invalid> - 2011-06-13 12:21 +0200
            Re: Converting Floats to Strings yields erratic results "io_x" <a@b.c.invalid> - 2011-06-13 22:31 +0200
          Re: Converting Floats to Strings yields erratic results Noob <root@127.0.0.1> - 2011-06-10 10:58 +0200
            Re: Converting Floats to Strings yields erratic results Seebs <usenet-nospam@seebs.net> - 2011-06-10 22:49 +0000
      Re: Converting Floats to Strings yields erratic results Eric Sosman <esosman@ieee-dot-org.invalid> - 2011-06-08 21:51 -0400
      Re: Converting Floats to Strings yields erratic results Mark Bluemel <mark_bluemel@pobox.com> - 2011-06-09 08:50 +0100
  Re: Converting Floats to Strings yields erratic results gordonb.9ycz5@burditt.org (Gordon Burditt) - 2011-06-07 18:13 -0500
  Re: Converting Floats to Strings yields erratic results Eric Sosman <esosman@ieee-dot-org.invalid> - 2011-06-07 20:47 -0400
    Re: Converting Floats to Strings yields erratic results Keith Thompson <kst-u@mib.org> - 2011-06-07 20:08 -0700
      Re: Converting Floats to Strings yields erratic results Eric Sosman <esosman@ieee-dot-org.invalid> - 2011-06-07 23:38 -0400
    Re: Converting Floats to Strings yields erratic results Eric Sosman <esosman@ieee-dot-org.invalid> - 2011-06-07 23:49 -0400
      Re: Converting Floats to Strings yields erratic results Shao Miller <sha0.miller@gmail.com> - 2011-06-08 00:54 -0500
  Re: Converting Floats to Strings yields erratic results Thad Smith <ThadSmith@acm.org> - 2011-06-07 20:38 -0700
    Re: Converting Floats to Strings yields erratic results Keith Thompson <kst-u@mib.org> - 2011-06-07 20:30 -0700
  Re: Converting Floats to Strings yields erratic results falk@rahul.net (Edward A. Falk) - 2011-06-08 20:54 +0000
    Re: Converting Floats to Strings yields erratic results Eric Sosman <esosman@ieee-dot-org.invalid> - 2011-06-08 21:56 -0400

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